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.
678 lines
23 KiB
C#
678 lines
23 KiB
C#
// 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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#define CHECKS
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namespace Accord.Math
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{
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using System;
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using Accord.Math.Decompositions;
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using Accord.Math.Comparers;
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using System.Collections.Generic;
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using System.Collections;
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using System.Runtime.CompilerServices;
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public static partial class Matrix
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{
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// TODO: Use T4 templates for the equality comparisons
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#region Transpose
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/// <summary>
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/// Gets the transpose of a matrix.
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/// </summary>
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///
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/// <param name="matrix">A matrix.</param>
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///
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/// <returns>The transpose of the given matrix.</returns>
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///
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public static T[][] Transpose<T>(this IList<T[]> matrix)
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{
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int rows = matrix.Count;
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if (rows == 0)
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return new T[rows][];
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int cols = matrix[0].Length;
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#if CHECKS
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if (!IsRectangular(matrix))
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throw new ArgumentException("Only rectangular matrices can be transposed.");
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#endif
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T[][] result = new T[cols][];
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for (int j = 0; j < cols; j++)
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{
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result[j] = new T[rows];
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for (int i = 0; i < rows; i++)
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result[j][i] = matrix[i][j];
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}
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return result;
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}
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/// <summary>
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/// Gets the transpose of a matrix.
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/// </summary>
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///
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/// <param name="matrix">A matrix.</param>
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///
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/// <returns>The transpose of the given matrix.</returns>
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///
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public static TItem[][] Transpose<TCollection, TItem>(this TCollection matrix)
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where TCollection : ICollection, IEnumerable<TItem[]>
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{
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int rows = matrix.Count;
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if (rows == 0)
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return new TItem[rows][];
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int cols = matrix.Columns();
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#if CHECKS
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if (!IsRectangular(matrix))
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throw new ArgumentException("Only rectangular matrices can be transposed.");
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#endif
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TItem[][] result = Jagged.Zeros<TItem>(cols, rows);
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int i = 0;
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foreach (TItem[] row in matrix)
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{
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for (int j = 0; j < result.Length; j++)
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result[j][i] = row[j];
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i++;
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}
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return result;
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}
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/// <summary>
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/// Gets the transpose of a matrix.
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/// </summary>
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///
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/// <param name="matrix">A matrix.</param>
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///
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/// <returns>The transpose of the given matrix.</returns>
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///
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public static T[][] Transpose<T>(this T[][] matrix)
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{
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return Transpose(matrix, false);
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}
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/// <summary>
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/// Gets the transpose of a matrix.
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/// </summary>
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///
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/// <param name="matrix">A matrix.</param>
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///
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/// <param name="inPlace">True to store the transpose over the same input
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/// <paramref name="matrix"/>, false otherwise. Default is false.</param>
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///
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/// <returns>The transpose of the given matrix.</returns>
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///
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public static T[][] Transpose<T>(this T[][] matrix, bool inPlace)
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{
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int rows = matrix.Length;
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if (rows == 0) return new T[rows][];
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int cols = matrix[0].Length;
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#if CHECKS
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if (!IsRectangular(matrix))
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throw new ArgumentException("Only rectangular matrices can be transposed.");
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#endif
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if (inPlace)
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{
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if (rows != cols)
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throw new ArgumentException("Only square matrices can be transposed in place.", "matrix");
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for (int i = 0; i < rows; i++)
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{
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for (int j = i; j < cols; j++)
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{
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T element = matrix[j][i];
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matrix[j][i] = matrix[i][j];
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matrix[i][j] = element;
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}
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}
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return matrix;
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}
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else
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{
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T[][] result = new T[cols][];
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for (int j = 0; j < cols; j++)
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{
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result[j] = new T[rows];
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for (int i = 0; i < rows; i++)
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result[j][i] = matrix[i][j];
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}
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return result;
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}
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}
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/// <summary>
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/// Gets the transpose of a row vector.
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/// </summary>
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///
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/// <param name="rowVector">A row vector.</param>
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/// <param name="result">The matrix where to store the transpose.</param>
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///
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/// <returns>The transpose of the given vector.</returns>
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///
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public static T[][] Transpose<T>(this T[] rowVector, out T[][] result)
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{
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result = new T[rowVector.Length][];
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for (int i = 0; i < rowVector.Length; i++)
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result[i] = new T[] { rowVector[i] };
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return result;
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}
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/// <summary>
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/// Gets the transpose of a row vector.
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/// </summary>
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///
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/// <param name="rowVector">A row vector.</param>
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/// <param name="result">The matrix where to store the transpose.</param>
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///
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/// <returns>The transpose of the given vector.</returns>
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///
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public static T[][] Transpose<T>(this T[] rowVector, T[][] result)
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{
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for (int i = 0; i < rowVector.Length; i++)
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result[i] = new T[] { rowVector[i] };
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return result;
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}
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#endregion
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#region Matrix Characteristics
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/// <summary>
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/// Gets the number of rows in a jagged matrix.
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/// </summary>
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///
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/// <typeparam name="T">The type of the elements in the matrix.</typeparam>
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/// <param name="matrix">The matrix whose number of rows must be computed.</param>
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///
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/// <returns>The number of rows in the matrix.</returns>
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///
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public static int Rows<T>(this T[][] matrix)
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{
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return matrix.Length;
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}
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/// <summary>
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/// Gets the number of columns in a jagged matrix.
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/// </summary>
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///
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/// <typeparam name="T">The type of the elements in the matrix.</typeparam>
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/// <param name="matrix">The matrix whose number of columns must be computed.</param>
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///
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/// <returns>The number of columns in the matrix.</returns>
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///
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public static int Columns<T>(this T[][] matrix)
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{
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if (matrix.Length == 0)
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return 0;
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return matrix[0].Length;
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}
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/// <summary>
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/// Gets the number of columns in a jagged matrix.
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/// </summary>
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///
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/// <typeparam name="T">The type of the elements in the matrix.</typeparam>
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/// <param name="matrix">The matrix whose number of columns must be computed.</param>
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///
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/// <returns>The number of columns in the matrix.</returns>
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///
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public static int Columns<T>(this IEnumerable<T[]> matrix)
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{
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foreach (var row in matrix)
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return row.Length;
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return 0;
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}
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/// <summary>
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/// Gets the number of columns in a jagged matrix.
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/// </summary>
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///
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/// <typeparam name="T">The type of the elements in the matrix.</typeparam>
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/// <param name="matrix">The matrix whose number of columns must be computed.</param>
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/// <param name="max">Whether to compute the maximum length across all rows (because
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/// rows can have different lengths in jagged matrices). Default is false.</param>
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///
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/// <returns>The number of columns in the matrix.</returns>
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///
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public static int Columns<T>(this T[][] matrix, bool max = false)
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{
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if (matrix.Length == 0)
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return 0;
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if (max)
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{
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int maxLength = matrix[0].Length;
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for (int i = 1; i < matrix.Length; i++)
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if (matrix[i].Length > maxLength)
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maxLength = matrix[i].Length;
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return maxLength;
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}
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return matrix[0].Length;
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}
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/// <summary>
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/// Gets the number of channels (planes) in a jagged matrix.
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/// </summary>
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///
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/// <typeparam name="T">The type of the elements in the matrix.</typeparam>
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/// <param name="matrix">The matrix whose number of channels must be computed.</param>
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/// <param name="max">Whether to compute the maximum length across all columns (because
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/// columns can have different lengths in jagged matrices). Default is false.</param>
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///
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/// <returns>The number of channels (planes) in the matrix.</returns>
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///
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public static int Depth<T>(this T[][][] matrix, bool max = false)
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{
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if (matrix.Length == 0 || matrix[0].Length == 0)
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return 0;
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if (max)
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{
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int maxLength = matrix[0][0].Length;
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for (int i = 0; i < matrix.Length; i++)
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for (int j = 0; j < matrix[i].Length; j++)
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if (matrix[i][j].Length > maxLength)
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maxLength = matrix[i][j].Length;
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return maxLength;
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}
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return matrix[0][0].Length;
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}
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/// <summary>
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/// Returns true if a matrix is upper triangular.
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/// </summary>
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public static bool IsUpperTriangular<T>(this T[][] matrix) where T : IComparable
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{
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T zero = default(T);
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if (matrix.Length != matrix[0].Length)
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return false;
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for (int i = 0; i < matrix.Length; i++)
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for (int j = 0; j < i; j++)
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if (matrix[i][j].CompareTo(zero) != 0)
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return false;
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return true;
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}
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/// <summary>
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/// Returns true if a matrix is lower triangular.
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/// </summary>
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public static bool IsLowerTriangular<T>(this T[][] matrix) where T : IComparable
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{
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T zero = default(T);
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if (matrix.Length != matrix[0].Length)
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return false;
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for (int i = 0; i < matrix.Length; i++)
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for (int j = i + 1; j < matrix[i].Length; j++)
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if (matrix[i][j].CompareTo(zero) != 0)
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return false;
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return true;
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}
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/// <summary>
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/// Gets the lower triangular part of a matrix.
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/// </summary>
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///
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public static T[][] GetLowerTriangle<T>(this T[][] matrix, bool includeDiagonal = true)
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{
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int s = includeDiagonal ? 1 : 0;
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var r = Jagged.CreateAs(matrix);
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for (int i = 0; i < matrix.Rows(); i++)
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for (int j = 0; j < i + s; j++)
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r[i][j] = matrix[i][j]; ;
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return r;
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}
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/// <summary>
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/// Gets the upper triangular part of a matrix.
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/// </summary>
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///
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public static T[][] GetUpperTriangle<T>(this T[][] matrix, bool includeDiagonal = false)
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{
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int s = includeDiagonal ? 0 : 1;
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var r = Jagged.CreateAs(matrix);
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for (int i = 0; i < matrix.Rows(); i++)
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for (int j = i + s; j < matrix.Columns(); j++)
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r[i][j] = matrix[i][j]; ;
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return r;
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}
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/// <summary>
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/// Transforms a triangular matrix in a symmetric matrix by copying
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/// its elements to the other, unfilled part of the matrix.
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/// </summary>
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///
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public static T[][] GetSymmetric<T>(this T[][] matrix, MatrixType type, T[][] result = null)
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{
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if (result == null)
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result = Jagged.CreateAs(matrix);
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switch (type)
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{
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case MatrixType.LowerTriangular:
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for (int i = 0; i < matrix.Rows(); i++)
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for (int j = 0; j <= i; j++)
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result[i][j] = result[j][i] = matrix[i][j];
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break;
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case MatrixType.UpperTriangular:
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for (int i = 0; i < matrix.Rows(); i++)
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for (int j = i; j <= matrix.Columns(); j++)
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result[i][j] = result[j][i] = matrix[i][j];
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break;
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default:
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throw new Exception("Matrix type can be either LowerTriangular or UpperTrianguler.");
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}
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return result;
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}
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/// <summary>
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/// Returns true if a matrix is diagonal.
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/// </summary>
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///
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public static bool IsDiagonal<T>(this T[][] matrix) where T : IComparable
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{
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if (matrix == null)
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throw new ArgumentNullException("matrix");
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T zero = default(T);
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if (matrix.Length != matrix[0].Length)
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return false;
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for (int i = 0; i < matrix.Length; i++)
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for (int j = 0; j < matrix[i].Length; j++)
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if (i != j && matrix[i][j].CompareTo(zero) != 0)
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return false;
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return true;
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}
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// TODO: Move to T4 template
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/// <summary>
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/// Gets the trace of a matrix.
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/// </summary>
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///
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/// <remarks>
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/// The trace of an n-by-n square matrix A is defined to be the sum of the
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/// elements on the main diagonal (the diagonal from the upper left to the
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/// lower right) of A.
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/// </remarks>
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///
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public static float Trace(this float[][] matrix)
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{
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float trace = 0.0f;
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for (int i = 0; i < matrix.Length; i++)
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trace += matrix[i][i];
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return trace;
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}
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/// <summary>
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/// Gets the diagonal vector from a matrix.
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/// </summary>
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///
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/// <param name="matrix">A matrix.</param>
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///
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/// <returns>The diagonal vector from the given matrix.</returns>
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///
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public static T[] Diagonal<T>(this T[][] matrix)
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{
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T[] r = new T[matrix.Length];
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for (int i = 0; i < r.Length; i++)
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r[i] = matrix[i][i];
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return r;
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}
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/// <summary>
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/// Gets whether a matrix is positive definite.
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/// </summary>
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///
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public static bool IsPositiveDefinite(this double[][] matrix)
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{
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return new JaggedCholeskyDecomposition(matrix).IsPositiveDefinite;
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}
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/// <summary>
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/// Determines whether the specified matrix is rectangular.
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/// </summary>
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///
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/// <param name="matrix">The matrix.</param>
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///
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/// <returns><c>true</c> if the specified matrix is rectangular; otherwise, <c>false</c>.</returns>
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///
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public static bool IsRectangular<T>(T[][] matrix)
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{
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int numberOfCols = matrix[0].Length;
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for (int i = 1; i < matrix.Length; i++)
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if (matrix[i].Length != numberOfCols)
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return false;
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return true;
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}
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/// <summary>
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/// Determines whether the specified matrix is rectangular.
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/// </summary>
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///
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/// <param name="matrix">The matrix.</param>
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///
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/// <returns><c>true</c> if the specified matrix is rectangular; otherwise, <c>false</c>.</returns>
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///
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public static bool IsRectangular<T>(this IEnumerable<T[]> matrix)
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{
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int numberOfCols = matrix.Columns();
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foreach (T[] row in matrix)
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if (row.Length != numberOfCols)
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return false;
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return true;
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}
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///// <summary>
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///// Determines whether a jagged array is a rectangular
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///// matrix (containing all inner arrays of same size).
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///// </summary>
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/////
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//public static bool IsRectangular<T>(this T[][] array)
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//{
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// if (array.Length == 0)
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// return true;
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// int cols = array[0].Length;
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// for (int i = 0; i < array.Length; i++)
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// {
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// if (array[0].Length != cols)
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// return false;
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// }
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// return true;
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//}
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#endregion
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#region Operation Mapping (Apply)
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/// <summary>
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/// Applies a function to every element of the array.
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/// </summary>
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///
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public static TResult[][] Apply<TInput, TResult>(TInput[][] matrix, Func<TInput, TResult> func)
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{
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return Apply(matrix, func, Jagged.CreateAs<TInput, TResult>(matrix));
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}
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/// <summary>
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/// Applies a function to every element of the array.
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/// </summary>
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///
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public static TResult[][] Apply<TInput, TResult>(this TInput[][] matrix, Func<TInput, int, int, TResult> func)
|
|
{
|
|
return Apply(matrix, func, Jagged.CreateAs<TInput, TResult>(matrix));
|
|
}
|
|
|
|
/// <summary>
|
|
/// Applies a function to every element of the array.
|
|
/// </summary>
|
|
///
|
|
public static TResult[][] Apply<TInput, TResult>(this TInput[][] matrix, Func<TInput, TResult> func, TResult[][] result)
|
|
{
|
|
for (int i = 0; i < matrix.Length; i++)
|
|
for (int j = 0; j < matrix[i].Length; j++)
|
|
result[i][j] = func(matrix[i][j]);
|
|
return result;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Applies a function to every element of the array.
|
|
/// </summary>
|
|
///
|
|
public static TResult[][] Apply<TInput, TResult>(this TInput[][] matrix, Func<TInput, int, int, TResult> func, TResult[][] result)
|
|
{
|
|
for (int i = 0; i < matrix.Length; i++)
|
|
for (int j = 0; j < matrix[i].Length; j++)
|
|
result[i][j] = func(matrix[i][j], i, j);
|
|
return result;
|
|
}
|
|
#endregion
|
|
|
|
|
|
/// <summary>
|
|
/// Creates a member-wise copy of a jagged matrix. Matrix elements
|
|
/// themselves are copied only in a shallowed manner (i.e. not cloned).
|
|
/// </summary>
|
|
///
|
|
public static T[][] MemberwiseClone<T>(this T[][] a)
|
|
{
|
|
T[][] clone = new T[a.Length][];
|
|
for (int i = 0; i < a.Length; i++)
|
|
clone[i] = (T[])a[i].Clone();
|
|
return clone;
|
|
}
|
|
|
|
/// <summary>
|
|
/// Creates a member-wise copy of a jagged matrix. Matrix elements
|
|
/// themselves are copied only in a shallowed manner (i.e. not cloned).
|
|
/// </summary>
|
|
///
|
|
public static T[][] Copy<T>(this T[][] a)
|
|
{
|
|
T[][] clone = new T[a.Length][];
|
|
for (int i = 0; i < a.Length; i++)
|
|
clone[i] = (T[])a[i].Clone();
|
|
return clone;
|
|
}
|
|
|
|
|
|
/// <summary>
|
|
/// Copies the content of an array to another array.
|
|
/// </summary>
|
|
///
|
|
/// <typeparam name="T">The type of the elements to be copied.</typeparam>
|
|
///
|
|
/// <param name="matrix">The source matrix to be copied.</param>
|
|
/// <param name="destination">The matrix where the elements should be copied to.</param>
|
|
/// <param name="transpose">Whether to transpose the matrix when copying or not. Default is false.</param>
|
|
///
|
|
public static void CopyTo<T>(this T[][] matrix, T[][] destination, bool transpose = false)
|
|
{
|
|
if (matrix == destination)
|
|
{
|
|
if (transpose)
|
|
matrix.Transpose(inPlace: true);
|
|
}
|
|
else
|
|
{
|
|
if (transpose)
|
|
{
|
|
int rows = Math.Min(matrix.Rows(), destination.Columns());
|
|
int cols = Math.Min(matrix.Columns(), destination.Rows());
|
|
for (int i = 0; i < rows; i++)
|
|
for (int j = 0; j < cols; j++)
|
|
destination[j][i] = matrix[i][j];
|
|
}
|
|
else
|
|
{
|
|
int rows = Math.Min(matrix.Rows(), destination.Rows());
|
|
int cols = Math.Min(matrix.Columns(), destination.Columns());
|
|
for (int i = 0; i < rows; i++)
|
|
for (int j = 0; j < cols; j++)
|
|
destination[i][j] = matrix[i][j];
|
|
}
|
|
}
|
|
}
|
|
|
|
/// <summary>
|
|
/// Copies the content of an array to another array.
|
|
/// </summary>
|
|
///
|
|
/// <typeparam name="T">The type of the elements to be copied.</typeparam>
|
|
///
|
|
/// <param name="vector">The source vector to be copied.</param>
|
|
/// <param name="destination">The matrix where the elements should be copied to.</param>
|
|
///
|
|
public static void CopyTo<T>(this T[] vector, T[] destination)
|
|
{
|
|
if (vector != destination)
|
|
for (int i = 0; i < vector.Length; i++)
|
|
destination[i] = vector[i];
|
|
}
|
|
|
|
/// <summary>
|
|
/// Copies the content of an array to another array.
|
|
/// </summary>
|
|
///
|
|
/// <typeparam name="T">The type of the elements to be copied.</typeparam>
|
|
///
|
|
/// <param name="matrix">The source matrix to be copied.</param>
|
|
/// <param name="destination">The matrix where the elements should be copied to.</param>
|
|
///
|
|
public static void CopyTo<T>(this T[][] matrix, T[,] destination)
|
|
{
|
|
for (int i = 0; i < matrix.Length; i++)
|
|
for (int j = 0; j < matrix[i].Length; j++)
|
|
destination[i, j] = matrix[i][j];
|
|
}
|
|
|
|
}
|
|
}
|
|
|