// <copyright file="DenseSvd.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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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System;
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using IStation.Numerics.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 singular value decomposition (SVD) for <see cref="DenseMatrix"/>.</para>
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/// <para>Suppose M is an m-by-n matrix whose entries are real numbers.
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/// Then there exists a factorization of the form M = UΣVT where:
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/// - U is an m-by-m unitary matrix;
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/// - Σ is m-by-n diagonal matrix with nonnegative real numbers on the diagonal;
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/// - VT denotes transpose of V, an n-by-n unitary matrix;
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/// Such a factorization is called a singular-value decomposition of M. A common convention is to order the diagonal
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/// entries Σ(i,i) in descending order. In this case, the diagonal matrix Σ is uniquely determined
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/// by M (though the matrices U and V are not). The diagonal entries of Σ are known as the singular values of M.</para>
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/// </summary>
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/// <remarks>
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/// The computation of the singular value decomposition is done at construction time.
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/// </remarks>
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internal sealed class DenseSvd : Svd
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{
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/// <summary>
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/// Initializes a new instance of the <see cref="DenseSvd"/> class. This object will compute the
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/// the singular value decomposition when the constructor is called and cache it's decomposition.
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/// </summary>
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/// <param name="matrix">The matrix to factor.</param>
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/// <param name="computeVectors">Compute the singular U and VT vectors or not.</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 SVD algorithm failed to converge with matrix <paramref name="matrix"/>.</exception>
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public static DenseSvd Create(DenseMatrix matrix, bool computeVectors)
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{
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var nm = Math.Min(matrix.RowCount, matrix.ColumnCount);
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var s = new DenseVector(nm);
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var u = new DenseMatrix(matrix.RowCount);
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var vt = new DenseMatrix(matrix.ColumnCount);
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LinearAlgebraControl.Provider.SingularValueDecomposition(computeVectors, ((DenseMatrix) matrix.Clone()).Values, matrix.RowCount, matrix.ColumnCount, s.Values, u.Values, vt.Values);
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return new DenseSvd(s, u, vt, computeVectors);
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}
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DenseSvd(Vector<double> s, Matrix<double> u, Matrix<double> vt, bool vectorsComputed)
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: base(s, u, vt, vectorsComputed)
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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 SVD 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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if (!VectorsComputed)
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{
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throw new InvalidOperationException("The singular vectors were not computed.");
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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 (U.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 (VT.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.SvdSolveFactored(U.RowCount, VT.ColumnCount, ((DenseVector) S).Values, ((DenseMatrix) U).Values, ((DenseMatrix) VT).Values, dinput.Values, input.ColumnCount, dresult.Values);
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}
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else
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{
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throw new NotSupportedException("Can only do SVD 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 SVD 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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if (!VectorsComputed)
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{
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throw new InvalidOperationException("The singular vectors were not computed.");
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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 (U.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 (VT.ColumnCount != result.Count)
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{
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throw Matrix.DimensionsDontMatch<ArgumentException>(VT, 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.SvdSolveFactored(U.RowCount, VT.ColumnCount, ((DenseVector) S).Values, ((DenseMatrix) U).Values, ((DenseMatrix) VT).Values, dinput.Values, 1, dresult.Values);
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}
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else
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{
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throw new NotSupportedException("Can only do SVD 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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