// <copyright file="FiniteDifferenceCoefficients.cs" company="Math.NET">
|
// Math.NET Numerics, part of the Math.NET Project
|
// http://numerics.mathdotnet.com
|
// http://github.com/mathnet/mathnet-numerics
|
//
|
// Copyright (c) 2009-2015 Math.NET
|
//
|
// Permission is hereby granted, free of charge, to any person
|
// obtaining a copy of this software and associated documentation
|
// files (the "Software"), to deal in the Software without
|
// restriction, including without limitation the rights to use,
|
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
// copies of the Software, and to permit persons to whom the
|
// Software is furnished to do so, subject to the following
|
// conditions:
|
//
|
// The above copyright notice and this permission notice shall be
|
// included in all copies or substantial portions of the Software.
|
//
|
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
// OTHER DEALINGS IN THE SOFTWARE.
|
// </copyright>
|
|
using System;
|
using IStation.Numerics.LinearAlgebra.Double;
|
|
namespace IStation.Numerics.Differentiation
|
{
|
/// <summary>
|
/// Class to calculate finite difference coefficients using Taylor series expansion method.
|
/// <remarks>
|
/// <para>
|
/// For n points, coefficients are calculated up to the maximum derivative order possible (n-1).
|
/// The current function value position specifies the "center" for surrounding coefficients.
|
/// Selecting the first, middle or last positions represent forward, backwards and central difference methods.
|
/// </para>
|
/// </remarks>
|
/// </summary>
|
public class FiniteDifferenceCoefficients
|
{
|
/// <summary>
|
/// Number of points for finite difference coefficients. Changing this value recalculates the coefficients table.
|
/// </summary>
|
public int Points
|
{
|
get => _points;
|
set
|
{
|
CalculateCoefficients(value);
|
_points = value;
|
}
|
}
|
|
private double[][,] _coefficients;
|
private int _points;
|
|
/// <summary>
|
/// Initializes a new instance of the <see cref="FiniteDifferenceCoefficients"/> class.
|
/// </summary>
|
/// <param name="points">Number of finite difference coefficients.</param>
|
public FiniteDifferenceCoefficients(int points)
|
{
|
Points = points;
|
CalculateCoefficients(Points);
|
}
|
|
/// <summary>
|
/// Gets the finite difference coefficients for a specified center and order.
|
/// </summary>
|
/// <param name="center">Current function position with respect to coefficients. Must be within point range.</param>
|
/// <param name="order">Order of finite difference coefficients.</param>
|
/// <returns>Vector of finite difference coefficients.</returns>
|
public double[] GetCoefficients(int center, int order)
|
{
|
if (center >= _coefficients.Length)
|
throw new ArgumentOutOfRangeException(nameof(center), "Center position must be within the point range.");
|
if (order >= _coefficients.Length)
|
throw new ArgumentOutOfRangeException(nameof(order), "Maximum difference order is points-1.");
|
|
// Return proper row
|
var columns = _coefficients[center].GetLength(1);
|
var array = new double[columns];
|
for (int i = 0; i < columns; ++i)
|
array[i] = _coefficients[center][order, i];
|
return array;
|
}
|
|
/// <summary>
|
/// Gets the finite difference coefficients for all orders at a specified center.
|
/// </summary>
|
/// <param name="center">Current function position with respect to coefficients. Must be within point range.</param>
|
/// <returns>Rectangular array of coefficients, with columns specifying order.</returns>
|
public double[,] GetCoefficientsForAllOrders(int center)
|
{
|
if (center >= _coefficients.Length)
|
throw new ArgumentOutOfRangeException(nameof(center), "Center position must be within the point range.");
|
|
return _coefficients[center];
|
}
|
|
private void CalculateCoefficients(int points)
|
{
|
var c = new double[points][,];
|
|
// For ever possible center given the number of points, compute ever possible coefficient for all possible orders.
|
for (int center = 0; center < points; center++)
|
{
|
// Deltas matrix for center located at 'center'.
|
var A = new DenseMatrix(points);
|
var l = points - center - 1;
|
for (int row = points - 1; row >= 0; row--)
|
{
|
A[row, 0] = 1.0;
|
for (int col = 1; col < points; col++)
|
{
|
A[row, col] = A[row, col - 1] * l / col;
|
}
|
l -= 1;
|
}
|
|
c[center] = A.Inverse().ToArray();
|
|
// "Polish" results by rounding.
|
var fac = SpecialFunctions.Factorial(points);
|
for (int j = 0; j < points; j++)
|
{
|
for (int k = 0; k < points; k++)
|
{
|
c[center][j, k] = (Math.Round(c[center][j, k] * fac, MidpointRounding.AwayFromZero)) / fac;
|
}
|
}
|
}
|
|
_coefficients = c;
|
}
|
}
|
}
|
