// <copyright file="DenseGramSchmidt.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2013 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System;
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using IStation.Numerics.LinearAlgebra.Factorization;
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using IStation.Numerics.Providers.LinearAlgebra;
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namespace IStation.Numerics.LinearAlgebra.Double.Factorization
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{
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/// <summary>
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/// <para>A class which encapsulates the functionality of the QR decomposition Modified Gram-Schmidt Orthogonalization.</para>
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/// <para>Any real square matrix A may be decomposed as A = QR where Q is an orthogonal mxn matrix and R is an nxn upper triangular matrix.</para>
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/// </summary>
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/// <remarks>
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/// The computation of the QR decomposition is done at construction time by modified Gram-Schmidt Orthogonalization.
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/// </remarks>
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internal sealed class DenseGramSchmidt : GramSchmidt
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{
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/// <summary>
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/// Initializes a new instance of the <see cref="DenseGramSchmidt"/> class. This object creates an orthogonal matrix
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/// using the modified Gram-Schmidt method.
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/// </summary>
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/// <param name="matrix">The matrix to factor.</param>
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/// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
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/// <exception cref="ArgumentException">If <paramref name="matrix"/> row count is less then column count</exception>
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/// <exception cref="ArgumentException">If <paramref name="matrix"/> is rank deficient</exception>
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public static DenseGramSchmidt Create(Matrix<double> matrix)
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{
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if (matrix.RowCount < matrix.ColumnCount)
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{
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throw Matrix.DimensionsDontMatch<ArgumentException>(matrix);
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}
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var q = (DenseMatrix)matrix.Clone();
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var r = new DenseMatrix(matrix.ColumnCount, matrix.ColumnCount);
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Factorize(q.Values, q.RowCount, q.ColumnCount, r.Values);
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return new DenseGramSchmidt(q, r);
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}
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DenseGramSchmidt(Matrix<double> q, Matrix<double> rFull)
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: base(q, rFull)
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{
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}
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/// <summary>
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/// Factorize matrix using the modified Gram-Schmidt method.
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/// </summary>
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/// <param name="q">Initial matrix. On exit is replaced by <see cref="Matrix{T}"/> Q.</param>
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/// <param name="rowsQ">Number of rows in <see cref="Matrix{T}"/> Q.</param>
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/// <param name="columnsQ">Number of columns in <see cref="Matrix{T}"/> Q.</param>
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/// <param name="r">On exit is filled by <see cref="Matrix{T}"/> R.</param>
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private static void Factorize(double[] q, int rowsQ, int columnsQ, double[] r)
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{
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for (var k = 0; k < columnsQ; k++)
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{
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var norm = 0.0;
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for (var i = 0; i < rowsQ; i++)
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{
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norm += q[(k * rowsQ) + i] * q[(k * rowsQ) + i];
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}
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norm = Math.Sqrt(norm);
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if (norm == 0.0)
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{
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throw new ArgumentException("Matrix must not be rank deficient.");
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}
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r[(k * columnsQ) + k] = norm;
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for (var i = 0; i < rowsQ; i++)
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{
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q[(k * rowsQ) + i] /= norm;
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}
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for (var j = k + 1; j < columnsQ; j++)
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{
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var k1 = k;
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var j1 = j;
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var dot = 0.0;
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for (var index = 0; index < rowsQ; index++)
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{
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dot += q[(k1 * rowsQ) + index] * q[(j1 * rowsQ) + index];
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}
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r[(j * columnsQ) + k] = dot;
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for (var i = 0; i < rowsQ; i++)
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{
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var value = q[(j * rowsQ) + i] - (q[(k * rowsQ) + i] * dot);
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q[(j * rowsQ) + i] = value;
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}
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}
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}
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}
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/// <summary>
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/// Solves a system of linear equations, <b>AX = B</b>, with A QR factorized.
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/// </summary>
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/// <param name="input">The right hand side <see cref="Matrix{T}"/>, <b>B</b>.</param>
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/// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>X</b>.</param>
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public override void Solve(Matrix<double> input, Matrix<double> result)
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{
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// The solution X should have the same number of columns as B
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if (input.ColumnCount != result.ColumnCount)
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{
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throw new ArgumentException("Matrix column dimensions must agree.");
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}
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// The dimension compatibility conditions for X = A\B require the two matrices A and B to have the same number of rows
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if (Q.RowCount != input.RowCount)
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{
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throw new ArgumentException("Matrix row dimensions must agree.");
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}
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// The solution X row dimension is equal to the column dimension of A
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if (Q.ColumnCount != result.RowCount)
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{
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throw new ArgumentException("Matrix column dimensions must agree.");
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}
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if (input is DenseMatrix dinput && result is DenseMatrix dresult)
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{
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LinearAlgebraControl.Provider.QRSolveFactored(((DenseMatrix) Q).Values, ((DenseMatrix) FullR).Values, Q.RowCount, FullR.ColumnCount, null, dinput.Values, input.ColumnCount, dresult.Values, QRMethod.Thin);
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}
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else
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{
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throw new NotSupportedException("Can only do GramSchmidt factorization for dense matrices at the moment.");
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}
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}
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/// <summary>
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/// Solves a system of linear equations, <b>Ax = b</b>, with A QR factorized.
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/// </summary>
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/// <param name="input">The right hand side vector, <b>b</b>.</param>
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/// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>x</b>.</param>
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public override void Solve(Vector<double> input, Vector<double> result)
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{
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// Ax=b where A is an m x n matrix
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// Check that b is a column vector with m entries
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if (Q.RowCount != input.Count)
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{
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throw new ArgumentException("All vectors must have the same dimensionality.");
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}
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// Check that x is a column vector with n entries
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if (Q.ColumnCount != result.Count)
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{
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throw Matrix.DimensionsDontMatch<ArgumentException>(Q, result);
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}
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if (input is DenseVector dinput && result is DenseVector dresult)
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{
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LinearAlgebraControl.Provider.QRSolveFactored(((DenseMatrix) Q).Values, ((DenseMatrix) FullR).Values, Q.RowCount, FullR.ColumnCount, null, dinput.Values, 1, dresult.Values, QRMethod.Thin);
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}
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else
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{
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throw new NotSupportedException("Can only do GramSchmidt factorization for dense vectors at the moment.");
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}
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}
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}
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}
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