// <copyright file="Differentiate.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2015 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System;
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using IStation.Numerics.Differentiation;
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namespace IStation.Numerics
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{
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/// <summary>
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/// Numerical Derivative.
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/// </summary>
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public static class Differentiate
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{
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/// <summary>
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/// Initialized a NumericalDerivative with the given points and center.
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/// </summary>
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public static NumericalDerivative Points(int points, int center)
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{
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return new NumericalDerivative(points, center);
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}
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/// <summary>
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/// Initialized a NumericalDerivative with the default points and center for the given order.
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/// </summary>
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public static NumericalDerivative Order(int order)
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{
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var points = order + (order.IsEven() ? 1 : 2);
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return new NumericalDerivative(points, points/2);
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}
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/// <summary>
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/// Evaluates the derivative of a scalar univariate function.
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/// </summary>
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/// <param name="f">Univariate function handle.</param>
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/// <param name="x">Point at which to evaluate the derivative.</param>
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/// <param name="order">Derivative order.</param>
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public static double Derivative(Func<double, double> f, double x, int order)
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{
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return Order(order).EvaluateDerivative(f, x, order);
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}
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/// <summary>
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/// Creates a function handle for the derivative of a scalar univariate function.
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/// </summary>
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/// <param name="f">Univariate function handle.</param>
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/// <param name="order">Derivative order.</param>
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public static Func<double, double> DerivativeFunc(Func<double, double> f, int order)
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{
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return Order(order).CreateDerivativeFunctionHandle(f, order);
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}
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/// <summary>
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/// Evaluates the first derivative of a scalar univariate function.
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/// </summary>
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/// <param name="f">Univariate function handle.</param>
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/// <param name="x">Point at which to evaluate the derivative.</param>
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public static double FirstDerivative(Func<double, double> f, double x)
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{
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return Order(1).EvaluateDerivative(f, x, 1);
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}
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/// <summary>
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/// Creates a function handle for the first derivative of a scalar univariate function.
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/// </summary>
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/// <param name="f">Univariate function handle.</param>
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public static Func<double, double> FirstDerivativeFunc(Func<double, double> f)
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{
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return Order(1).CreateDerivativeFunctionHandle(f, 1);
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}
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/// <summary>
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/// Evaluates the second derivative of a scalar univariate function.
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/// </summary>
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/// <param name="f">Univariate function handle.</param>
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/// <param name="x">Point at which to evaluate the derivative.</param>
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public static double SecondDerivative(Func<double, double> f, double x)
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{
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return Order(2).EvaluateDerivative(f, x, 2);
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}
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/// <summary>
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/// Creates a function handle for the second derivative of a scalar univariate function.
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/// </summary>
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/// <param name="f">Univariate function handle.</param>
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public static Func<double, double> SecondDerivativeFunc(Func<double, double> f)
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{
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return Order(2).CreateDerivativeFunctionHandle(f, 2);
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}
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/// <summary>
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/// Evaluates the partial derivative of a multivariate function.
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/// </summary>
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/// <param name="f">Multivariate function handle.</param>
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/// <param name="x">Vector at which to evaluate the derivative.</param>
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/// <param name="parameterIndex">Index of independent variable for partial derivative.</param>
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/// <param name="order">Derivative order.</param>
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public static double PartialDerivative(Func<double[], double> f, double[] x, int parameterIndex, int order)
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{
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return Order(order).EvaluatePartialDerivative(f, x, parameterIndex, order);
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}
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/// <summary>
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/// Creates a function handle for the partial derivative of a multivariate function.
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/// </summary>
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/// <param name="f">Multivariate function handle.</param>
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/// <param name="parameterIndex">Index of independent variable for partial derivative.</param>
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/// <param name="order">Derivative order.</param>
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public static Func<double[], double> PartialDerivativeFunc(Func<double[], double> f, int parameterIndex, int order)
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{
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return Order(order).CreatePartialDerivativeFunctionHandle(f, parameterIndex, order);
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}
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/// <summary>
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/// Evaluates the first partial derivative of a multivariate function.
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/// </summary>
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/// <param name="f">Multivariate function handle.</param>
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/// <param name="x">Vector at which to evaluate the derivative.</param>
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/// <param name="parameterIndex">Index of independent variable for partial derivative.</param>
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public static double FirstPartialDerivative(Func<double[], double> f, double[] x, int parameterIndex)
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{
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return PartialDerivative(f, x, parameterIndex, 1);
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}
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/// <summary>
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/// Creates a function handle for the first partial derivative of a multivariate function.
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/// </summary>
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/// <param name="f">Multivariate function handle.</param>
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/// <param name="parameterIndex">Index of independent variable for partial derivative.</param>
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public static Func<double[], double> FirstPartialDerivativeFunc(Func<double[], double> f, int parameterIndex)
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{
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return PartialDerivativeFunc(f, parameterIndex, 1);
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}
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/// <summary>
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/// Evaluates the partial derivative of a bivariate function.
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/// </summary>
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/// <param name="f">Bivariate function handle.</param>
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/// <param name="x">First argument at which to evaluate the derivative.</param>
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/// <param name="y">Second argument at which to evaluate the derivative.</param>
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/// <param name="parameterIndex">Index of independent variable for partial derivative.</param>
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/// <param name="order">Derivative order.</param>
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public static double PartialDerivative2(Func<double, double, double> f, double x, double y, int parameterIndex, int order)
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{
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return Order(order).EvaluatePartialDerivative(array => f(array[0], array[1]), new[] { x, y }, parameterIndex, order);
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}
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/// <summary>
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/// Creates a function handle for the partial derivative of a bivariate function.
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/// </summary>
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/// <param name="f">Bivariate function handle.</param>
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/// <param name="parameterIndex">Index of independent variable for partial derivative.</param>
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/// <param name="order">Derivative order.</param>
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public static Func<double, double, double> PartialDerivative2Func(Func<double, double, double> f, int parameterIndex, int order)
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{
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var handle = Order(order).CreatePartialDerivativeFunctionHandle(array => f(array[0], array[1]), parameterIndex, order);
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return (x, y) => handle(new[] { x, y });
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}
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/// <summary>
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/// Evaluates the first partial derivative of a bivariate function.
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/// </summary>
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/// <param name="f">Bivariate function handle.</param>
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/// <param name="x">First argument at which to evaluate the derivative.</param>
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/// <param name="y">Second argument at which to evaluate the derivative.</param>
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/// <param name="parameterIndex">Index of independent variable for partial derivative.</param>
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public static double FirstPartialDerivative2(Func<double, double, double> f, double x, double y, int parameterIndex)
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{
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return PartialDerivative2(f, x, y, parameterIndex, 1);
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}
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/// <summary>
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/// Creates a function handle for the first partial derivative of a bivariate function.
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/// </summary>
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/// <param name="f">Bivariate function handle.</param>
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/// <param name="parameterIndex">Index of independent variable for partial derivative.</param>
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public static Func<double, double, double> FirstPartialDerivative2Func(Func<double, double, double> f, int parameterIndex)
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{
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return PartialDerivative2Func(f, parameterIndex, 1);
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}
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}
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}
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