mirror of
https://github.com/hanzoai/jube-fork.git
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richard-churchman
cc0a2bee21
Included open-source Accord.net library code natively to the solution given the deprecated state of that project. Accord.net will be supported inside Jube for own needs (such as upgrading to .Net 7+). Accord.net libraries modified to compile to .Net 6. Modified Accord.net libraries to better support Newtonsoft Json.net serialisation. Included annotations in the Accord.net libraries to house important dependency statistics. Serialised json can be used independently of Jube to recall a Neural Network. Removal of Binary Serializer totally as a precursor to the projects support of .Net 7+. Extensive bug fixing in crucial functions of Neural Network training and recall. While this part of the system remains in Alpha, it is substantially more fit for purpose.
782 lines
29 KiB
Plaintext
782 lines
29 KiB
Plaintext
<#@ template debug="false" hostspecific="true" language="C#" #>
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<#@ output extension="Generated.cs" #>
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<#@ import namespace="Microsoft.VisualStudio.TextTemplating" #>
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<#@ include file="T4Toolbox.tt" #>
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// Accord Math Library
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// The Accord.NET Framework
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// http://accord-framework.net
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//
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// Copyright © César Souza, 2009-2017
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// cesarsouza at gmail.com
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//
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// This library is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 2.1 of the License, or (at your option) any later version.
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//
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// This library is distributed in the hope that it will be useful,
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// but WITHOUT ANY WARRANTY; without even the implied warranty of
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// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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// Lesser General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License along with this library; if not, write to the Free Software
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// Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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//
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// ======================================================================
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// This code has been generated by a tool; do not edit manually. Instead,
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// edit the T4 template Matrix.Elementwise.tt so this file can be regenerated.
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// ======================================================================
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namespace Accord.Math
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{
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using System;
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using System.CodeDom.Compiler;
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using Accord.Math;
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using System.Runtime.CompilerServices;
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using Accord.Math.Decompositions;
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//[GeneratedCode("Accord.NET T4 Templates", "3.1")]
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public static partial class Matrix
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{
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<#
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string[][] types =
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{
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new[] { "Double", "" },
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new[] { "Single", "F" },
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new[] { "Decimal", "D" },
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};
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foreach (string[] a in types)
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{
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string type = a[0];
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string suffix = a[1];
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#>
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/// <summary>
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/// Returns the solution matrix if the matrix is square or the least squares solution otherwise.
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/// </summary>
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///
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/// <param name="matrix">The matrix for the linear problem.</param>
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/// <param name="rightSide">The right side <c>b</c>.</param>
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/// <param name="leastSquares">True to produce a solution even if the
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/// <paramref name="matrix"/> is singular; false otherwise. Default is false.</param>
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///
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/// <remarks>
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/// Please note that this does not check if the matrix is non-singular
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/// before attempting to solve. If a least squares solution is desired
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/// in case the matrix is singular, pass true to the <paramref name="leastSquares"/>
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/// parameter when calling this function.
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/// </remarks>
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///
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/// <example>
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/// <code>
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/// // Create a matrix. Please note that this matrix
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/// // is singular (i.e. not invertible), so only a
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/// // least squares solution would be feasible here.
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///
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/// <#=type#>[,] matrix =
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/// {
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/// { 1, 2, 3 },
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/// { 4, 5, 6 },
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/// { 7, 8, 9 },
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/// };
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///
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/// // Define a right side matrix b:
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/// <#=type#>[,] rightSide = { {1}, {2}, {3} };
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///
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/// // Solve the linear system Ax = b by finding x:
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/// <#=type#>[,] x = Matrix.Solve(matrix, rightSide, leastSquares: true);
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///
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/// // The answer should be { {-1/18}, {2/18}, {5/18} }.
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/// </code>
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/// </example>
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///
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public static <#=type#>[,] Solve(this <#=type#>[,] matrix, <#=type#>[,] rightSide, bool leastSquares = false)
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{
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int rows = matrix.GetLength(0);
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int cols = matrix.GetLength(1);
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if (rows != rightSide.GetLength(0))
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throw new DimensionMismatchException("rightSide",
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"The number of rows in the right hand side matrix must be "
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+ "equal to the number of rows in the problem matrix.");
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if (leastSquares)
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{
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return new SingularValueDecomposition<#=suffix#>(matrix,
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computeLeftSingularVectors: true,
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computeRightSingularVectors: true,
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autoTranspose: true).Solve(rightSide);
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}
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if (rows == cols)
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{
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// Solve by LU Decomposition if matrix is square.
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return new LuDecomposition<#=suffix#>(matrix).Solve(rightSide);
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}
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else
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{
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if (cols < rows)
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{
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// Solve by QR Decomposition if not.
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return new QrDecomposition<#=suffix#>(matrix).Solve(rightSide);
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}
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else
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{
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return new SingularValueDecomposition<#=suffix#>(matrix,
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computeLeftSingularVectors: true,
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computeRightSingularVectors: true,
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autoTranspose: true).Solve(rightSide);
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}
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}
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}
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/// <summary>
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/// Returns the solution matrix if the matrix is square or the least squares solution otherwise.
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/// </summary>
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///
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/// <param name="matrix">The matrix for the linear problem.</param>
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/// <param name="rightSide">The right side <c>b</c>.</param>
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/// <param name="leastSquares">True to produce a solution even if the
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/// <paramref name="matrix"/> is singular; false otherwise. Default is false.</param>
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///
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/// <remarks>
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/// Please note that this does not check if the matrix is non-singular
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/// before attempting to solve. If a least squares solution is desired
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/// in case the matrix is singular, pass true to the <paramref name="leastSquares"/>
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/// parameter when calling this function.
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/// </remarks>
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///
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/// <example>
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/// <code>
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/// // Create a matrix. Please note that this matrix
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/// // is singular (i.e. not invertible), so only a
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/// // least squares solution would be feasible here.
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///
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/// <#=type#>[,] matrix =
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/// {
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/// { 1, 2, 3 },
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/// { 4, 5, 6 },
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/// { 7, 8, 9 },
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/// };
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///
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/// // Define a right side vector b:
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/// <#=type#>[] rightSide = { 1, 2, 3 };
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///
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/// // Solve the linear system Ax = b by finding x:
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/// <#=type#>[] x = Matrix.Solve(matrix, rightSide, leastSquares: true);
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///
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/// // The answer should be { -1/18, 2/18, 5/18 }.
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/// </code>
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/// </example>
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///
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public static <#=type#>[] Solve(this <#=type#>[,] matrix, <#=type#>[] rightSide, bool leastSquares = false)
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{
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if (matrix == null)
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throw new ArgumentNullException("matrix");
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if (rightSide == null)
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throw new ArgumentNullException("rightSide");
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int rows = matrix.GetLength(0);
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int cols = matrix.GetLength(1);
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if (rows != rightSide.Length)
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throw new DimensionMismatchException("rightSide",
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"The right hand side vector must have the same length"
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+ "as there are rows of the problem matrix.");
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if (leastSquares)
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{
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return new SingularValueDecomposition<#=suffix#>(matrix,
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computeLeftSingularVectors: true,
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computeRightSingularVectors: true,
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autoTranspose: true).Solve(rightSide);
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}
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if (rows == cols)
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{
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// Solve by LU Decomposition if matrix is square.
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return new LuDecomposition<#=suffix#>(matrix).Solve(rightSide);
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}
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else
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{
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if (cols < rows)
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{
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// Solve by QR Decomposition if not.
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return new QrDecomposition<#=suffix#>(matrix).Solve(rightSide);
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}
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else
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{
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return new SingularValueDecomposition<#=suffix#>(matrix,
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computeLeftSingularVectors: true,
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computeRightSingularVectors: true,
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autoTranspose: true).Solve(rightSide);
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}
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}
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}
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/// <summary>
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/// Computes the inverse of a matrix.
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/// </summary>
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///
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/// <example>
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/// <code source="Unit Tests\Accord.Tests.Math\Matrix\MatrixTest.cs" region="doc_inverse" />
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/// </example>
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///
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public static <#=type#>[,] Inverse(this <#=type#>[,] matrix)
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{
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return Inverse(matrix, false);
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}
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/// <summary>
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/// Computes the inverse of a matrix.
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/// </summary>
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///
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/// <example>
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/// <code source="Unit Tests\Accord.Tests.Math\Matrix\MatrixTest.cs" region="doc_inverse" />
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/// </example>
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///
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public static <#=type#>[,] Inverse(this <#=type#>[,] matrix, bool inPlace)
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{
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int rows = matrix.GetLength(0);
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int cols = matrix.GetLength(1);
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if (rows != cols)
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throw new ArgumentException("Matrix must be square", "matrix");
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if (rows == 3)
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{
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// Special case for 3x3 matrices
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<#=type#> a = matrix[0, 0], b = matrix[0, 1], c = matrix[0, 2];
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<#=type#> d = matrix[1, 0], e = matrix[1, 1], f = matrix[1, 2];
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<#=type#> g = matrix[2, 0], h = matrix[2, 1], i = matrix[2, 2];
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<#=type#> den = a * (e * i - f * h) -
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b * (d * i - f * g) +
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c * (d * h - e * g);
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if (den == 0)
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throw new SingularMatrixException();
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<#=type#> m = 1 / den;
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var inv = (inPlace) ? matrix : new <#=type#>[3, 3];
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inv[0, 0] = m * (e * i - f * h);
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inv[0, 1] = m * (c * h - b * i);
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inv[0, 2] = m * (b * f - c * e);
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inv[1, 0] = m * (f * g - d * i);
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inv[1, 1] = m * (a * i - c * g);
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inv[1, 2] = m * (c * d - a * f);
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inv[2, 0] = m * (d * h - e * g);
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inv[2, 1] = m * (b * g - a * h);
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inv[2, 2] = m * (a * e - b * d);
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return inv;
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}
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if (rows == 2)
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{
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// Special case for 2x2 matrices
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<#=type#> a = matrix[0, 0], b = matrix[0, 1];
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<#=type#> c = matrix[1, 0], d = matrix[1, 1];
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<#=type#> den = a * d - b * c;
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if (den == 0)
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throw new SingularMatrixException();
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<#=type#> m = 1 / den;
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var inv = (inPlace) ? matrix : new <#=type#>[2, 2];
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inv[0, 0] = +m * d;
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inv[0, 1] = -m * b;
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inv[1, 0] = -m * c;
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inv[1, 1] = +m * a;
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return inv;
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}
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return new LuDecomposition<#=suffix#>(matrix, false, inPlace).Inverse();
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}
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/// <summary>
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/// Computes the pseudo-inverse of a matrix.
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/// </summary>
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///
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/// <example>
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/// <code source="Unit Tests\Accord.Tests.Math\Matrix\MatrixTest.cs" region="doc_pseudoinverse" />
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/// </example>
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///
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public static <#=type#>[,] PseudoInverse(this <#=type#>[,] matrix)
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{
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return new SingularValueDecomposition<#=suffix#>(matrix,
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computeLeftSingularVectors: true,
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computeRightSingularVectors: true,
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autoTranspose: true).Inverse();
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}
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/// <summary>
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/// Returns the solution matrix if the matrix is square or the least squares solution otherwise.
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/// </summary>
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///
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/// <param name="matrix">The matrix for the linear problem.</param>
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/// <param name="rightSide">The right side <c>b</c>.</param>
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/// <param name="leastSquares">True to produce a solution even if the
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/// <paramref name="matrix"/> is singular; false otherwise. Default is false.</param>
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///
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/// <remarks>
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/// Please note that this does not check if the matrix is non-singular
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/// before attempting to solve. If a least squares solution is desired
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/// in case the matrix is singular, pass true to the <paramref name="leastSquares"/>
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/// parameter when calling this function.
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/// </remarks>
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///
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/// <example>
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/// <code>
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/// // Create a matrix. Please note that this matrix
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/// // is singular (i.e. not invertible), so only a
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/// // least squares solution would be feasible here.
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///
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/// <#=type#>[,] matrix =
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/// {
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/// { 1, 2, 3 },
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/// { 4, 5, 6 },
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/// { 7, 8, 9 },
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/// };
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///
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/// // Define a right side matrix b:
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/// <#=type#>[,] rightSide = { {1}, {2}, {3} };
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///
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/// // Solve the linear system Ax = b by finding x:
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/// <#=type#>[,] x = Matrix.Solve(matrix, rightSide, leastSquares: true);
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///
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/// // The answer should be { {-1/18}, {2/18}, {5/18} }.
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/// </code>
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/// </example>
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///
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public static <#=type#>[][] Solve(this <#=type#>[][] matrix, <#=type#>[][] rightSide, bool leastSquares = false)
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{
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if (matrix.Length != rightSide.Length)
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{
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throw new DimensionMismatchException("rightSide",
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"The number of rows in the right hand side matrix must be "
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+ "equal to the number of rows in the problem matrix.");
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}
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return matrix.Decompose(leastSquares).Solve(rightSide);
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}
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/// <summary>
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/// Returns the solution matrix if the matrix is square or the least squares solution otherwise.
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/// </summary>
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///
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/// <param name="matrix">The matrix for the linear problem.</param>
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/// <param name="rightSide">The right side <c>b</c>.</param>
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/// <param name="leastSquares">True to produce a solution even if the
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/// <paramref name="matrix"/> is singular; false otherwise. Default is false.</param>
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///
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/// <remarks>
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/// Please note that this does not check if the matrix is non-singular
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/// before attempting to solve. If a least squares solution is desired
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/// in case the matrix is singular, pass true to the <paramref name="leastSquares"/>
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/// parameter when calling this function.
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/// </remarks>
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///
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/// <example>
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/// <code>
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/// // Create a matrix. Please note that this matrix
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/// // is singular (i.e. not invertible), so only a
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/// // least squares solution would be feasible here.
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///
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/// <#=type#>[,] matrix =
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/// {
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/// { 1, 2, 3 },
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/// { 4, 5, 6 },
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/// { 7, 8, 9 },
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/// };
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///
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/// // Define a right side vector b:
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/// <#=type#>[] rightSide = { 1, 2, 3 };
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///
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/// // Solve the linear system Ax = b by finding x:
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/// <#=type#>[] x = Matrix.Solve(matrix, rightSide, leastSquares: true);
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///
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/// // The answer should be { -1/18, 2/18, 5/18 }.
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/// </code>
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/// </example>
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///
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public static <#=type#>[] Solve(this <#=type#>[][] matrix, <#=type#>[] rightSide, bool leastSquares = false)
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{
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if (matrix.Length != rightSide.Length)
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{
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throw new DimensionMismatchException("rightSide",
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"The right hand side vector must have the same length"
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+ "as there are rows of the problem matrix.");
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}
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return matrix.Decompose(leastSquares).Solve(rightSide);
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}
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/// <summary>
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/// Returns the solution matrix for a linear system involving a diagonal matrix ion the right-hand side.
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/// </summary>
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///
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/// <param name="matrix">The matrix for the linear problem.</param>
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/// <param name="diagonalRightSide">The right side <c>b</c>.</param>
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/// <param name="leastSquares">True to produce a solution even if the
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|
/// <paramref name="matrix"/> is singular; false otherwise. Default is false.</param>
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|
///
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|
/// <remarks>
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|
/// Please note that this does not check if the matrix is non-singular
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|
/// before attempting to solve. If a least squares solution is desired
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|
/// in case the matrix is singular, pass true to the <paramref name="leastSquares"/>
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/// parameter when calling this function.
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/// </remarks>
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///
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public static <#=type#>[][] SolveForDiagonal(this <#=type#>[][] matrix, <#=type#>[] diagonalRightSide, bool leastSquares = false)
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{
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if (matrix.Length != diagonalRightSide.Length)
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{
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throw new DimensionMismatchException("diagonalRightSide",
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"The right hand side matrix must have the same length"
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|
+ "as there are rows of the problem matrix.");
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}
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return matrix.Decompose(leastSquares).SolveForDiagonal(diagonalRightSide);
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}
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|
|
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/// <summary>
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|
/// Creates a matrix decomposition that be used to compute the solution matrix if the
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/// matrix is square or the least squares solution otherwise.
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/// </summary>
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///
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public static ISolverMatrixDecomposition<<#=type#>> Decompose(this <#=type#>[,] matrix, bool leastSquares = false)
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{
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int rows = matrix.Rows();
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int cols = matrix.Columns();
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|
|
if (leastSquares)
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{
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return new SingularValueDecomposition<#=suffix#>(matrix,
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|
computeLeftSingularVectors: true,
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|
computeRightSingularVectors: true,
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|
autoTranspose: true);
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|
}
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|
if (rows == cols)
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|
{
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|
// Solve by LU Decomposition if matrix is square.
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|
return new LuDecomposition<#=suffix#>(matrix);
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|
}
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|
else
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|
{
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|
if (cols < rows)
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|
{
|
|
// Solve by QR Decomposition if not.
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|
return new QrDecomposition<#=suffix#>(matrix);
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|
}
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|
else
|
|
{
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|
return new SingularValueDecomposition<#=suffix#>(matrix,
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|
computeLeftSingularVectors: true,
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|
computeRightSingularVectors: true,
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|
autoTranspose: true);
|
|
}
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a matrix decomposition that be used to compute the solution matrix if the
|
|
/// matrix is square or the least squares solution otherwise.
|
|
/// </summary>
|
|
///
|
|
public static ISolverArrayDecomposition<<#=type#>> Decompose(this <#=type#>[][] matrix, bool leastSquares = false)
|
|
{
|
|
int rows = matrix.Rows();
|
|
int cols = matrix.Columns();
|
|
|
|
if (leastSquares)
|
|
{
|
|
return new JaggedSingularValueDecomposition<#=suffix#>(matrix,
|
|
computeLeftSingularVectors: true,
|
|
computeRightSingularVectors: true,
|
|
autoTranspose: true);
|
|
}
|
|
|
|
if (rows == cols)
|
|
{
|
|
// Solve by LU Decomposition if matrix is square.
|
|
return new JaggedLuDecomposition<#=suffix#>(matrix);
|
|
}
|
|
else
|
|
{
|
|
if (cols < rows)
|
|
{
|
|
// Solve by QR Decomposition if not.
|
|
return new JaggedQrDecomposition<#=suffix#>(matrix);
|
|
}
|
|
else
|
|
{
|
|
return new JaggedSingularValueDecomposition<#=suffix#>(matrix,
|
|
computeLeftSingularVectors: true,
|
|
computeRightSingularVectors: true,
|
|
autoTranspose: true);
|
|
}
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Computes the inverse of a matrix.
|
|
/// </summary>
|
|
///
|
|
///
|
|
/// <example>
|
|
/// <code source="Unit Tests\Accord.Tests.Math\Matrix\MatrixTest.cs" region="doc_inverse" />
|
|
/// </example>
|
|
///
|
|
public static <#=type#>[][] Inverse(this <#=type#>[][] matrix)
|
|
{
|
|
return Inverse(matrix, false);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Computes the inverse of a matrix.
|
|
/// </summary>
|
|
///
|
|
/// <example>
|
|
/// <code source="Unit Tests\Accord.Tests.Math\Matrix\MatrixTest.cs" region="doc_inverse" />
|
|
/// </example>
|
|
///
|
|
public static <#=type#>[][] Inverse(this <#=type#>[][] matrix, bool inPlace)
|
|
{
|
|
int rows = matrix.Length;
|
|
int cols = matrix[0].Length;
|
|
|
|
if (rows != cols)
|
|
throw new ArgumentException("Matrix must be square", "matrix");
|
|
|
|
if (rows == 3)
|
|
{
|
|
// Special case for 3x3 matrices
|
|
<#=type#> a = matrix[0][0], b = matrix[0][1], c = matrix[0][2];
|
|
<#=type#> d = matrix[1][0], e = matrix[1][1], f = matrix[1][2];
|
|
<#=type#> g = matrix[2][0], h = matrix[2][1], i = matrix[2][2];
|
|
|
|
<#=type#> den = a * (e * i - f * h) -
|
|
b * (d * i - f * g) +
|
|
c * (d * h - e * g);
|
|
|
|
if (den == 0)
|
|
throw new SingularMatrixException();
|
|
|
|
<#=type#> m = 1 / den;
|
|
|
|
var inv = matrix;
|
|
if (!inPlace)
|
|
{
|
|
inv = new <#=type#>[3][];
|
|
for (int j = 0; j < inv.Length; j++)
|
|
inv[j] = new <#=type#>[3];
|
|
}
|
|
|
|
inv[0][0] = m * (e * i - f * h);
|
|
inv[0][1] = m * (c * h - b * i);
|
|
inv[0][2] = m * (b * f - c * e);
|
|
inv[1][0] = m * (f * g - d * i);
|
|
inv[1][1] = m * (a * i - c * g);
|
|
inv[1][2] = m * (c * d - a * f);
|
|
inv[2][0] = m * (d * h - e * g);
|
|
inv[2][1] = m * (b * g - a * h);
|
|
inv[2][2] = m * (a * e - b * d);
|
|
|
|
return inv;
|
|
}
|
|
|
|
if (rows == 2)
|
|
{
|
|
// Special case for 2x2 matrices
|
|
<#=type#> a = matrix[0][0], b = matrix[0][1];
|
|
<#=type#> c = matrix[1][0], d = matrix[1][1];
|
|
|
|
<#=type#> den = a * d - b * c;
|
|
|
|
if (den == 0)
|
|
throw new SingularMatrixException();
|
|
|
|
<#=type#> m = 1 / den;
|
|
|
|
var inv = matrix;
|
|
if (!inPlace)
|
|
{
|
|
inv = new <#=type#>[2][];
|
|
for (int j = 0; j < inv.Length; j++)
|
|
inv[j] = new <#=type#>[2];
|
|
}
|
|
|
|
inv[0][0] = +m * d;
|
|
inv[0][1] = -m * b;
|
|
inv[1][0] = -m * c;
|
|
inv[1][1] = +m * a;
|
|
|
|
return inv;
|
|
}
|
|
|
|
return new JaggedLuDecomposition<#=suffix#>(matrix, false, inPlace).Inverse();
|
|
}
|
|
|
|
/// <summary>
|
|
/// Computes the pseudo-inverse of a matrix.
|
|
/// </summary>
|
|
///
|
|
/// <example>
|
|
/// <code source="Unit Tests\Accord.Tests.Math\Matrix\MatrixTest.cs" region="doc_pseudoinverse" />
|
|
/// </example>
|
|
///
|
|
public static <#=type#>[][] PseudoInverse(this <#=type#>[][] matrix)
|
|
{
|
|
return new JaggedSingularValueDecomposition<#=suffix#>(matrix,
|
|
computeLeftSingularVectors: true,
|
|
computeRightSingularVectors: true,
|
|
autoTranspose: true).Inverse();
|
|
}
|
|
|
|
/// <summary>
|
|
/// Divides two matrices by multiplying A by the inverse of B.
|
|
/// </summary>
|
|
///
|
|
/// <param name="a">The first matrix.</param>
|
|
/// <param name="b">The second matrix (which will be inverted).</param>
|
|
/// <param name="leastSquares">True to produce a solution even if the
|
|
/// <paramref name="b"/> is singular; false otherwise. Default is false.</param>
|
|
///
|
|
/// <returns>The result from the division <c>AB^-1</c> of the given matrices.</returns>
|
|
///
|
|
public static <#=type#>[,] Divide(this <#=type#>[,] a, <#=type#>[,] b, bool leastSquares = false)
|
|
{
|
|
int rows = b.Rows();
|
|
int cols = b.Columns();
|
|
|
|
if (leastSquares)
|
|
{
|
|
return new SingularValueDecomposition<#=suffix#>(b.Transpose(),
|
|
computeLeftSingularVectors: true,
|
|
computeRightSingularVectors: true,
|
|
autoTranspose: true).Solve(a.Transpose()).Transpose();
|
|
}
|
|
|
|
|
|
if (rows == cols && cols == a.Rows())
|
|
{
|
|
// Solve by LU Decomposition if matrix is square.
|
|
return new LuDecomposition<#=suffix#>(b, true).SolveTranspose(a);
|
|
}
|
|
else
|
|
{
|
|
if (rows <= cols)
|
|
{
|
|
// Solve by QR Decomposition if not.
|
|
return new QrDecomposition<#=suffix#>(b, true).SolveTranspose(a);
|
|
}
|
|
else
|
|
{
|
|
return new SingularValueDecomposition<#=suffix#>(b.Transpose(),
|
|
computeLeftSingularVectors: true,
|
|
computeRightSingularVectors: true,
|
|
autoTranspose: true).Solve(a.Transpose()).Transpose();
|
|
}
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Divides two matrices by multiplying A by the inverse of B.
|
|
/// </summary>
|
|
///
|
|
/// <param name="a">The first matrix.</param>
|
|
/// <param name="b">The second matrix (which will be inverted).</param>
|
|
/// <param name="leastSquares">True to produce a solution even if the
|
|
/// <paramref name="b"/> is singular; false otherwise. Default is false.</param>
|
|
///
|
|
/// <returns>The result from the division <c>AB^-1</c> of the given matrices.</returns>
|
|
///
|
|
public static <#=type#>[][] Divide(this <#=type#>[][] a, <#=type#>[][] b, bool leastSquares = false)
|
|
{
|
|
int rows = b.Rows();
|
|
int cols = b.Columns();
|
|
|
|
if (leastSquares)
|
|
{
|
|
return new JaggedSingularValueDecomposition<#=suffix#>(b.Transpose(),
|
|
computeLeftSingularVectors: true,
|
|
computeRightSingularVectors: true,
|
|
autoTranspose: true).Solve(a.Transpose()).Transpose();
|
|
}
|
|
|
|
|
|
if (rows == cols && cols == a.Rows())
|
|
{
|
|
// Solve by LU Decomposition if matrix is square.
|
|
return new JaggedLuDecomposition<#=suffix#>(b, true).SolveTranspose(a);
|
|
}
|
|
else
|
|
{
|
|
if (rows <= cols)
|
|
{
|
|
// Solve by QR Decomposition if not.
|
|
return new JaggedQrDecomposition<#=suffix#>(b, true).SolveTranspose(a);
|
|
}
|
|
else
|
|
{
|
|
return new JaggedSingularValueDecomposition<#=suffix#>(b.Transpose(),
|
|
computeLeftSingularVectors: true,
|
|
computeRightSingularVectors: true,
|
|
autoTranspose: true).Solve(a.Transpose()).Transpose();
|
|
}
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Gets the null-space of a column vector.
|
|
/// </summary>
|
|
///
|
|
public static <#=type#>[][] Null(this <#=type#>[] vector)
|
|
{
|
|
return Null(Jagged.ColumnVector(vector));
|
|
}
|
|
|
|
/// <summary>
|
|
/// Gets the null-space of a matrix.
|
|
/// </summary>
|
|
///
|
|
public static <#=type#>[][] Null(this <#=type#>[][] matrix)
|
|
{
|
|
var qr = new JaggedQrDecomposition<#=suffix#>(matrix, economy: false);
|
|
var Q = qr.OrthogonalFactor;
|
|
var threshold = matrix.GetLength().Max() * Constants.<#=type#>Epsilon;
|
|
int[] idx = qr.Diagonal.Find(x => (<#=type#>)Math.Abs(x) < threshold);
|
|
return Q.GetColumns(idx);
|
|
}
|
|
|
|
/// <summary>
|
|
/// Gets the null-space of a matrix.
|
|
/// </summary>
|
|
///
|
|
public static <#=type#>[,] Null(this <#=type#>[,] matrix)
|
|
{
|
|
var qr = new QrDecomposition<#=suffix#>(matrix, economy: false);
|
|
var Q = qr.OrthogonalFactor;
|
|
var threshold = matrix.GetLength().Max() * Constants.<#=type#>Epsilon;
|
|
int[] idx = qr.Diagonal.Find(x => (<#=type#>)Math.Abs(x) < threshold);
|
|
return Q.GetColumns(idx);
|
|
}
|
|
<#
|
|
}
|
|
#>
|
|
}
|
|
} |