上传commons-math3

fine-commons-math3/pom.xml

@@ -0,0 +1,35 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project xmlns="http://maven.apache.org/POM/4.0.0"
+         xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
+         xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd">
+    <modelVersion>4.0.0</modelVersion>
+    <groupId>com.fr.third</groupId>
+    <artifactId>commons-math3</artifactId>
+    <version>3.6.1</version>
+    <build>
+        <sourceDirectory>${basedir}/src</sourceDirectory>
+        <plugins>
+            <!-- 使用 maven-Assembly-plugin插件打可执行包-->
+            <plugin>
+                <groupId>org.apache.maven.plugins</groupId>
+                <artifactId>maven-assembly-plugin</artifactId>
+                <version>2.6</version>
+                <configuration>
+                    <!-- get all project dependencies -->
+                    <descriptorRefs>
+                        <descriptorRef>jar-with-dependencies</descriptorRef>
+                    </descriptorRefs>
+                </configuration>
+                <executions>
+                    <execution>
+                        <id>make-assembly</id>
+                        <phase>package</phase>
+                        <goals>
+                            <goal>single</goal>
+                        </goals>
+                    </execution>
+                </executions>
+            </plugin>
+        </plugins>
+    </build>
+</project>

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/Field.java

@@ -0,0 +1,58 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3;
+
+/**
+ * Interface representing a <a href="http://mathworld.wolfram.com/Field.html">field</a>.
+ * <p>
+ * Classes implementing this interface will often be singletons.
+ * </p>
+ * @param <T> the type of the field elements
+ * @see FieldElement
+ * @since 2.0
+ */
+public interface Field<T> {
+
+    /** Get the additive identity of the field.
+     * <p>
+     * The additive identity is the element e<sub>0</sub> of the field such that
+     * for all elements a of the field, the equalities a + e<sub>0</sub> =
+     * e<sub>0</sub> + a = a hold.
+     * </p>
+     * @return additive identity of the field
+     */
+    T getZero();
+
+    /** Get the multiplicative identity of the field.
+     * <p>
+     * The multiplicative identity is the element e<sub>1</sub> of the field such that
+     * for all elements a of the field, the equalities a &times; e<sub>1</sub> =
+     * e<sub>1</sub> &times; a = a hold.
+     * </p>
+     * @return multiplicative identity of the field
+     */
+    T getOne();
+
+    /**
+     * Returns the runtime class of the FieldElement.
+     *
+     * @return The {@code Class} object that represents the runtime
+     *         class of this object.
+     */
+    Class<? extends FieldElement<T>> getRuntimeClass();
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/FieldElement.java

@@ -0,0 +1,87 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3;
+
+import com.fr.third.org.apache.commons.math3.exception.MathArithmeticException;
+import com.fr.third.org.apache.commons.math3.exception.NullArgumentException;
+
+
+/**
+ * Interface representing <a href="http://mathworld.wolfram.com/Field.html">field</a> elements.
+ * @param <T> the type of the field elements
+ * @see Field
+ * @since 2.0
+ */
+public interface FieldElement<T> {
+
+    /** Compute this + a.
+     * @param a element to add
+     * @return a new element representing this + a
+     * @throws NullArgumentException if {@code a} is {@code null}.
+     */
+    T add(T a) throws NullArgumentException;
+
+    /** Compute this - a.
+     * @param a element to subtract
+     * @return a new element representing this - a
+     * @throws NullArgumentException if {@code a} is {@code null}.
+     */
+    T subtract(T a) throws NullArgumentException;
+
+    /**
+     * Returns the additive inverse of {@code this} element.
+     * @return the opposite of {@code this}.
+     */
+    T negate();
+
+    /** Compute n &times; this. Multiplication by an integer number is defined
+     * as the following sum
+     * <center>
+     * n &times; this = &sum;<sub>i=1</sub><sup>n</sup> this.
+     * </center>
+     * @param n Number of times {@code this} must be added to itself.
+     * @return A new element representing n &times; this.
+     */
+    T multiply(int n);
+
+    /** Compute this &times; a.
+     * @param a element to multiply
+     * @return a new element representing this &times; a
+     * @throws NullArgumentException if {@code a} is {@code null}.
+     */
+    T multiply(T a) throws NullArgumentException;
+
+    /** Compute this &divide; a.
+     * @param a element to divide by
+     * @return a new element representing this &divide; a
+     * @throws NullArgumentException if {@code a} is {@code null}.
+     * @throws MathArithmeticException if {@code a} is zero
+     */
+    T divide(T a) throws NullArgumentException, MathArithmeticException;
+
+    /**
+     * Returns the multiplicative inverse of {@code this} element.
+     * @return the inverse of {@code this}.
+     * @throws MathArithmeticException if {@code this} is zero
+     */
+    T reciprocal() throws MathArithmeticException;
+
+    /** Get the {@link Field} to which the instance belongs.
+     * @return {@link Field} to which the instance belongs
+     */
+    Field<T> getField();
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/RealFieldElement.java

@@ -0,0 +1,402 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3;
+
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+
+/**
+ * Interface representing a <a href="http://mathworld.wolfram.com/RealNumber.html">real</a>
+ * <a href="http://mathworld.wolfram.com/Field.html">field</a>.
+ * @param <T> the type of the field elements
+ * @see FieldElement
+ * @since 3.2
+ */
+public interface RealFieldElement<T> extends FieldElement<T> {
+
+    /** Get the real value of the number.
+     * @return real value
+     */
+    double getReal();
+
+    /** '+' operator.
+     * @param a right hand side parameter of the operator
+     * @return this+a
+     */
+    T add(double a);
+
+    /** '-' operator.
+     * @param a right hand side parameter of the operator
+     * @return this-a
+     */
+    T subtract(double a);
+
+    /** '&times;' operator.
+     * @param a right hand side parameter of the operator
+     * @return this&times;a
+     */
+    T multiply(double a);
+
+    /** '&divide;' operator.
+     * @param a right hand side parameter of the operator
+     * @return this&divide;a
+     */
+    T divide(double a);
+
+    /** IEEE remainder operator.
+     * @param a right hand side parameter of the operator
+     * @return this - n &times; a where n is the closest integer to this/a
+     * (the even integer is chosen for n if this/a is halfway between two integers)
+     */
+    T remainder(double a);
+
+    /** IEEE remainder operator.
+     * @param a right hand side parameter of the operator
+     * @return this - n &times; a where n is the closest integer to this/a
+     * (the even integer is chosen for n if this/a is halfway between two integers)
+     * @exception DimensionMismatchException if number of free parameters or orders are inconsistent
+     */
+    T remainder(T a)
+        throws DimensionMismatchException;
+
+    /** absolute value.
+     * @return abs(this)
+     */
+    T abs();
+
+    /** Get the smallest whole number larger than instance.
+     * @return ceil(this)
+     */
+    T ceil();
+
+    /** Get the largest whole number smaller than instance.
+     * @return floor(this)
+     */
+    T floor();
+
+    /** Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.
+     * @return a double number r such that r is an integer r - 0.5 &le; this &le; r + 0.5
+     */
+    T rint();
+
+    /** Get the closest long to instance value.
+     * @return closest long to {@link #getReal()}
+     */
+    long round();
+
+    /** Compute the signum of the instance.
+     * The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise
+     * @return -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a
+     */
+    T signum();
+
+    /**
+     * Returns the instance with the sign of the argument.
+     * A NaN {@code sign} argument is treated as positive.
+     *
+     * @param sign the sign for the returned value
+     * @return the instance with the same sign as the {@code sign} argument
+     */
+    T copySign(T sign);
+
+    /**
+     * Returns the instance with the sign of the argument.
+     * A NaN {@code sign} argument is treated as positive.
+     *
+     * @param sign the sign for the returned value
+     * @return the instance with the same sign as the {@code sign} argument
+     */
+    T copySign(double sign);
+
+    /**
+     * Multiply the instance by a power of 2.
+     * @param n power of 2
+     * @return this &times; 2<sup>n</sup>
+     */
+    T scalb(int n);
+
+    /**
+     * Returns the hypotenuse of a triangle with sides {@code this} and {@code y}
+     * - sqrt(<i>this</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)
+     * avoiding intermediate overflow or underflow.
+     *
+     * <ul>
+     * <li> If either argument is infinite, then the result is positive infinity.</li>
+     * <li> else, if either argument is NaN then the result is NaN.</li>
+     * </ul>
+     *
+     * @param y a value
+     * @return sqrt(<i>this</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)
+     * @exception DimensionMismatchException if number of free parameters or orders are inconsistent
+     */
+    T hypot(T y)
+        throws DimensionMismatchException;
+
+    /** {@inheritDoc} */
+    T reciprocal();
+
+    /** Square root.
+     * @return square root of the instance
+     */
+    T sqrt();
+
+    /** Cubic root.
+     * @return cubic root of the instance
+     */
+    T cbrt();
+
+    /** N<sup>th</sup> root.
+     * @param n order of the root
+     * @return n<sup>th</sup> root of the instance
+     */
+    T rootN(int n);
+
+    /** Power operation.
+     * @param p power to apply
+     * @return this<sup>p</sup>
+     */
+    T pow(double p);
+
+    /** Integer power operation.
+     * @param n power to apply
+     * @return this<sup>n</sup>
+     */
+    T pow(int n);
+
+    /** Power operation.
+     * @param e exponent
+     * @return this<sup>e</sup>
+     * @exception DimensionMismatchException if number of free parameters or orders are inconsistent
+     */
+    T pow(T e)
+        throws DimensionMismatchException;
+
+    /** Exponential.
+     * @return exponential of the instance
+     */
+    T exp();
+
+    /** Exponential minus 1.
+     * @return exponential minus one of the instance
+     */
+    T expm1();
+
+    /** Natural logarithm.
+     * @return logarithm of the instance
+     */
+    T log();
+
+    /** Shifted natural logarithm.
+     * @return logarithm of one plus the instance
+     */
+    T log1p();
+
+//    TODO: add this method in 4.0, as it is not possible to do it in 3.2
+//          due to incompatibility of the return type in the Dfp class
+//    /** Base 10 logarithm.
+//     * @return base 10 logarithm of the instance
+//     */
+//    T log10();
+
+    /** Cosine operation.
+     * @return cos(this)
+     */
+    T cos();
+
+    /** Sine operation.
+     * @return sin(this)
+     */
+    T sin();
+
+    /** Tangent operation.
+     * @return tan(this)
+     */
+    T tan();
+
+    /** Arc cosine operation.
+     * @return acos(this)
+     */
+    T acos();
+
+    /** Arc sine operation.
+     * @return asin(this)
+     */
+    T asin();
+
+    /** Arc tangent operation.
+     * @return atan(this)
+     */
+    T atan();
+
+    /** Two arguments arc tangent operation.
+     * @param x second argument of the arc tangent
+     * @return atan2(this, x)
+     * @exception DimensionMismatchException if number of free parameters or orders are inconsistent
+     */
+    T atan2(T x)
+        throws DimensionMismatchException;
+
+    /** Hyperbolic cosine operation.
+     * @return cosh(this)
+     */
+    T cosh();
+
+    /** Hyperbolic sine operation.
+     * @return sinh(this)
+     */
+    T sinh();
+
+    /** Hyperbolic tangent operation.
+     * @return tanh(this)
+     */
+    T tanh();
+
+    /** Inverse hyperbolic cosine operation.
+     * @return acosh(this)
+     */
+    T acosh();
+
+    /** Inverse hyperbolic sine operation.
+     * @return asin(this)
+     */
+    T asinh();
+
+    /** Inverse hyperbolic  tangent operation.
+     * @return atanh(this)
+     */
+    T atanh();
+
+    /**
+     * Compute a linear combination.
+     * @param a Factors.
+     * @param b Factors.
+     * @return <code>&Sigma;<sub>i</sub> a<sub>i</sub> b<sub>i</sub></code>.
+     * @throws DimensionMismatchException if arrays dimensions don't match
+     * @since 3.2
+     */
+    T linearCombination(T[] a, T[] b)
+        throws DimensionMismatchException;
+
+    /**
+     * Compute a linear combination.
+     * @param a Factors.
+     * @param b Factors.
+     * @return <code>&Sigma;<sub>i</sub> a<sub>i</sub> b<sub>i</sub></code>.
+     * @throws DimensionMismatchException if arrays dimensions don't match
+     * @since 3.2
+     */
+    T linearCombination(double[] a, T[] b)
+        throws DimensionMismatchException;
+
+    /**
+     * Compute a linear combination.
+     * @param a1 first factor of the first term
+     * @param b1 second factor of the first term
+     * @param a2 first factor of the second term
+     * @param b2 second factor of the second term
+     * @return a<sub>1</sub>&times;b<sub>1</sub> +
+     * a<sub>2</sub>&times;b<sub>2</sub>
+     * @see #linearCombination(Object, Object, Object, Object, Object, Object)
+     * @see #linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)
+     * @since 3.2
+     */
+    T linearCombination(T a1, T b1, T a2, T b2);
+
+    /**
+     * Compute a linear combination.
+     * @param a1 first factor of the first term
+     * @param b1 second factor of the first term
+     * @param a2 first factor of the second term
+     * @param b2 second factor of the second term
+     * @return a<sub>1</sub>&times;b<sub>1</sub> +
+     * a<sub>2</sub>&times;b<sub>2</sub>
+     * @see #linearCombination(double, Object, double, Object, double, Object)
+     * @see #linearCombination(double, Object, double, Object, double, Object, double, Object)
+     * @since 3.2
+     */
+    T linearCombination(double a1, T b1, double a2, T b2);
+
+    /**
+     * Compute a linear combination.
+     * @param a1 first factor of the first term
+     * @param b1 second factor of the first term
+     * @param a2 first factor of the second term
+     * @param b2 second factor of the second term
+     * @param a3 first factor of the third term
+     * @param b3 second factor of the third term
+     * @return a<sub>1</sub>&times;b<sub>1</sub> +
+     * a<sub>2</sub>&times;b<sub>2</sub> + a<sub>3</sub>&times;b<sub>3</sub>
+     * @see #linearCombination(Object, Object, Object, Object)
+     * @see #linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)
+     * @since 3.2
+     */
+    T linearCombination(T a1, T b1, T a2, T b2, T a3, T b3);
+
+    /**
+     * Compute a linear combination.
+     * @param a1 first factor of the first term
+     * @param b1 second factor of the first term
+     * @param a2 first factor of the second term
+     * @param b2 second factor of the second term
+     * @param a3 first factor of the third term
+     * @param b3 second factor of the third term
+     * @return a<sub>1</sub>&times;b<sub>1</sub> +
+     * a<sub>2</sub>&times;b<sub>2</sub> + a<sub>3</sub>&times;b<sub>3</sub>
+     * @see #linearCombination(double, Object, double, Object)
+     * @see #linearCombination(double, Object, double, Object, double, Object, double, Object)
+     * @since 3.2
+     */
+    T linearCombination(double a1, T b1,  double a2, T b2, double a3, T b3);
+
+    /**
+     * Compute a linear combination.
+     * @param a1 first factor of the first term
+     * @param b1 second factor of the first term
+     * @param a2 first factor of the second term
+     * @param b2 second factor of the second term
+     * @param a3 first factor of the third term
+     * @param b3 second factor of the third term
+     * @param a4 first factor of the third term
+     * @param b4 second factor of the third term
+     * @return a<sub>1</sub>&times;b<sub>1</sub> +
+     * a<sub>2</sub>&times;b<sub>2</sub> + a<sub>3</sub>&times;b<sub>3</sub> +
+     * a<sub>4</sub>&times;b<sub>4</sub>
+     * @see #linearCombination(Object, Object, Object, Object)
+     * @see #linearCombination(Object, Object, Object, Object, Object, Object)
+     * @since 3.2
+     */
+    T linearCombination(T a1, T b1, T a2, T b2, T a3, T b3, T a4, T b4);
+
+    /**
+     * Compute a linear combination.
+     * @param a1 first factor of the first term
+     * @param b1 second factor of the first term
+     * @param a2 first factor of the second term
+     * @param b2 second factor of the second term
+     * @param a3 first factor of the third term
+     * @param b3 second factor of the third term
+     * @param a4 first factor of the third term
+     * @param b4 second factor of the third term
+     * @return a<sub>1</sub>&times;b<sub>1</sub> +
+     * a<sub>2</sub>&times;b<sub>2</sub> + a<sub>3</sub>&times;b<sub>3</sub> +
+     * a<sub>4</sub>&times;b<sub>4</sub>
+     * @see #linearCombination(double, Object, double, Object)
+     * @see #linearCombination(double, Object, double, Object, double, Object)
+     * @since 3.2
+     */
+    T linearCombination(double a1, T b1, double a2, T b2, double a3, T b3, double a4, T b4);
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/BivariateFunction.java

@@ -0,0 +1,35 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis;
+
+/**
+ * An interface representing a bivariate real function.
+ *
+ * @since 2.1
+ */
+public interface BivariateFunction {
+    /**
+     * Compute the value for the function.
+     *
+     * @param x Abscissa for which the function value should be computed.
+     * @param y Ordinate for which the function value should be computed.
+     * @return the value.
+     */
+    double value(double x, double y);
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/DifferentiableMultivariateFunction.java

@@ -0,0 +1,54 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableFunction;
+
+/**
+ * Extension of {@link MultivariateFunction} representing a differentiable
+ * multivariate real function.
+ * @since 2.0
+ * @deprecated as of 3.1 replaced by {@link MultivariateDifferentiableFunction}
+ */
+@Deprecated
+public interface DifferentiableMultivariateFunction extends MultivariateFunction {
+
+    /**
+     * Returns the partial derivative of the function with respect to a point coordinate.
+     * <p>
+     * The partial derivative is defined with respect to point coordinate
+     * x<sub>k</sub>. If the partial derivatives with respect to all coordinates are
+     * needed, it may be more efficient to use the {@link #gradient()} method which will
+     * compute them all at once.
+     * </p>
+     * @param k index of the coordinate with respect to which the partial
+     * derivative is computed
+     * @return the partial derivative function with respect to k<sup>th</sup> point coordinate
+     */
+    MultivariateFunction partialDerivative(int k);
+
+    /**
+     * Returns the gradient function.
+     * <p>If only one partial derivative with respect to a specific coordinate is
+     * needed, it may be more efficient to use the {@link #partialDerivative(int)} method
+     * which will compute only the specified component.</p>
+     * @return the gradient function
+     */
+    MultivariateVectorFunction gradient();
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/DifferentiableMultivariateVectorFunction.java

@@ -0,0 +1,38 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction;
+
+/**
+ * Extension of {@link MultivariateVectorFunction} representing a differentiable
+ * multivariate vectorial function.
+ * @since 2.0
+ * @deprecated as of 3.1 replaced by {@link MultivariateDifferentiableVectorFunction}
+ */
+@Deprecated
+public interface DifferentiableMultivariateVectorFunction
+    extends MultivariateVectorFunction {
+
+    /**
+     * Returns the jacobian function.
+     * @return the jacobian function
+     */
+    MultivariateMatrixFunction jacobian();
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/DifferentiableUnivariateFunction.java

@@ -0,0 +1,37 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+
+/**
+ * Extension of {@link UnivariateFunction} representing a differentiable univariate real function.
+ *
+ * @deprecated as of 3.1 replaced by {@link UnivariateDifferentiableFunction}
+ */
+@Deprecated
+public interface DifferentiableUnivariateFunction
+    extends UnivariateFunction {
+
+    /**
+     * Returns the derivative of the function
+     *
+     * @return  the derivative function
+     */
+    UnivariateFunction derivative();
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/DifferentiableUnivariateMatrixFunction.java

@@ -0,0 +1,38 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableMatrixFunction;
+
+/**
+ * Extension of {@link UnivariateMatrixFunction} representing a differentiable univariate matrix function.
+ *
+ * @since 2.0
+ * @deprecated as of 3.1 replaced by  {@link UnivariateDifferentiableMatrixFunction}
+ */
+@Deprecated
+public interface DifferentiableUnivariateMatrixFunction
+    extends UnivariateMatrixFunction {
+
+    /**
+     * Returns the derivative of the function
+     *
+     * @return  the derivative function
+     */
+    UnivariateMatrixFunction derivative();
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/DifferentiableUnivariateVectorFunction.java

@@ -0,0 +1,38 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableVectorFunction;
+
+/**
+ * Extension of {@link UnivariateVectorFunction} representing a differentiable univariate vectorial function.
+ *
+ * @since 2.0
+ * @deprecated as of 3.1 replaced by {@link UnivariateDifferentiableVectorFunction}
+ */
+@Deprecated
+public interface DifferentiableUnivariateVectorFunction
+    extends UnivariateVectorFunction {
+
+    /**
+     * Returns the derivative of the function
+     *
+     * @return  the derivative function
+     */
+    UnivariateVectorFunction derivative();
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/FunctionUtils.java

@@ -0,0 +1,806 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.MultivariateDifferentiableVectorFunction;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.function.Identity;
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import com.fr.third.org.apache.commons.math3.exception.NumberIsTooLargeException;
+import com.fr.third.org.apache.commons.math3.exception.util.LocalizedFormats;
+
+/**
+ * Utilities for manipulating function objects.
+ *
+ * @since 3.0
+ */
+public class FunctionUtils {
+    /**
+     * Class only contains static methods.
+     */
+    private FunctionUtils() {}
+
+    /**
+     * Composes functions.
+     * <p>
+     * The functions in the argument list are composed sequentially, in the
+     * given order.  For example, compose(f1,f2,f3) acts like f1(f2(f3(x))).</p>
+     *
+     * @param f List of functions.
+     * @return the composite function.
+     */
+    public static UnivariateFunction compose(final UnivariateFunction ... f) {
+        return new UnivariateFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                double r = x;
+                for (int i = f.length - 1; i >= 0; i--) {
+                    r = f[i].value(r);
+                }
+                return r;
+            }
+        };
+    }
+
+    /**
+     * Composes functions.
+     * <p>
+     * The functions in the argument list are composed sequentially, in the
+     * given order.  For example, compose(f1,f2,f3) acts like f1(f2(f3(x))).</p>
+     *
+     * @param f List of functions.
+     * @return the composite function.
+     * @since 3.1
+     */
+    public static UnivariateDifferentiableFunction compose(final UnivariateDifferentiableFunction ... f) {
+        return new UnivariateDifferentiableFunction() {
+
+            /** {@inheritDoc} */
+            public double value(final double t) {
+                double r = t;
+                for (int i = f.length - 1; i >= 0; i--) {
+                    r = f[i].value(r);
+                }
+                return r;
+            }
+
+            /** {@inheritDoc} */
+            public DerivativeStructure value(final DerivativeStructure t) {
+                DerivativeStructure r = t;
+                for (int i = f.length - 1; i >= 0; i--) {
+                    r = f[i].value(r);
+                }
+                return r;
+            }
+
+        };
+    }
+
+    /**
+     * Composes functions.
+     * <p>
+     * The functions in the argument list are composed sequentially, in the
+     * given order.  For example, compose(f1,f2,f3) acts like f1(f2(f3(x))).</p>
+     *
+     * @param f List of functions.
+     * @return the composite function.
+     * @deprecated as of 3.1 replaced by {@link #compose(UnivariateDifferentiableFunction...)}
+     */
+    @Deprecated
+    public static DifferentiableUnivariateFunction compose(final DifferentiableUnivariateFunction ... f) {
+        return new DifferentiableUnivariateFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                double r = x;
+                for (int i = f.length - 1; i >= 0; i--) {
+                    r = f[i].value(r);
+                }
+                return r;
+            }
+
+            /** {@inheritDoc} */
+            public UnivariateFunction derivative() {
+                return new UnivariateFunction() {
+                    /** {@inheritDoc} */
+                    public double value(double x) {
+                        double p = 1;
+                        double r = x;
+                        for (int i = f.length - 1; i >= 0; i--) {
+                            p *= f[i].derivative().value(r);
+                            r = f[i].value(r);
+                        }
+                        return p;
+                    }
+                };
+            }
+        };
+    }
+
+    /**
+     * Adds functions.
+     *
+     * @param f List of functions.
+     * @return a function that computes the sum of the functions.
+     */
+    public static UnivariateFunction add(final UnivariateFunction ... f) {
+        return new UnivariateFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                double r = f[0].value(x);
+                for (int i = 1; i < f.length; i++) {
+                    r += f[i].value(x);
+                }
+                return r;
+            }
+        };
+    }
+
+    /**
+     * Adds functions.
+     *
+     * @param f List of functions.
+     * @return a function that computes the sum of the functions.
+     * @since 3.1
+     */
+    public static UnivariateDifferentiableFunction add(final UnivariateDifferentiableFunction ... f) {
+        return new UnivariateDifferentiableFunction() {
+
+            /** {@inheritDoc} */
+            public double value(final double t) {
+                double r = f[0].value(t);
+                for (int i = 1; i < f.length; i++) {
+                    r += f[i].value(t);
+                }
+                return r;
+            }
+
+            /** {@inheritDoc}
+             * @throws DimensionMismatchException if functions are not consistent with each other
+             */
+            public DerivativeStructure value(final DerivativeStructure t)
+                throws DimensionMismatchException {
+                DerivativeStructure r = f[0].value(t);
+                for (int i = 1; i < f.length; i++) {
+                    r = r.add(f[i].value(t));
+                }
+                return r;
+            }
+
+        };
+    }
+
+    /**
+     * Adds functions.
+     *
+     * @param f List of functions.
+     * @return a function that computes the sum of the functions.
+     * @deprecated as of 3.1 replaced by {@link #add(UnivariateDifferentiableFunction...)}
+     */
+    @Deprecated
+    public static DifferentiableUnivariateFunction add(final DifferentiableUnivariateFunction ... f) {
+        return new DifferentiableUnivariateFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                double r = f[0].value(x);
+                for (int i = 1; i < f.length; i++) {
+                    r += f[i].value(x);
+                }
+                return r;
+            }
+
+            /** {@inheritDoc} */
+            public UnivariateFunction derivative() {
+                return new UnivariateFunction() {
+                    /** {@inheritDoc} */
+                    public double value(double x) {
+                        double r = f[0].derivative().value(x);
+                        for (int i = 1; i < f.length; i++) {
+                            r += f[i].derivative().value(x);
+                        }
+                        return r;
+                    }
+                };
+            }
+        };
+    }
+
+    /**
+     * Multiplies functions.
+     *
+     * @param f List of functions.
+     * @return a function that computes the product of the functions.
+     */
+    public static UnivariateFunction multiply(final UnivariateFunction ... f) {
+        return new UnivariateFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                double r = f[0].value(x);
+                for (int i = 1; i < f.length; i++) {
+                    r *= f[i].value(x);
+                }
+                return r;
+            }
+        };
+    }
+
+    /**
+     * Multiplies functions.
+     *
+     * @param f List of functions.
+     * @return a function that computes the product of the functions.
+     * @since 3.1
+     */
+    public static UnivariateDifferentiableFunction multiply(final UnivariateDifferentiableFunction ... f) {
+        return new UnivariateDifferentiableFunction() {
+
+            /** {@inheritDoc} */
+            public double value(final double t) {
+                double r = f[0].value(t);
+                for (int i = 1; i < f.length; i++) {
+                    r  *= f[i].value(t);
+                }
+                return r;
+            }
+
+            /** {@inheritDoc} */
+            public DerivativeStructure value(final DerivativeStructure t) {
+                DerivativeStructure r = f[0].value(t);
+                for (int i = 1; i < f.length; i++) {
+                    r = r.multiply(f[i].value(t));
+                }
+                return r;
+            }
+
+        };
+    }
+
+    /**
+     * Multiplies functions.
+     *
+     * @param f List of functions.
+     * @return a function that computes the product of the functions.
+     * @deprecated as of 3.1 replaced by {@link #multiply(UnivariateDifferentiableFunction...)}
+     */
+    @Deprecated
+    public static DifferentiableUnivariateFunction multiply(final DifferentiableUnivariateFunction ... f) {
+        return new DifferentiableUnivariateFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                double r = f[0].value(x);
+                for (int i = 1; i < f.length; i++) {
+                    r *= f[i].value(x);
+                }
+                return r;
+            }
+
+            /** {@inheritDoc} */
+            public UnivariateFunction derivative() {
+                return new UnivariateFunction() {
+                    /** {@inheritDoc} */
+                    public double value(double x) {
+                        double sum = 0;
+                        for (int i = 0; i < f.length; i++) {
+                            double prod = f[i].derivative().value(x);
+                            for (int j = 0; j < f.length; j++) {
+                                if (i != j) {
+                                    prod *= f[j].value(x);
+                                }
+                            }
+                            sum += prod;
+                        }
+                        return sum;
+                    }
+                };
+            }
+        };
+    }
+
+    /**
+     * Returns the univariate function
+     * {@code h(x) = combiner(f(x), g(x)).}
+     *
+     * @param combiner Combiner function.
+     * @param f Function.
+     * @param g Function.
+     * @return the composite function.
+     */
+    public static UnivariateFunction combine(final BivariateFunction combiner,
+                                             final UnivariateFunction f,
+                                             final UnivariateFunction g) {
+        return new UnivariateFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return combiner.value(f.value(x), g.value(x));
+            }
+        };
+    }
+
+    /**
+     * Returns a MultivariateFunction h(x[]) defined by <pre> <code>
+     * h(x[]) = combiner(...combiner(combiner(initialValue,f(x[0])),f(x[1]))...),f(x[x.length-1]))
+     * </code></pre>
+     *
+     * @param combiner Combiner function.
+     * @param f Function.
+     * @param initialValue Initial value.
+     * @return a collector function.
+     */
+    public static MultivariateFunction collector(final BivariateFunction combiner,
+                                                 final UnivariateFunction f,
+                                                 final double initialValue) {
+        return new MultivariateFunction() {
+            /** {@inheritDoc} */
+            public double value(double[] point) {
+                double result = combiner.value(initialValue, f.value(point[0]));
+                for (int i = 1; i < point.length; i++) {
+                    result = combiner.value(result, f.value(point[i]));
+                }
+                return result;
+            }
+        };
+    }
+
+    /**
+     * Returns a MultivariateFunction h(x[]) defined by <pre> <code>
+     * h(x[]) = combiner(...combiner(combiner(initialValue,x[0]),x[1])...),x[x.length-1])
+     * </code></pre>
+     *
+     * @param combiner Combiner function.
+     * @param initialValue Initial value.
+     * @return a collector function.
+     */
+    public static MultivariateFunction collector(final BivariateFunction combiner,
+                                                 final double initialValue) {
+        return collector(combiner, new Identity(), initialValue);
+    }
+
+    /**
+     * Creates a unary function by fixing the first argument of a binary function.
+     *
+     * @param f Binary function.
+     * @param fixed value to which the first argument of {@code f} is set.
+     * @return the unary function h(x) = f(fixed, x)
+     */
+    public static UnivariateFunction fix1stArgument(final BivariateFunction f,
+                                                    final double fixed) {
+        return new UnivariateFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return f.value(fixed, x);
+            }
+        };
+    }
+    /**
+     * Creates a unary function by fixing the second argument of a binary function.
+     *
+     * @param f Binary function.
+     * @param fixed value to which the second argument of {@code f} is set.
+     * @return the unary function h(x) = f(x, fixed)
+     */
+    public static UnivariateFunction fix2ndArgument(final BivariateFunction f,
+                                                    final double fixed) {
+        return new UnivariateFunction() {
+            /** {@inheritDoc} */
+            public double value(double x) {
+                return f.value(x, fixed);
+            }
+        };
+    }
+
+    /**
+     * Samples the specified univariate real function on the specified interval.
+     * <p>
+     * The interval is divided equally into {@code n} sections and sample points
+     * are taken from {@code min} to {@code max - (max - min) / n}; therefore
+     * {@code f} is not sampled at the upper bound {@code max}.</p>
+     *
+     * @param f Function to be sampled
+     * @param min Lower bound of the interval (included).
+     * @param max Upper bound of the interval (excluded).
+     * @param n Number of sample points.
+     * @return the array of samples.
+     * @throws NumberIsTooLargeException if the lower bound {@code min} is
+     * greater than, or equal to the upper bound {@code max}.
+     * @throws NotStrictlyPositiveException if the number of sample points
+     * {@code n} is negative.
+     */
+    public static double[] sample(UnivariateFunction f, double min, double max, int n)
+       throws NumberIsTooLargeException, NotStrictlyPositiveException {
+
+        if (n <= 0) {
+            throw new NotStrictlyPositiveException(
+                    LocalizedFormats.NOT_POSITIVE_NUMBER_OF_SAMPLES,
+                    Integer.valueOf(n));
+        }
+        if (min >= max) {
+            throw new NumberIsTooLargeException(min, max, false);
+        }
+
+        final double[] s = new double[n];
+        final double h = (max - min) / n;
+        for (int i = 0; i < n; i++) {
+            s[i] = f.value(min + i * h);
+        }
+        return s;
+    }
+
+    /**
+     * Convert a {@link UnivariateDifferentiableFunction} into a {@link DifferentiableUnivariateFunction}.
+     *
+     * @param f function to convert
+     * @return converted function
+     * @deprecated this conversion method is temporary in version 3.1, as the {@link
+     * DifferentiableUnivariateFunction} interface itself is deprecated
+     */
+    @Deprecated
+    public static DifferentiableUnivariateFunction toDifferentiableUnivariateFunction(final UnivariateDifferentiableFunction f) {
+        return new DifferentiableUnivariateFunction() {
+
+            /** {@inheritDoc} */
+            public double value(final double x) {
+                return f.value(x);
+            }
+
+            /** {@inheritDoc} */
+            public UnivariateFunction derivative() {
+                return new UnivariateFunction() {
+                    /** {@inheritDoc} */
+                    public double value(final double x) {
+                        return f.value(new DerivativeStructure(1, 1, 0, x)).getPartialDerivative(1);
+                    }
+                };
+            }
+
+        };
+    }
+
+    /**
+     * Convert a {@link DifferentiableUnivariateFunction} into a {@link UnivariateDifferentiableFunction}.
+     * <p>
+     * Note that the converted function is able to handle {@link DerivativeStructure} up to order one.
+     * If the function is called with higher order, a {@link NumberIsTooLargeException} is thrown.
+     * </p>
+     * @param f function to convert
+     * @return converted function
+     * @deprecated this conversion method is temporary in version 3.1, as the {@link
+     * DifferentiableUnivariateFunction} interface itself is deprecated
+     */
+    @Deprecated
+    public static UnivariateDifferentiableFunction toUnivariateDifferential(final DifferentiableUnivariateFunction f) {
+        return new UnivariateDifferentiableFunction() {
+
+            /** {@inheritDoc} */
+            public double value(final double x) {
+                return f.value(x);
+            }
+
+            /** {@inheritDoc}
+             * @exception NumberIsTooLargeException if derivation order is greater than 1
+             */
+            public DerivativeStructure value(final DerivativeStructure t)
+                throws NumberIsTooLargeException {
+                switch (t.getOrder()) {
+                    case 0 :
+                        return new DerivativeStructure(t.getFreeParameters(), 0, f.value(t.getValue()));
+                    case 1 : {
+                        final int parameters = t.getFreeParameters();
+                        final double[] derivatives = new double[parameters + 1];
+                        derivatives[0] = f.value(t.getValue());
+                        final double fPrime = f.derivative().value(t.getValue());
+                        int[] orders = new int[parameters];
+                        for (int i = 0; i < parameters; ++i) {
+                            orders[i] = 1;
+                            derivatives[i + 1] = fPrime * t.getPartialDerivative(orders);
+                            orders[i] = 0;
+                        }
+                        return new DerivativeStructure(parameters, 1, derivatives);
+                    }
+                    default :
+                        throw new NumberIsTooLargeException(t.getOrder(), 1, true);
+                }
+            }
+
+        };
+    }
+
+    /**
+     * Convert a {@link MultivariateDifferentiableFunction} into a {@link DifferentiableMultivariateFunction}.
+     *
+     * @param f function to convert
+     * @return converted function
+     * @deprecated this conversion method is temporary in version 3.1, as the {@link
+     * DifferentiableMultivariateFunction} interface itself is deprecated
+     */
+    @Deprecated
+    public static DifferentiableMultivariateFunction toDifferentiableMultivariateFunction(final MultivariateDifferentiableFunction f) {
+        return new DifferentiableMultivariateFunction() {
+
+            /** {@inheritDoc} */
+            public double value(final double[] x) {
+                return f.value(x);
+            }
+
+            /** {@inheritDoc} */
+            public MultivariateFunction partialDerivative(final int k) {
+                return new MultivariateFunction() {
+                    /** {@inheritDoc} */
+                    public double value(final double[] x) {
+
+                        final int n = x.length;
+
+                        // delegate computation to underlying function
+                        final DerivativeStructure[] dsX = new DerivativeStructure[n];
+                        for (int i = 0; i < n; ++i) {
+                            if (i == k) {
+                                dsX[i] = new DerivativeStructure(1, 1, 0, x[i]);
+                            } else {
+                                dsX[i] = new DerivativeStructure(1, 1, x[i]);
+                            }
+                        }
+                        final DerivativeStructure y = f.value(dsX);
+
+                        // extract partial derivative
+                        return y.getPartialDerivative(1);
+
+                    }
+                };
+            }
+
+            /** {@inheritDoc} */
+            public MultivariateVectorFunction gradient() {
+                return new MultivariateVectorFunction() {
+                    /** {@inheritDoc} */
+                    public double[] value(final double[] x) {
+
+                        final int n = x.length;
+
+                        // delegate computation to underlying function
+                        final DerivativeStructure[] dsX = new DerivativeStructure[n];
+                        for (int i = 0; i < n; ++i) {
+                            dsX[i] = new DerivativeStructure(n, 1, i, x[i]);
+                        }
+                        final DerivativeStructure y = f.value(dsX);
+
+                        // extract gradient
+                        final double[] gradient = new double[n];
+                        final int[] orders = new int[n];
+                        for (int i = 0; i < n; ++i) {
+                            orders[i]   = 1;
+                            gradient[i] = y.getPartialDerivative(orders);
+                            orders[i]   = 0;
+                        }
+
+                        return gradient;
+
+                    }
+                };
+            }
+
+        };
+    }
+
+    /**
+     * Convert a {@link DifferentiableMultivariateFunction} into a {@link MultivariateDifferentiableFunction}.
+     * <p>
+     * Note that the converted function is able to handle {@link DerivativeStructure} elements
+     * that all have the same number of free parameters and order, and with order at most 1.
+     * If the function is called with inconsistent numbers of free parameters or higher order, a
+     * {@link DimensionMismatchException} or a {@link NumberIsTooLargeException} will be thrown.
+     * </p>
+     * @param f function to convert
+     * @return converted function
+     * @deprecated this conversion method is temporary in version 3.1, as the {@link
+     * DifferentiableMultivariateFunction} interface itself is deprecated
+     */
+    @Deprecated
+    public static MultivariateDifferentiableFunction toMultivariateDifferentiableFunction(final DifferentiableMultivariateFunction f) {
+        return new MultivariateDifferentiableFunction() {
+
+            /** {@inheritDoc} */
+            public double value(final double[] x) {
+                return f.value(x);
+            }
+
+            /** {@inheritDoc}
+             * @exception NumberIsTooLargeException if derivation order is higher than 1
+             * @exception DimensionMismatchException if numbers of free parameters are inconsistent
+             */
+            public DerivativeStructure value(final DerivativeStructure[] t)
+                throws DimensionMismatchException, NumberIsTooLargeException {
+
+                // check parameters and orders limits
+                final int parameters = t[0].getFreeParameters();
+                final int order      = t[0].getOrder();
+                final int n          = t.length;
+                if (order > 1) {
+                    throw new NumberIsTooLargeException(order, 1, true);
+                }
+
+                // check all elements in the array are consistent
+                for (int i = 0; i < n; ++i) {
+                    if (t[i].getFreeParameters() != parameters) {
+                        throw new DimensionMismatchException(t[i].getFreeParameters(), parameters);
+                    }
+
+                    if (t[i].getOrder() != order) {
+                        throw new DimensionMismatchException(t[i].getOrder(), order);
+                    }
+                }
+
+                // delegate computation to underlying function
+                final double[] point = new double[n];
+                for (int i = 0; i < n; ++i) {
+                    point[i] = t[i].getValue();
+                }
+                final double value      = f.value(point);
+                final double[] gradient = f.gradient().value(point);
+
+                // merge value and gradient into one DerivativeStructure
+                final double[] derivatives = new double[parameters + 1];
+                derivatives[0] = value;
+                final int[] orders = new int[parameters];
+                for (int i = 0; i < parameters; ++i) {
+                    orders[i] = 1;
+                    for (int j = 0; j < n; ++j) {
+                        derivatives[i + 1] += gradient[j] * t[j].getPartialDerivative(orders);
+                    }
+                    orders[i] = 0;
+                }
+
+                return new DerivativeStructure(parameters, order, derivatives);
+
+            }
+
+        };
+    }
+
+    /**
+     * Convert a {@link MultivariateDifferentiableVectorFunction} into a {@link DifferentiableMultivariateVectorFunction}.
+     *
+     * @param f function to convert
+     * @return converted function
+     * @deprecated this conversion method is temporary in version 3.1, as the {@link
+     * DifferentiableMultivariateVectorFunction} interface itself is deprecated
+     */
+    @Deprecated
+    public static DifferentiableMultivariateVectorFunction toDifferentiableMultivariateVectorFunction(final MultivariateDifferentiableVectorFunction f) {
+        return new DifferentiableMultivariateVectorFunction() {
+
+            /** {@inheritDoc} */
+            public double[] value(final double[] x) {
+                return f.value(x);
+            }
+
+            /** {@inheritDoc} */
+            public MultivariateMatrixFunction jacobian() {
+                return new MultivariateMatrixFunction() {
+                    /** {@inheritDoc} */
+                    public double[][] value(final double[] x) {
+
+                        final int n = x.length;
+
+                        // delegate computation to underlying function
+                        final DerivativeStructure[] dsX = new DerivativeStructure[n];
+                        for (int i = 0; i < n; ++i) {
+                            dsX[i] = new DerivativeStructure(n, 1, i, x[i]);
+                        }
+                        final DerivativeStructure[] y = f.value(dsX);
+
+                        // extract Jacobian
+                        final double[][] jacobian = new double[y.length][n];
+                        final int[] orders = new int[n];
+                        for (int i = 0; i < y.length; ++i) {
+                            for (int j = 0; j < n; ++j) {
+                                orders[j]      = 1;
+                                jacobian[i][j] = y[i].getPartialDerivative(orders);
+                                orders[j]      = 0;
+                            }
+                        }
+
+                        return jacobian;
+
+                    }
+                };
+            }
+
+        };
+    }
+
+    /**
+     * Convert a {@link DifferentiableMultivariateVectorFunction} into a {@link MultivariateDifferentiableVectorFunction}.
+     * <p>
+     * Note that the converted function is able to handle {@link DerivativeStructure} elements
+     * that all have the same number of free parameters and order, and with order at most 1.
+     * If the function is called with inconsistent numbers of free parameters or higher order, a
+     * {@link DimensionMismatchException} or a {@link NumberIsTooLargeException} will be thrown.
+     * </p>
+     * @param f function to convert
+     * @return converted function
+     * @deprecated this conversion method is temporary in version 3.1, as the {@link
+     * DifferentiableMultivariateFunction} interface itself is deprecated
+     */
+    @Deprecated
+    public static MultivariateDifferentiableVectorFunction toMultivariateDifferentiableVectorFunction(final DifferentiableMultivariateVectorFunction f) {
+        return new MultivariateDifferentiableVectorFunction() {
+
+            /** {@inheritDoc} */
+            public double[] value(final double[] x) {
+                return f.value(x);
+            }
+
+            /** {@inheritDoc}
+             * @exception NumberIsTooLargeException if derivation order is higher than 1
+             * @exception DimensionMismatchException if numbers of free parameters are inconsistent
+             */
+            public DerivativeStructure[] value(final DerivativeStructure[] t)
+                throws DimensionMismatchException, NumberIsTooLargeException {
+
+                // check parameters and orders limits
+                final int parameters = t[0].getFreeParameters();
+                final int order      = t[0].getOrder();
+                final int n          = t.length;
+                if (order > 1) {
+                    throw new NumberIsTooLargeException(order, 1, true);
+                }
+
+                // check all elements in the array are consistent
+                for (int i = 0; i < n; ++i) {
+                    if (t[i].getFreeParameters() != parameters) {
+                        throw new DimensionMismatchException(t[i].getFreeParameters(), parameters);
+                    }
+
+                    if (t[i].getOrder() != order) {
+                        throw new DimensionMismatchException(t[i].getOrder(), order);
+                    }
+                }
+
+                // delegate computation to underlying function
+                final double[] point = new double[n];
+                for (int i = 0; i < n; ++i) {
+                    point[i] = t[i].getValue();
+                }
+                final double[] value      = f.value(point);
+                final double[][] jacobian = f.jacobian().value(point);
+
+                // merge value and Jacobian into a DerivativeStructure array
+                final DerivativeStructure[] merged = new DerivativeStructure[value.length];
+                for (int k = 0; k < merged.length; ++k) {
+                    final double[] derivatives = new double[parameters + 1];
+                    derivatives[0] = value[k];
+                    final int[] orders = new int[parameters];
+                    for (int i = 0; i < parameters; ++i) {
+                        orders[i] = 1;
+                        for (int j = 0; j < n; ++j) {
+                            derivatives[i + 1] += jacobian[k][j] * t[j].getPartialDerivative(orders);
+                        }
+                        orders[i] = 0;
+                    }
+                    merged[k] = new DerivativeStructure(parameters, order, derivatives);
+                }
+
+                return merged;
+
+            }
+
+        };
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/MultivariateFunction.java

@@ -0,0 +1,45 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis;
+
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.exception.MathIllegalArgumentException;
+
+/**
+ * An interface representing a multivariate real function.
+ *
+ * @since 2.0
+ */
+public interface MultivariateFunction {
+
+    /**
+     * Compute the value for the function at the given point.
+     *
+     * @param point Point at which the function must be evaluated.
+     * @return the function value for the given point.
+     * @throws DimensionMismatchException
+     * if the parameter's dimension is wrong for the function being evaluated.
+     * @throws MathIllegalArgumentException
+     * when the activated method itself can ascertain that preconditions,
+     * specified in the API expressed at the level of the activated method,
+     * have been violated.  In the vast majority of cases where Commons Math
+     * throws this exception, it is the result of argument checking of actual
+     * parameters immediately passed to a method.
+     */
+    double value(double[] point);
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/MultivariateMatrixFunction.java

@@ -0,0 +1,35 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis;
+
+/**
+ * An interface representing a multivariate matrix function.
+ * @since 2.0
+ */
+public interface MultivariateMatrixFunction {
+
+    /**
+     * Compute the value for the function at the given point.
+     * @param point point at which the function must be evaluated
+     * @return function value for the given point
+     * @exception IllegalArgumentException if point's dimension is wrong
+     */
+    double[][] value(double[] point)
+        throws IllegalArgumentException;
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/MultivariateVectorFunction.java

@@ -0,0 +1,35 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis;
+
+/**
+ * An interface representing a multivariate vectorial function.
+ * @since 2.0
+ */
+public interface MultivariateVectorFunction {
+
+    /**
+     * Compute the value for the function at the given point.
+     * @param point point at which the function must be evaluated
+     * @return function value for the given point
+     * @exception IllegalArgumentException if point's dimension is wrong
+     */
+    double[] value(double[] point)
+        throws IllegalArgumentException;
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/ParametricUnivariateFunction.java

@@ -0,0 +1,44 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis;
+
+/**
+ * An interface representing a real function that depends on one independent
+ * variable plus some extra parameters.
+ *
+ * @since 3.0
+ */
+public interface ParametricUnivariateFunction {
+    /**
+     * Compute the value of the function.
+     *
+     * @param x Point for which the function value should be computed.
+     * @param parameters Function parameters.
+     * @return the value.
+     */
+    double value(double x, double ... parameters);
+
+    /**
+     * Compute the gradient of the function with respect to its parameters.
+     *
+     * @param x Point for which the function value should be computed.
+     * @param parameters Function parameters.
+     * @return the value.
+     */
+    double[] gradient(double x, double ... parameters);
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/RealFieldUnivariateFunction.java

@@ -0,0 +1,86 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis;
+
+import com.fr.third.org.apache.commons.math3.RealFieldElement;
+
+/**
+ * An interface representing a univariate real function.
+ * <p>
+ * When a <em>user-defined</em> function encounters an error during
+ * evaluation, the {@link #value(RealFieldElement) value} method should throw a
+ * <em>user-defined</em> unchecked exception.</p>
+ * <p>
+ * The following code excerpt shows the recommended way to do that using
+ * a root solver as an example, but the same construct is applicable to
+ * ODE integrators or optimizers.</p>
+ *
+ * <pre>
+ * private static class LocalException extends RuntimeException {
+ *     // The x value that caused the problem.
+ *     private final SomeFieldType x;
+ *
+ *     public LocalException(SomeFieldType x) {
+ *         this.x = x;
+ *     }
+ *
+ *     public double getX() {
+ *         return x;
+ *     }
+ * }
+ *
+ * private static class MyFunction implements FieldUnivariateFunction&lt;SomeFieldType&gt; {
+ *     public SomeFieldType value(SomeFieldType x) {
+ *         SomeFieldType y = hugeFormula(x);
+ *         if (somethingBadHappens) {
+ *           throw new LocalException(x);
+ *         }
+ *         return y;
+ *     }
+ * }
+ *
+ * public void compute() {
+ *     try {
+ *         solver.solve(maxEval, new MyFunction(a, b, c), min, max);
+ *     } catch (LocalException le) {
+ *         // Retrieve the x value.
+ *     }
+ * }
+ * </pre>
+ *
+ * As shown, the exception is local to the user's code and it is guaranteed
+ * that Apache Commons Math will not catch it.
+ *
+ * @param <T> the type of the field elements
+ * @since 3.6
+ * @see UnivariateFunction
+ */
+public interface RealFieldUnivariateFunction<T extends RealFieldElement<T>> {
+    /**
+     * Compute the value of the function.
+     *
+     * @param x Point at which the function value should be computed.
+     * @return the value of the function.
+     * @throws IllegalArgumentException when the activated method itself can
+     * ascertain that a precondition, specified in the API expressed at the
+     * level of the activated method, has been violated.
+     * When Commons Math throws an {@code IllegalArgumentException}, it is
+     * usually the consequence of checking the actual parameters passed to
+     * the method.
+     */
+    T value(T x);
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/TrivariateFunction.java

@@ -0,0 +1,35 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis;
+
+/**
+ * An interface representing a trivariate real function.
+ *
+ * @since 2.2
+ */
+public interface TrivariateFunction {
+    /**
+     * Compute the value for the function.
+     *
+     * @param x x-coordinate for which the function value should be computed.
+     * @param y y-coordinate for which the function value should be computed.
+     * @param z z-coordinate for which the function value should be computed.
+     * @return the value.
+     */
+    double value(double x, double y, double z);
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/UnivariateFunction.java

@@ -0,0 +1,81 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis;
+
+/**
+ * An interface representing a univariate real function.
+ * <p>
+ * When a <em>user-defined</em> function encounters an error during
+ * evaluation, the {@link #value(double) value} method should throw a
+ * <em>user-defined</em> unchecked exception.</p>
+ * <p>
+ * The following code excerpt shows the recommended way to do that using
+ * a root solver as an example, but the same construct is applicable to
+ * ODE integrators or optimizers.</p>
+ *
+ * <pre>
+ * private static class LocalException extends RuntimeException {
+ *     // The x value that caused the problem.
+ *     private final double x;
+ *
+ *     public LocalException(double x) {
+ *         this.x = x;
+ *     }
+ *
+ *     public double getX() {
+ *         return x;
+ *     }
+ * }
+ *
+ * private static class MyFunction implements UnivariateFunction {
+ *     public double value(double x) {
+ *         double y = hugeFormula(x);
+ *         if (somethingBadHappens) {
+ *           throw new LocalException(x);
+ *         }
+ *         return y;
+ *     }
+ * }
+ *
+ * public void compute() {
+ *     try {
+ *         solver.solve(maxEval, new MyFunction(a, b, c), min, max);
+ *     } catch (LocalException le) {
+ *         // Retrieve the x value.
+ *     }
+ * }
+ * </pre>
+ *
+ * As shown, the exception is local to the user's code and it is guaranteed
+ * that Apache Commons Math will not catch it.
+ *
+ */
+public interface UnivariateFunction {
+    /**
+     * Compute the value of the function.
+     *
+     * @param x Point at which the function value should be computed.
+     * @return the value of the function.
+     * @throws IllegalArgumentException when the activated method itself can
+     * ascertain that a precondition, specified in the API expressed at the
+     * level of the activated method, has been violated.
+     * When Commons Math throws an {@code IllegalArgumentException}, it is
+     * usually the consequence of checking the actual parameters passed to
+     * the method.
+     */
+    double value(double x);
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/UnivariateMatrixFunction.java

@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis;
+
+/**
+ * An interface representing a univariate matrix function.
+ *
+ * @since 2.0
+ */
+public interface UnivariateMatrixFunction {
+
+    /**
+     * Compute the value for the function.
+     * @param x the point for which the function value should be computed
+     * @return the value
+     */
+    double[][] value(double x);
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/UnivariateVectorFunction.java

@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis;
+
+/**
+ * An interface representing a univariate vectorial function.
+ *
+ * @since 2.0
+ */
+public interface UnivariateVectorFunction {
+
+    /**
+     * Compute the value for the function.
+     * @param x the point for which the function value should be computed
+     * @return the value
+     */
+    double[] value(double x);
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/differentiation/FiniteDifferencesDifferentiator.java

@@ -0,0 +1,384 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.differentiation;
+
+import java.io.Serializable;
+
+import com.fr.third.org.apache.commons.math3.exception.MathIllegalArgumentException;
+import com.fr.third.org.apache.commons.math3.exception.NotPositiveException;
+import com.fr.third.org.apache.commons.math3.exception.NumberIsTooLargeException;
+import com.fr.third.org.apache.commons.math3.exception.NumberIsTooSmallException;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateMatrixFunction;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateVectorFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/** Univariate functions differentiator using finite differences.
+ * <p>
+ * This class creates some wrapper objects around regular
+ * {@link UnivariateFunction univariate functions} (or {@link
+ * UnivariateVectorFunction univariate vector functions} or {@link
+ * UnivariateMatrixFunction univariate matrix functions}). These
+ * wrapper objects compute derivatives in addition to function
+ * values.
+ * </p>
+ * <p>
+ * The wrapper objects work by calling the underlying function on
+ * a sampling grid around the current point and performing polynomial
+ * interpolation. A finite differences scheme with n points is
+ * theoretically able to compute derivatives up to order n-1, but
+ * it is generally better to have a slight margin. The step size must
+ * also be small enough in order for the polynomial approximation to
+ * be good in the current point neighborhood, but it should not be too
+ * small because numerical instability appears quickly (there are several
+ * differences of close points). Choosing the number of points and
+ * the step size is highly problem dependent.
+ * </p>
+ * <p>
+ * As an example of good and bad settings, lets consider the quintic
+ * polynomial function {@code f(x) = (x-1)*(x-0.5)*x*(x+0.5)*(x+1)}.
+ * Since it is a polynomial, finite differences with at least 6 points
+ * should theoretically recover the exact same polynomial and hence
+ * compute accurate derivatives for any order. However, due to numerical
+ * errors, we get the following results for a 7 points finite differences
+ * for abscissae in the [-10, 10] range:
+ * <ul>
+ *   <li>step size = 0.25, second order derivative error about 9.97e-10</li>
+ *   <li>step size = 0.25, fourth order derivative error about 5.43e-8</li>
+ *   <li>step size = 1.0e-6, second order derivative error about 148</li>
+ *   <li>step size = 1.0e-6, fourth order derivative error about 6.35e+14</li>
+ * </ul>
+ * <p>
+ * This example shows that the small step size is really bad, even simply
+ * for second order derivative!</p>
+ *
+ * @since 3.1
+ */
+public class FiniteDifferencesDifferentiator
+    implements UnivariateFunctionDifferentiator, UnivariateVectorFunctionDifferentiator,
+               UnivariateMatrixFunctionDifferentiator, Serializable {
+
+    /** Serializable UID. */
+    private static final long serialVersionUID = 20120917L;
+
+    /** Number of points to use. */
+    private final int nbPoints;
+
+    /** Step size. */
+    private final double stepSize;
+
+    /** Half sample span. */
+    private final double halfSampleSpan;
+
+    /** Lower bound for independent variable. */
+    private final double tMin;
+
+    /** Upper bound for independent variable. */
+    private final double tMax;
+
+    /**
+     * Build a differentiator with number of points and step size when independent variable is unbounded.
+     * <p>
+     * Beware that wrong settings for the finite differences differentiator
+     * can lead to highly unstable and inaccurate results, especially for
+     * high derivation orders. Using very small step sizes is often a
+     * <em>bad</em> idea.
+     * </p>
+     * @param nbPoints number of points to use
+     * @param stepSize step size (gap between each point)
+     * @exception NotPositiveException if {@code stepsize <= 0} (note that
+     * {@link NotPositiveException} extends {@link NumberIsTooSmallException})
+     * @exception NumberIsTooSmallException {@code nbPoint <= 1}
+     */
+    public FiniteDifferencesDifferentiator(final int nbPoints, final double stepSize)
+        throws NotPositiveException, NumberIsTooSmallException {
+        this(nbPoints, stepSize, Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);
+    }
+
+    /**
+     * Build a differentiator with number of points and step size when independent variable is bounded.
+     * <p>
+     * When the independent variable is bounded (tLower &lt; t &lt; tUpper), the sampling
+     * points used for differentiation will be adapted to ensure the constraint holds
+     * even near the boundaries. This means the sample will not be centered anymore in
+     * these cases. At an extreme case, computing derivatives exactly at the lower bound
+     * will lead the sample to be entirely on the right side of the derivation point.
+     * </p>
+     * <p>
+     * Note that the boundaries are considered to be excluded for function evaluation.
+     * </p>
+     * <p>
+     * Beware that wrong settings for the finite differences differentiator
+     * can lead to highly unstable and inaccurate results, especially for
+     * high derivation orders. Using very small step sizes is often a
+     * <em>bad</em> idea.
+     * </p>
+     * @param nbPoints number of points to use
+     * @param stepSize step size (gap between each point)
+     * @param tLower lower bound for independent variable (may be {@code Double.NEGATIVE_INFINITY}
+     * if there are no lower bounds)
+     * @param tUpper upper bound for independent variable (may be {@code Double.POSITIVE_INFINITY}
+     * if there are no upper bounds)
+     * @exception NotPositiveException if {@code stepsize <= 0} (note that
+     * {@link NotPositiveException} extends {@link NumberIsTooSmallException})
+     * @exception NumberIsTooSmallException {@code nbPoint <= 1}
+     * @exception NumberIsTooLargeException {@code stepSize * (nbPoints - 1) >= tUpper - tLower}
+     */
+    public FiniteDifferencesDifferentiator(final int nbPoints, final double stepSize,
+                                           final double tLower, final double tUpper)
+            throws NotPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
+
+        if (nbPoints <= 1) {
+            throw new NumberIsTooSmallException(stepSize, 1, false);
+        }
+        this.nbPoints = nbPoints;
+
+        if (stepSize <= 0) {
+            throw new NotPositiveException(stepSize);
+        }
+        this.stepSize = stepSize;
+
+        halfSampleSpan = 0.5 * stepSize * (nbPoints - 1);
+        if (2 * halfSampleSpan >= tUpper - tLower) {
+            throw new NumberIsTooLargeException(2 * halfSampleSpan, tUpper - tLower, false);
+        }
+        final double safety = FastMath.ulp(halfSampleSpan);
+        this.tMin = tLower + halfSampleSpan + safety;
+        this.tMax = tUpper - halfSampleSpan - safety;
+
+    }
+
+    /**
+     * Get the number of points to use.
+     * @return number of points to use
+     */
+    public int getNbPoints() {
+        return nbPoints;
+    }
+
+    /**
+     * Get the step size.
+     * @return step size
+     */
+    public double getStepSize() {
+        return stepSize;
+    }
+
+    /**
+     * Evaluate derivatives from a sample.
+     * <p>
+     * Evaluation is done using divided differences.
+     * </p>
+     * @param t evaluation abscissa value and derivatives
+     * @param t0 first sample point abscissa
+     * @param y function values sample {@code y[i] = f(t[i]) = f(t0 + i * stepSize)}
+     * @return value and derivatives at {@code t}
+     * @exception NumberIsTooLargeException if the requested derivation order
+     * is larger or equal to the number of points
+     */
+    private DerivativeStructure evaluate(final DerivativeStructure t, final double t0,
+                                         final double[] y)
+        throws NumberIsTooLargeException {
+
+        // create divided differences diagonal arrays
+        final double[] top    = new double[nbPoints];
+        final double[] bottom = new double[nbPoints];
+
+        for (int i = 0; i < nbPoints; ++i) {
+
+            // update the bottom diagonal of the divided differences array
+            bottom[i] = y[i];
+            for (int j = 1; j <= i; ++j) {
+                bottom[i - j] = (bottom[i - j + 1] - bottom[i - j]) / (j * stepSize);
+            }
+
+            // update the top diagonal of the divided differences array
+            top[i] = bottom[0];
+
+        }
+
+        // evaluate interpolation polynomial (represented by top diagonal) at t
+        final int order            = t.getOrder();
+        final int parameters       = t.getFreeParameters();
+        final double[] derivatives = t.getAllDerivatives();
+        final double dt0           = t.getValue() - t0;
+        DerivativeStructure interpolation = new DerivativeStructure(parameters, order, 0.0);
+        DerivativeStructure monomial = null;
+        for (int i = 0; i < nbPoints; ++i) {
+            if (i == 0) {
+                // start with monomial(t) = 1
+                monomial = new DerivativeStructure(parameters, order, 1.0);
+            } else {
+                // monomial(t) = (t - t0) * (t - t1) * ... * (t - t(i-1))
+                derivatives[0] = dt0 - (i - 1) * stepSize;
+                final DerivativeStructure deltaX = new DerivativeStructure(parameters, order, derivatives);
+                monomial = monomial.multiply(deltaX);
+            }
+            interpolation = interpolation.add(monomial.multiply(top[i]));
+        }
+
+        return interpolation;
+
+    }
+
+    /** {@inheritDoc}
+     * <p>The returned object cannot compute derivatives to arbitrary orders. The
+     * value function will throw a {@link NumberIsTooLargeException} if the requested
+     * derivation order is larger or equal to the number of points.
+     * </p>
+     */
+    public UnivariateDifferentiableFunction differentiate(final UnivariateFunction function) {
+        return new UnivariateDifferentiableFunction() {
+
+            /** {@inheritDoc} */
+            public double value(final double x) throws MathIllegalArgumentException {
+                return function.value(x);
+            }
+
+            /** {@inheritDoc} */
+            public DerivativeStructure value(final DerivativeStructure t)
+                throws MathIllegalArgumentException {
+
+                // check we can achieve the requested derivation order with the sample
+                if (t.getOrder() >= nbPoints) {
+                    throw new NumberIsTooLargeException(t.getOrder(), nbPoints, false);
+                }
+
+                // compute sample position, trying to be centered if possible
+                final double t0 = FastMath.max(FastMath.min(t.getValue(), tMax), tMin) - halfSampleSpan;
+
+                // compute sample points
+                final double[] y = new double[nbPoints];
+                for (int i = 0; i < nbPoints; ++i) {
+                    y[i] = function.value(t0 + i * stepSize);
+                }
+
+                // evaluate derivatives
+                return evaluate(t, t0, y);
+
+            }
+
+        };
+    }
+
+    /** {@inheritDoc}
+     * <p>The returned object cannot compute derivatives to arbitrary orders. The
+     * value function will throw a {@link NumberIsTooLargeException} if the requested
+     * derivation order is larger or equal to the number of points.
+     * </p>
+     */
+    public UnivariateDifferentiableVectorFunction differentiate(final UnivariateVectorFunction function) {
+        return new UnivariateDifferentiableVectorFunction() {
+
+            /** {@inheritDoc} */
+            public double[]value(final double x) throws MathIllegalArgumentException {
+                return function.value(x);
+            }
+
+            /** {@inheritDoc} */
+            public DerivativeStructure[] value(final DerivativeStructure t)
+                throws MathIllegalArgumentException {
+
+                // check we can achieve the requested derivation order with the sample
+                if (t.getOrder() >= nbPoints) {
+                    throw new NumberIsTooLargeException(t.getOrder(), nbPoints, false);
+                }
+
+                // compute sample position, trying to be centered if possible
+                final double t0 = FastMath.max(FastMath.min(t.getValue(), tMax), tMin) - halfSampleSpan;
+
+                // compute sample points
+                double[][] y = null;
+                for (int i = 0; i < nbPoints; ++i) {
+                    final double[] v = function.value(t0 + i * stepSize);
+                    if (i == 0) {
+                        y = new double[v.length][nbPoints];
+                    }
+                    for (int j = 0; j < v.length; ++j) {
+                        y[j][i] = v[j];
+                    }
+                }
+
+                // evaluate derivatives
+                final DerivativeStructure[] value = new DerivativeStructure[y.length];
+                for (int j = 0; j < value.length; ++j) {
+                    value[j] = evaluate(t, t0, y[j]);
+                }
+
+                return value;
+
+            }
+
+        };
+    }
+
+    /** {@inheritDoc}
+     * <p>The returned object cannot compute derivatives to arbitrary orders. The
+     * value function will throw a {@link NumberIsTooLargeException} if the requested
+     * derivation order is larger or equal to the number of points.
+     * </p>
+     */
+    public UnivariateDifferentiableMatrixFunction differentiate(final UnivariateMatrixFunction function) {
+        return new UnivariateDifferentiableMatrixFunction() {
+
+            /** {@inheritDoc} */
+            public double[][]  value(final double x) throws MathIllegalArgumentException {
+                return function.value(x);
+            }
+
+            /** {@inheritDoc} */
+            public DerivativeStructure[][]  value(final DerivativeStructure t)
+                throws MathIllegalArgumentException {
+
+                // check we can achieve the requested derivation order with the sample
+                if (t.getOrder() >= nbPoints) {
+                    throw new NumberIsTooLargeException(t.getOrder(), nbPoints, false);
+                }
+
+                // compute sample position, trying to be centered if possible
+                final double t0 = FastMath.max(FastMath.min(t.getValue(), tMax), tMin) - halfSampleSpan;
+
+                // compute sample points
+                double[][][] y = null;
+                for (int i = 0; i < nbPoints; ++i) {
+                    final double[][] v = function.value(t0 + i * stepSize);
+                    if (i == 0) {
+                        y = new double[v.length][v[0].length][nbPoints];
+                    }
+                    for (int j = 0; j < v.length; ++j) {
+                        for (int k = 0; k < v[j].length; ++k) {
+                            y[j][k][i] = v[j][k];
+                        }
+                    }
+                }
+
+                // evaluate derivatives
+                final DerivativeStructure[][] value = new DerivativeStructure[y.length][y[0].length];
+                for (int j = 0; j < value.length; ++j) {
+                    for (int k = 0; k < y[j].length; ++k) {
+                        value[j][k] = evaluate(t, t0, y[j][k]);
+                    }
+                }
+
+                return value;
+
+            }
+
+        };
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/differentiation/GradientFunction.java

@@ -0,0 +1,65 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.differentiation;
+
+import com.fr.third.org.apache.commons.math3.analysis.MultivariateVectorFunction;
+
+/** Class representing the gradient of a multivariate function.
+ * <p>
+ * The vectorial components of the function represent the derivatives
+ * with respect to each function parameters.
+ * </p>
+ * @since 3.1
+ */
+public class GradientFunction implements MultivariateVectorFunction {
+
+    /** Underlying real-valued function. */
+    private final MultivariateDifferentiableFunction f;
+
+    /** Simple constructor.
+     * @param f underlying real-valued function
+     */
+    public GradientFunction(final MultivariateDifferentiableFunction f) {
+        this.f = f;
+    }
+
+    /** {@inheritDoc} */
+    public double[] value(double[] point) {
+
+        // set up parameters
+        final DerivativeStructure[] dsX = new DerivativeStructure[point.length];
+        for (int i = 0; i < point.length; ++i) {
+            dsX[i] = new DerivativeStructure(point.length, 1, i, point[i]);
+        }
+
+        // compute the derivatives
+        final DerivativeStructure dsY = f.value(dsX);
+
+        // extract the gradient
+        final double[] y = new double[point.length];
+        final int[] orders = new int[point.length];
+        for (int i = 0; i < point.length; ++i) {
+            orders[i] = 1;
+            y[i] = dsY.getPartialDerivative(orders);
+            orders[i] = 0;
+        }
+
+        return y;
+
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/differentiation/JacobianFunction.java

@@ -0,0 +1,69 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.differentiation;
+
+import com.fr.third.org.apache.commons.math3.analysis.MultivariateMatrixFunction;
+
+/** Class representing the Jacobian of a multivariate vector function.
+ * <p>
+ * The rows iterate on the model functions while the columns iterate on the parameters; thus,
+ * the numbers of rows is equal to the dimension of the underlying function vector
+ * value and the number of columns is equal to the number of free parameters of
+ * the underlying function.
+ * </p>
+ * @since 3.1
+ */
+public class JacobianFunction implements MultivariateMatrixFunction {
+
+    /** Underlying vector-valued function. */
+    private final MultivariateDifferentiableVectorFunction f;
+
+    /** Simple constructor.
+     * @param f underlying vector-valued function
+     */
+    public JacobianFunction(final MultivariateDifferentiableVectorFunction f) {
+        this.f = f;
+    }
+
+    /** {@inheritDoc} */
+    public double[][] value(double[] point) {
+
+        // set up parameters
+        final DerivativeStructure[] dsX = new DerivativeStructure[point.length];
+        for (int i = 0; i < point.length; ++i) {
+            dsX[i] = new DerivativeStructure(point.length, 1, i, point[i]);
+        }
+
+        // compute the derivatives
+        final DerivativeStructure[] dsY = f.value(dsX);
+
+        // extract the Jacobian
+        final double[][] y = new double[dsY.length][point.length];
+        final int[] orders = new int[point.length];
+        for (int i = 0; i < dsY.length; ++i) {
+            for (int j = 0; j < point.length; ++j) {
+                orders[j] = 1;
+                y[i][j] = dsY[i].getPartialDerivative(orders);
+                orders[j] = 0;
+            }
+        }
+
+        return y;
+
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/differentiation/MultivariateDifferentiableFunction.java

@@ -0,0 +1,42 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.differentiation;
+
+import com.fr.third.org.apache.commons.math3.exception.MathIllegalArgumentException;
+import com.fr.third.org.apache.commons.math3.analysis.MultivariateFunction;
+
+/**
+ * Extension of {@link MultivariateFunction} representing a
+ * multivariate differentiable real function.
+ * @since 3.1
+ */
+public interface MultivariateDifferentiableFunction extends MultivariateFunction {
+
+    /**
+     * Compute the value for the function at the given point.
+     *
+     * @param point Point at which the function must be evaluated.
+     * @return the function value for the given point.
+     * @exception MathIllegalArgumentException if {@code point} does not
+     * satisfy the function's constraints (wrong dimension, argument out of bound,
+     * or unsupported derivative order for example)
+     */
+    DerivativeStructure value(DerivativeStructure[] point)
+        throws MathIllegalArgumentException;
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/differentiation/MultivariateDifferentiableVectorFunction.java

@@ -0,0 +1,43 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.differentiation;
+
+import com.fr.third.org.apache.commons.math3.exception.MathIllegalArgumentException;
+import com.fr.third.org.apache.commons.math3.analysis.MultivariateVectorFunction;
+
+
+/**
+ * Extension of {@link MultivariateVectorFunction} representing a
+ * multivariate differentiable vectorial function.
+ * @since 3.1
+ */
+public interface MultivariateDifferentiableVectorFunction
+    extends MultivariateVectorFunction {
+
+    /**
+     * Compute the value for the function at the given point.
+     * @param point point at which the function must be evaluated
+     * @return function value for the given point
+     * @exception MathIllegalArgumentException if {@code point} does not
+     * satisfy the function's constraints (wrong dimension, argument out of bound,
+     * or unsupported derivative order for example)
+     */
+    DerivativeStructure[] value(DerivativeStructure[] point)
+        throws MathIllegalArgumentException;
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/differentiation/SparseGradient.java

@@ -0,0 +1,877 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.differentiation;
+
+import java.io.Serializable;
+import java.util.Collections;
+import java.util.HashMap;
+import java.util.Map;
+
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.Field;
+import com.fr.third.org.apache.commons.math3.FieldElement;
+import com.fr.third.org.apache.commons.math3.RealFieldElement;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+import com.fr.third.org.apache.commons.math3.util.MathArrays;
+import com.fr.third.org.apache.commons.math3.util.MathUtils;
+import com.fr.third.org.apache.commons.math3.util.Precision;
+
+/**
+ * First derivative computation with large number of variables.
+ * <p>
+ * This class plays a similar role to {@link DerivativeStructure}, with
+ * a focus on efficiency when dealing with large number of independent variables
+ * and most computation depend only on a few of them, and when only first derivative
+ * is desired. When these conditions are met, this class should be much faster than
+ * {@link DerivativeStructure} and use less memory.
+ * </p>
+ *
+ * @since 3.3
+ */
+public class SparseGradient implements RealFieldElement<SparseGradient>, Serializable {
+
+    /** Serializable UID. */
+    private static final long serialVersionUID = 20131025L;
+
+    /** Value of the calculation. */
+    private double value;
+
+    /** Stored derivative, each key representing a different independent variable. */
+    private final Map<Integer, Double> derivatives;
+
+    /** Internal constructor.
+     * @param value value of the function
+     * @param derivatives derivatives map, a deep copy will be performed,
+     * so the map given here will remain safe from changes in the new instance,
+     * may be null to create an empty derivatives map, i.e. a constant value
+     */
+    private SparseGradient(final double value, final Map<Integer, Double> derivatives) {
+        this.value = value;
+        this.derivatives = new HashMap<Integer, Double>();
+        if (derivatives != null) {
+            this.derivatives.putAll(derivatives);
+        }
+    }
+
+    /** Internal constructor.
+     * @param value value of the function
+     * @param scale scaling factor to apply to all derivatives
+     * @param derivatives derivatives map, a deep copy will be performed,
+     * so the map given here will remain safe from changes in the new instance,
+     * may be null to create an empty derivatives map, i.e. a constant value
+     */
+    private SparseGradient(final double value, final double scale,
+                             final Map<Integer, Double> derivatives) {
+        this.value = value;
+        this.derivatives = new HashMap<Integer, Double>();
+        if (derivatives != null) {
+            for (final Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
+                this.derivatives.put(entry.getKey(), scale * entry.getValue());
+            }
+        }
+    }
+
+    /** Factory method creating a constant.
+     * @param value value of the constant
+     * @return a new instance
+     */
+    public static SparseGradient createConstant(final double value) {
+        return new SparseGradient(value, Collections.<Integer, Double> emptyMap());
+    }
+
+    /** Factory method creating an independent variable.
+     * @param idx index of the variable
+     * @param value value of the variable
+     * @return a new instance
+     */
+    public static SparseGradient createVariable(final int idx, final double value) {
+        return new SparseGradient(value, Collections.singletonMap(idx, 1.0));
+    }
+
+    /**
+     * Find the number of variables.
+     * @return number of variables
+     */
+    public int numVars() {
+        return derivatives.size();
+    }
+
+    /**
+     * Get the derivative with respect to a particular index variable.
+     *
+     * @param index index to differentiate with.
+     * @return derivative with respect to a particular index variable
+     */
+    public double getDerivative(final int index) {
+        final Double out = derivatives.get(index);
+        return (out == null) ? 0.0 : out;
+    }
+
+    /**
+     * Get the value of the function.
+     * @return value of the function.
+     */
+    public double getValue() {
+        return value;
+    }
+
+    /** {@inheritDoc} */
+    public double getReal() {
+        return value;
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient add(final SparseGradient a) {
+        final SparseGradient out = new SparseGradient(value + a.value, derivatives);
+        for (Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
+            final int id = entry.getKey();
+            final Double old = out.derivatives.get(id);
+            if (old == null) {
+                out.derivatives.put(id, entry.getValue());
+            } else {
+                out.derivatives.put(id, old + entry.getValue());
+            }
+        }
+
+        return out;
+    }
+
+    /**
+     * Add in place.
+     * <p>
+     * This method is designed to be faster when used multiple times in a loop.
+     * </p>
+     * <p>
+     * The instance is changed here, in order to not change the
+     * instance the {@link #add(SparseGradient)} method should
+     * be used.
+     * </p>
+     * @param a instance to add
+     */
+    public void addInPlace(final SparseGradient a) {
+        value += a.value;
+        for (final Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
+            final int id = entry.getKey();
+            final Double old = derivatives.get(id);
+            if (old == null) {
+                derivatives.put(id, entry.getValue());
+            } else {
+                derivatives.put(id, old + entry.getValue());
+            }
+        }
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient add(final double c) {
+        final SparseGradient out = new SparseGradient(value + c, derivatives);
+        return out;
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient subtract(final SparseGradient a) {
+        final SparseGradient out = new SparseGradient(value - a.value, derivatives);
+        for (Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
+            final int id = entry.getKey();
+            final Double old = out.derivatives.get(id);
+            if (old == null) {
+                out.derivatives.put(id, -entry.getValue());
+            } else {
+                out.derivatives.put(id, old - entry.getValue());
+            }
+        }
+        return out;
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient subtract(double c) {
+        return new SparseGradient(value - c, derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient multiply(final SparseGradient a) {
+        final SparseGradient out =
+            new SparseGradient(value * a.value, Collections.<Integer, Double> emptyMap());
+
+        // Derivatives.
+        for (Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
+            out.derivatives.put(entry.getKey(), a.value * entry.getValue());
+        }
+        for (Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
+            final int id = entry.getKey();
+            final Double old = out.derivatives.get(id);
+            if (old == null) {
+                out.derivatives.put(id, value * entry.getValue());
+            } else {
+                out.derivatives.put(id, old + value * entry.getValue());
+            }
+        }
+        return out;
+    }
+
+    /**
+     * Multiply in place.
+     * <p>
+     * This method is designed to be faster when used multiple times in a loop.
+     * </p>
+     * <p>
+     * The instance is changed here, in order to not change the
+     * instance the {@link #add(SparseGradient)} method should
+     * be used.
+     * </p>
+     * @param a instance to multiply
+     */
+    public void multiplyInPlace(final SparseGradient a) {
+        // Derivatives.
+        for (Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
+            derivatives.put(entry.getKey(), a.value * entry.getValue());
+        }
+        for (Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
+            final int id = entry.getKey();
+            final Double old = derivatives.get(id);
+            if (old == null) {
+                derivatives.put(id, value * entry.getValue());
+            } else {
+                derivatives.put(id, old + value * entry.getValue());
+            }
+        }
+        value *= a.value;
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient multiply(final double c) {
+        return new SparseGradient(value * c, c, derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient multiply(final int n) {
+        return new SparseGradient(value * n, n, derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient divide(final SparseGradient a) {
+        final SparseGradient out = new SparseGradient(value / a.value, Collections.<Integer, Double> emptyMap());
+
+        // Derivatives.
+        for (Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
+            out.derivatives.put(entry.getKey(), entry.getValue() / a.value);
+        }
+        for (Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
+            final int id = entry.getKey();
+            final Double old = out.derivatives.get(id);
+            if (old == null) {
+                out.derivatives.put(id, -out.value / a.value * entry.getValue());
+            } else {
+                out.derivatives.put(id, old - out.value / a.value * entry.getValue());
+            }
+        }
+        return out;
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient divide(final double c) {
+        return new SparseGradient(value / c, 1.0 / c, derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient negate() {
+        return new SparseGradient(-value, -1.0, derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public Field<SparseGradient> getField() {
+        return new Field<SparseGradient>() {
+
+            /** {@inheritDoc} */
+            public SparseGradient getZero() {
+                return createConstant(0);
+            }
+
+            /** {@inheritDoc} */
+            public SparseGradient getOne() {
+                return createConstant(1);
+            }
+
+            /** {@inheritDoc} */
+            public Class<? extends FieldElement<SparseGradient>> getRuntimeClass() {
+                return SparseGradient.class;
+            }
+
+        };
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient remainder(final double a) {
+        return new SparseGradient(FastMath.IEEEremainder(value, a), derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient remainder(final SparseGradient a) {
+
+        // compute k such that lhs % rhs = lhs - k rhs
+        final double rem = FastMath.IEEEremainder(value, a.value);
+        final double k   = FastMath.rint((value - rem) / a.value);
+
+        return subtract(a.multiply(k));
+
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient abs() {
+        if (Double.doubleToLongBits(value) < 0) {
+            // we use the bits representation to also handle -0.0
+            return negate();
+        } else {
+            return this;
+        }
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient ceil() {
+        return createConstant(FastMath.ceil(value));
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient floor() {
+        return createConstant(FastMath.floor(value));
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient rint() {
+        return createConstant(FastMath.rint(value));
+    }
+
+    /** {@inheritDoc} */
+    public long round() {
+        return FastMath.round(value);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient signum() {
+        return createConstant(FastMath.signum(value));
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient copySign(final SparseGradient sign) {
+        final long m = Double.doubleToLongBits(value);
+        final long s = Double.doubleToLongBits(sign.value);
+        if ((m >= 0 && s >= 0) || (m < 0 && s < 0)) { // Sign is currently OK
+            return this;
+        }
+        return negate(); // flip sign
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient copySign(final double sign) {
+        final long m = Double.doubleToLongBits(value);
+        final long s = Double.doubleToLongBits(sign);
+        if ((m >= 0 && s >= 0) || (m < 0 && s < 0)) { // Sign is currently OK
+            return this;
+        }
+        return negate(); // flip sign
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient scalb(final int n) {
+        final SparseGradient out = new SparseGradient(FastMath.scalb(value, n), Collections.<Integer, Double> emptyMap());
+        for (Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
+            out.derivatives.put(entry.getKey(), FastMath.scalb(entry.getValue(), n));
+        }
+        return out;
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient hypot(final SparseGradient y) {
+        if (Double.isInfinite(value) || Double.isInfinite(y.value)) {
+            return createConstant(Double.POSITIVE_INFINITY);
+        } else if (Double.isNaN(value) || Double.isNaN(y.value)) {
+            return createConstant(Double.NaN);
+        } else {
+
+            final int expX = FastMath.getExponent(value);
+            final int expY = FastMath.getExponent(y.value);
+            if (expX > expY + 27) {
+                // y is negligible with respect to x
+                return abs();
+            } else if (expY > expX + 27) {
+                // x is negligible with respect to y
+                return y.abs();
+            } else {
+
+                // find an intermediate scale to avoid both overflow and underflow
+                final int middleExp = (expX + expY) / 2;
+
+                // scale parameters without losing precision
+                final SparseGradient scaledX = scalb(-middleExp);
+                final SparseGradient scaledY = y.scalb(-middleExp);
+
+                // compute scaled hypotenuse
+                final SparseGradient scaledH =
+                        scaledX.multiply(scaledX).add(scaledY.multiply(scaledY)).sqrt();
+
+                // remove scaling
+                return scaledH.scalb(middleExp);
+
+            }
+
+        }
+    }
+
+    /**
+     * Returns the hypotenuse of a triangle with sides {@code x} and {@code y}
+     * - sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)
+     * avoiding intermediate overflow or underflow.
+     *
+     * <ul>
+     * <li> If either argument is infinite, then the result is positive infinity.</li>
+     * <li> else, if either argument is NaN then the result is NaN.</li>
+     * </ul>
+     *
+     * @param x a value
+     * @param y a value
+     * @return sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)
+     */
+    public static SparseGradient hypot(final SparseGradient x, final SparseGradient y) {
+        return x.hypot(y);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient reciprocal() {
+        return new SparseGradient(1.0 / value, -1.0 / (value * value), derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient sqrt() {
+        final double sqrt = FastMath.sqrt(value);
+        return new SparseGradient(sqrt, 0.5 / sqrt, derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient cbrt() {
+        final double cbrt = FastMath.cbrt(value);
+        return new SparseGradient(cbrt, 1.0 / (3 * cbrt * cbrt), derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient rootN(final int n) {
+        if (n == 2) {
+            return sqrt();
+        } else if (n == 3) {
+            return cbrt();
+        } else {
+            final double root = FastMath.pow(value, 1.0 / n);
+            return new SparseGradient(root, 1.0 / (n * FastMath.pow(root, n - 1)), derivatives);
+        }
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient pow(final double p) {
+        return new SparseGradient(FastMath.pow(value,  p), p * FastMath.pow(value,  p - 1), derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient pow(final int n) {
+        if (n == 0) {
+            return getField().getOne();
+        } else {
+            final double valueNm1 = FastMath.pow(value,  n - 1);
+            return new SparseGradient(value * valueNm1, n * valueNm1, derivatives);
+        }
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient pow(final SparseGradient e) {
+        return log().multiply(e).exp();
+    }
+
+    /** Compute a<sup>x</sup> where a is a double and x a {@link SparseGradient}
+     * @param a number to exponentiate
+     * @param x power to apply
+     * @return a<sup>x</sup>
+     */
+    public static SparseGradient pow(final double a, final SparseGradient x) {
+        if (a == 0) {
+            if (x.value == 0) {
+                return x.compose(1.0, Double.NEGATIVE_INFINITY);
+            } else if (x.value < 0) {
+                return x.compose(Double.NaN, Double.NaN);
+            } else {
+                return x.getField().getZero();
+            }
+        } else {
+            final double ax = FastMath.pow(a, x.value);
+            return new SparseGradient(ax, ax * FastMath.log(a), x.derivatives);
+        }
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient exp() {
+        final double e = FastMath.exp(value);
+        return new SparseGradient(e, e, derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient expm1() {
+        return new SparseGradient(FastMath.expm1(value), FastMath.exp(value), derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient log() {
+        return new SparseGradient(FastMath.log(value), 1.0 / value, derivatives);
+    }
+
+    /** Base 10 logarithm.
+     * @return base 10 logarithm of the instance
+     */
+    public SparseGradient log10() {
+        return new SparseGradient(FastMath.log10(value), 1.0 / (FastMath.log(10.0) * value), derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient log1p() {
+        return new SparseGradient(FastMath.log1p(value), 1.0 / (1.0 + value), derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient cos() {
+        return new SparseGradient(FastMath.cos(value), -FastMath.sin(value), derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient sin() {
+        return new SparseGradient(FastMath.sin(value), FastMath.cos(value), derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient tan() {
+        final double t = FastMath.tan(value);
+        return new SparseGradient(t, 1 + t * t, derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient acos() {
+        return new SparseGradient(FastMath.acos(value), -1.0 / FastMath.sqrt(1 - value * value), derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient asin() {
+        return new SparseGradient(FastMath.asin(value), 1.0 / FastMath.sqrt(1 - value * value), derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient atan() {
+        return new SparseGradient(FastMath.atan(value), 1.0 / (1 + value * value), derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient atan2(final SparseGradient x) {
+
+        // compute r = sqrt(x^2+y^2)
+        final SparseGradient r = multiply(this).add(x.multiply(x)).sqrt();
+
+        final SparseGradient a;
+        if (x.value >= 0) {
+
+            // compute atan2(y, x) = 2 atan(y / (r + x))
+            a = divide(r.add(x)).atan().multiply(2);
+
+        } else {
+
+            // compute atan2(y, x) = +/- pi - 2 atan(y / (r - x))
+            final SparseGradient tmp = divide(r.subtract(x)).atan().multiply(-2);
+            a = tmp.add(tmp.value <= 0 ? -FastMath.PI : FastMath.PI);
+
+        }
+
+        // fix value to take special cases (+0/+0, +0/-0, -0/+0, -0/-0, +/-infinity) correctly
+        a.value = FastMath.atan2(value, x.value);
+
+        return a;
+
+    }
+
+    /** Two arguments arc tangent operation.
+     * @param y first argument of the arc tangent
+     * @param x second argument of the arc tangent
+     * @return atan2(y, x)
+     */
+    public static SparseGradient atan2(final SparseGradient y, final SparseGradient x) {
+        return y.atan2(x);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient cosh() {
+        return new SparseGradient(FastMath.cosh(value), FastMath.sinh(value), derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient sinh() {
+        return new SparseGradient(FastMath.sinh(value), FastMath.cosh(value), derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient tanh() {
+        final double t = FastMath.tanh(value);
+        return new SparseGradient(t, 1 - t * t, derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient acosh() {
+        return new SparseGradient(FastMath.acosh(value), 1.0 / FastMath.sqrt(value * value - 1.0), derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient asinh() {
+        return new SparseGradient(FastMath.asinh(value), 1.0 / FastMath.sqrt(value * value + 1.0), derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient atanh() {
+        return new SparseGradient(FastMath.atanh(value), 1.0 / (1.0 - value * value), derivatives);
+    }
+
+    /** Convert radians to degrees, with error of less than 0.5 ULP
+     *  @return instance converted into degrees
+     */
+    public SparseGradient toDegrees() {
+        return new SparseGradient(FastMath.toDegrees(value), FastMath.toDegrees(1.0), derivatives);
+    }
+
+    /** Convert degrees to radians, with error of less than 0.5 ULP
+     *  @return instance converted into radians
+     */
+    public SparseGradient toRadians() {
+        return new SparseGradient(FastMath.toRadians(value), FastMath.toRadians(1.0), derivatives);
+    }
+
+    /** Evaluate Taylor expansion of a sparse gradient.
+     * @param delta parameters offsets (&Delta;x, &Delta;y, ...)
+     * @return value of the Taylor expansion at x + &Delta;x, y + &Delta;y, ...
+     */
+    public double taylor(final double ... delta) {
+        double y = value;
+        for (int i = 0; i < delta.length; ++i) {
+            y += delta[i] * getDerivative(i);
+        }
+        return y;
+    }
+
+    /** Compute composition of the instance by a univariate function.
+     * @param f0 value of the function at (i.e. f({@link #getValue()}))
+     * @param f1 first derivative of the function at
+     * the current point (i.e. f'({@link #getValue()}))
+     * @return f(this)
+    */
+    public SparseGradient compose(final double f0, final double f1) {
+        return new SparseGradient(f0, f1, derivatives);
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient linearCombination(final SparseGradient[] a,
+                                              final SparseGradient[] b)
+        throws DimensionMismatchException {
+
+        // compute a simple value, with all partial derivatives
+        SparseGradient out = a[0].getField().getZero();
+        for (int i = 0; i < a.length; ++i) {
+            out = out.add(a[i].multiply(b[i]));
+        }
+
+        // recompute an accurate value, taking care of cancellations
+        final double[] aDouble = new double[a.length];
+        for (int i = 0; i < a.length; ++i) {
+            aDouble[i] = a[i].getValue();
+        }
+        final double[] bDouble = new double[b.length];
+        for (int i = 0; i < b.length; ++i) {
+            bDouble[i] = b[i].getValue();
+        }
+        out.value = MathArrays.linearCombination(aDouble, bDouble);
+
+        return out;
+
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient linearCombination(final double[] a, final SparseGradient[] b) {
+
+        // compute a simple value, with all partial derivatives
+        SparseGradient out = b[0].getField().getZero();
+        for (int i = 0; i < a.length; ++i) {
+            out = out.add(b[i].multiply(a[i]));
+        }
+
+        // recompute an accurate value, taking care of cancellations
+        final double[] bDouble = new double[b.length];
+        for (int i = 0; i < b.length; ++i) {
+            bDouble[i] = b[i].getValue();
+        }
+        out.value = MathArrays.linearCombination(a, bDouble);
+
+        return out;
+
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient linearCombination(final SparseGradient a1, final SparseGradient b1,
+                                              final SparseGradient a2, final SparseGradient b2) {
+
+        // compute a simple value, with all partial derivatives
+        SparseGradient out = a1.multiply(b1).add(a2.multiply(b2));
+
+        // recompute an accurate value, taking care of cancellations
+        out.value = MathArrays.linearCombination(a1.value, b1.value, a2.value, b2.value);
+
+        return out;
+
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient linearCombination(final double a1, final SparseGradient b1,
+                                              final double a2, final SparseGradient b2) {
+
+        // compute a simple value, with all partial derivatives
+        SparseGradient out = b1.multiply(a1).add(b2.multiply(a2));
+
+        // recompute an accurate value, taking care of cancellations
+        out.value = MathArrays.linearCombination(a1, b1.value, a2, b2.value);
+
+        return out;
+
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient linearCombination(final SparseGradient a1, final SparseGradient b1,
+                                              final SparseGradient a2, final SparseGradient b2,
+                                              final SparseGradient a3, final SparseGradient b3) {
+
+        // compute a simple value, with all partial derivatives
+        SparseGradient out = a1.multiply(b1).add(a2.multiply(b2)).add(a3.multiply(b3));
+
+        // recompute an accurate value, taking care of cancellations
+        out.value = MathArrays.linearCombination(a1.value, b1.value,
+                                                 a2.value, b2.value,
+                                                 a3.value, b3.value);
+
+        return out;
+
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient linearCombination(final double a1, final SparseGradient b1,
+                                              final double a2, final SparseGradient b2,
+                                              final double a3, final SparseGradient b3) {
+
+        // compute a simple value, with all partial derivatives
+        SparseGradient out = b1.multiply(a1).add(b2.multiply(a2)).add(b3.multiply(a3));
+
+        // recompute an accurate value, taking care of cancellations
+        out.value = MathArrays.linearCombination(a1, b1.value,
+                                                 a2, b2.value,
+                                                 a3, b3.value);
+
+        return out;
+
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient linearCombination(final SparseGradient a1, final SparseGradient b1,
+                                              final SparseGradient a2, final SparseGradient b2,
+                                              final SparseGradient a3, final SparseGradient b3,
+                                              final SparseGradient a4, final SparseGradient b4) {
+
+        // compute a simple value, with all partial derivatives
+        SparseGradient out = a1.multiply(b1).add(a2.multiply(b2)).add(a3.multiply(b3)).add(a4.multiply(b4));
+
+        // recompute an accurate value, taking care of cancellations
+        out.value = MathArrays.linearCombination(a1.value, b1.value,
+                                                 a2.value, b2.value,
+                                                 a3.value, b3.value,
+                                                 a4.value, b4.value);
+
+        return out;
+
+    }
+
+    /** {@inheritDoc} */
+    public SparseGradient linearCombination(final double a1, final SparseGradient b1,
+                                              final double a2, final SparseGradient b2,
+                                              final double a3, final SparseGradient b3,
+                                              final double a4, final SparseGradient b4) {
+
+        // compute a simple value, with all partial derivatives
+        SparseGradient out = b1.multiply(a1).add(b2.multiply(a2)).add(b3.multiply(a3)).add(b4.multiply(a4));
+
+        // recompute an accurate value, taking care of cancellations
+        out.value = MathArrays.linearCombination(a1, b1.value,
+                                                 a2, b2.value,
+                                                 a3, b3.value,
+                                                 a4, b4.value);
+
+        return out;
+
+    }
+
+    /**
+     * Test for the equality of two sparse gradients.
+     * <p>
+     * Sparse gradients are considered equal if they have the same value
+     * and the same derivatives.
+     * </p>
+     * @param other Object to test for equality to this
+     * @return true if two sparse gradients are equal
+     */
+    @Override
+    public boolean equals(Object other) {
+
+        if (this == other) {
+            return true;
+        }
+
+        if (other instanceof SparseGradient) {
+            final SparseGradient rhs = (SparseGradient)other;
+            if (!Precision.equals(value, rhs.value, 1)) {
+                return false;
+            }
+            if (derivatives.size() != rhs.derivatives.size()) {
+                return false;
+            }
+            for (final Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
+                if (!rhs.derivatives.containsKey(entry.getKey())) {
+                    return false;
+                }
+                if (!Precision.equals(entry.getValue(), rhs.derivatives.get(entry.getKey()), 1)) {
+                    return false;
+                }
+            }
+            return true;
+        }
+
+        return false;
+
+    }
+
+    /**
+     * Get a hashCode for the derivative structure.
+     * @return a hash code value for this object
+     * @since 3.2
+     */
+    @Override
+    public int hashCode() {
+        return 743 + 809 * MathUtils.hash(value) + 167 * derivatives.hashCode();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/differentiation/UnivariateDifferentiableFunction.java

@@ -0,0 +1,43 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.differentiation;
+
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+
+/** Interface for univariate functions derivatives.
+ * <p>This interface represents a simple function which computes
+ * both the value and the first derivative of a mathematical function.
+ * The derivative is computed with respect to the input variable.</p>
+ * @see UnivariateDifferentiableFunction
+ * @see UnivariateFunctionDifferentiator
+ * @since 3.1
+ */
+public interface UnivariateDifferentiableFunction extends UnivariateFunction {
+
+    /** Simple mathematical function.
+     * <p>{@link UnivariateDifferentiableFunction} classes compute both the
+     * value and the first derivative of the function.</p>
+     * @param t function input value
+     * @return function result
+     * @exception DimensionMismatchException if t is inconsistent with the
+     * function's free parameters or order
+     */
+    DerivativeStructure value(DerivativeStructure t)
+        throws DimensionMismatchException;
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/differentiation/UnivariateDifferentiableMatrixFunction.java

@@ -0,0 +1,40 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.differentiation;
+
+import com.fr.third.org.apache.commons.math3.exception.MathIllegalArgumentException;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateMatrixFunction;
+
+/**
+ * Extension of {@link UnivariateMatrixFunction} representing a univariate differentiable matrix function.
+ *
+ * @since 3.1
+ */
+public interface UnivariateDifferentiableMatrixFunction
+    extends UnivariateMatrixFunction {
+
+    /**
+     * Compute the value for the function.
+     * @param x the point for which the function value should be computed
+     * @return the value
+     * @exception MathIllegalArgumentException if {@code x} does not
+     * satisfy the function's constraints (argument out of bound, or unsupported
+     * derivative order for example)
+     */
+    DerivativeStructure[][] value(DerivativeStructure x) throws MathIllegalArgumentException;
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/differentiation/UnivariateDifferentiableVectorFunction.java

@@ -0,0 +1,40 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.differentiation;
+
+import com.fr.third.org.apache.commons.math3.exception.MathIllegalArgumentException;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateVectorFunction;
+
+/**
+ * Extension of {@link UnivariateVectorFunction} representing a univariate differentiable vectorial function.
+ *
+ * @since 3.1
+ */
+public interface UnivariateDifferentiableVectorFunction
+    extends UnivariateVectorFunction {
+
+    /**
+     * Compute the value for the function.
+     * @param x the point for which the function value should be computed
+     * @return the value
+     * @exception MathIllegalArgumentException if {@code x} does not
+     * satisfy the function's constraints (argument out of bound, or unsupported
+     * derivative order for example)
+     */
+    DerivativeStructure[] value(DerivativeStructure x) throws MathIllegalArgumentException;
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/differentiation/UnivariateFunctionDifferentiator.java

@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.differentiation;
+
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+
+/** Interface defining the function differentiation operation.
+ * @since 3.1
+ */
+public interface UnivariateFunctionDifferentiator {
+
+    /** Create an implementation of a {@link UnivariateDifferentiableFunction
+     * differential} from a regular {@link UnivariateFunction function}.
+     * @param function function to differentiate
+     * @return differential function
+     */
+    UnivariateDifferentiableFunction differentiate(UnivariateFunction function);
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/differentiation/UnivariateMatrixFunctionDifferentiator.java

@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.differentiation;
+
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateMatrixFunction;
+
+/** Interface defining the function differentiation operation.
+ * @since 3.1
+ */
+public interface UnivariateMatrixFunctionDifferentiator {
+
+    /** Create an implementation of a {@link UnivariateDifferentiableMatrixFunction
+     * differential} from a regular {@link UnivariateMatrixFunction matrix function}.
+     * @param function function to differentiate
+     * @return differential function
+     */
+    UnivariateDifferentiableMatrixFunction differentiate(UnivariateMatrixFunction function);
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/differentiation/UnivariateVectorFunctionDifferentiator.java

@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.differentiation;
+
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateVectorFunction;
+
+/** Interface defining the function differentiation operation.
+ * @since 3.1
+ */
+public interface UnivariateVectorFunctionDifferentiator {
+
+    /** Create an implementation of a {@link UnivariateDifferentiableVectorFunction
+     * differential} from a regular {@link UnivariateVectorFunction vector function}.
+     * @param function function to differentiate
+     * @return differential function
+     */
+    UnivariateDifferentiableVectorFunction differentiate(UnivariateVectorFunction function);
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/differentiation/package-info.java

@@ -0,0 +1,42 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+/**
+ *
+ * <p>
+ *   This package holds the main interfaces and basic building block classes
+ *   dealing with differentiation.
+ *   The core class is {@link com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure
+ *   DerivativeStructure} which holds the value and the differentials of a function. This class
+ *   handles some arbitrary number of free parameters and arbitrary differentiation order. It is used
+ *   both as the input and the output type for the {@link
+ *   com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction
+ *   UnivariateDifferentiableFunction} interface. Any differentiable function should implement this
+ *   interface.
+ * </p>
+ * <p>
+ *   The {@link com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateFunctionDifferentiator
+ *   UnivariateFunctionDifferentiator} interface defines a way to differentiate a simple {@link
+ *   com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction UnivariateFunction} and get a {@link
+ *   com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction
+ *   UnivariateDifferentiableFunction}.
+ * </p>
+ * <p>
+ *   Similar interfaces also exist for multivariate functions and for vector or matrix valued functions.
+ * </p>
+ *
+ */
+package com.fr.third.org.apache.commons.math3.analysis.differentiation;

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Abs.java

@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Absolute value function.
+ *
+ * @since 3.0
+ */
+public class Abs implements UnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.abs(x);
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Acos.java

@@ -0,0 +1,53 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Arc-cosine function.
+ *
+ * @since 3.0
+ */
+public class Acos implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.acos(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.acos();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Acosh.java

@@ -0,0 +1,53 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Hyperbolic arc-cosine function.
+ *
+ * @since 3.0
+ */
+public class Acosh implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.acosh(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.acosh();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Add.java

@@ -0,0 +1,32 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.BivariateFunction;
+
+/**
+ * Add the two operands.
+ *
+ * @since 3.0
+ */
+public class Add implements BivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x, double y) {
+        return x + y;
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Asin.java

@@ -0,0 +1,53 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Arc-sine function.
+ *
+ * @since 3.0
+ */
+public class Asin implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.asin(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.asin();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Asinh.java

@@ -0,0 +1,53 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Hyperbolic arc-sine function.
+ *
+ * @since 3.0
+ */
+public class Asinh implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.asinh(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.asinh();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Atan.java

@@ -0,0 +1,53 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Arc-tangent function.
+ *
+ * @since 3.0
+ */
+public class Atan implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.atan(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.atan();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Atan2.java

@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.BivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Arc-tangent function.
+ *
+ * @since 3.0
+ */
+public class Atan2 implements BivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x, double y) {
+        return FastMath.atan2(x, y);
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Atanh.java

@@ -0,0 +1,53 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Hyperbolic arc-tangent function.
+ *
+ * @since 3.0
+ */
+public class Atanh implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.atanh(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.atanh();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Cbrt.java

@@ -0,0 +1,53 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Cube root function.
+ *
+ * @since 3.0
+ */
+public class Cbrt implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.cbrt(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.cbrt();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Ceil.java

@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * {@code ceil} function.
+ *
+ * @since 3.0
+ */
+public class Ceil implements UnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.ceil(x);
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Constant.java

@@ -0,0 +1,60 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+
+/**
+ * Constant function.
+ *
+ * @since 3.0
+ */
+public class Constant implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** Constant. */
+    private final double c;
+
+    /**
+     * @param c Constant.
+     */
+    public Constant(double c) {
+        this.c = c;
+    }
+
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return c;
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public DifferentiableUnivariateFunction derivative() {
+        return new Constant(0);
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return new DerivativeStructure(t.getFreeParameters(), t.getOrder(), c);
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Cos.java

@@ -0,0 +1,53 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Cosine function.
+ *
+ * @since 3.0
+ */
+public class Cos implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.cos(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.cos();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Cosh.java

@@ -0,0 +1,51 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Hyperbolic cosine function.
+ *
+ * @since 3.0
+ */
+public class Cosh implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.cosh(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public DifferentiableUnivariateFunction derivative() {
+        return new Sinh();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.cosh();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Divide.java

@@ -0,0 +1,32 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.BivariateFunction;
+
+/**
+ * Divide the first operand by the second.
+ *
+ * @since 3.0
+ */
+public class Divide implements BivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x, double y) {
+        return x / y;
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Exp.java

@@ -0,0 +1,53 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Exponential function.
+ *
+ * @since 3.0
+ */
+public class Exp implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.exp(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.exp();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Expm1.java

@@ -0,0 +1,53 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * <code>e<sup>x</sup>-1</code> function.
+ *
+ * @since 3.0
+ */
+public class Expm1 implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.expm1(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.expm1();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Floor.java

@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * {@code floor} function.
+ *
+ * @since 3.0
+ */
+public class Floor implements UnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.floor(x);
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Gaussian.java

@@ -0,0 +1,259 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import java.util.Arrays;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import com.fr.third.org.apache.commons.math3.exception.NullArgumentException;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.ParametricUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+import com.fr.third.org.apache.commons.math3.util.Precision;
+
+/**
+ * <a href="http://en.wikipedia.org/wiki/Gaussian_function">
+ *  Gaussian</a> function.
+ *
+ * @since 3.0
+ */
+public class Gaussian implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** Mean. */
+    private final double mean;
+    /** Inverse of the standard deviation. */
+    private final double is;
+    /** Inverse of twice the square of the standard deviation. */
+    private final double i2s2;
+    /** Normalization factor. */
+    private final double norm;
+
+    /**
+     * Gaussian with given normalization factor, mean and standard deviation.
+     *
+     * @param norm Normalization factor.
+     * @param mean Mean.
+     * @param sigma Standard deviation.
+     * @throws NotStrictlyPositiveException if {@code sigma <= 0}.
+     */
+    public Gaussian(double norm,
+                    double mean,
+                    double sigma)
+        throws NotStrictlyPositiveException {
+        if (sigma <= 0) {
+            throw new NotStrictlyPositiveException(sigma);
+        }
+
+        this.norm = norm;
+        this.mean = mean;
+        this.is   = 1 / sigma;
+        this.i2s2 = 0.5 * is * is;
+    }
+
+    /**
+     * Normalized gaussian with given mean and standard deviation.
+     *
+     * @param mean Mean.
+     * @param sigma Standard deviation.
+     * @throws NotStrictlyPositiveException if {@code sigma <= 0}.
+     */
+    public Gaussian(double mean,
+                    double sigma)
+        throws NotStrictlyPositiveException {
+        this(1 / (sigma * FastMath.sqrt(2 * Math.PI)), mean, sigma);
+    }
+
+    /**
+     * Normalized gaussian with zero mean and unit standard deviation.
+     */
+    public Gaussian() {
+        this(0, 1);
+    }
+
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return value(x - mean, norm, i2s2);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /**
+     * Parametric function where the input array contains the parameters of
+     * the Gaussian, ordered as follows:
+     * <ul>
+     *  <li>Norm</li>
+     *  <li>Mean</li>
+     *  <li>Standard deviation</li>
+     * </ul>
+     */
+    public static class Parametric implements ParametricUnivariateFunction {
+        /**
+         * Computes the value of the Gaussian at {@code x}.
+         *
+         * @param x Value for which the function must be computed.
+         * @param param Values of norm, mean and standard deviation.
+         * @return the value of the function.
+         * @throws NullArgumentException if {@code param} is {@code null}.
+         * @throws DimensionMismatchException if the size of {@code param} is
+         * not 3.
+         * @throws NotStrictlyPositiveException if {@code param[2]} is negative.
+         */
+        public double value(double x, double ... param)
+            throws NullArgumentException,
+                   DimensionMismatchException,
+                   NotStrictlyPositiveException {
+            validateParameters(param);
+
+            final double diff = x - param[1];
+            final double i2s2 = 1 / (2 * param[2] * param[2]);
+            return Gaussian.value(diff, param[0], i2s2);
+        }
+
+        /**
+         * Computes the value of the gradient at {@code x}.
+         * The components of the gradient vector are the partial
+         * derivatives of the function with respect to each of the
+         * <em>parameters</em> (norm, mean and standard deviation).
+         *
+         * @param x Value at which the gradient must be computed.
+         * @param param Values of norm, mean and standard deviation.
+         * @return the gradient vector at {@code x}.
+         * @throws NullArgumentException if {@code param} is {@code null}.
+         * @throws DimensionMismatchException if the size of {@code param} is
+         * not 3.
+         * @throws NotStrictlyPositiveException if {@code param[2]} is negative.
+         */
+        public double[] gradient(double x, double ... param)
+            throws NullArgumentException,
+                   DimensionMismatchException,
+                   NotStrictlyPositiveException {
+            validateParameters(param);
+
+            final double norm = param[0];
+            final double diff = x - param[1];
+            final double sigma = param[2];
+            final double i2s2 = 1 / (2 * sigma * sigma);
+
+            final double n = Gaussian.value(diff, 1, i2s2);
+            final double m = norm * n * 2 * i2s2 * diff;
+            final double s = m * diff / sigma;
+
+            return new double[] { n, m, s };
+        }
+
+        /**
+         * Validates parameters to ensure they are appropriate for the evaluation of
+         * the {@link #value(double,double[])} and {@link #gradient(double,double[])}
+         * methods.
+         *
+         * @param param Values of norm, mean and standard deviation.
+         * @throws NullArgumentException if {@code param} is {@code null}.
+         * @throws DimensionMismatchException if the size of {@code param} is
+         * not 3.
+         * @throws NotStrictlyPositiveException if {@code param[2]} is negative.
+         */
+        private void validateParameters(double[] param)
+            throws NullArgumentException,
+                   DimensionMismatchException,
+                   NotStrictlyPositiveException {
+            if (param == null) {
+                throw new NullArgumentException();
+            }
+            if (param.length != 3) {
+                throw new DimensionMismatchException(param.length, 3);
+            }
+            if (param[2] <= 0) {
+                throw new NotStrictlyPositiveException(param[2]);
+            }
+        }
+    }
+
+    /**
+     * @param xMinusMean {@code x - mean}.
+     * @param norm Normalization factor.
+     * @param i2s2 Inverse of twice the square of the standard deviation.
+     * @return the value of the Gaussian at {@code x}.
+     */
+    private static double value(double xMinusMean,
+                                double norm,
+                                double i2s2) {
+        return norm * FastMath.exp(-xMinusMean * xMinusMean * i2s2);
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t)
+        throws DimensionMismatchException {
+
+        final double u = is * (t.getValue() - mean);
+        double[] f = new double[t.getOrder() + 1];
+
+        // the nth order derivative of the Gaussian has the form:
+        // dn(g(x)/dxn = (norm / s^n) P_n(u) exp(-u^2/2) with u=(x-m)/s
+        // where P_n(u) is a degree n polynomial with same parity as n
+        // P_0(u) = 1, P_1(u) = -u, P_2(u) = u^2 - 1, P_3(u) = -u^3 + 3 u...
+        // the general recurrence relation for P_n is:
+        // P_n(u) = P_(n-1)'(u) - u P_(n-1)(u)
+        // as per polynomial parity, we can store coefficients of both P_(n-1) and P_n in the same array
+        final double[] p = new double[f.length];
+        p[0] = 1;
+        final double u2 = u * u;
+        double coeff = norm * FastMath.exp(-0.5 * u2);
+        if (coeff <= Precision.SAFE_MIN) {
+            Arrays.fill(f, 0.0);
+        } else {
+            f[0] = coeff;
+            for (int n = 1; n < f.length; ++n) {
+
+                // update and evaluate polynomial P_n(x)
+                double v = 0;
+                p[n] = -p[n - 1];
+                for (int k = n; k >= 0; k -= 2) {
+                    v = v * u2 + p[k];
+                    if (k > 2) {
+                        p[k - 2] = (k - 1) * p[k - 1] - p[k - 3];
+                    } else if (k == 2) {
+                        p[0] = p[1];
+                    }
+                }
+                if ((n & 0x1) == 1) {
+                    v *= u;
+                }
+
+                coeff *= is;
+                f[n] = coeff * v;
+
+            }
+        }
+
+        return t.compose(f);
+
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/HarmonicOscillator.java

@@ -0,0 +1,183 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.exception.NullArgumentException;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.ParametricUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * <a href="http://en.wikipedia.org/wiki/Harmonic_oscillator">
+ *  simple harmonic oscillator</a> function.
+ *
+ * @since 3.0
+ */
+public class HarmonicOscillator implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** Amplitude. */
+    private final double amplitude;
+    /** Angular frequency. */
+    private final double omega;
+    /** Phase. */
+    private final double phase;
+
+    /**
+     * Harmonic oscillator function.
+     *
+     * @param amplitude Amplitude.
+     * @param omega Angular frequency.
+     * @param phase Phase.
+     */
+    public HarmonicOscillator(double amplitude,
+                              double omega,
+                              double phase) {
+        this.amplitude = amplitude;
+        this.omega = omega;
+        this.phase = phase;
+    }
+
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return value(omega * x + phase, amplitude);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /**
+     * Parametric function where the input array contains the parameters of
+     * the harmonic oscillator function, ordered as follows:
+     * <ul>
+     *  <li>Amplitude</li>
+     *  <li>Angular frequency</li>
+     *  <li>Phase</li>
+     * </ul>
+     */
+    public static class Parametric implements ParametricUnivariateFunction {
+        /**
+         * Computes the value of the harmonic oscillator at {@code x}.
+         *
+         * @param x Value for which the function must be computed.
+         * @param param Values of norm, mean and standard deviation.
+         * @return the value of the function.
+         * @throws NullArgumentException if {@code param} is {@code null}.
+         * @throws DimensionMismatchException if the size of {@code param} is
+         * not 3.
+         */
+        public double value(double x, double ... param)
+            throws NullArgumentException,
+                   DimensionMismatchException {
+            validateParameters(param);
+            return HarmonicOscillator.value(x * param[1] + param[2], param[0]);
+        }
+
+        /**
+         * Computes the value of the gradient at {@code x}.
+         * The components of the gradient vector are the partial
+         * derivatives of the function with respect to each of the
+         * <em>parameters</em> (amplitude, angular frequency and phase).
+         *
+         * @param x Value at which the gradient must be computed.
+         * @param param Values of amplitude, angular frequency and phase.
+         * @return the gradient vector at {@code x}.
+         * @throws NullArgumentException if {@code param} is {@code null}.
+         * @throws DimensionMismatchException if the size of {@code param} is
+         * not 3.
+         */
+        public double[] gradient(double x, double ... param)
+            throws NullArgumentException,
+                   DimensionMismatchException {
+            validateParameters(param);
+
+            final double amplitude = param[0];
+            final double omega = param[1];
+            final double phase = param[2];
+
+            final double xTimesOmegaPlusPhase = omega * x + phase;
+            final double a = HarmonicOscillator.value(xTimesOmegaPlusPhase, 1);
+            final double p = -amplitude * FastMath.sin(xTimesOmegaPlusPhase);
+            final double w = p * x;
+
+            return new double[] { a, w, p };
+        }
+
+        /**
+         * Validates parameters to ensure they are appropriate for the evaluation of
+         * the {@link #value(double,double[])} and {@link #gradient(double,double[])}
+         * methods.
+         *
+         * @param param Values of norm, mean and standard deviation.
+         * @throws NullArgumentException if {@code param} is {@code null}.
+         * @throws DimensionMismatchException if the size of {@code param} is
+         * not 3.
+         */
+        private void validateParameters(double[] param)
+            throws NullArgumentException,
+                   DimensionMismatchException {
+            if (param == null) {
+                throw new NullArgumentException();
+            }
+            if (param.length != 3) {
+                throw new DimensionMismatchException(param.length, 3);
+            }
+        }
+    }
+
+    /**
+     * @param xTimesOmegaPlusPhase {@code omega * x + phase}.
+     * @param amplitude Amplitude.
+     * @return the value of the harmonic oscillator function at {@code x}.
+     */
+    private static double value(double xTimesOmegaPlusPhase,
+                                double amplitude) {
+        return amplitude * FastMath.cos(xTimesOmegaPlusPhase);
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t)
+        throws DimensionMismatchException {
+        final double x = t.getValue();
+        double[] f = new double[t.getOrder() + 1];
+
+        final double alpha = omega * x + phase;
+        f[0] = amplitude * FastMath.cos(alpha);
+        if (f.length > 1) {
+            f[1] = -amplitude * omega * FastMath.sin(alpha);
+            final double mo2 = - omega * omega;
+            for (int i = 2; i < f.length; ++i) {
+                f[i] = mo2 * f[i - 2];
+            }
+        }
+
+        return t.compose(f);
+
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Identity.java

@@ -0,0 +1,50 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+
+/**
+ * Identity function.
+ *
+ * @since 3.0
+ */
+public class Identity implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return x;
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public DifferentiableUnivariateFunction derivative() {
+        return new Constant(1);
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t;
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Inverse.java

@@ -0,0 +1,52 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+
+/**
+ * Inverse function.
+ *
+ * @since 3.0
+ */
+public class Inverse implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return 1 / x;
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.reciprocal();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Log.java

@@ -0,0 +1,53 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Natural logarithm function.
+ *
+ * @since 3.0
+ */
+public class Log implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.log(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.log();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Log10.java

@@ -0,0 +1,54 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Base 10 logarithm function.
+ *
+ * @since 3.0
+ */
+public class Log10 implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.log10(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.log10();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Log1p.java

@@ -0,0 +1,53 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * <code>log(1 + p)</code> function.
+ *
+ * @since 3.0
+ */
+public class Log1p implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.log1p(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.log1p();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Logistic.java

@@ -0,0 +1,228 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import com.fr.third.org.apache.commons.math3.exception.NullArgumentException;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.ParametricUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * <a href="http://en.wikipedia.org/wiki/Generalised_logistic_function">
+ *  Generalised logistic</a> function.
+ *
+ * @since 3.0
+ */
+public class Logistic implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** Lower asymptote. */
+    private final double a;
+    /** Upper asymptote. */
+    private final double k;
+    /** Growth rate. */
+    private final double b;
+    /** Parameter that affects near which asymptote maximum growth occurs. */
+    private final double oneOverN;
+    /** Parameter that affects the position of the curve along the ordinate axis. */
+    private final double q;
+    /** Abscissa of maximum growth. */
+    private final double m;
+
+    /**
+     * @param k If {@code b > 0}, value of the function for x going towards +&infin;.
+     * If {@code b < 0}, value of the function for x going towards -&infin;.
+     * @param m Abscissa of maximum growth.
+     * @param b Growth rate.
+     * @param q Parameter that affects the position of the curve along the
+     * ordinate axis.
+     * @param a If {@code b > 0}, value of the function for x going towards -&infin;.
+     * If {@code b < 0}, value of the function for x going towards +&infin;.
+     * @param n Parameter that affects near which asymptote the maximum
+     * growth occurs.
+     * @throws NotStrictlyPositiveException if {@code n <= 0}.
+     */
+    public Logistic(double k,
+                    double m,
+                    double b,
+                    double q,
+                    double a,
+                    double n)
+        throws NotStrictlyPositiveException {
+        if (n <= 0) {
+            throw new NotStrictlyPositiveException(n);
+        }
+
+        this.k = k;
+        this.m = m;
+        this.b = b;
+        this.q = q;
+        this.a = a;
+        oneOverN = 1 / n;
+    }
+
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return value(m - x, k, b, q, a, oneOverN);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /**
+     * Parametric function where the input array contains the parameters of
+     * the {@link Logistic#Logistic(double,double,double,double,double,double)
+     * logistic function}, ordered as follows:
+     * <ul>
+     *  <li>k</li>
+     *  <li>m</li>
+     *  <li>b</li>
+     *  <li>q</li>
+     *  <li>a</li>
+     *  <li>n</li>
+     * </ul>
+     */
+    public static class Parametric implements ParametricUnivariateFunction {
+        /**
+         * Computes the value of the sigmoid at {@code x}.
+         *
+         * @param x Value for which the function must be computed.
+         * @param param Values for {@code k}, {@code m}, {@code b}, {@code q},
+         * {@code a} and  {@code n}.
+         * @return the value of the function.
+         * @throws NullArgumentException if {@code param} is {@code null}.
+         * @throws DimensionMismatchException if the size of {@code param} is
+         * not 6.
+         * @throws NotStrictlyPositiveException if {@code param[5] <= 0}.
+         */
+        public double value(double x, double ... param)
+            throws NullArgumentException,
+                   DimensionMismatchException,
+                   NotStrictlyPositiveException {
+            validateParameters(param);
+            return Logistic.value(param[1] - x, param[0],
+                                  param[2], param[3],
+                                  param[4], 1 / param[5]);
+        }
+
+        /**
+         * Computes the value of the gradient at {@code x}.
+         * The components of the gradient vector are the partial
+         * derivatives of the function with respect to each of the
+         * <em>parameters</em>.
+         *
+         * @param x Value at which the gradient must be computed.
+         * @param param Values for {@code k}, {@code m}, {@code b}, {@code q},
+         * {@code a} and  {@code n}.
+         * @return the gradient vector at {@code x}.
+         * @throws NullArgumentException if {@code param} is {@code null}.
+         * @throws DimensionMismatchException if the size of {@code param} is
+         * not 6.
+         * @throws NotStrictlyPositiveException if {@code param[5] <= 0}.
+         */
+        public double[] gradient(double x, double ... param)
+            throws NullArgumentException,
+                   DimensionMismatchException,
+                   NotStrictlyPositiveException {
+            validateParameters(param);
+
+            final double b = param[2];
+            final double q = param[3];
+
+            final double mMinusX = param[1] - x;
+            final double oneOverN = 1 / param[5];
+            final double exp = FastMath.exp(b * mMinusX);
+            final double qExp = q * exp;
+            final double qExp1 = qExp + 1;
+            final double factor1 = (param[0] - param[4]) * oneOverN / FastMath.pow(qExp1, oneOverN);
+            final double factor2 = -factor1 / qExp1;
+
+            // Components of the gradient.
+            final double gk = Logistic.value(mMinusX, 1, b, q, 0, oneOverN);
+            final double gm = factor2 * b * qExp;
+            final double gb = factor2 * mMinusX * qExp;
+            final double gq = factor2 * exp;
+            final double ga = Logistic.value(mMinusX, 0, b, q, 1, oneOverN);
+            final double gn = factor1 * FastMath.log(qExp1) * oneOverN;
+
+            return new double[] { gk, gm, gb, gq, ga, gn };
+        }
+
+        /**
+         * Validates parameters to ensure they are appropriate for the evaluation of
+         * the {@link #value(double,double[])} and {@link #gradient(double,double[])}
+         * methods.
+         *
+         * @param param Values for {@code k}, {@code m}, {@code b}, {@code q},
+         * {@code a} and {@code n}.
+         * @throws NullArgumentException if {@code param} is {@code null}.
+         * @throws DimensionMismatchException if the size of {@code param} is
+         * not 6.
+         * @throws NotStrictlyPositiveException if {@code param[5] <= 0}.
+         */
+        private void validateParameters(double[] param)
+            throws NullArgumentException,
+                   DimensionMismatchException,
+                   NotStrictlyPositiveException {
+            if (param == null) {
+                throw new NullArgumentException();
+            }
+            if (param.length != 6) {
+                throw new DimensionMismatchException(param.length, 6);
+            }
+            if (param[5] <= 0) {
+                throw new NotStrictlyPositiveException(param[5]);
+            }
+        }
+    }
+
+    /**
+     * @param mMinusX {@code m - x}.
+     * @param k {@code k}.
+     * @param b {@code b}.
+     * @param q {@code q}.
+     * @param a {@code a}.
+     * @param oneOverN {@code 1 / n}.
+     * @return the value of the function.
+     */
+    private static double value(double mMinusX,
+                                double k,
+                                double b,
+                                double q,
+                                double a,
+                                double oneOverN) {
+        return a + (k - a) / FastMath.pow(1 + q * FastMath.exp(b * mMinusX), oneOverN);
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.negate().add(m).multiply(b).exp().multiply(q).add(1).pow(oneOverN).reciprocal().multiply(k - a).add(a);
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Logit.java

@@ -0,0 +1,212 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.exception.NullArgumentException;
+import com.fr.third.org.apache.commons.math3.exception.OutOfRangeException;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.ParametricUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * <a href="http://en.wikipedia.org/wiki/Logit">
+ *  Logit</a> function.
+ * It is the inverse of the {@link Sigmoid sigmoid} function.
+ *
+ * @since 3.0
+ */
+public class Logit implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** Lower bound. */
+    private final double lo;
+    /** Higher bound. */
+    private final double hi;
+
+    /**
+     * Usual logit function, where the lower bound is 0 and the higher
+     * bound is 1.
+     */
+    public Logit() {
+        this(0, 1);
+    }
+
+    /**
+     * Logit function.
+     *
+     * @param lo Lower bound of the function domain.
+     * @param hi Higher bound of the function domain.
+     */
+    public Logit(double lo,
+                 double hi) {
+        this.lo = lo;
+        this.hi = hi;
+    }
+
+    /** {@inheritDoc} */
+    public double value(double x)
+        throws OutOfRangeException {
+        return value(x, lo, hi);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /**
+     * Parametric function where the input array contains the parameters of
+     * the logit function, ordered as follows:
+     * <ul>
+     *  <li>Lower bound</li>
+     *  <li>Higher bound</li>
+     * </ul>
+     */
+    public static class Parametric implements ParametricUnivariateFunction {
+        /**
+         * Computes the value of the logit at {@code x}.
+         *
+         * @param x Value for which the function must be computed.
+         * @param param Values of lower bound and higher bounds.
+         * @return the value of the function.
+         * @throws NullArgumentException if {@code param} is {@code null}.
+         * @throws DimensionMismatchException if the size of {@code param} is
+         * not 2.
+         */
+        public double value(double x, double ... param)
+            throws NullArgumentException,
+                   DimensionMismatchException {
+            validateParameters(param);
+            return Logit.value(x, param[0], param[1]);
+        }
+
+        /**
+         * Computes the value of the gradient at {@code x}.
+         * The components of the gradient vector are the partial
+         * derivatives of the function with respect to each of the
+         * <em>parameters</em> (lower bound and higher bound).
+         *
+         * @param x Value at which the gradient must be computed.
+         * @param param Values for lower and higher bounds.
+         * @return the gradient vector at {@code x}.
+         * @throws NullArgumentException if {@code param} is {@code null}.
+         * @throws DimensionMismatchException if the size of {@code param} is
+         * not 2.
+         */
+        public double[] gradient(double x, double ... param)
+            throws NullArgumentException,
+                   DimensionMismatchException {
+            validateParameters(param);
+
+            final double lo = param[0];
+            final double hi = param[1];
+
+            return new double[] { 1 / (lo - x), 1 / (hi - x) };
+        }
+
+        /**
+         * Validates parameters to ensure they are appropriate for the evaluation of
+         * the {@link #value(double,double[])} and {@link #gradient(double,double[])}
+         * methods.
+         *
+         * @param param Values for lower and higher bounds.
+         * @throws NullArgumentException if {@code param} is {@code null}.
+         * @throws DimensionMismatchException if the size of {@code param} is
+         * not 2.
+         */
+        private void validateParameters(double[] param)
+            throws NullArgumentException,
+                   DimensionMismatchException {
+            if (param == null) {
+                throw new NullArgumentException();
+            }
+            if (param.length != 2) {
+                throw new DimensionMismatchException(param.length, 2);
+            }
+        }
+    }
+
+    /**
+     * @param x Value at which to compute the logit.
+     * @param lo Lower bound.
+     * @param hi Higher bound.
+     * @return the value of the logit function at {@code x}.
+     * @throws OutOfRangeException if {@code x < lo} or {@code x > hi}.
+     */
+    private static double value(double x,
+                                double lo,
+                                double hi)
+        throws OutOfRangeException {
+        if (x < lo || x > hi) {
+            throw new OutOfRangeException(x, lo, hi);
+        }
+        return FastMath.log((x - lo) / (hi - x));
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     * @exception OutOfRangeException if parameter is outside of function domain
+     */
+    public DerivativeStructure value(final DerivativeStructure t)
+        throws OutOfRangeException {
+        final double x = t.getValue();
+        if (x < lo || x > hi) {
+            throw new OutOfRangeException(x, lo, hi);
+        }
+        double[] f = new double[t.getOrder() + 1];
+
+        // function value
+        f[0] = FastMath.log((x - lo) / (hi - x));
+
+        if (Double.isInfinite(f[0])) {
+
+            if (f.length > 1) {
+                f[1] = Double.POSITIVE_INFINITY;
+            }
+            // fill the array with infinities
+            // (for x close to lo the signs will flip between -inf and +inf,
+            //  for x close to hi the signs will always be +inf)
+            // this is probably overkill, since the call to compose at the end
+            // of the method will transform most infinities into NaN ...
+            for (int i = 2; i < f.length; ++i) {
+                f[i] = f[i - 2];
+            }
+
+        } else {
+
+            // function derivatives
+            final double invL = 1.0 / (x - lo);
+            double xL = invL;
+            final double invH = 1.0 / (hi - x);
+            double xH = invH;
+            for (int i = 1; i < f.length; ++i) {
+                f[i] = xL + xH;
+                xL  *= -i * invL;
+                xH  *=  i * invH;
+            }
+        }
+
+        return t.compose(f);
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Max.java

@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.BivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Maximum function.
+ *
+ * @since 3.0
+ */
+public class Max implements BivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x, double y) {
+        return FastMath.max(x, y);
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Min.java

@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.BivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Minimum function.
+ *
+ * @since 3.0
+ */
+public class Min implements BivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x, double y) {
+        return FastMath.min(x, y);
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Minus.java

@@ -0,0 +1,50 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+
+/**
+ * Minus function.
+ *
+ * @since 3.0
+ */
+public class Minus implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return -x;
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public DifferentiableUnivariateFunction derivative() {
+        return new Constant(-1);
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.negate();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Multiply.java

@@ -0,0 +1,32 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.BivariateFunction;
+
+/**
+ * Multiply the two operands.
+ *
+ * @since 3.0
+ */
+public class Multiply implements BivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x, double y) {
+        return x * y;
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Pow.java

@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.BivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Power function.
+ *
+ * @since 3.0
+ */
+public class Pow implements BivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x, double y) {
+        return FastMath.pow(x, y);
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Power.java

@@ -0,0 +1,63 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Power function.
+ *
+ * @since 3.0
+ */
+public class Power implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** Power. */
+    private final double p;
+
+    /**
+     * @param p Power.
+     */
+    public Power(double p) {
+        this.p = p;
+    }
+
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.pow(x, p);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.pow(p);
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Rint.java

@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * {@code rint} function.
+ *
+ * @since 3.0
+ */
+public class Rint implements UnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.rint(x);
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Sigmoid.java

@@ -0,0 +1,218 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import java.util.Arrays;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.exception.NullArgumentException;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.ParametricUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * <a href="http://en.wikipedia.org/wiki/Sigmoid_function">
+ *  Sigmoid</a> function.
+ * It is the inverse of the {@link Logit logit} function.
+ * A more flexible version, the generalised logistic, is implemented
+ * by the {@link Logistic} class.
+ *
+ * @since 3.0
+ */
+public class Sigmoid implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** Lower asymptote. */
+    private final double lo;
+    /** Higher asymptote. */
+    private final double hi;
+
+    /**
+     * Usual sigmoid function, where the lower asymptote is 0 and the higher
+     * asymptote is 1.
+     */
+    public Sigmoid() {
+        this(0, 1);
+    }
+
+    /**
+     * Sigmoid function.
+     *
+     * @param lo Lower asymptote.
+     * @param hi Higher asymptote.
+     */
+    public Sigmoid(double lo,
+                   double hi) {
+        this.lo = lo;
+        this.hi = hi;
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return value(x, lo, hi);
+    }
+
+    /**
+     * Parametric function where the input array contains the parameters of
+     * the {@link Sigmoid#Sigmoid(double,double) sigmoid function}, ordered
+     * as follows:
+     * <ul>
+     *  <li>Lower asymptote</li>
+     *  <li>Higher asymptote</li>
+     * </ul>
+     */
+    public static class Parametric implements ParametricUnivariateFunction {
+        /**
+         * Computes the value of the sigmoid at {@code x}.
+         *
+         * @param x Value for which the function must be computed.
+         * @param param Values of lower asymptote and higher asymptote.
+         * @return the value of the function.
+         * @throws NullArgumentException if {@code param} is {@code null}.
+         * @throws DimensionMismatchException if the size of {@code param} is
+         * not 2.
+         */
+        public double value(double x, double ... param)
+            throws NullArgumentException,
+                   DimensionMismatchException {
+            validateParameters(param);
+            return Sigmoid.value(x, param[0], param[1]);
+        }
+
+        /**
+         * Computes the value of the gradient at {@code x}.
+         * The components of the gradient vector are the partial
+         * derivatives of the function with respect to each of the
+         * <em>parameters</em> (lower asymptote and higher asymptote).
+         *
+         * @param x Value at which the gradient must be computed.
+         * @param param Values for lower asymptote and higher asymptote.
+         * @return the gradient vector at {@code x}.
+         * @throws NullArgumentException if {@code param} is {@code null}.
+         * @throws DimensionMismatchException if the size of {@code param} is
+         * not 2.
+         */
+        public double[] gradient(double x, double ... param)
+            throws NullArgumentException,
+                   DimensionMismatchException {
+            validateParameters(param);
+
+            final double invExp1 = 1 / (1 + FastMath.exp(-x));
+
+            return new double[] { 1 - invExp1, invExp1 };
+        }
+
+        /**
+         * Validates parameters to ensure they are appropriate for the evaluation of
+         * the {@link #value(double,double[])} and {@link #gradient(double,double[])}
+         * methods.
+         *
+         * @param param Values for lower and higher asymptotes.
+         * @throws NullArgumentException if {@code param} is {@code null}.
+         * @throws DimensionMismatchException if the size of {@code param} is
+         * not 2.
+         */
+        private void validateParameters(double[] param)
+            throws NullArgumentException,
+                   DimensionMismatchException {
+            if (param == null) {
+                throw new NullArgumentException();
+            }
+            if (param.length != 2) {
+                throw new DimensionMismatchException(param.length, 2);
+            }
+        }
+    }
+
+    /**
+     * @param x Value at which to compute the sigmoid.
+     * @param lo Lower asymptote.
+     * @param hi Higher asymptote.
+     * @return the value of the sigmoid function at {@code x}.
+     */
+    private static double value(double x,
+                                double lo,
+                                double hi) {
+        return lo + (hi - lo) / (1 + FastMath.exp(-x));
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t)
+        throws DimensionMismatchException {
+
+        double[] f = new double[t.getOrder() + 1];
+        final double exp = FastMath.exp(-t.getValue());
+        if (Double.isInfinite(exp)) {
+
+            // special handling near lower boundary, to avoid NaN
+            f[0] = lo;
+            Arrays.fill(f, 1, f.length, 0.0);
+
+        } else {
+
+            // the nth order derivative of sigmoid has the form:
+            // dn(sigmoid(x)/dxn = P_n(exp(-x)) / (1+exp(-x))^(n+1)
+            // where P_n(t) is a degree n polynomial with normalized higher term
+            // P_0(t) = 1, P_1(t) = t, P_2(t) = t^2 - t, P_3(t) = t^3 - 4 t^2 + t...
+            // the general recurrence relation for P_n is:
+            // P_n(x) = n t P_(n-1)(t) - t (1 + t) P_(n-1)'(t)
+            final double[] p = new double[f.length];
+
+            final double inv   = 1 / (1 + exp);
+            double coeff = hi - lo;
+            for (int n = 0; n < f.length; ++n) {
+
+                // update and evaluate polynomial P_n(t)
+                double v = 0;
+                p[n] = 1;
+                for (int k = n; k >= 0; --k) {
+                    v = v * exp + p[k];
+                    if (k > 1) {
+                        p[k - 1] = (n - k + 2) * p[k - 2] - (k - 1) * p[k - 1];
+                    } else {
+                        p[0] = 0;
+                    }
+                }
+
+                coeff *= inv;
+                f[n]   = coeff * v;
+
+            }
+
+            // fix function value
+            f[0] += lo;
+
+        }
+
+        return t.compose(f);
+
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Signum.java

@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * {@code signum} function.
+ *
+ * @since 3.0
+ */
+public class Signum implements UnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.signum(x);
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Sin.java

@@ -0,0 +1,51 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Sine function.
+ *
+ * @since 3.0
+ */
+public class Sin implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.sin(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public DifferentiableUnivariateFunction derivative() {
+        return new Cos();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.sin();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Sinc.java

@@ -0,0 +1,205 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * <a href="http://en.wikipedia.org/wiki/Sinc_function">Sinc</a> function,
+ * defined by
+ * <pre><code>
+ *   sinc(x) = 1            if x = 0,
+ *             sin(x) / x   otherwise.
+ * </code></pre>
+ *
+ * @since 3.0
+ */
+public class Sinc implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /**
+     * Value below which the computations are done using Taylor series.
+     * <p>
+     * The Taylor series for sinc even order derivatives are:
+     * <pre>
+     * d^(2n)sinc/dx^(2n)     = Sum_(k>=0) (-1)^(n+k) / ((2k)!(2n+2k+1)) x^(2k)
+     *                        = (-1)^n     [ 1/(2n+1) - x^2/(4n+6) + x^4/(48n+120) - x^6/(1440n+5040) + O(x^8) ]
+     * </pre>
+     * </p>
+     * <p>
+     * The Taylor series for sinc odd order derivatives are:
+     * <pre>
+     * d^(2n+1)sinc/dx^(2n+1) = Sum_(k>=0) (-1)^(n+k+1) / ((2k+1)!(2n+2k+3)) x^(2k+1)
+     *                        = (-1)^(n+1) [ x/(2n+3) - x^3/(12n+30) + x^5/(240n+840) - x^7/(10080n+45360) + O(x^9) ]
+     * </pre>
+     * </p>
+     * <p>
+     * So the ratio of the fourth term with respect to the first term
+     * is always smaller than x^6/720, for all derivative orders.
+     * This implies that neglecting this term and using only the first three terms induces
+     * a relative error bounded by x^6/720. The SHORTCUT value is chosen such that this
+     * relative error is below double precision accuracy when |x| <= SHORTCUT.
+     * </p>
+     */
+    private static final double SHORTCUT = 6.0e-3;
+    /** For normalized sinc function. */
+    private final boolean normalized;
+
+    /**
+     * The sinc function, {@code sin(x) / x}.
+     */
+    public Sinc() {
+        this(false);
+    }
+
+    /**
+     * Instantiates the sinc function.
+     *
+     * @param normalized If {@code true}, the function is
+     * <code> sin(&pi;x) / &pi;x</code>, otherwise {@code sin(x) / x}.
+     */
+    public Sinc(boolean normalized) {
+        this.normalized = normalized;
+    }
+
+    /** {@inheritDoc} */
+    public double value(final double x) {
+        final double scaledX = normalized ? FastMath.PI * x : x;
+        if (FastMath.abs(scaledX) <= SHORTCUT) {
+            // use Taylor series
+            final double scaledX2 = scaledX * scaledX;
+            return ((scaledX2 - 20) * scaledX2 + 120) / 120;
+        } else {
+            // use definition expression
+            return FastMath.sin(scaledX) / scaledX;
+        }
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t)
+        throws DimensionMismatchException {
+
+        final double scaledX  = (normalized ? FastMath.PI : 1) * t.getValue();
+        final double scaledX2 = scaledX * scaledX;
+
+        double[] f = new double[t.getOrder() + 1];
+
+        if (FastMath.abs(scaledX) <= SHORTCUT) {
+
+            for (int i = 0; i < f.length; ++i) {
+                final int k = i / 2;
+                if ((i & 0x1) == 0) {
+                    // even derivation order
+                    f[i] = (((k & 0x1) == 0) ? 1 : -1) *
+                           (1.0 / (i + 1) - scaledX2 * (1.0 / (2 * i + 6) - scaledX2 / (24 * i + 120)));
+                } else {
+                    // odd derivation order
+                    f[i] = (((k & 0x1) == 0) ? -scaledX : scaledX) *
+                           (1.0 / (i + 2) - scaledX2 * (1.0 / (6 * i + 24) - scaledX2 / (120 * i + 720)));
+                }
+            }
+
+        } else {
+
+            final double inv = 1 / scaledX;
+            final double cos = FastMath.cos(scaledX);
+            final double sin = FastMath.sin(scaledX);
+
+            f[0] = inv * sin;
+
+            // the nth order derivative of sinc has the form:
+            // dn(sinc(x)/dxn = [S_n(x) sin(x) + C_n(x) cos(x)] / x^(n+1)
+            // where S_n(x) is an even polynomial with degree n-1 or n (depending on parity)
+            // and C_n(x) is an odd polynomial with degree n-1 or n (depending on parity)
+            // S_0(x) = 1, S_1(x) = -1, S_2(x) = -x^2 + 2, S_3(x) = 3x^2 - 6...
+            // C_0(x) = 0, C_1(x) = x, C_2(x) = -2x, C_3(x) = -x^3 + 6x...
+            // the general recurrence relations for S_n and C_n are:
+            // S_n(x) = x S_(n-1)'(x) - n S_(n-1)(x) - x C_(n-1)(x)
+            // C_n(x) = x C_(n-1)'(x) - n C_(n-1)(x) + x S_(n-1)(x)
+            // as per polynomials parity, we can store both S_n and C_n in the same array
+            final double[] sc = new double[f.length];
+            sc[0] = 1;
+
+            double coeff = inv;
+            for (int n = 1; n < f.length; ++n) {
+
+                double s = 0;
+                double c = 0;
+
+                // update and evaluate polynomials S_n(x) and C_n(x)
+                final int kStart;
+                if ((n & 0x1) == 0) {
+                    // even derivation order, S_n is degree n and C_n is degree n-1
+                    sc[n] = 0;
+                    kStart = n;
+                } else {
+                    // odd derivation order, S_n is degree n-1 and C_n is degree n
+                    sc[n] = sc[n - 1];
+                    c = sc[n];
+                    kStart = n - 1;
+                }
+
+                // in this loop, k is always even
+                for (int k = kStart; k > 1; k -= 2) {
+
+                    // sine part
+                    sc[k]     = (k - n) * sc[k] - sc[k - 1];
+                    s         = s * scaledX2 + sc[k];
+
+                    // cosine part
+                    sc[k - 1] = (k - 1 - n) * sc[k - 1] + sc[k -2];
+                    c         = c * scaledX2 + sc[k - 1];
+
+                }
+                sc[0] *= -n;
+                s      = s * scaledX2 + sc[0];
+
+                coeff *= inv;
+                f[n]   = coeff * (s * sin + c * scaledX * cos);
+
+            }
+
+        }
+
+        if (normalized) {
+            double scale = FastMath.PI;
+            for (int i = 1; i < f.length; ++i) {
+                f[i]  *= scale;
+                scale *= FastMath.PI;
+            }
+        }
+
+        return t.compose(f);
+
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Sinh.java

@@ -0,0 +1,51 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Hyperbolic sine function.
+ *
+ * @since 3.0
+ */
+public class Sinh implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.sinh(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public DifferentiableUnivariateFunction derivative() {
+        return new Cosh();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.sinh();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Sqrt.java

@@ -0,0 +1,53 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Square-root function.
+ *
+ * @since 3.0
+ */
+public class Sqrt implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.sqrt(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.sqrt();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/StepFunction.java

@@ -0,0 +1,101 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import java.util.Arrays;
+
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.exception.NoDataException;
+import com.fr.third.org.apache.commons.math3.exception.NonMonotonicSequenceException;
+import com.fr.third.org.apache.commons.math3.exception.NullArgumentException;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.MathArrays;
+
+/**
+ * <a href="http://en.wikipedia.org/wiki/Step_function">
+ *  Step function</a>.
+ *
+ * @since 3.0
+ */
+public class StepFunction implements UnivariateFunction {
+    /** Abscissae. */
+    private final double[] abscissa;
+    /** Ordinates. */
+    private final double[] ordinate;
+
+    /**
+     * Builds a step function from a list of arguments and the corresponding
+     * values. Specifically, returns the function h(x) defined by <pre><code>
+     * h(x) = y[0] for all x &lt; x[1]
+     *        y[1] for x[1] &le; x &lt; x[2]
+     *        ...
+     *        y[y.length - 1] for x &ge; x[x.length - 1]
+     * </code></pre>
+     * The value of {@code x[0]} is ignored, but it must be strictly less than
+     * {@code x[1]}.
+     *
+     * @param x Domain values where the function changes value.
+     * @param y Values of the function.
+     * @throws NonMonotonicSequenceException
+     * if the {@code x} array is not sorted in strictly increasing order.
+     * @throws NullArgumentException if {@code x} or {@code y} are {@code null}.
+     * @throws NoDataException if {@code x} or {@code y} are zero-length.
+     * @throws DimensionMismatchException if {@code x} and {@code y} do not
+     * have the same length.
+     */
+    public StepFunction(double[] x,
+                        double[] y)
+        throws NullArgumentException, NoDataException,
+               DimensionMismatchException, NonMonotonicSequenceException {
+        if (x == null ||
+            y == null) {
+            throw new NullArgumentException();
+        }
+        if (x.length == 0 ||
+            y.length == 0) {
+            throw new NoDataException();
+        }
+        if (y.length != x.length) {
+            throw new DimensionMismatchException(y.length, x.length);
+        }
+        MathArrays.checkOrder(x);
+
+        abscissa = MathArrays.copyOf(x);
+        ordinate = MathArrays.copyOf(y);
+    }
+
+    /** {@inheritDoc} */
+    public double value(double x) {
+        int index = Arrays.binarySearch(abscissa, x);
+        double fx = 0;
+
+        if (index < -1) {
+            // "x" is between "abscissa[-index-2]" and "abscissa[-index-1]".
+            fx = ordinate[-index-2];
+        } else if (index >= 0) {
+            // "x" is exactly "abscissa[index]".
+            fx = ordinate[index];
+        } else {
+            // Otherwise, "x" is smaller than the first value in "abscissa"
+            // (hence the returned value should be "ordinate[0]").
+            fx = ordinate[0];
+        }
+
+        return fx;
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Subtract.java

@@ -0,0 +1,32 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.BivariateFunction;
+
+/**
+ * Subtract the second operand from the first.
+ *
+ * @since 3.0
+ */
+public class Subtract implements BivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x, double y) {
+        return x - y;
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Tan.java

@@ -0,0 +1,53 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Tangent function.
+ *
+ * @since 3.0
+ */
+public class Tan implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.tan(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.tan();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Tanh.java

@@ -0,0 +1,53 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.DerivativeStructure;
+import com.fr.third.org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;
+import com.fr.third.org.apache.commons.math3.analysis.FunctionUtils;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Hyperbolic tangent function.
+ *
+ * @since 3.0
+ */
+public class Tanh implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.tanh(x);
+    }
+
+    /** {@inheritDoc}
+     * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}
+     */
+    @Deprecated
+    public UnivariateFunction derivative() {
+        return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();
+    }
+
+    /** {@inheritDoc}
+     * @since 3.1
+     */
+    public DerivativeStructure value(final DerivativeStructure t) {
+        return t.tanh();
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/Ulp.java

@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package com.fr.third.org.apache.commons.math3.analysis.function;
+
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * {@code ulp} function.
+ *
+ * @since 3.0
+ */
+public class Ulp implements UnivariateFunction {
+    /** {@inheritDoc} */
+    public double value(double x) {
+        return FastMath.ulp(x);
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/function/package-info.java

@@ -0,0 +1,26 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+/**
+ *
+ *    <p>
+ *      The {@code function} package contains function objects that wrap the
+ *      methods contained in {@link java.lang.Math}, as well as common
+ *      mathematical functions such as the gaussian and sinc functions.
+ *    </p>
+ *
+ */
+package com.fr.third.org.apache.commons.math3.analysis.function;

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/integration/BaseAbstractUnivariateIntegrator.java

@@ -0,0 +1,299 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.integration;
+
+import com.fr.third.org.apache.commons.math3.exception.MathIllegalArgumentException;
+import com.fr.third.org.apache.commons.math3.exception.MaxCountExceededException;
+import com.fr.third.org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import com.fr.third.org.apache.commons.math3.exception.NullArgumentException;
+import com.fr.third.org.apache.commons.math3.exception.NumberIsTooSmallException;
+import com.fr.third.org.apache.commons.math3.exception.TooManyEvaluationsException;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.solvers.UnivariateSolverUtils;
+import com.fr.third.org.apache.commons.math3.util.Incrementor;
+import com.fr.third.org.apache.commons.math3.util.IntegerSequence;
+import com.fr.third.org.apache.commons.math3.util.Precision;
+import com.fr.third.org.apache.commons.math3.util.MathUtils;
+
+/**
+ * Provide a default implementation for several generic functions.
+ *
+ * @since 1.2
+ */
+public abstract class BaseAbstractUnivariateIntegrator implements UnivariateIntegrator {
+
+    /** Default absolute accuracy. */
+    public static final double DEFAULT_ABSOLUTE_ACCURACY = 1.0e-15;
+
+    /** Default relative accuracy. */
+    public static final double DEFAULT_RELATIVE_ACCURACY = 1.0e-6;
+
+    /** Default minimal iteration count. */
+    public static final int DEFAULT_MIN_ITERATIONS_COUNT = 3;
+
+    /** Default maximal iteration count. */
+    public static final int DEFAULT_MAX_ITERATIONS_COUNT = Integer.MAX_VALUE;
+
+    /** The iteration count.
+     * @deprecated as of 3.6, this field has been replaced with {@link #incrementCount()}
+     */
+    @Deprecated
+    protected Incrementor iterations;
+
+    /** The iteration count. */
+    private IntegerSequence.Incrementor count;
+
+    /** Maximum absolute error. */
+    private final double absoluteAccuracy;
+
+    /** Maximum relative error. */
+    private final double relativeAccuracy;
+
+    /** minimum number of iterations */
+    private final int minimalIterationCount;
+
+    /** The functions evaluation count. */
+    private IntegerSequence.Incrementor evaluations;
+
+    /** Function to integrate. */
+    private UnivariateFunction function;
+
+    /** Lower bound for the interval. */
+    private double min;
+
+    /** Upper bound for the interval. */
+    private double max;
+
+    /**
+     * Construct an integrator with given accuracies and iteration counts.
+     * <p>
+     * The meanings of the various parameters are:
+     * <ul>
+     *   <li>relative accuracy:
+     *       this is used to stop iterations if the absolute accuracy can't be
+     *       achieved due to large values or short mantissa length. If this
+     *       should be the primary criterion for convergence rather then a
+     *       safety measure, set the absolute accuracy to a ridiculously small value,
+     *       like {@link Precision#SAFE_MIN Precision.SAFE_MIN}.</li>
+     *   <li>absolute accuracy:
+     *       The default is usually chosen so that results in the interval
+     *       -10..-0.1 and +0.1..+10 can be found with a reasonable accuracy. If the
+     *       expected absolute value of your results is of much smaller magnitude, set
+     *       this to a smaller value.</li>
+     *   <li>minimum number of iterations:
+     *       minimal iteration is needed to avoid false early convergence, e.g.
+     *       the sample points happen to be zeroes of the function. Users can
+     *       use the default value or choose one that they see as appropriate.</li>
+     *   <li>maximum number of iterations:
+     *       usually a high iteration count indicates convergence problems. However,
+     *       the "reasonable value" varies widely for different algorithms. Users are
+     *       advised to use the default value supplied by the algorithm.</li>
+     * </ul>
+     *
+     * @param relativeAccuracy relative accuracy of the result
+     * @param absoluteAccuracy absolute accuracy of the result
+     * @param minimalIterationCount minimum number of iterations
+     * @param maximalIterationCount maximum number of iterations
+     * @exception NotStrictlyPositiveException if minimal number of iterations
+     * is not strictly positive
+     * @exception NumberIsTooSmallException if maximal number of iterations
+     * is lesser than or equal to the minimal number of iterations
+     */
+    protected BaseAbstractUnivariateIntegrator(final double relativeAccuracy,
+                                               final double absoluteAccuracy,
+                                               final int minimalIterationCount,
+                                               final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException {
+
+        // accuracy settings
+        this.relativeAccuracy      = relativeAccuracy;
+        this.absoluteAccuracy      = absoluteAccuracy;
+
+        // iterations count settings
+        if (minimalIterationCount <= 0) {
+            throw new NotStrictlyPositiveException(minimalIterationCount);
+        }
+        if (maximalIterationCount <= minimalIterationCount) {
+            throw new NumberIsTooSmallException(maximalIterationCount, minimalIterationCount, false);
+        }
+        this.minimalIterationCount = minimalIterationCount;
+        this.count                 = IntegerSequence.Incrementor.create().withMaximalCount(maximalIterationCount);
+
+        @SuppressWarnings("deprecation")
+        Incrementor wrapped =
+                        Incrementor.wrap(count);
+        this.iterations = wrapped;
+
+        // prepare evaluations counter, but do not set it yet
+        evaluations = IntegerSequence.Incrementor.create();
+
+    }
+
+    /**
+     * Construct an integrator with given accuracies.
+     * @param relativeAccuracy relative accuracy of the result
+     * @param absoluteAccuracy absolute accuracy of the result
+     */
+    protected BaseAbstractUnivariateIntegrator(final double relativeAccuracy,
+                                           final double absoluteAccuracy) {
+        this(relativeAccuracy, absoluteAccuracy,
+             DEFAULT_MIN_ITERATIONS_COUNT, DEFAULT_MAX_ITERATIONS_COUNT);
+    }
+
+    /**
+     * Construct an integrator with given iteration counts.
+     * @param minimalIterationCount minimum number of iterations
+     * @param maximalIterationCount maximum number of iterations
+     * @exception NotStrictlyPositiveException if minimal number of iterations
+     * is not strictly positive
+     * @exception NumberIsTooSmallException if maximal number of iterations
+     * is lesser than or equal to the minimal number of iterations
+     */
+    protected BaseAbstractUnivariateIntegrator(final int minimalIterationCount,
+                                           final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException {
+        this(DEFAULT_RELATIVE_ACCURACY, DEFAULT_ABSOLUTE_ACCURACY,
+             minimalIterationCount, maximalIterationCount);
+    }
+
+    /** {@inheritDoc} */
+    public double getRelativeAccuracy() {
+        return relativeAccuracy;
+    }
+
+    /** {@inheritDoc} */
+    public double getAbsoluteAccuracy() {
+        return absoluteAccuracy;
+    }
+
+    /** {@inheritDoc} */
+    public int getMinimalIterationCount() {
+        return minimalIterationCount;
+    }
+
+    /** {@inheritDoc} */
+    public int getMaximalIterationCount() {
+        return count.getMaximalCount();
+    }
+
+    /** {@inheritDoc} */
+    public int getEvaluations() {
+        return evaluations.getCount();
+    }
+
+    /** {@inheritDoc} */
+    public int getIterations() {
+        return count.getCount();
+    }
+
+    /** Increment the number of iterations.
+     * @exception MaxCountExceededException if the number of iterations
+     * exceeds the allowed maximum number
+     */
+    protected void incrementCount() throws MaxCountExceededException {
+        count.increment();
+    }
+
+    /**
+     * @return the lower bound.
+     */
+    protected double getMin() {
+        return min;
+    }
+    /**
+     * @return the upper bound.
+     */
+    protected double getMax() {
+        return max;
+    }
+
+    /**
+     * Compute the objective function value.
+     *
+     * @param point Point at which the objective function must be evaluated.
+     * @return the objective function value at specified point.
+     * @throws TooManyEvaluationsException if the maximal number of function
+     * evaluations is exceeded.
+     */
+    protected double computeObjectiveValue(final double point)
+        throws TooManyEvaluationsException {
+        try {
+            evaluations.increment();
+        } catch (MaxCountExceededException e) {
+            throw new TooManyEvaluationsException(e.getMax());
+        }
+        return function.value(point);
+    }
+
+    /**
+     * Prepare for computation.
+     * Subclasses must call this method if they override any of the
+     * {@code solve} methods.
+     *
+     * @param maxEval Maximum number of evaluations.
+     * @param f the integrand function
+     * @param lower the min bound for the interval
+     * @param upper the upper bound for the interval
+     * @throws NullArgumentException if {@code f} is {@code null}.
+     * @throws MathIllegalArgumentException if {@code min >= max}.
+     */
+    protected void setup(final int maxEval,
+                         final UnivariateFunction f,
+                         final double lower, final double upper)
+        throws NullArgumentException, MathIllegalArgumentException {
+
+        // Checks.
+        MathUtils.checkNotNull(f);
+        UnivariateSolverUtils.verifyInterval(lower, upper);
+
+        // Reset.
+        min = lower;
+        max = upper;
+        function = f;
+        evaluations = evaluations.withMaximalCount(maxEval).withStart(0);
+        count       = count.withStart(0);
+
+    }
+
+    /** {@inheritDoc} */
+    public double integrate(final int maxEval, final UnivariateFunction f,
+                            final double lower, final double upper)
+        throws TooManyEvaluationsException, MaxCountExceededException,
+               MathIllegalArgumentException, NullArgumentException {
+
+        // Initialization.
+        setup(maxEval, f, lower, upper);
+
+        // Perform computation.
+        return doIntegrate();
+
+    }
+
+    /**
+     * Method for implementing actual integration algorithms in derived
+     * classes.
+     *
+     * @return the root.
+     * @throws TooManyEvaluationsException if the maximal number of evaluations
+     * is exceeded.
+     * @throws MaxCountExceededException if the maximum iteration count is exceeded
+     * or the integrator detects convergence problems otherwise
+     */
+    protected abstract double doIntegrate()
+        throws TooManyEvaluationsException, MaxCountExceededException;
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/integration/IterativeLegendreGaussIntegrator.java

@@ -0,0 +1,183 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.integration;
+
+import com.fr.third.org.apache.commons.math3.exception.MathIllegalArgumentException;
+import com.fr.third.org.apache.commons.math3.exception.MaxCountExceededException;
+import com.fr.third.org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import com.fr.third.org.apache.commons.math3.exception.NumberIsTooSmallException;
+import com.fr.third.org.apache.commons.math3.exception.TooManyEvaluationsException;
+import com.fr.third.org.apache.commons.math3.exception.util.LocalizedFormats;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.analysis.integration.gauss.GaussIntegratorFactory;
+import com.fr.third.org.apache.commons.math3.analysis.integration.gauss.GaussIntegrator;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * This algorithm divides the integration interval into equally-sized
+ * sub-interval and on each of them performs a
+ * <a href="http://mathworld.wolfram.com/Legendre-GaussQuadrature.html">
+ * Legendre-Gauss</a> quadrature.
+ * Because of its <em>non-adaptive</em> nature, this algorithm can
+ * converge to a wrong value for the integral (for example, if the
+ * function is significantly different from zero toward the ends of the
+ * integration interval).
+ * In particular, a change of variables aimed at estimating integrals
+ * over infinite intervals as proposed
+ * <a href="http://en.wikipedia.org/w/index.php?title=Numerical_integration#Integrals_over_infinite_intervals">
+ *  here</a> should be avoided when using this class.
+ *
+ * @since 3.1
+ */
+
+public class IterativeLegendreGaussIntegrator
+    extends BaseAbstractUnivariateIntegrator {
+    /** Factory that computes the points and weights. */
+    private static final GaussIntegratorFactory FACTORY
+        = new GaussIntegratorFactory();
+    /** Number of integration points (per interval). */
+    private final int numberOfPoints;
+
+    /**
+     * Builds an integrator with given accuracies and iterations counts.
+     *
+     * @param n Number of integration points.
+     * @param relativeAccuracy Relative accuracy of the result.
+     * @param absoluteAccuracy Absolute accuracy of the result.
+     * @param minimalIterationCount Minimum number of iterations.
+     * @param maximalIterationCount Maximum number of iterations.
+     * @throws NotStrictlyPositiveException if minimal number of iterations
+     * or number of points are not strictly positive.
+     * @throws NumberIsTooSmallException if maximal number of iterations
+     * is smaller than or equal to the minimal number of iterations.
+     */
+    public IterativeLegendreGaussIntegrator(final int n,
+                                            final double relativeAccuracy,
+                                            final double absoluteAccuracy,
+                                            final int minimalIterationCount,
+                                            final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException {
+        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
+        if (n <= 0) {
+            throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_POINTS, n);
+        }
+       numberOfPoints = n;
+    }
+
+    /**
+     * Builds an integrator with given accuracies.
+     *
+     * @param n Number of integration points.
+     * @param relativeAccuracy Relative accuracy of the result.
+     * @param absoluteAccuracy Absolute accuracy of the result.
+     * @throws NotStrictlyPositiveException if {@code n < 1}.
+     */
+    public IterativeLegendreGaussIntegrator(final int n,
+                                            final double relativeAccuracy,
+                                            final double absoluteAccuracy)
+        throws NotStrictlyPositiveException {
+        this(n, relativeAccuracy, absoluteAccuracy,
+             DEFAULT_MIN_ITERATIONS_COUNT, DEFAULT_MAX_ITERATIONS_COUNT);
+    }
+
+    /**
+     * Builds an integrator with given iteration counts.
+     *
+     * @param n Number of integration points.
+     * @param minimalIterationCount Minimum number of iterations.
+     * @param maximalIterationCount Maximum number of iterations.
+     * @throws NotStrictlyPositiveException if minimal number of iterations
+     * is not strictly positive.
+     * @throws NumberIsTooSmallException if maximal number of iterations
+     * is smaller than or equal to the minimal number of iterations.
+     * @throws NotStrictlyPositiveException if {@code n < 1}.
+     */
+    public IterativeLegendreGaussIntegrator(final int n,
+                                            final int minimalIterationCount,
+                                            final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException {
+        this(n, DEFAULT_RELATIVE_ACCURACY, DEFAULT_ABSOLUTE_ACCURACY,
+             minimalIterationCount, maximalIterationCount);
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected double doIntegrate()
+        throws MathIllegalArgumentException, TooManyEvaluationsException, MaxCountExceededException {
+        // Compute first estimate with a single step.
+        double oldt = stage(1);
+
+        int n = 2;
+        while (true) {
+            // Improve integral with a larger number of steps.
+            final double t = stage(n);
+
+            // Estimate the error.
+            final double delta = FastMath.abs(t - oldt);
+            final double limit =
+                FastMath.max(getAbsoluteAccuracy(),
+                             getRelativeAccuracy() * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5);
+
+            // check convergence
+            if (getIterations() + 1 >= getMinimalIterationCount() &&
+                delta <= limit) {
+                return t;
+            }
+
+            // Prepare next iteration.
+            final double ratio = FastMath.min(4, FastMath.pow(delta / limit, 0.5 / numberOfPoints));
+            n = FastMath.max((int) (ratio * n), n + 1);
+            oldt = t;
+            incrementCount();
+        }
+    }
+
+    /**
+     * Compute the n-th stage integral.
+     *
+     * @param n Number of steps.
+     * @return the value of n-th stage integral.
+     * @throws TooManyEvaluationsException if the maximum number of evaluations
+     * is exceeded.
+     */
+    private double stage(final int n)
+        throws TooManyEvaluationsException {
+        // Function to be integrated is stored in the base class.
+        final UnivariateFunction f = new UnivariateFunction() {
+                /** {@inheritDoc} */
+                public double value(double x)
+                    throws MathIllegalArgumentException, TooManyEvaluationsException {
+                    return computeObjectiveValue(x);
+                }
+            };
+
+        final double min = getMin();
+        final double max = getMax();
+        final double step = (max - min) / n;
+
+        double sum = 0;
+        for (int i = 0; i < n; i++) {
+            // Integrate over each sub-interval [a, b].
+            final double a = min + i * step;
+            final double b = a + step;
+            final GaussIntegrator g = FACTORY.legendreHighPrecision(numberOfPoints, a, b);
+            sum += g.integrate(f);
+        }
+
+        return sum;
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/integration/LegendreGaussIntegrator.java

@@ -0,0 +1,265 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.integration;
+
+import com.fr.third.org.apache.commons.math3.exception.MathIllegalArgumentException;
+import com.fr.third.org.apache.commons.math3.exception.MaxCountExceededException;
+import com.fr.third.org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import com.fr.third.org.apache.commons.math3.exception.NumberIsTooSmallException;
+import com.fr.third.org.apache.commons.math3.exception.TooManyEvaluationsException;
+import com.fr.third.org.apache.commons.math3.exception.util.LocalizedFormats;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Implements the <a href="http://mathworld.wolfram.com/Legendre-GaussQuadrature.html">
+ * Legendre-Gauss</a> quadrature formula.
+ * <p>
+ * Legendre-Gauss integrators are efficient integrators that can
+ * accurately integrate functions with few function evaluations. A
+ * Legendre-Gauss integrator using an n-points quadrature formula can
+ * integrate 2n-1 degree polynomials exactly.
+ * </p>
+ * <p>
+ * These integrators evaluate the function on n carefully chosen
+ * abscissas in each step interval (mapped to the canonical [-1,1] interval).
+ * The evaluation abscissas are not evenly spaced and none of them are
+ * at the interval endpoints. This implies the function integrated can be
+ * undefined at integration interval endpoints.
+ * </p>
+ * <p>
+ * The evaluation abscissas x<sub>i</sub> are the roots of the degree n
+ * Legendre polynomial. The weights a<sub>i</sub> of the quadrature formula
+ * integrals from -1 to +1 &int; Li<sup>2</sup> where Li (x) =
+ * &prod; (x-x<sub>k</sub>)/(x<sub>i</sub>-x<sub>k</sub>) for k != i.
+ * </p>
+ * <p>
+ * @since 1.2
+ * @deprecated As of 3.1 (to be removed in 4.0). Please use
+ * {@link IterativeLegendreGaussIntegrator} instead.
+ */
+@Deprecated
+public class LegendreGaussIntegrator extends BaseAbstractUnivariateIntegrator {
+
+    /** Abscissas for the 2 points method. */
+    private static final double[] ABSCISSAS_2 = {
+        -1.0 / FastMath.sqrt(3.0),
+         1.0 / FastMath.sqrt(3.0)
+    };
+
+    /** Weights for the 2 points method. */
+    private static final double[] WEIGHTS_2 = {
+        1.0,
+        1.0
+    };
+
+    /** Abscissas for the 3 points method. */
+    private static final double[] ABSCISSAS_3 = {
+        -FastMath.sqrt(0.6),
+         0.0,
+         FastMath.sqrt(0.6)
+    };
+
+    /** Weights for the 3 points method. */
+    private static final double[] WEIGHTS_3 = {
+        5.0 / 9.0,
+        8.0 / 9.0,
+        5.0 / 9.0
+    };
+
+    /** Abscissas for the 4 points method. */
+    private static final double[] ABSCISSAS_4 = {
+        -FastMath.sqrt((15.0 + 2.0 * FastMath.sqrt(30.0)) / 35.0),
+        -FastMath.sqrt((15.0 - 2.0 * FastMath.sqrt(30.0)) / 35.0),
+         FastMath.sqrt((15.0 - 2.0 * FastMath.sqrt(30.0)) / 35.0),
+         FastMath.sqrt((15.0 + 2.0 * FastMath.sqrt(30.0)) / 35.0)
+    };
+
+    /** Weights for the 4 points method. */
+    private static final double[] WEIGHTS_4 = {
+        (90.0 - 5.0 * FastMath.sqrt(30.0)) / 180.0,
+        (90.0 + 5.0 * FastMath.sqrt(30.0)) / 180.0,
+        (90.0 + 5.0 * FastMath.sqrt(30.0)) / 180.0,
+        (90.0 - 5.0 * FastMath.sqrt(30.0)) / 180.0
+    };
+
+    /** Abscissas for the 5 points method. */
+    private static final double[] ABSCISSAS_5 = {
+        -FastMath.sqrt((35.0 + 2.0 * FastMath.sqrt(70.0)) / 63.0),
+        -FastMath.sqrt((35.0 - 2.0 * FastMath.sqrt(70.0)) / 63.0),
+         0.0,
+         FastMath.sqrt((35.0 - 2.0 * FastMath.sqrt(70.0)) / 63.0),
+         FastMath.sqrt((35.0 + 2.0 * FastMath.sqrt(70.0)) / 63.0)
+    };
+
+    /** Weights for the 5 points method. */
+    private static final double[] WEIGHTS_5 = {
+        (322.0 - 13.0 * FastMath.sqrt(70.0)) / 900.0,
+        (322.0 + 13.0 * FastMath.sqrt(70.0)) / 900.0,
+        128.0 / 225.0,
+        (322.0 + 13.0 * FastMath.sqrt(70.0)) / 900.0,
+        (322.0 - 13.0 * FastMath.sqrt(70.0)) / 900.0
+    };
+
+    /** Abscissas for the current method. */
+    private final double[] abscissas;
+
+    /** Weights for the current method. */
+    private final double[] weights;
+
+    /**
+     * Build a Legendre-Gauss integrator with given accuracies and iterations counts.
+     * @param n number of points desired (must be between 2 and 5 inclusive)
+     * @param relativeAccuracy relative accuracy of the result
+     * @param absoluteAccuracy absolute accuracy of the result
+     * @param minimalIterationCount minimum number of iterations
+     * @param maximalIterationCount maximum number of iterations
+     * @exception MathIllegalArgumentException if number of points is out of [2; 5]
+     * @exception NotStrictlyPositiveException if minimal number of iterations
+     * is not strictly positive
+     * @exception NumberIsTooSmallException if maximal number of iterations
+     * is lesser than or equal to the minimal number of iterations
+     */
+    public LegendreGaussIntegrator(final int n,
+                                   final double relativeAccuracy,
+                                   final double absoluteAccuracy,
+                                   final int minimalIterationCount,
+                                   final int maximalIterationCount)
+        throws MathIllegalArgumentException, NotStrictlyPositiveException, NumberIsTooSmallException {
+        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
+        switch(n) {
+        case 2 :
+            abscissas = ABSCISSAS_2;
+            weights   = WEIGHTS_2;
+            break;
+        case 3 :
+            abscissas = ABSCISSAS_3;
+            weights   = WEIGHTS_3;
+            break;
+        case 4 :
+            abscissas = ABSCISSAS_4;
+            weights   = WEIGHTS_4;
+            break;
+        case 5 :
+            abscissas = ABSCISSAS_5;
+            weights   = WEIGHTS_5;
+            break;
+        default :
+            throw new MathIllegalArgumentException(
+                    LocalizedFormats.N_POINTS_GAUSS_LEGENDRE_INTEGRATOR_NOT_SUPPORTED,
+                    n, 2, 5);
+        }
+
+    }
+
+    /**
+     * Build a Legendre-Gauss integrator with given accuracies.
+     * @param n number of points desired (must be between 2 and 5 inclusive)
+     * @param relativeAccuracy relative accuracy of the result
+     * @param absoluteAccuracy absolute accuracy of the result
+     * @exception MathIllegalArgumentException if number of points is out of [2; 5]
+     */
+    public LegendreGaussIntegrator(final int n,
+                                   final double relativeAccuracy,
+                                   final double absoluteAccuracy)
+        throws MathIllegalArgumentException {
+        this(n, relativeAccuracy, absoluteAccuracy,
+             DEFAULT_MIN_ITERATIONS_COUNT, DEFAULT_MAX_ITERATIONS_COUNT);
+    }
+
+    /**
+     * Build a Legendre-Gauss integrator with given iteration counts.
+     * @param n number of points desired (must be between 2 and 5 inclusive)
+     * @param minimalIterationCount minimum number of iterations
+     * @param maximalIterationCount maximum number of iterations
+     * @exception MathIllegalArgumentException if number of points is out of [2; 5]
+     * @exception NotStrictlyPositiveException if minimal number of iterations
+     * is not strictly positive
+     * @exception NumberIsTooSmallException if maximal number of iterations
+     * is lesser than or equal to the minimal number of iterations
+     */
+    public LegendreGaussIntegrator(final int n,
+                                   final int minimalIterationCount,
+                                   final int maximalIterationCount)
+        throws MathIllegalArgumentException {
+        this(n, DEFAULT_RELATIVE_ACCURACY, DEFAULT_ABSOLUTE_ACCURACY,
+             minimalIterationCount, maximalIterationCount);
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected double doIntegrate()
+        throws MathIllegalArgumentException, TooManyEvaluationsException, MaxCountExceededException {
+
+        // compute first estimate with a single step
+        double oldt = stage(1);
+
+        int n = 2;
+        while (true) {
+
+            // improve integral with a larger number of steps
+            final double t = stage(n);
+
+            // estimate error
+            final double delta = FastMath.abs(t - oldt);
+            final double limit =
+                FastMath.max(getAbsoluteAccuracy(),
+                             getRelativeAccuracy() * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5);
+
+            // check convergence
+            if ((getIterations() + 1 >= getMinimalIterationCount()) && (delta <= limit)) {
+                return t;
+            }
+
+            // prepare next iteration
+            double ratio = FastMath.min(4, FastMath.pow(delta / limit, 0.5 / abscissas.length));
+            n = FastMath.max((int) (ratio * n), n + 1);
+            oldt = t;
+            incrementCount();
+
+        }
+
+    }
+
+    /**
+     * Compute the n-th stage integral.
+     * @param n number of steps
+     * @return the value of n-th stage integral
+     * @throws TooManyEvaluationsException if the maximum number of evaluations
+     * is exceeded.
+     */
+    private double stage(final int n)
+        throws TooManyEvaluationsException {
+
+        // set up the step for the current stage
+        final double step     = (getMax() - getMin()) / n;
+        final double halfStep = step / 2.0;
+
+        // integrate over all elementary steps
+        double midPoint = getMin() + halfStep;
+        double sum = 0.0;
+        for (int i = 0; i < n; ++i) {
+            for (int j = 0; j < abscissas.length; ++j) {
+                sum += weights[j] * computeObjectiveValue(midPoint + halfStep * abscissas[j]);
+            }
+            midPoint += step;
+        }
+
+        return halfStep * sum;
+
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/integration/MidPointIntegrator.java

@@ -0,0 +1,169 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.integration;
+
+import com.fr.third.org.apache.commons.math3.exception.MathIllegalArgumentException;
+import com.fr.third.org.apache.commons.math3.exception.MaxCountExceededException;
+import com.fr.third.org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import com.fr.third.org.apache.commons.math3.exception.NumberIsTooLargeException;
+import com.fr.third.org.apache.commons.math3.exception.NumberIsTooSmallException;
+import com.fr.third.org.apache.commons.math3.exception.TooManyEvaluationsException;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Implements the <a href="http://en.wikipedia.org/wiki/Midpoint_method">
+ * Midpoint Rule</a> for integration of real univariate functions. For
+ * reference, see <b>Numerical Mathematics</b>, ISBN 0387989595,
+ * chapter 9.2.
+ * <p>
+ * The function should be integrable.</p>
+ *
+ * @since 3.3
+ */
+public class MidPointIntegrator extends BaseAbstractUnivariateIntegrator {
+
+    /** Maximum number of iterations for midpoint. */
+    public static final int MIDPOINT_MAX_ITERATIONS_COUNT = 64;
+
+    /**
+     * Build a midpoint integrator with given accuracies and iterations counts.
+     * @param relativeAccuracy relative accuracy of the result
+     * @param absoluteAccuracy absolute accuracy of the result
+     * @param minimalIterationCount minimum number of iterations
+     * @param maximalIterationCount maximum number of iterations
+     * (must be less than or equal to {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
+     * @exception NotStrictlyPositiveException if minimal number of iterations
+     * is not strictly positive
+     * @exception NumberIsTooSmallException if maximal number of iterations
+     * is lesser than or equal to the minimal number of iterations
+     * @exception NumberIsTooLargeException if maximal number of iterations
+     * is greater than {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
+     */
+    public MidPointIntegrator(final double relativeAccuracy,
+                              final double absoluteAccuracy,
+                              final int minimalIterationCount,
+                              final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
+        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
+        if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) {
+            throw new NumberIsTooLargeException(maximalIterationCount,
+                                                MIDPOINT_MAX_ITERATIONS_COUNT, false);
+        }
+    }
+
+    /**
+     * Build a midpoint integrator with given iteration counts.
+     * @param minimalIterationCount minimum number of iterations
+     * @param maximalIterationCount maximum number of iterations
+     * (must be less than or equal to {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
+     * @exception NotStrictlyPositiveException if minimal number of iterations
+     * is not strictly positive
+     * @exception NumberIsTooSmallException if maximal number of iterations
+     * is lesser than or equal to the minimal number of iterations
+     * @exception NumberIsTooLargeException if maximal number of iterations
+     * is greater than {@link #MIDPOINT_MAX_ITERATIONS_COUNT}
+     */
+    public MidPointIntegrator(final int minimalIterationCount,
+                              final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
+        super(minimalIterationCount, maximalIterationCount);
+        if (maximalIterationCount > MIDPOINT_MAX_ITERATIONS_COUNT) {
+            throw new NumberIsTooLargeException(maximalIterationCount,
+                                                MIDPOINT_MAX_ITERATIONS_COUNT, false);
+        }
+    }
+
+    /**
+     * Construct a midpoint integrator with default settings.
+     * (max iteration count set to {@link #MIDPOINT_MAX_ITERATIONS_COUNT})
+     */
+    public MidPointIntegrator() {
+        super(DEFAULT_MIN_ITERATIONS_COUNT, MIDPOINT_MAX_ITERATIONS_COUNT);
+    }
+
+    /**
+     * Compute the n-th stage integral of midpoint rule.
+     * This function should only be called by API <code>integrate()</code> in the package.
+     * To save time it does not verify arguments - caller does.
+     * <p>
+     * The interval is divided equally into 2^n sections rather than an
+     * arbitrary m sections because this configuration can best utilize the
+     * already computed values.</p>
+     *
+     * @param n the stage of 1/2 refinement. Must be larger than 0.
+     * @param previousStageResult Result from the previous call to the
+     * {@code stage} method.
+     * @param min Lower bound of the integration interval.
+     * @param diffMaxMin Difference between the lower bound and upper bound
+     * of the integration interval.
+     * @return the value of n-th stage integral
+     * @throws TooManyEvaluationsException if the maximal number of evaluations
+     * is exceeded.
+     */
+    private double stage(final int n,
+                         double previousStageResult,
+                         double min,
+                         double diffMaxMin)
+        throws TooManyEvaluationsException {
+
+        // number of new points in this stage
+        final long np = 1L << (n - 1);
+        double sum = 0;
+
+        // spacing between adjacent new points
+        final double spacing = diffMaxMin / np;
+
+        // the first new point
+        double x = min + 0.5 * spacing;
+        for (long i = 0; i < np; i++) {
+            sum += computeObjectiveValue(x);
+            x += spacing;
+        }
+        // add the new sum to previously calculated result
+        return 0.5 * (previousStageResult + sum * spacing);
+    }
+
+
+    /** {@inheritDoc} */
+    @Override
+    protected double doIntegrate()
+        throws MathIllegalArgumentException, TooManyEvaluationsException, MaxCountExceededException {
+
+        final double min = getMin();
+        final double diff = getMax() - min;
+        final double midPoint = min + 0.5 * diff;
+
+        double oldt = diff * computeObjectiveValue(midPoint);
+
+        while (true) {
+            incrementCount();
+            final int i = getIterations();
+            final double t = stage(i, oldt, min, diff);
+            if (i >= getMinimalIterationCount()) {
+                final double delta = FastMath.abs(t - oldt);
+                final double rLimit =
+                        getRelativeAccuracy() * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5;
+                if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
+                    return t;
+                }
+            }
+            oldt = t;
+        }
+
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/integration/RombergIntegrator.java

@@ -0,0 +1,142 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.integration;
+
+import com.fr.third.org.apache.commons.math3.exception.MaxCountExceededException;
+import com.fr.third.org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import com.fr.third.org.apache.commons.math3.exception.NumberIsTooLargeException;
+import com.fr.third.org.apache.commons.math3.exception.NumberIsTooSmallException;
+import com.fr.third.org.apache.commons.math3.exception.TooManyEvaluationsException;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Implements the <a href="http://mathworld.wolfram.com/RombergIntegration.html">
+ * Romberg Algorithm</a> for integration of real univariate functions. For
+ * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
+ * chapter 3.
+ * <p>
+ * Romberg integration employs k successive refinements of the trapezoid
+ * rule to remove error terms less than order O(N^(-2k)). Simpson's rule
+ * is a special case of k = 2.</p>
+ *
+ * @since 1.2
+ */
+public class RombergIntegrator extends BaseAbstractUnivariateIntegrator {
+
+    /** Maximal number of iterations for Romberg. */
+    public static final int ROMBERG_MAX_ITERATIONS_COUNT = 32;
+
+    /**
+     * Build a Romberg integrator with given accuracies and iterations counts.
+     * @param relativeAccuracy relative accuracy of the result
+     * @param absoluteAccuracy absolute accuracy of the result
+     * @param minimalIterationCount minimum number of iterations
+     * @param maximalIterationCount maximum number of iterations
+     * (must be less than or equal to {@link #ROMBERG_MAX_ITERATIONS_COUNT})
+     * @exception NotStrictlyPositiveException if minimal number of iterations
+     * is not strictly positive
+     * @exception NumberIsTooSmallException if maximal number of iterations
+     * is lesser than or equal to the minimal number of iterations
+     * @exception NumberIsTooLargeException if maximal number of iterations
+     * is greater than {@link #ROMBERG_MAX_ITERATIONS_COUNT}
+     */
+    public RombergIntegrator(final double relativeAccuracy,
+                             final double absoluteAccuracy,
+                             final int minimalIterationCount,
+                             final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
+        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
+        if (maximalIterationCount > ROMBERG_MAX_ITERATIONS_COUNT) {
+            throw new NumberIsTooLargeException(maximalIterationCount,
+                                                ROMBERG_MAX_ITERATIONS_COUNT, false);
+        }
+    }
+
+    /**
+     * Build a Romberg integrator with given iteration counts.
+     * @param minimalIterationCount minimum number of iterations
+     * @param maximalIterationCount maximum number of iterations
+     * (must be less than or equal to {@link #ROMBERG_MAX_ITERATIONS_COUNT})
+     * @exception NotStrictlyPositiveException if minimal number of iterations
+     * is not strictly positive
+     * @exception NumberIsTooSmallException if maximal number of iterations
+     * is lesser than or equal to the minimal number of iterations
+     * @exception NumberIsTooLargeException if maximal number of iterations
+     * is greater than {@link #ROMBERG_MAX_ITERATIONS_COUNT}
+     */
+    public RombergIntegrator(final int minimalIterationCount,
+                             final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
+        super(minimalIterationCount, maximalIterationCount);
+        if (maximalIterationCount > ROMBERG_MAX_ITERATIONS_COUNT) {
+            throw new NumberIsTooLargeException(maximalIterationCount,
+                                                ROMBERG_MAX_ITERATIONS_COUNT, false);
+        }
+    }
+
+    /**
+     * Construct a Romberg integrator with default settings
+     * (max iteration count set to {@link #ROMBERG_MAX_ITERATIONS_COUNT})
+     */
+    public RombergIntegrator() {
+        super(DEFAULT_MIN_ITERATIONS_COUNT, ROMBERG_MAX_ITERATIONS_COUNT);
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected double doIntegrate()
+        throws TooManyEvaluationsException, MaxCountExceededException {
+
+        final int m = getMaximalIterationCount() + 1;
+        double previousRow[] = new double[m];
+        double currentRow[]  = new double[m];
+
+        TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
+        currentRow[0] = qtrap.stage(this, 0);
+        incrementCount();
+        double olds = currentRow[0];
+        while (true) {
+
+            final int i = getIterations();
+
+            // switch rows
+            final double[] tmpRow = previousRow;
+            previousRow = currentRow;
+            currentRow = tmpRow;
+
+            currentRow[0] = qtrap.stage(this, i);
+            incrementCount();
+            for (int j = 1; j <= i; j++) {
+                // Richardson extrapolation coefficient
+                final double r = (1L << (2 * j)) - 1;
+                final double tIJm1 = currentRow[j - 1];
+                currentRow[j] = tIJm1 + (tIJm1 - previousRow[j - 1]) / r;
+            }
+            final double s = currentRow[i];
+            if (i >= getMinimalIterationCount()) {
+                final double delta  = FastMath.abs(s - olds);
+                final double rLimit = getRelativeAccuracy() * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5;
+                if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
+                    return s;
+                }
+            }
+            olds = s;
+        }
+
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/integration/SimpsonIntegrator.java

@@ -0,0 +1,129 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.integration;
+
+import com.fr.third.org.apache.commons.math3.exception.MaxCountExceededException;
+import com.fr.third.org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import com.fr.third.org.apache.commons.math3.exception.NumberIsTooLargeException;
+import com.fr.third.org.apache.commons.math3.exception.NumberIsTooSmallException;
+import com.fr.third.org.apache.commons.math3.exception.TooManyEvaluationsException;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Implements <a href="http://mathworld.wolfram.com/SimpsonsRule.html">
+ * Simpson's Rule</a> for integration of real univariate functions. For
+ * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
+ * chapter 3.
+ * <p>
+ * This implementation employs the basic trapezoid rule to calculate Simpson's
+ * rule.</p>
+ *
+ * @since 1.2
+ */
+public class SimpsonIntegrator extends BaseAbstractUnivariateIntegrator {
+
+    /** Maximal number of iterations for Simpson. */
+    public static final int SIMPSON_MAX_ITERATIONS_COUNT = 64;
+
+    /**
+     * Build a Simpson integrator with given accuracies and iterations counts.
+     * @param relativeAccuracy relative accuracy of the result
+     * @param absoluteAccuracy absolute accuracy of the result
+     * @param minimalIterationCount minimum number of iterations
+     * @param maximalIterationCount maximum number of iterations
+     * (must be less than or equal to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
+     * @exception NotStrictlyPositiveException if minimal number of iterations
+     * is not strictly positive
+     * @exception NumberIsTooSmallException if maximal number of iterations
+     * is lesser than or equal to the minimal number of iterations
+     * @exception NumberIsTooLargeException if maximal number of iterations
+     * is greater than {@link #SIMPSON_MAX_ITERATIONS_COUNT}
+     */
+    public SimpsonIntegrator(final double relativeAccuracy,
+                             final double absoluteAccuracy,
+                             final int minimalIterationCount,
+                             final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
+        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
+        if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
+            throw new NumberIsTooLargeException(maximalIterationCount,
+                                                SIMPSON_MAX_ITERATIONS_COUNT, false);
+        }
+    }
+
+    /**
+     * Build a Simpson integrator with given iteration counts.
+     * @param minimalIterationCount minimum number of iterations
+     * @param maximalIterationCount maximum number of iterations
+     * (must be less than or equal to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
+     * @exception NotStrictlyPositiveException if minimal number of iterations
+     * is not strictly positive
+     * @exception NumberIsTooSmallException if maximal number of iterations
+     * is lesser than or equal to the minimal number of iterations
+     * @exception NumberIsTooLargeException if maximal number of iterations
+     * is greater than {@link #SIMPSON_MAX_ITERATIONS_COUNT}
+     */
+    public SimpsonIntegrator(final int minimalIterationCount,
+                             final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
+        super(minimalIterationCount, maximalIterationCount);
+        if (maximalIterationCount > SIMPSON_MAX_ITERATIONS_COUNT) {
+            throw new NumberIsTooLargeException(maximalIterationCount,
+                                                SIMPSON_MAX_ITERATIONS_COUNT, false);
+        }
+    }
+
+    /**
+     * Construct an integrator with default settings.
+     * (max iteration count set to {@link #SIMPSON_MAX_ITERATIONS_COUNT})
+     */
+    public SimpsonIntegrator() {
+        super(DEFAULT_MIN_ITERATIONS_COUNT, SIMPSON_MAX_ITERATIONS_COUNT);
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected double doIntegrate()
+        throws TooManyEvaluationsException, MaxCountExceededException {
+
+        TrapezoidIntegrator qtrap = new TrapezoidIntegrator();
+        if (getMinimalIterationCount() == 1) {
+            return (4 * qtrap.stage(this, 1) - qtrap.stage(this, 0)) / 3.0;
+        }
+
+        // Simpson's rule requires at least two trapezoid stages.
+        double olds = 0;
+        double oldt = qtrap.stage(this, 0);
+        while (true) {
+            final double t = qtrap.stage(this, getIterations());
+            incrementCount();
+            final double s = (4 * t - oldt) / 3.0;
+            if (getIterations() >= getMinimalIterationCount()) {
+                final double delta = FastMath.abs(s - olds);
+                final double rLimit =
+                    getRelativeAccuracy() * (FastMath.abs(olds) + FastMath.abs(s)) * 0.5;
+                if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
+                    return s;
+                }
+            }
+            olds = s;
+            oldt = t;
+        }
+
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/integration/TrapezoidIntegrator.java

@@ -0,0 +1,168 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.integration;
+
+import com.fr.third.org.apache.commons.math3.exception.MathIllegalArgumentException;
+import com.fr.third.org.apache.commons.math3.exception.MaxCountExceededException;
+import com.fr.third.org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import com.fr.third.org.apache.commons.math3.exception.NumberIsTooLargeException;
+import com.fr.third.org.apache.commons.math3.exception.NumberIsTooSmallException;
+import com.fr.third.org.apache.commons.math3.exception.TooManyEvaluationsException;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Implements the <a href="http://mathworld.wolfram.com/TrapezoidalRule.html">
+ * Trapezoid Rule</a> for integration of real univariate functions. For
+ * reference, see <b>Introduction to Numerical Analysis</b>, ISBN 038795452X,
+ * chapter 3.
+ * <p>
+ * The function should be integrable.</p>
+ *
+ * @since 1.2
+ */
+public class TrapezoidIntegrator extends BaseAbstractUnivariateIntegrator {
+
+    /** Maximum number of iterations for trapezoid. */
+    public static final int TRAPEZOID_MAX_ITERATIONS_COUNT = 64;
+
+    /** Intermediate result. */
+    private double s;
+
+    /**
+     * Build a trapezoid integrator with given accuracies and iterations counts.
+     * @param relativeAccuracy relative accuracy of the result
+     * @param absoluteAccuracy absolute accuracy of the result
+     * @param minimalIterationCount minimum number of iterations
+     * @param maximalIterationCount maximum number of iterations
+     * (must be less than or equal to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
+     * @exception NotStrictlyPositiveException if minimal number of iterations
+     * is not strictly positive
+     * @exception NumberIsTooSmallException if maximal number of iterations
+     * is lesser than or equal to the minimal number of iterations
+     * @exception NumberIsTooLargeException if maximal number of iterations
+     * is greater than {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
+     */
+    public TrapezoidIntegrator(final double relativeAccuracy,
+                               final double absoluteAccuracy,
+                               final int minimalIterationCount,
+                               final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
+        super(relativeAccuracy, absoluteAccuracy, minimalIterationCount, maximalIterationCount);
+        if (maximalIterationCount > TRAPEZOID_MAX_ITERATIONS_COUNT) {
+            throw new NumberIsTooLargeException(maximalIterationCount,
+                                                TRAPEZOID_MAX_ITERATIONS_COUNT, false);
+        }
+    }
+
+    /**
+     * Build a trapezoid integrator with given iteration counts.
+     * @param minimalIterationCount minimum number of iterations
+     * @param maximalIterationCount maximum number of iterations
+     * (must be less than or equal to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
+     * @exception NotStrictlyPositiveException if minimal number of iterations
+     * is not strictly positive
+     * @exception NumberIsTooSmallException if maximal number of iterations
+     * is lesser than or equal to the minimal number of iterations
+     * @exception NumberIsTooLargeException if maximal number of iterations
+     * is greater than {@link #TRAPEZOID_MAX_ITERATIONS_COUNT}
+     */
+    public TrapezoidIntegrator(final int minimalIterationCount,
+                               final int maximalIterationCount)
+        throws NotStrictlyPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
+        super(minimalIterationCount, maximalIterationCount);
+        if (maximalIterationCount > TRAPEZOID_MAX_ITERATIONS_COUNT) {
+            throw new NumberIsTooLargeException(maximalIterationCount,
+                                                TRAPEZOID_MAX_ITERATIONS_COUNT, false);
+        }
+    }
+
+    /**
+     * Construct a trapezoid integrator with default settings.
+     * (max iteration count set to {@link #TRAPEZOID_MAX_ITERATIONS_COUNT})
+     */
+    public TrapezoidIntegrator() {
+        super(DEFAULT_MIN_ITERATIONS_COUNT, TRAPEZOID_MAX_ITERATIONS_COUNT);
+    }
+
+    /**
+     * Compute the n-th stage integral of trapezoid rule. This function
+     * should only be called by API <code>integrate()</code> in the package.
+     * To save time it does not verify arguments - caller does.
+     * <p>
+     * The interval is divided equally into 2^n sections rather than an
+     * arbitrary m sections because this configuration can best utilize the
+     * already computed values.</p>
+     *
+     * @param baseIntegrator integrator holding integration parameters
+     * @param n the stage of 1/2 refinement, n = 0 is no refinement
+     * @return the value of n-th stage integral
+     * @throws TooManyEvaluationsException if the maximal number of evaluations
+     * is exceeded.
+     */
+    double stage(final BaseAbstractUnivariateIntegrator baseIntegrator, final int n)
+        throws TooManyEvaluationsException {
+
+        if (n == 0) {
+            final double max = baseIntegrator.getMax();
+            final double min = baseIntegrator.getMin();
+            s = 0.5 * (max - min) *
+                      (baseIntegrator.computeObjectiveValue(min) +
+                       baseIntegrator.computeObjectiveValue(max));
+            return s;
+        } else {
+            final long np = 1L << (n-1);           // number of new points in this stage
+            double sum = 0;
+            final double max = baseIntegrator.getMax();
+            final double min = baseIntegrator.getMin();
+            // spacing between adjacent new points
+            final double spacing = (max - min) / np;
+            double x = min + 0.5 * spacing;    // the first new point
+            for (long i = 0; i < np; i++) {
+                sum += baseIntegrator.computeObjectiveValue(x);
+                x += spacing;
+            }
+            // add the new sum to previously calculated result
+            s = 0.5 * (s + sum * spacing);
+            return s;
+        }
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected double doIntegrate()
+        throws MathIllegalArgumentException, TooManyEvaluationsException, MaxCountExceededException {
+
+        double oldt = stage(this, 0);
+        incrementCount();
+        while (true) {
+            final int i = getIterations();
+            final double t = stage(this, i);
+            if (i >= getMinimalIterationCount()) {
+                final double delta = FastMath.abs(t - oldt);
+                final double rLimit =
+                    getRelativeAccuracy() * (FastMath.abs(oldt) + FastMath.abs(t)) * 0.5;
+                if ((delta <= rLimit) || (delta <= getAbsoluteAccuracy())) {
+                    return t;
+                }
+            }
+            oldt = t;
+            incrementCount();
+        }
+
+    }
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/integration/UnivariateIntegrator.java

@@ -0,0 +1,95 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.integration;
+
+import com.fr.third.org.apache.commons.math3.exception.MathIllegalArgumentException;
+import com.fr.third.org.apache.commons.math3.exception.MaxCountExceededException;
+import com.fr.third.org.apache.commons.math3.exception.NullArgumentException;
+import com.fr.third.org.apache.commons.math3.exception.TooManyEvaluationsException;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+
+/**
+ * Interface for univariate real integration algorithms.
+ *
+ * @since 1.2
+ */
+public interface UnivariateIntegrator {
+
+    /**
+     * Get the relative accuracy.
+     *
+     * @return the accuracy
+     */
+    double getRelativeAccuracy();
+
+    /**
+     * Get the absolute accuracy.
+     *
+     * @return the accuracy
+     */
+    double getAbsoluteAccuracy();
+
+    /**
+     * Get the min limit for the number of iterations.
+     *
+     * @return the actual min limit
+     */
+    int getMinimalIterationCount();
+
+    /**
+     * Get the upper limit for the number of iterations.
+     *
+     * @return the actual upper limit
+     */
+    int getMaximalIterationCount();
+
+    /**
+     * Integrate the function in the given interval.
+     *
+     * @param maxEval Maximum number of evaluations.
+     * @param f the integrand function
+     * @param min the lower bound for the interval
+     * @param max the upper bound for the interval
+     * @return the value of integral
+     * @throws TooManyEvaluationsException if the maximum number of function
+     * evaluations is exceeded
+     * @throws MaxCountExceededException if the maximum iteration count is exceeded
+     * or the integrator detects convergence problems otherwise
+     * @throws MathIllegalArgumentException if {@code min > max} or the endpoints do not
+     * satisfy the requirements specified by the integrator
+     * @throws NullArgumentException if {@code f} is {@code null}.
+     */
+    double integrate(int maxEval, UnivariateFunction f, double min,
+                     double max)
+        throws TooManyEvaluationsException, MaxCountExceededException,
+               MathIllegalArgumentException, NullArgumentException;
+
+    /**
+     * Get the number of function evaluations of the last run of the integrator.
+     *
+     * @return number of function evaluations
+     */
+    int getEvaluations();
+
+    /**
+     * Get the number of iterations of the last run of the integrator.
+     *
+     * @return number of iterations
+     */
+    int getIterations();
+
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/integration/gauss/BaseRuleFactory.java

@@ -0,0 +1,154 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.integration.gauss;
+
+import java.util.Map;
+import java.util.TreeMap;
+
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import com.fr.third.org.apache.commons.math3.exception.util.LocalizedFormats;
+import com.fr.third.org.apache.commons.math3.util.Pair;
+
+/**
+ * Base class for rules that determines the integration nodes and their
+ * weights.
+ * Subclasses must implement the {@link #computeRule(int) computeRule} method.
+ *
+ * @param <T> Type of the number used to represent the points and weights of
+ * the quadrature rules.
+ *
+ * @since 3.1
+ */
+public abstract class BaseRuleFactory<T extends Number> {
+    /** List of points and weights, indexed by the order of the rule. */
+    private final Map<Integer, Pair<T[], T[]>> pointsAndWeights
+        = new TreeMap<Integer, Pair<T[], T[]>>();
+    /** Cache for double-precision rules. */
+    private final Map<Integer, Pair<double[], double[]>> pointsAndWeightsDouble
+        = new TreeMap<Integer, Pair<double[], double[]>>();
+
+    /**
+     * Gets a copy of the quadrature rule with the given number of integration
+     * points.
+     *
+     * @param numberOfPoints Number of integration points.
+     * @return a copy of the integration rule.
+     * @throws NotStrictlyPositiveException if {@code numberOfPoints < 1}.
+     * @throws DimensionMismatchException if the elements of the rule pair do not
+     * have the same length.
+     */
+    public Pair<double[], double[]> getRule(int numberOfPoints)
+        throws NotStrictlyPositiveException, DimensionMismatchException {
+
+        if (numberOfPoints <= 0) {
+            throw new NotStrictlyPositiveException(LocalizedFormats.NUMBER_OF_POINTS,
+                                                   numberOfPoints);
+        }
+
+        // Try to obtain the rule from the cache.
+        Pair<double[], double[]> cached = pointsAndWeightsDouble.get(numberOfPoints);
+
+        if (cached == null) {
+            // Rule not computed yet.
+
+            // Compute the rule.
+            final Pair<T[], T[]> rule = getRuleInternal(numberOfPoints);
+            cached = convertToDouble(rule);
+
+            // Cache it.
+            pointsAndWeightsDouble.put(numberOfPoints, cached);
+        }
+
+        // Return a copy.
+        return new Pair<double[], double[]>(cached.getFirst().clone(),
+                                            cached.getSecond().clone());
+    }
+
+    /**
+     * Gets a rule.
+     * Synchronization ensures that rules will be computed and added to the
+     * cache at most once.
+     * The returned rule is a reference into the cache.
+     *
+     * @param numberOfPoints Order of the rule to be retrieved.
+     * @return the points and weights corresponding to the given order.
+     * @throws DimensionMismatchException if the elements of the rule pair do not
+     * have the same length.
+     */
+    protected synchronized Pair<T[], T[]> getRuleInternal(int numberOfPoints)
+        throws DimensionMismatchException {
+        final Pair<T[], T[]> rule = pointsAndWeights.get(numberOfPoints);
+        if (rule == null) {
+            addRule(computeRule(numberOfPoints));
+            // The rule should be available now.
+            return getRuleInternal(numberOfPoints);
+        }
+        return rule;
+    }
+
+    /**
+     * Stores a rule.
+     *
+     * @param rule Rule to be stored.
+     * @throws DimensionMismatchException if the elements of the pair do not
+     * have the same length.
+     */
+    protected void addRule(Pair<T[], T[]> rule) throws DimensionMismatchException {
+        if (rule.getFirst().length != rule.getSecond().length) {
+            throw new DimensionMismatchException(rule.getFirst().length,
+                                                 rule.getSecond().length);
+        }
+
+        pointsAndWeights.put(rule.getFirst().length, rule);
+    }
+
+    /**
+     * Computes the rule for the given order.
+     *
+     * @param numberOfPoints Order of the rule to be computed.
+     * @return the computed rule.
+     * @throws DimensionMismatchException if the elements of the pair do not
+     * have the same length.
+     */
+    protected abstract Pair<T[], T[]> computeRule(int numberOfPoints)
+        throws DimensionMismatchException;
+
+    /**
+     * Converts the from the actual {@code Number} type to {@code double}
+     *
+     * @param <T> Type of the number used to represent the points and
+     * weights of the quadrature rules.
+     * @param rule Points and weights.
+     * @return points and weights as {@code double}s.
+     */
+    private static <T extends Number> Pair<double[], double[]> convertToDouble(Pair<T[], T[]> rule) {
+        final T[] pT = rule.getFirst();
+        final T[] wT = rule.getSecond();
+
+        final int len = pT.length;
+        final double[] pD = new double[len];
+        final double[] wD = new double[len];
+
+        for (int i = 0; i < len; i++) {
+            pD[i] = pT[i].doubleValue();
+            wD[i] = wT[i].doubleValue();
+        }
+
+        return new Pair<double[], double[]>(pD, wD);
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/integration/gauss/GaussIntegrator.java

@@ -0,0 +1,129 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.integration.gauss;
+
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.exception.NonMonotonicSequenceException;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.MathArrays;
+import com.fr.third.org.apache.commons.math3.util.Pair;
+
+/**
+ * Class that implements the Gaussian rule for
+ * {@link #integrate(UnivariateFunction) integrating} a weighted
+ * function.
+ *
+ * @since 3.1
+ */
+public class GaussIntegrator {
+    /** Nodes. */
+    private final double[] points;
+    /** Nodes weights. */
+    private final double[] weights;
+
+    /**
+     * Creates an integrator from the given {@code points} and {@code weights}.
+     * The integration interval is defined by the first and last value of
+     * {@code points} which must be sorted in increasing order.
+     *
+     * @param points Integration points.
+     * @param weights Weights of the corresponding integration nodes.
+     * @throws NonMonotonicSequenceException if the {@code points} are not
+     * sorted in increasing order.
+     * @throws DimensionMismatchException if points and weights don't have the same length
+     */
+    public GaussIntegrator(double[] points,
+                           double[] weights)
+        throws NonMonotonicSequenceException, DimensionMismatchException {
+        if (points.length != weights.length) {
+            throw new DimensionMismatchException(points.length,
+                                                 weights.length);
+        }
+
+        MathArrays.checkOrder(points, MathArrays.OrderDirection.INCREASING, true, true);
+
+        this.points = points.clone();
+        this.weights = weights.clone();
+    }
+
+    /**
+     * Creates an integrator from the given pair of points (first element of
+     * the pair) and weights (second element of the pair.
+     *
+     * @param pointsAndWeights Integration points and corresponding weights.
+     * @throws NonMonotonicSequenceException if the {@code points} are not
+     * sorted in increasing order.
+     *
+     * @see #GaussIntegrator(double[], double[])
+     */
+    public GaussIntegrator(Pair<double[], double[]> pointsAndWeights)
+        throws NonMonotonicSequenceException {
+        this(pointsAndWeights.getFirst(), pointsAndWeights.getSecond());
+    }
+
+    /**
+     * Returns an estimate of the integral of {@code f(x) * w(x)},
+     * where {@code w} is a weight function that depends on the actual
+     * flavor of the Gauss integration scheme.
+     * The algorithm uses the points and associated weights, as passed
+     * to the {@link #GaussIntegrator(double[],double[]) constructor}.
+     *
+     * @param f Function to integrate.
+     * @return the integral of the weighted function.
+     */
+    public double integrate(UnivariateFunction f) {
+        double s = 0;
+        double c = 0;
+        for (int i = 0; i < points.length; i++) {
+            final double x = points[i];
+            final double w = weights[i];
+            final double y = w * f.value(x) - c;
+            final double t = s + y;
+            c = (t - s) - y;
+            s = t;
+        }
+        return s;
+    }
+
+    /**
+     * @return the order of the integration rule (the number of integration
+     * points).
+     */
+    public int getNumberOfPoints() {
+        return points.length;
+    }
+
+    /**
+     * Gets the integration point at the given index.
+     * The index must be in the valid range but no check is performed.
+     * @param index index of the integration point
+     * @return the integration point.
+     */
+    public double getPoint(int index) {
+        return points[index];
+    }
+
+    /**
+     * Gets the weight of the integration point at the given index.
+     * The index must be in the valid range but no check is performed.
+     * @param index index of the integration point
+     * @return the weight.
+     */
+    public double getWeight(int index) {
+        return weights[index];
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/integration/gauss/GaussIntegratorFactory.java

@@ -0,0 +1,168 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.integration.gauss;
+
+import java.math.BigDecimal;
+
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.exception.NotStrictlyPositiveException;
+import com.fr.third.org.apache.commons.math3.util.Pair;
+
+/**
+ * Class that provides different ways to compute the nodes and weights to be
+ * used by the {@link GaussIntegrator Gaussian integration rule}.
+ *
+ * @since 3.1
+ */
+public class GaussIntegratorFactory {
+    /** Generator of Gauss-Legendre integrators. */
+    private final BaseRuleFactory<Double> legendre = new LegendreRuleFactory();
+    /** Generator of Gauss-Legendre integrators. */
+    private final BaseRuleFactory<BigDecimal> legendreHighPrecision = new LegendreHighPrecisionRuleFactory();
+    /** Generator of Gauss-Hermite integrators. */
+    private final BaseRuleFactory<Double> hermite = new HermiteRuleFactory();
+
+    /**
+     * Creates a Gauss-Legendre integrator of the given order.
+     * The call to the
+     * {@link GaussIntegrator#integrate(UnivariateFunction)
+     * integrate} method will perform an integration on the natural interval
+     * {@code [-1 , 1]}.
+     *
+     * @param numberOfPoints Order of the integration rule.
+     * @return a Gauss-Legendre integrator.
+     */
+    public GaussIntegrator legendre(int numberOfPoints) {
+        return new GaussIntegrator(getRule(legendre, numberOfPoints));
+    }
+
+    /**
+     * Creates a Gauss-Legendre integrator of the given order.
+     * The call to the
+     * {@link GaussIntegrator#integrate(UnivariateFunction)
+     * integrate} method will perform an integration on the given interval.
+     *
+     * @param numberOfPoints Order of the integration rule.
+     * @param lowerBound Lower bound of the integration interval.
+     * @param upperBound Upper bound of the integration interval.
+     * @return a Gauss-Legendre integrator.
+     * @throws NotStrictlyPositiveException if number of points is not positive
+     */
+    public GaussIntegrator legendre(int numberOfPoints,
+                                    double lowerBound,
+                                    double upperBound)
+        throws NotStrictlyPositiveException {
+        return new GaussIntegrator(transform(getRule(legendre, numberOfPoints),
+                                             lowerBound, upperBound));
+    }
+
+    /**
+     * Creates a Gauss-Legendre integrator of the given order.
+     * The call to the
+     * {@link GaussIntegrator#integrate(UnivariateFunction)
+     * integrate} method will perform an integration on the natural interval
+     * {@code [-1 , 1]}.
+     *
+     * @param numberOfPoints Order of the integration rule.
+     * @return a Gauss-Legendre integrator.
+     * @throws NotStrictlyPositiveException if number of points is not positive
+     */
+    public GaussIntegrator legendreHighPrecision(int numberOfPoints)
+        throws NotStrictlyPositiveException {
+        return new GaussIntegrator(getRule(legendreHighPrecision, numberOfPoints));
+    }
+
+    /**
+     * Creates an integrator of the given order, and whose call to the
+     * {@link GaussIntegrator#integrate(UnivariateFunction)
+     * integrate} method will perform an integration on the given interval.
+     *
+     * @param numberOfPoints Order of the integration rule.
+     * @param lowerBound Lower bound of the integration interval.
+     * @param upperBound Upper bound of the integration interval.
+     * @return a Gauss-Legendre integrator.
+     * @throws NotStrictlyPositiveException if number of points is not positive
+     */
+    public GaussIntegrator legendreHighPrecision(int numberOfPoints,
+                                                 double lowerBound,
+                                                 double upperBound)
+        throws NotStrictlyPositiveException {
+        return new GaussIntegrator(transform(getRule(legendreHighPrecision, numberOfPoints),
+                                             lowerBound, upperBound));
+    }
+
+    /**
+     * Creates a Gauss-Hermite integrator of the given order.
+     * The call to the
+     * {@link SymmetricGaussIntegrator#integrate(UnivariateFunction)
+     * integrate} method will perform a weighted integration on the interval
+     * \([-\infty, +\infty]\): the computed value is the improper integral of
+     * \(e^{-x^2}f(x)\)
+     * where \(f(x)\) is the function passed to the
+     * {@link SymmetricGaussIntegrator#integrate(UnivariateFunction)
+     * integrate} method.
+     *
+     * @param numberOfPoints Order of the integration rule.
+     * @return a Gauss-Hermite integrator.
+     */
+    public SymmetricGaussIntegrator hermite(int numberOfPoints) {
+        return new SymmetricGaussIntegrator(getRule(hermite, numberOfPoints));
+    }
+
+    /**
+     * @param factory Integration rule factory.
+     * @param numberOfPoints Order of the integration rule.
+     * @return the integration nodes and weights.
+     * @throws NotStrictlyPositiveException if number of points is not positive
+     * @throws DimensionMismatchException if the elements of the rule pair do not
+     * have the same length.
+     */
+    private static Pair<double[], double[]> getRule(BaseRuleFactory<? extends Number> factory,
+                                                    int numberOfPoints)
+        throws NotStrictlyPositiveException, DimensionMismatchException {
+        return factory.getRule(numberOfPoints);
+    }
+
+    /**
+     * Performs a change of variable so that the integration can be performed
+     * on an arbitrary interval {@code [a, b]}.
+     * It is assumed that the natural interval is {@code [-1, 1]}.
+     *
+     * @param rule Original points and weights.
+     * @param a Lower bound of the integration interval.
+     * @param b Lower bound of the integration interval.
+     * @return the points and weights adapted to the new interval.
+     */
+    private static Pair<double[], double[]> transform(Pair<double[], double[]> rule,
+                                                      double a,
+                                                      double b) {
+        final double[] points = rule.getFirst();
+        final double[] weights = rule.getSecond();
+
+        // Scaling
+        final double scale = (b - a) / 2;
+        final double shift = a + scale;
+
+        for (int i = 0; i < points.length; i++) {
+            points[i] = points[i] * scale + shift;
+            weights[i] *= scale;
+        }
+
+        return new Pair<double[], double[]>(points, weights);
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/integration/gauss/HermiteRuleFactory.java

@@ -0,0 +1,177 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.integration.gauss;
+
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.util.Pair;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+
+/**
+ * Factory that creates a
+ * <a href="http://en.wikipedia.org/wiki/Gauss-Hermite_quadrature">
+ * Gauss-type quadrature rule using Hermite polynomials</a>
+ * of the first kind.
+ * Such a quadrature rule allows the calculation of improper integrals
+ * of a function
+ * <p>
+ *  \(f(x) e^{-x^2}\)
+ * </p><p>
+ * Recurrence relation and weights computation follow
+ * <a href="http://en.wikipedia.org/wiki/Abramowitz_and_Stegun">
+ * Abramowitz and Stegun, 1964</a>.
+ * </p><p>
+ * The coefficients of the standard Hermite polynomials grow very rapidly.
+ * In order to avoid overflows, each Hermite polynomial is normalized with
+ * respect to the underlying scalar product.
+ * The initial interval for the application of the bisection method is
+ * based on the roots of the previous Hermite polynomial (interlacing).
+ * Upper and lower bounds of these roots are provided by </p>
+ * <blockquote>
+ *  I. Krasikov,
+ *  <em>Nonnegative quadratic forms and bounds on orthogonal polynomials</em>,
+ *  Journal of Approximation theory <b>111</b>, 31-49
+ * </blockquote>
+ *
+ * @since 3.3
+ */
+public class HermiteRuleFactory extends BaseRuleFactory<Double> {
+    /** &pi;<sup>1/2</sup> */
+    private static final double SQRT_PI = 1.77245385090551602729;
+    /** &pi;<sup>-1/4</sup> */
+    private static final double H0 = 7.5112554446494248286e-1;
+    /** &pi;<sup>-1/4</sup> &radic;2 */
+    private static final double H1 = 1.0622519320271969145;
+
+    /** {@inheritDoc} */
+    @Override
+    protected Pair<Double[], Double[]> computeRule(int numberOfPoints)
+        throws DimensionMismatchException {
+
+        if (numberOfPoints == 1) {
+            // Break recursion.
+            return new Pair<Double[], Double[]>(new Double[] { 0d },
+                                                new Double[] { SQRT_PI });
+        }
+
+        // Get previous rule.
+        // If it has not been computed yet it will trigger a recursive call
+        // to this method.
+        final int lastNumPoints = numberOfPoints - 1;
+        final Double[] previousPoints = getRuleInternal(lastNumPoints).getFirst();
+
+        // Compute next rule.
+        final Double[] points = new Double[numberOfPoints];
+        final Double[] weights = new Double[numberOfPoints];
+
+        final double sqrtTwoTimesLastNumPoints = FastMath.sqrt(2 * lastNumPoints);
+        final double sqrtTwoTimesNumPoints = FastMath.sqrt(2 * numberOfPoints);
+
+        // Find i-th root of H[n+1] by bracketing.
+        final int iMax = numberOfPoints / 2;
+        for (int i = 0; i < iMax; i++) {
+            // Lower-bound of the interval.
+            double a = (i == 0) ? -sqrtTwoTimesLastNumPoints : previousPoints[i - 1].doubleValue();
+            // Upper-bound of the interval.
+            double b = (iMax == 1) ? -0.5 : previousPoints[i].doubleValue();
+
+            // H[j-1](a)
+            double hma = H0;
+            // H[j](a)
+            double ha = H1 * a;
+            // H[j-1](b)
+            double hmb = H0;
+            // H[j](b)
+            double hb = H1 * b;
+            for (int j = 1; j < numberOfPoints; j++) {
+                // Compute H[j+1](a) and H[j+1](b)
+                final double jp1 = j + 1;
+                final double s = FastMath.sqrt(2 / jp1);
+                final double sm = FastMath.sqrt(j / jp1);
+                final double hpa = s * a * ha - sm * hma;
+                final double hpb = s * b * hb - sm * hmb;
+                hma = ha;
+                ha = hpa;
+                hmb = hb;
+                hb = hpb;
+            }
+
+            // Now ha = H[n+1](a), and hma = H[n](a) (same holds for b).
+            // Middle of the interval.
+            double c = 0.5 * (a + b);
+            // P[j-1](c)
+            double hmc = H0;
+            // P[j](c)
+            double hc = H1 * c;
+            boolean done = false;
+            while (!done) {
+                done = b - a <= Math.ulp(c);
+                hmc = H0;
+                hc = H1 * c;
+                for (int j = 1; j < numberOfPoints; j++) {
+                    // Compute H[j+1](c)
+                    final double jp1 = j + 1;
+                    final double s = FastMath.sqrt(2 / jp1);
+                    final double sm = FastMath.sqrt(j / jp1);
+                    final double hpc = s * c * hc - sm * hmc;
+                    hmc = hc;
+                    hc = hpc;
+                }
+                // Now h = H[n+1](c) and hm = H[n](c).
+                if (!done) {
+                    if (ha * hc < 0) {
+                        b = c;
+                        hmb = hmc;
+                        hb = hc;
+                    } else {
+                        a = c;
+                        hma = hmc;
+                        ha = hc;
+                    }
+                    c = 0.5 * (a + b);
+                }
+            }
+            final double d = sqrtTwoTimesNumPoints * hmc;
+            final double w = 2 / (d * d);
+
+            points[i] = c;
+            weights[i] = w;
+
+            final int idx = lastNumPoints - i;
+            points[idx] = -c;
+            weights[idx] = w;
+        }
+
+        // If "numberOfPoints" is odd, 0 is a root.
+        // Note: as written, the test for oddness will work for negative
+        // integers too (although it is not necessary here), preventing
+        // a FindBugs warning.
+        if (numberOfPoints % 2 != 0) {
+            double hm = H0;
+            for (int j = 1; j < numberOfPoints; j += 2) {
+                final double jp1 = j + 1;
+                hm = -FastMath.sqrt(j / jp1) * hm;
+            }
+            final double d = sqrtTwoTimesNumPoints * hm;
+            final double w = 2 / (d * d);
+
+            points[iMax] = 0d;
+            weights[iMax] = w;
+        }
+
+        return new Pair<Double[], Double[]>(points, weights);
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/integration/gauss/LegendreHighPrecisionRuleFactory.java

@@ -0,0 +1,215 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.integration.gauss;
+
+import java.math.BigDecimal;
+import java.math.MathContext;
+
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.util.Pair;
+
+/**
+ * Factory that creates Gauss-type quadrature rule using Legendre polynomials.
+ * In this implementation, the lower and upper bounds of the natural interval
+ * of integration are -1 and 1, respectively.
+ * The Legendre polynomials are evaluated using the recurrence relation
+ * presented in <a href="http://en.wikipedia.org/wiki/Abramowitz_and_Stegun">
+ * Abramowitz and Stegun, 1964</a>.
+ *
+ * @since 3.1
+ */
+public class LegendreHighPrecisionRuleFactory extends BaseRuleFactory<BigDecimal> {
+    /** Settings for enhanced precision computations. */
+    private final MathContext mContext;
+    /** The number {@code 2}. */
+    private final BigDecimal two;
+    /** The number {@code -1}. */
+    private final BigDecimal minusOne;
+    /** The number {@code 0.5}. */
+    private final BigDecimal oneHalf;
+
+    /**
+     * Default precision is {@link MathContext#DECIMAL128 DECIMAL128}.
+     */
+    public LegendreHighPrecisionRuleFactory() {
+        this(MathContext.DECIMAL128);
+    }
+
+    /**
+     * @param mContext Precision setting for computing the quadrature rules.
+     */
+    public LegendreHighPrecisionRuleFactory(MathContext mContext) {
+        this.mContext = mContext;
+        two = new BigDecimal("2", mContext);
+        minusOne = new BigDecimal("-1", mContext);
+        oneHalf = new BigDecimal("0.5", mContext);
+    }
+
+    /** {@inheritDoc} */
+    @Override
+    protected Pair<BigDecimal[], BigDecimal[]> computeRule(int numberOfPoints)
+        throws DimensionMismatchException {
+
+        if (numberOfPoints == 1) {
+            // Break recursion.
+            return new Pair<BigDecimal[], BigDecimal[]>(new BigDecimal[] { BigDecimal.ZERO },
+                                                        new BigDecimal[] { two });
+        }
+
+        // Get previous rule.
+        // If it has not been computed yet it will trigger a recursive call
+        // to this method.
+        final BigDecimal[] previousPoints = getRuleInternal(numberOfPoints - 1).getFirst();
+
+        // Compute next rule.
+        final BigDecimal[] points = new BigDecimal[numberOfPoints];
+        final BigDecimal[] weights = new BigDecimal[numberOfPoints];
+
+        // Find i-th root of P[n+1] by bracketing.
+        final int iMax = numberOfPoints / 2;
+        for (int i = 0; i < iMax; i++) {
+            // Lower-bound of the interval.
+            BigDecimal a = (i == 0) ? minusOne : previousPoints[i - 1];
+            // Upper-bound of the interval.
+            BigDecimal b = (iMax == 1) ? BigDecimal.ONE : previousPoints[i];
+            // P[j-1](a)
+            BigDecimal pma = BigDecimal.ONE;
+            // P[j](a)
+            BigDecimal pa = a;
+            // P[j-1](b)
+            BigDecimal pmb = BigDecimal.ONE;
+            // P[j](b)
+            BigDecimal pb = b;
+            for (int j = 1; j < numberOfPoints; j++) {
+                final BigDecimal b_two_j_p_1 = new BigDecimal(2 * j + 1, mContext);
+                final BigDecimal b_j = new BigDecimal(j, mContext);
+                final BigDecimal b_j_p_1 = new BigDecimal(j + 1, mContext);
+
+                // Compute P[j+1](a)
+                // ppa = ((2 * j + 1) * a * pa - j * pma) / (j + 1);
+
+                BigDecimal tmp1 = a.multiply(b_two_j_p_1, mContext);
+                tmp1 = pa.multiply(tmp1, mContext);
+                BigDecimal tmp2 = pma.multiply(b_j, mContext);
+                // P[j+1](a)
+                BigDecimal ppa = tmp1.subtract(tmp2, mContext);
+                ppa = ppa.divide(b_j_p_1, mContext);
+
+                // Compute P[j+1](b)
+                // ppb = ((2 * j + 1) * b * pb - j * pmb) / (j + 1);
+
+                tmp1 = b.multiply(b_two_j_p_1, mContext);
+                tmp1 = pb.multiply(tmp1, mContext);
+                tmp2 = pmb.multiply(b_j, mContext);
+                // P[j+1](b)
+                BigDecimal ppb = tmp1.subtract(tmp2, mContext);
+                ppb = ppb.divide(b_j_p_1, mContext);
+
+                pma = pa;
+                pa = ppa;
+                pmb = pb;
+                pb = ppb;
+            }
+            // Now pa = P[n+1](a), and pma = P[n](a). Same holds for b.
+            // Middle of the interval.
+            BigDecimal c = a.add(b, mContext).multiply(oneHalf, mContext);
+            // P[j-1](c)
+            BigDecimal pmc = BigDecimal.ONE;
+            // P[j](c)
+            BigDecimal pc = c;
+            boolean done = false;
+            while (!done) {
+                BigDecimal tmp1 = b.subtract(a, mContext);
+                BigDecimal tmp2 = c.ulp().multiply(BigDecimal.TEN, mContext);
+                done = tmp1.compareTo(tmp2) <= 0;
+                pmc = BigDecimal.ONE;
+                pc = c;
+                for (int j = 1; j < numberOfPoints; j++) {
+                    final BigDecimal b_two_j_p_1 = new BigDecimal(2 * j + 1, mContext);
+                    final BigDecimal b_j = new BigDecimal(j, mContext);
+                    final BigDecimal b_j_p_1 = new BigDecimal(j + 1, mContext);
+
+                    // Compute P[j+1](c)
+                    tmp1 = c.multiply(b_two_j_p_1, mContext);
+                    tmp1 = pc.multiply(tmp1, mContext);
+                    tmp2 = pmc.multiply(b_j, mContext);
+                    // P[j+1](c)
+                    BigDecimal ppc = tmp1.subtract(tmp2, mContext);
+                    ppc = ppc.divide(b_j_p_1, mContext);
+
+                    pmc = pc;
+                    pc = ppc;
+                }
+                // Now pc = P[n+1](c) and pmc = P[n](c).
+                if (!done) {
+                    if (pa.signum() * pc.signum() <= 0) {
+                        b = c;
+                        pmb = pmc;
+                        pb = pc;
+                    } else {
+                        a = c;
+                        pma = pmc;
+                        pa = pc;
+                    }
+                    c = a.add(b, mContext).multiply(oneHalf, mContext);
+                }
+            }
+            final BigDecimal nP = new BigDecimal(numberOfPoints, mContext);
+            BigDecimal tmp1 = pmc.subtract(c.multiply(pc, mContext), mContext);
+            tmp1 = tmp1.multiply(nP);
+            tmp1 = tmp1.pow(2, mContext);
+            BigDecimal tmp2 = c.pow(2, mContext);
+            tmp2 = BigDecimal.ONE.subtract(tmp2, mContext);
+            tmp2 = tmp2.multiply(two, mContext);
+            tmp2 = tmp2.divide(tmp1, mContext);
+
+            points[i] = c;
+            weights[i] = tmp2;
+
+            final int idx = numberOfPoints - i - 1;
+            points[idx] = c.negate(mContext);
+            weights[idx] = tmp2;
+        }
+        // If "numberOfPoints" is odd, 0 is a root.
+        // Note: as written, the test for oddness will work for negative
+        // integers too (although it is not necessary here), preventing
+        // a FindBugs warning.
+        if (numberOfPoints % 2 != 0) {
+            BigDecimal pmc = BigDecimal.ONE;
+            for (int j = 1; j < numberOfPoints; j += 2) {
+                final BigDecimal b_j = new BigDecimal(j, mContext);
+                final BigDecimal b_j_p_1 = new BigDecimal(j + 1, mContext);
+
+                // pmc = -j * pmc / (j + 1);
+                pmc = pmc.multiply(b_j, mContext);
+                pmc = pmc.divide(b_j_p_1, mContext);
+                pmc = pmc.negate(mContext);
+            }
+
+            // 2 / pow(numberOfPoints * pmc, 2);
+            final BigDecimal nP = new BigDecimal(numberOfPoints, mContext);
+            BigDecimal tmp1 = pmc.multiply(nP, mContext);
+            tmp1 = tmp1.pow(2, mContext);
+            BigDecimal tmp2 = two.divide(tmp1, mContext);
+
+            points[iMax] = BigDecimal.ZERO;
+            weights[iMax] = tmp2;
+        }
+
+        return new Pair<BigDecimal[], BigDecimal[]>(points, weights);
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/integration/gauss/LegendreRuleFactory.java

@@ -0,0 +1,140 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.integration.gauss;
+
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.util.Pair;
+
+/**
+ * Factory that creates Gauss-type quadrature rule using Legendre polynomials.
+ * In this implementation, the lower and upper bounds of the natural interval
+ * of integration are -1 and 1, respectively.
+ * The Legendre polynomials are evaluated using the recurrence relation
+ * presented in <a href="http://en.wikipedia.org/wiki/Abramowitz_and_Stegun">
+ * Abramowitz and Stegun, 1964</a>.
+ *
+ * @since 3.1
+ */
+public class LegendreRuleFactory extends BaseRuleFactory<Double> {
+    /** {@inheritDoc} */
+    @Override
+    protected Pair<Double[], Double[]> computeRule(int numberOfPoints)
+        throws DimensionMismatchException {
+
+        if (numberOfPoints == 1) {
+            // Break recursion.
+            return new Pair<Double[], Double[]>(new Double[] { 0d },
+                                                new Double[] { 2d });
+        }
+
+        // Get previous rule.
+        // If it has not been computed yet it will trigger a recursive call
+        // to this method.
+        final Double[] previousPoints = getRuleInternal(numberOfPoints - 1).getFirst();
+
+        // Compute next rule.
+        final Double[] points = new Double[numberOfPoints];
+        final Double[] weights = new Double[numberOfPoints];
+
+        // Find i-th root of P[n+1] by bracketing.
+        final int iMax = numberOfPoints / 2;
+        for (int i = 0; i < iMax; i++) {
+            // Lower-bound of the interval.
+            double a = (i == 0) ? -1 : previousPoints[i - 1].doubleValue();
+            // Upper-bound of the interval.
+            double b = (iMax == 1) ? 1 : previousPoints[i].doubleValue();
+            // P[j-1](a)
+            double pma = 1;
+            // P[j](a)
+            double pa = a;
+            // P[j-1](b)
+            double pmb = 1;
+            // P[j](b)
+            double pb = b;
+            for (int j = 1; j < numberOfPoints; j++) {
+                final int two_j_p_1 = 2 * j + 1;
+                final int j_p_1 = j + 1;
+                // P[j+1](a)
+                final double ppa = (two_j_p_1 * a * pa - j * pma) / j_p_1;
+                // P[j+1](b)
+                final double ppb = (two_j_p_1 * b * pb - j * pmb) / j_p_1;
+                pma = pa;
+                pa = ppa;
+                pmb = pb;
+                pb = ppb;
+            }
+            // Now pa = P[n+1](a), and pma = P[n](a) (same holds for b).
+            // Middle of the interval.
+            double c = 0.5 * (a + b);
+            // P[j-1](c)
+            double pmc = 1;
+            // P[j](c)
+            double pc = c;
+            boolean done = false;
+            while (!done) {
+                done = b - a <= Math.ulp(c);
+                pmc = 1;
+                pc = c;
+                for (int j = 1; j < numberOfPoints; j++) {
+                    // P[j+1](c)
+                    final double ppc = ((2 * j + 1) * c * pc - j * pmc) / (j + 1);
+                    pmc = pc;
+                    pc = ppc;
+                }
+                // Now pc = P[n+1](c) and pmc = P[n](c).
+                if (!done) {
+                    if (pa * pc <= 0) {
+                        b = c;
+                        pmb = pmc;
+                        pb = pc;
+                    } else {
+                        a = c;
+                        pma = pmc;
+                        pa = pc;
+                    }
+                    c = 0.5 * (a + b);
+                }
+            }
+            final double d = numberOfPoints * (pmc - c * pc);
+            final double w = 2 * (1 - c * c) / (d * d);
+
+            points[i] = c;
+            weights[i] = w;
+
+            final int idx = numberOfPoints - i - 1;
+            points[idx] = -c;
+            weights[idx] = w;
+        }
+        // If "numberOfPoints" is odd, 0 is a root.
+        // Note: as written, the test for oddness will work for negative
+        // integers too (although it is not necessary here), preventing
+        // a FindBugs warning.
+        if (numberOfPoints % 2 != 0) {
+            double pmc = 1;
+            for (int j = 1; j < numberOfPoints; j += 2) {
+                pmc = -j * pmc / (j + 1);
+            }
+            final double d = numberOfPoints * pmc;
+            final double w = 2 / (d * d);
+
+            points[iMax] = 0d;
+            weights[iMax] = w;
+        }
+
+        return new Pair<Double[], Double[]>(points, weights);
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/integration/gauss/SymmetricGaussIntegrator.java

@@ -0,0 +1,103 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.integration.gauss;
+
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.exception.NonMonotonicSequenceException;
+import com.fr.third.org.apache.commons.math3.analysis.UnivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.Pair;
+
+/**
+ * This class's implements {@link #integrate(UnivariateFunction) integrate}
+ * method assuming that the integral is symmetric about 0.
+ * This allows to reduce numerical errors.
+ *
+ * @since 3.3
+ */
+public class SymmetricGaussIntegrator extends GaussIntegrator {
+    /**
+     * Creates an integrator from the given {@code points} and {@code weights}.
+     * The integration interval is defined by the first and last value of
+     * {@code points} which must be sorted in increasing order.
+     *
+     * @param points Integration points.
+     * @param weights Weights of the corresponding integration nodes.
+     * @throws NonMonotonicSequenceException if the {@code points} are not
+     * sorted in increasing order.
+     * @throws DimensionMismatchException if points and weights don't have the same length
+     */
+    public SymmetricGaussIntegrator(double[] points,
+                                    double[] weights)
+        throws NonMonotonicSequenceException, DimensionMismatchException {
+        super(points, weights);
+    }
+
+    /**
+     * Creates an integrator from the given pair of points (first element of
+     * the pair) and weights (second element of the pair.
+     *
+     * @param pointsAndWeights Integration points and corresponding weights.
+     * @throws NonMonotonicSequenceException if the {@code points} are not
+     * sorted in increasing order.
+     *
+     * @see #SymmetricGaussIntegrator(double[], double[])
+     */
+    public SymmetricGaussIntegrator(Pair<double[], double[]> pointsAndWeights)
+        throws NonMonotonicSequenceException {
+        this(pointsAndWeights.getFirst(), pointsAndWeights.getSecond());
+    }
+
+    /**
+     * {@inheritDoc}
+     */
+    @Override
+    public double integrate(UnivariateFunction f) {
+        final int ruleLength = getNumberOfPoints();
+
+        if (ruleLength == 1) {
+            return getWeight(0) * f.value(0d);
+        }
+
+        final int iMax = ruleLength / 2;
+        double s = 0;
+        double c = 0;
+        for (int i = 0; i < iMax; i++) {
+            final double p = getPoint(i);
+            final double w = getWeight(i);
+
+            final double f1 = f.value(p);
+            final double f2 = f.value(-p);
+
+            final double y = w * (f1 + f2) - c;
+            final double t = s + y;
+
+            c = (t - s) - y;
+            s = t;
+        }
+
+        if (ruleLength % 2 != 0) {
+            final double w = getWeight(iMax);
+
+            final double y = w * f.value(0d) - c;
+            final double t = s + y;
+
+            s = t;
+        }
+
+        return s;
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/integration/gauss/package-info.java

@@ -0,0 +1,22 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+/**
+ *
+ * Gauss family of quadrature schemes.
+ *
+ */
+package com.fr.third.org.apache.commons.math3.analysis.integration.gauss;

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/integration/package-info.java

@@ -0,0 +1,22 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+/**
+ *
+ *     Numerical integration (quadrature) algorithms for univariate real functions.
+ *
+ */
+package com.fr.third.org.apache.commons.math3.analysis.integration;

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/interpolation/AkimaSplineInterpolator.java

@@ -0,0 +1,215 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.interpolation;
+
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.exception.NonMonotonicSequenceException;
+import com.fr.third.org.apache.commons.math3.exception.NullArgumentException;
+import com.fr.third.org.apache.commons.math3.exception.NumberIsTooSmallException;
+import com.fr.third.org.apache.commons.math3.exception.util.LocalizedFormats;
+import com.fr.third.org.apache.commons.math3.analysis.polynomials.PolynomialFunction;
+import com.fr.third.org.apache.commons.math3.analysis.polynomials.PolynomialSplineFunction;
+import com.fr.third.org.apache.commons.math3.util.FastMath;
+import com.fr.third.org.apache.commons.math3.util.MathArrays;
+import com.fr.third.org.apache.commons.math3.util.Precision;
+
+/**
+ * Computes a cubic spline interpolation for the data set using the Akima
+ * algorithm, as originally formulated by Hiroshi Akima in his 1970 paper
+ * "A New Method of Interpolation and Smooth Curve Fitting Based on Local Procedures."
+ * J. ACM 17, 4 (October 1970), 589-602. DOI=10.1145/321607.321609
+ * http://doi.acm.org/10.1145/321607.321609
+ * <p>
+ * This implementation is based on the Akima implementation in the CubicSpline
+ * class in the Math.NET Numerics library. The method referenced is
+ * CubicSpline.InterpolateAkimaSorted
+ * </p>
+ * <p>
+ * The {@link #interpolate(double[], double[]) interpolate} method returns a
+ * {@link PolynomialSplineFunction} consisting of n cubic polynomials, defined
+ * over the subintervals determined by the x values, {@code x[0] < x[i] ... < x[n]}.
+ * The Akima algorithm requires that {@code n >= 5}.
+ * </p>
+ */
+public class AkimaSplineInterpolator
+    implements UnivariateInterpolator {
+    /** The minimum number of points that are needed to compute the function. */
+    private static final int MINIMUM_NUMBER_POINTS = 5;
+
+    /**
+     * Computes an interpolating function for the data set.
+     *
+     * @param xvals the arguments for the interpolation points
+     * @param yvals the values for the interpolation points
+     * @return a function which interpolates the data set
+     * @throws DimensionMismatchException if {@code xvals} and {@code yvals} have
+     *         different sizes.
+     * @throws NonMonotonicSequenceException if {@code xvals} is not sorted in
+     *         strict increasing order.
+     * @throws NumberIsTooSmallException if the size of {@code xvals} is smaller
+     *         than 5.
+     */
+    public PolynomialSplineFunction interpolate(double[] xvals,
+                                                double[] yvals)
+        throws DimensionMismatchException,
+               NumberIsTooSmallException,
+               NonMonotonicSequenceException {
+        if (xvals == null ||
+            yvals == null) {
+            throw new NullArgumentException();
+        }
+
+        if (xvals.length != yvals.length) {
+            throw new DimensionMismatchException(xvals.length, yvals.length);
+        }
+
+        if (xvals.length < MINIMUM_NUMBER_POINTS) {
+            throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
+                                                xvals.length,
+                                                MINIMUM_NUMBER_POINTS, true);
+        }
+
+        MathArrays.checkOrder(xvals);
+
+        final int numberOfDiffAndWeightElements = xvals.length - 1;
+
+        final double[] differences = new double[numberOfDiffAndWeightElements];
+        final double[] weights = new double[numberOfDiffAndWeightElements];
+
+        for (int i = 0; i < differences.length; i++) {
+            differences[i] = (yvals[i + 1] - yvals[i]) / (xvals[i + 1] - xvals[i]);
+        }
+
+        for (int i = 1; i < weights.length; i++) {
+            weights[i] = FastMath.abs(differences[i] - differences[i - 1]);
+        }
+
+        // Prepare Hermite interpolation scheme.
+        final double[] firstDerivatives = new double[xvals.length];
+
+        for (int i = 2; i < firstDerivatives.length - 2; i++) {
+            final double wP = weights[i + 1];
+            final double wM = weights[i - 1];
+            if (Precision.equals(wP, 0.0) &&
+                Precision.equals(wM, 0.0)) {
+                final double xv = xvals[i];
+                final double xvP = xvals[i + 1];
+                final double xvM = xvals[i - 1];
+                firstDerivatives[i] = (((xvP - xv) * differences[i - 1]) + ((xv - xvM) * differences[i])) / (xvP - xvM);
+            } else {
+                firstDerivatives[i] = ((wP * differences[i - 1]) + (wM * differences[i])) / (wP + wM);
+            }
+        }
+
+        firstDerivatives[0] = differentiateThreePoint(xvals, yvals, 0, 0, 1, 2);
+        firstDerivatives[1] = differentiateThreePoint(xvals, yvals, 1, 0, 1, 2);
+        firstDerivatives[xvals.length - 2] = differentiateThreePoint(xvals, yvals, xvals.length - 2,
+                                                                     xvals.length - 3, xvals.length - 2,
+                                                                     xvals.length - 1);
+        firstDerivatives[xvals.length - 1] = differentiateThreePoint(xvals, yvals, xvals.length - 1,
+                                                                     xvals.length - 3, xvals.length - 2,
+                                                                     xvals.length - 1);
+
+        return interpolateHermiteSorted(xvals, yvals, firstDerivatives);
+    }
+
+    /**
+     * Three point differentiation helper, modeled off of the same method in the
+     * Math.NET CubicSpline class. This is used by both the Apache Math and the
+     * Math.NET Akima Cubic Spline algorithms
+     *
+     * @param xvals x values to calculate the numerical derivative with
+     * @param yvals y values to calculate the numerical derivative with
+     * @param indexOfDifferentiation index of the elemnt we are calculating the derivative around
+     * @param indexOfFirstSample index of the first element to sample for the three point method
+     * @param indexOfSecondsample index of the second element to sample for the three point method
+     * @param indexOfThirdSample index of the third element to sample for the three point method
+     * @return the derivative
+     */
+    private double differentiateThreePoint(double[] xvals, double[] yvals,
+                                           int indexOfDifferentiation,
+                                           int indexOfFirstSample,
+                                           int indexOfSecondsample,
+                                           int indexOfThirdSample) {
+        final double x0 = yvals[indexOfFirstSample];
+        final double x1 = yvals[indexOfSecondsample];
+        final double x2 = yvals[indexOfThirdSample];
+
+        final double t = xvals[indexOfDifferentiation] - xvals[indexOfFirstSample];
+        final double t1 = xvals[indexOfSecondsample] - xvals[indexOfFirstSample];
+        final double t2 = xvals[indexOfThirdSample] - xvals[indexOfFirstSample];
+
+        final double a = (x2 - x0 - (t2 / t1 * (x1 - x0))) / (t2 * t2 - t1 * t2);
+        final double b = (x1 - x0 - a * t1 * t1) / t1;
+
+        return (2 * a * t) + b;
+    }
+
+    /**
+     * Creates a Hermite cubic spline interpolation from the set of (x,y) value
+     * pairs and their derivatives. This is modeled off of the
+     * InterpolateHermiteSorted method in the Math.NET CubicSpline class.
+     *
+     * @param xvals x values for interpolation
+     * @param yvals y values for interpolation
+     * @param firstDerivatives first derivative values of the function
+     * @return polynomial that fits the function
+     */
+    private PolynomialSplineFunction interpolateHermiteSorted(double[] xvals,
+                                                              double[] yvals,
+                                                              double[] firstDerivatives) {
+        if (xvals.length != yvals.length) {
+            throw new DimensionMismatchException(xvals.length, yvals.length);
+        }
+
+        if (xvals.length != firstDerivatives.length) {
+            throw new DimensionMismatchException(xvals.length,
+                                                 firstDerivatives.length);
+        }
+
+        final int minimumLength = 2;
+        if (xvals.length < minimumLength) {
+            throw new NumberIsTooSmallException(LocalizedFormats.NUMBER_OF_POINTS,
+                                                xvals.length, minimumLength,
+                                                true);
+        }
+
+        final int size = xvals.length - 1;
+        final PolynomialFunction[] polynomials = new PolynomialFunction[size];
+        final double[] coefficients = new double[4];
+
+        for (int i = 0; i < polynomials.length; i++) {
+            final double w = xvals[i + 1] - xvals[i];
+            final double w2 = w * w;
+
+            final double yv = yvals[i];
+            final double yvP = yvals[i + 1];
+
+            final double fd = firstDerivatives[i];
+            final double fdP = firstDerivatives[i + 1];
+
+            coefficients[0] = yv;
+            coefficients[1] = firstDerivatives[i];
+            coefficients[2] = (3 * (yvP - yv) / w - 2 * fd - fdP) / w;
+            coefficients[3] = (2 * (yv - yvP) / w + fd + fdP) / w2;
+            polynomials[i] = new PolynomialFunction(coefficients);
+        }
+
+        return new PolynomialSplineFunction(xvals, polynomials);
+
+    }
+}

fine-commons-math3/src/com/fr/third/org/apache/commons/math3/analysis/interpolation/BicubicInterpolatingFunction.java

@@ -0,0 +1,326 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *      http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package com.fr.third.org.apache.commons.math3.analysis.interpolation;
+
+import java.util.Arrays;
+
+import com.fr.third.org.apache.commons.math3.exception.DimensionMismatchException;
+import com.fr.third.org.apache.commons.math3.exception.NoDataException;
+import com.fr.third.org.apache.commons.math3.exception.NonMonotonicSequenceException;
+import com.fr.third.org.apache.commons.math3.exception.OutOfRangeException;
+import com.fr.third.org.apache.commons.math3.analysis.BivariateFunction;
+import com.fr.third.org.apache.commons.math3.util.MathArrays;
+
+/**
+ * Function that implements the
+ * <a href="http://en.wikipedia.org/wiki/Bicubic_interpolation">
+ * bicubic spline interpolation</a>.
+ *
+ * @since 3.4
+ */
+public class BicubicInterpolatingFunction
+    implements BivariateFunction {
+    /** Number of coefficients. */
+    private static final int NUM_COEFF = 16;
+    /**
+     * Matrix to compute the spline coefficients from the function values
+     * and function derivatives values
+     */
+    private static final double[][] AINV = {
+        { 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
+        { 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0 },
+        { -3,3,0,0,-2,-1,0,0,0,0,0,0,0,0,0,0 },
+        { 2,-2,0,0,1,1,0,0,0,0,0,0,0,0,0,0 },
+        { 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0 },
+        { 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0 },
+        { 0,0,0,0,0,0,0,0,-3,3,0,0,-2,-1,0,0 },
+        { 0,0,0,0,0,0,0,0,2,-2,0,0,1,1,0,0 },
+        { -3,0,3,0,0,0,0,0,-2,0,-1,0,0,0,0,0 },
+        { 0,0,0,0,-3,0,3,0,0,0,0,0,-2,0,-1,0 },
+        { 9,-9,-9,9,6,3,-6,-3,6,-6,3,-3,4,2,2,1 },
+        { -6,6,6,-6,-3,-3,3,3,-4,4,-2,2,-2,-2,-1,-1 },
+        { 2,0,-2,0,0,0,0,0,1,0,1,0,0,0,0,0 },
+        { 0,0,0,0,2,0,-2,0,0,0,0,0,1,0,1,0 },
+        { -6,6,6,-6,-4,-2,4,2,-3,3,-3,3,-2,-1,-2,-1 },
+        { 4,-4,-4,4,2,2,-2,-2,2,-2,2,-2,1,1,1,1 }
+    };
+
+    /** Samples x-coordinates */
+    private final double[] xval;
+    /** Samples y-coordinates */
+    private final double[] yval;
+    /** Set of cubic splines patching the whole data grid */
+    private final BicubicFunction[][] splines;
+
+    /**
+     * @param x Sample values of the x-coordinate, in increasing order.
+     * @param y Sample values of the y-coordinate, in increasing order.
+     * @param f Values of the function on every grid point.
+     * @param dFdX Values of the partial derivative of function with respect
+     * to x on every grid point.
+     * @param dFdY Values of the partial derivative of function with respect
+     * to y on every grid point.
+     * @param d2FdXdY Values of the cross partial derivative of function on
+     * every grid point.
+     * @throws DimensionMismatchException if the various arrays do not contain
+     * the expected number of elements.
+     * @throws NonMonotonicSequenceException if {@code x} or {@code y} are
+     * not strictly increasing.
+     * @throws NoDataException if any of the arrays has zero length.
+     */
+    public BicubicInterpolatingFunction(double[] x,
+                                        double[] y,
+                                        double[][] f,
+                                        double[][] dFdX,
+                                        double[][] dFdY,
+                                        double[][] d2FdXdY)
+        throws DimensionMismatchException,
+               NoDataException,
+               NonMonotonicSequenceException {
+        final int xLen = x.length;
+        final int yLen = y.length;
+
+        if (xLen == 0 || yLen == 0 || f.length == 0 || f[0].length == 0) {
+            throw new NoDataException();
+        }
+        if (xLen != f.length) {
+            throw new DimensionMismatchException(xLen, f.length);
+        }
+        if (xLen != dFdX.length) {
+            throw new DimensionMismatchException(xLen, dFdX.length);
+        }
+        if (xLen != dFdY.length) {
+            throw new DimensionMismatchException(xLen, dFdY.length);
+        }
+        if (xLen != d2FdXdY.length) {
+            throw new DimensionMismatchException(xLen, d2FdXdY.length);
+        }
+
+        MathArrays.checkOrder(x);
+        MathArrays.checkOrder(y);
+
+        xval = x.clone();
+        yval = y.clone();
+
+        final int lastI = xLen - 1;
+        final int lastJ = yLen - 1;
+        splines = new BicubicFunction[lastI][lastJ];
+
+        for (int i = 0; i < lastI; i++) {
+            if (f[i].length != yLen) {
+                throw new DimensionMismatchException(f[i].length, yLen);
+            }
+            if (dFdX[i].length != yLen) {
+                throw new DimensionMismatchException(dFdX[i].length, yLen);
+            }
+            if (dFdY[i].length != yLen) {
+                throw new DimensionMismatchException(dFdY[i].length, yLen);
+            }
+            if (d2FdXdY[i].length != yLen) {
+                throw new DimensionMismatchException(d2FdXdY[i].length, yLen);
+            }
+            final int ip1 = i + 1;
+            final double xR = xval[ip1] - xval[i];
+            for (int j = 0; j < lastJ; j++) {
+                final int jp1 = j + 1;
+                final double yR = yval[jp1] - yval[j];
+                final double xRyR = xR * yR;
+                final double[] beta = new double[] {
+                    f[i][j], f[ip1][j], f[i][jp1], f[ip1][jp1],
+                    dFdX[i][j] * xR, dFdX[ip1][j] * xR, dFdX[i][jp1] * xR, dFdX[ip1][jp1] * xR,
+                    dFdY[i][j] * yR, dFdY[ip1][j] * yR, dFdY[i][jp1] * yR, dFdY[ip1][jp1] * yR,
+                    d2FdXdY[i][j] * xRyR, d2FdXdY[ip1][j] * xRyR, d2FdXdY[i][jp1] * xRyR, d2FdXdY[ip1][jp1] * xRyR
+                };
+
+                splines[i][j] = new BicubicFunction(computeSplineCoefficients(beta));
+            }
+        }
+    }
+
+    /**
+     * {@inheritDoc}
+     */
+    public double value(double x, double y)
+        throws OutOfRangeException {
+        final int i = searchIndex(x, xval);
+        final int j = searchIndex(y, yval);
+
+        final double xN = (x - xval[i]) / (xval[i + 1] - xval[i]);
+        final double yN = (y - yval[j]) / (yval[j + 1] - yval[j]);
+
+        return splines[i][j].value(xN, yN);
+    }
+
+    /**
+     * Indicates whether a point is within the interpolation range.
+     *
+     * @param x First coordinate.
+     * @param y Second coordinate.
+     * @return {@code true} if (x, y) is a valid point.
+     */
+    public boolean isValidPoint(double x, double y) {
+        if (x < xval[0] ||
+            x > xval[xval.length - 1] ||
+            y < yval[0] ||
+            y > yval[yval.length - 1]) {
+            return false;
+        } else {
+            return true;
+        }
+    }
+
+    /**
+     * @param c Coordinate.
+     * @param val Coordinate samples.
+     * @return the index in {@code val} corresponding to the interval
+     * containing {@code c}.
+     * @throws OutOfRangeException if {@code c} is out of the
+     * range defined by the boundary values of {@code val}.
+     */
+    private int searchIndex(double c, double[] val) {
+        final int r = Arrays.binarySearch(val, c);
+
+        if (r == -1 ||
+            r == -val.length - 1) {
+            throw new OutOfRangeException(c, val[0], val[val.length - 1]);
+        }
+
+        if (r < 0) {
+            // "c" in within an interpolation sub-interval: Return the
+            // index of the sample at the lower end of the sub-interval.
+            return -r - 2;
+        }
+        final int last = val.length - 1;
+        if (r == last) {
+            // "c" is the last sample of the range: Return the index
+            // of the sample at the lower end of the last sub-interval.
+            return last - 1;
+        }
+
+        // "c" is another sample point.
+        return r;
+    }
+
+    /**
+     * Compute the spline coefficients from the list of function values and
+     * function partial derivatives values at the four corners of a grid
+     * element. They must be specified in the following order:
+     * <ul>
+     *  <li>f(0,0)</li>
+     *  <li>f(1,0)</li>
+     *  <li>f(0,1)</li>
+     *  <li>f(1,1)</li>
+     *  <li>f<sub>x</sub>(0,0)</li>
+     *  <li>f<sub>x</sub>(1,0)</li>
+     *  <li>f<sub>x</sub>(0,1)</li>
+     *  <li>f<sub>x</sub>(1,1)</li>
+     *  <li>f<sub>y</sub>(0,0)</li>
+     *  <li>f<sub>y</sub>(1,0)</li>
+     *  <li>f<sub>y</sub>(0,1)</li>
+     *  <li>f<sub>y</sub>(1,1)</li>
+     *  <li>f<sub>xy</sub>(0,0)</li>
+     *  <li>f<sub>xy</sub>(1,0)</li>
+     *  <li>f<sub>xy</sub>(0,1)</li>
+     *  <li>f<sub>xy</sub>(1,1)</li>
+     * </ul>
+     * where the subscripts indicate the partial derivative with respect to
+     * the corresponding variable(s).
+     *
+     * @param beta List of function values and function partial derivatives
+     * values.
+     * @return the spline coefficients.
+     */
+    private double[] computeSplineCoefficients(double[] beta) {
+        final double[] a = new double[NUM_COEFF];
+
+        for (int i = 0; i < NUM_COEFF; i++) {
+            double result = 0;
+            final double[] row = AINV[i];
+            for (int j = 0; j < NUM_COEFF; j++) {
+                result += row[j] * beta[j];
+            }
+            a[i] = result;
+        }
+
+        return a;
+    }
+}
+
+/**
+ * Bicubic function.
+ */
+class BicubicFunction implements BivariateFunction {
+    /** Number of points. */
+    private static final short N = 4;
+    /** Coefficients */
+    private final double[][] a;
+
+    /**
+     * Simple constructor.
+     *
+     * @param coeff Spline coefficients.
+     */
+    BicubicFunction(double[] coeff) {
+        a = new double[N][N];
+        for (int j = 0; j < N; j++) {
+            final double[] aJ = a[j];
+            for (int i = 0; i < N; i++) {
+                aJ[i] = coeff[i * N + j];
+            }
+        }
+    }
+
+    /**
+     * {@inheritDoc}
+     */
+    public double value(double x, double y) {
+        if (x < 0 || x > 1) {
+            throw new OutOfRangeException(x, 0, 1);
+        }
+        if (y < 0 || y > 1) {
+            throw new OutOfRangeException(y, 0, 1);
+        }
+
+        final double x2 = x * x;
+        final double x3 = x2 * x;
+        final double[] pX = {1, x, x2, x3};
+
+        final double y2 = y * y;
+        final double y3 = y2 * y;
+        final double[] pY = {1, y, y2, y3};
+
+        return apply(pX, pY, a);
+    }
+
+    /**
+     * Compute the value of the bicubic polynomial.
+     *
+     * @param pX Powers of the x-coordinate.
+     * @param pY Powers of the y-coordinate.
+     * @param coeff Spline coefficients.
+     * @return the interpolated value.
+     */
+    private double apply(double[] pX, double[] pY, double[][] coeff) {
+        double result = 0;
+        for (int i = 0; i < N; i++) {
+            final double r = MathArrays.linearCombination(coeff[i], pY);
+            result += r * pX[i];
+        }
+
+        return result;
+    }
+}