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@ -4,7 +4,7 @@ |
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// http://github.com/mathnet/mathnet-numerics
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// http://github.com/mathnet/mathnet-numerics
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// http://mathnetnumerics.codeplex.com
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// http://mathnetnumerics.codeplex.com
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//
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//
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// Copyright (c) 2009-2010 Math.NET
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// Copyright (c) 2009-2013 Math.NET
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//
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//
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// Permission is hereby granted, free of charge, to any person
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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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// obtaining a copy of this software and associated documentation
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@ -28,11 +28,11 @@ |
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// OTHER DEALINGS IN THE SOFTWARE.
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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// </copyright>
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using System; |
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using System.Linq; |
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using MathNet.Numerics.LinearAlgebra.Factorization; |
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using MathNet.Numerics.LinearAlgebra.Factorization; |
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using MathNet.Numerics.Properties; |
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using MathNet.Numerics.Properties; |
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using MathNet.Numerics.Threading; |
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using MathNet.Numerics.Threading; |
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using System; |
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using System.Linq; |
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namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization |
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namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization |
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{ |
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{ |
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@ -47,7 +47,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization |
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/// <remarks>
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/// <remarks>
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/// The computation of the QR decomposition is done at construction time by Householder transformation.
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/// The computation of the QR decomposition is done at construction time by Householder transformation.
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/// </remarks>
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/// </remarks>
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public class UserQR : QR |
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public sealed class UserQR : QR |
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{ |
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{ |
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/// <summary>
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/// <summary>
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/// Initializes a new instance of the <see cref="UserQR"/> class. This object will compute the
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/// Initializes a new instance of the <see cref="UserQR"/> class. This object will compute the
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@ -56,71 +56,70 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization |
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/// <param name="matrix">The matrix to factor.</param>
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/// <param name="matrix">The matrix to factor.</param>
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/// <param name="method">The QR factorization method to use.</param>
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/// <param name="method">The QR factorization method to use.</param>
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/// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
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/// <exception cref="ArgumentNullException">If <paramref name="matrix"/> is <c>null</c>.</exception>
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public UserQR(Matrix<Complex32> matrix, QRMethod method = QRMethod.Full) |
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public static UserQR Create(Matrix<Complex32> matrix, QRMethod method = QRMethod.Full) |
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{ |
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{ |
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if (matrix == null) |
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{ |
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throw new ArgumentNullException("matrix"); |
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} |
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if (matrix.RowCount < matrix.ColumnCount) |
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if (matrix.RowCount < matrix.ColumnCount) |
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{ |
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{ |
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throw Matrix.DimensionsDontMatch<ArgumentException>(matrix); |
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throw Matrix.DimensionsDontMatch<ArgumentException>(matrix); |
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} |
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} |
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QrMethod = method; |
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Matrix<Complex32> q; |
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Matrix<Complex32> r; |
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var minmn = Math.Min(matrix.RowCount, matrix.ColumnCount); |
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var minmn = Math.Min(matrix.RowCount, matrix.ColumnCount); |
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var u = new Complex32[minmn][]; |
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var u = new Complex32[minmn][]; |
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if (method == QRMethod.Full) |
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if (method == QRMethod.Full) |
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{ |
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{ |
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MatrixR = matrix.Clone(); |
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r = matrix.Clone(); |
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Q = matrix.CreateMatrix(matrix.RowCount, matrix.RowCount); |
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q = matrix.CreateMatrix(matrix.RowCount, matrix.RowCount); |
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for (var i = 0; i < matrix.RowCount; i++) |
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for (var i = 0; i < matrix.RowCount; i++) |
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{ |
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{ |
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Q.At(i, i, 1.0f); |
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q.At(i, i, 1.0f); |
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} |
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} |
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for (var i = 0; i < minmn; i++) |
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for (var i = 0; i < minmn; i++) |
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{ |
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{ |
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u[i] = GenerateColumn(MatrixR, i, i); |
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u[i] = GenerateColumn(r, i, i); |
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ComputeQR(u[i], MatrixR, i, matrix.RowCount, i + 1, matrix.ColumnCount, |
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ComputeQR(u[i], r, i, matrix.RowCount, i + 1, matrix.ColumnCount, Control.NumberOfParallelWorkerThreads); |
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Control.NumberOfParallelWorkerThreads); |
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} |
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} |
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for (var i = minmn - 1; i >= 0; i--) |
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for (var i = minmn - 1; i >= 0; i--) |
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{ |
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{ |
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ComputeQR(u[i], Q, i, matrix.RowCount, i, matrix.RowCount, |
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ComputeQR(u[i], q, i, matrix.RowCount, i, matrix.RowCount, Control.NumberOfParallelWorkerThreads); |
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Control.NumberOfParallelWorkerThreads); |
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} |
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} |
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} |
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} |
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else |
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else |
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{ |
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{ |
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MatrixR = matrix.CreateMatrix(matrix.ColumnCount, matrix.ColumnCount); |
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q = matrix.Clone(); |
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Q = matrix.Clone(); |
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for (var i = 0; i < minmn; i++) |
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for (var i = 0; i < minmn; i++) |
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{ |
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{ |
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u[i] = GenerateColumn(Q, i, i); |
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u[i] = GenerateColumn(q, i, i); |
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ComputeQR(u[i], Q, i, matrix.RowCount, i + 1, matrix.ColumnCount, |
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ComputeQR(u[i], q, i, matrix.RowCount, i + 1, matrix.ColumnCount, Control.NumberOfParallelWorkerThreads); |
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Control.NumberOfParallelWorkerThreads); |
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} |
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} |
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MatrixR = Q.SubMatrix(0, matrix.ColumnCount, 0, matrix.ColumnCount); |
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r = q.SubMatrix(0, matrix.ColumnCount, 0, matrix.ColumnCount); |
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Q.Clear(); |
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q.Clear(); |
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for (var i = 0; i < matrix.ColumnCount; i++) |
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for (var i = 0; i < matrix.ColumnCount; i++) |
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{ |
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{ |
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Q.At(i, i, 1.0f); |
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q.At(i, i, 1.0f); |
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} |
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} |
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for (var i = minmn - 1; i >= 0; i--) |
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for (var i = minmn - 1; i >= 0; i--) |
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{ |
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{ |
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ComputeQR(u[i], Q, i, matrix.RowCount, i, matrix.ColumnCount, |
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ComputeQR(u[i], q, i, matrix.RowCount, i, matrix.ColumnCount, Control.NumberOfParallelWorkerThreads); |
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Control.NumberOfParallelWorkerThreads); |
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} |
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} |
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} |
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} |
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return new UserQR(q, r, method); |
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} |
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UserQR(Matrix<Complex32> q, Matrix<Complex32> rFull, QRMethod method) |
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: base(q, rFull, method) |
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{ |
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} |
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} |
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/// <summary>
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/// <summary>
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@ -130,7 +129,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization |
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/// <param name="row">The first row</param>
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/// <param name="row">The first row</param>
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/// <param name="column">Column index</param>
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/// <param name="column">Column index</param>
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/// <returns>Generated vector</returns>
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/// <returns>Generated vector</returns>
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private static Complex32[] GenerateColumn(Matrix<Complex32> a, int row, int column) |
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static Complex32[] GenerateColumn(Matrix<Complex32> a, int row, int column) |
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{ |
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{ |
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var ru = a.RowCount - row; |
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var ru = a.RowCount - row; |
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var u = new Complex32[ru]; |
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var u = new Complex32[ru]; |
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@ -141,19 +140,19 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization |
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a.At(i, column, 0.0f); |
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a.At(i, column, 0.0f); |
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} |
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} |
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var norm = u.Aggregate(Complex32.Zero, (current, t) => current + (t.Magnitude * t.Magnitude)); |
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var norm = u.Aggregate(Complex32.Zero, (current, t) => current + (t.Magnitude*t.Magnitude)); |
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norm = norm.SquareRoot(); |
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norm = norm.SquareRoot(); |
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if (row == a.RowCount - 1 || norm.Magnitude == 0) |
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if (row == a.RowCount - 1 || norm.Magnitude == 0) |
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{ |
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{ |
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a.At(row, column, -u[0]); |
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a.At(row, column, -u[0]); |
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u[0] = (float)Constants.Sqrt2; |
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u[0] = (float) Constants.Sqrt2; |
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return u; |
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return u; |
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} |
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} |
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if (u[0].Magnitude != 0.0f) |
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if (u[0].Magnitude != 0.0f) |
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{ |
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{ |
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norm = norm.Magnitude * (u[0] / u[0].Magnitude); |
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norm = norm.Magnitude*(u[0]/u[0].Magnitude); |
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} |
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} |
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a.At(row, column, -norm); |
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a.At(row, column, -norm); |
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@ -165,10 +164,10 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization |
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u[0] += 1.0f; |
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u[0] += 1.0f; |
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var s = (1.0f / u[0]).SquareRoot(); |
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var s = (1.0f/u[0]).SquareRoot(); |
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for (var i = 0; i < ru; i++) |
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for (var i = 0; i < ru; i++) |
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{ |
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{ |
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u[i] = u[i].Conjugate() * s; |
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u[i] = u[i].Conjugate()*s; |
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} |
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} |
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return u; |
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return u; |
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@ -184,7 +183,7 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization |
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/// <param name="columnStart">The first column</param>
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/// <param name="columnStart">The first column</param>
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/// <param name="columnDim">The last column</param>
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/// <param name="columnDim">The last column</param>
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/// <param name="availableCores">Number of available CPUs</param>
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/// <param name="availableCores">Number of available CPUs</param>
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private static void ComputeQR(Complex32[] u, Matrix<Complex32> a, int rowStart, int rowDim, int columnStart, int columnDim, int availableCores) |
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static void ComputeQR(Complex32[] u, Matrix<Complex32> a, int rowStart, int rowDim, int columnStart, int columnDim, int availableCores) |
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{ |
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{ |
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if (rowDim < rowStart || columnDim < columnStart) |
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if (rowDim < rowStart || columnDim < columnStart) |
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{ |
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{ |
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@ -195,8 +194,8 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization |
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if ((availableCores > 1) && (tmpColCount > 200)) |
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if ((availableCores > 1) && (tmpColCount > 200)) |
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{ |
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{ |
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var tmpSplit = columnStart + (tmpColCount / 2); |
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var tmpSplit = columnStart + (tmpColCount/2); |
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var tmpCores = availableCores / 2; |
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var tmpCores = availableCores/2; |
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CommonParallel.Invoke( |
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CommonParallel.Invoke( |
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() => ComputeQR(u, a, rowStart, rowDim, columnStart, tmpSplit, tmpCores), |
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() => ComputeQR(u, a, rowStart, rowDim, columnStart, tmpSplit, tmpCores), |
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@ -209,12 +208,12 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization |
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var scale = Complex32.Zero; |
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var scale = Complex32.Zero; |
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for (var i = rowStart; i < rowDim; i++) |
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for (var i = rowStart; i < rowDim; i++) |
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{ |
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{ |
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scale += u[i - rowStart] * a.At(i, j); |
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scale += u[i - rowStart]*a.At(i, j); |
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} |
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} |
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for (var i = rowStart; i < rowDim; i++) |
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for (var i = rowStart; i < rowDim; i++) |
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{ |
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{ |
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a.At(i, j, a.At(i, j) - (u[i - rowStart].Conjugate() * scale)); |
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a.At(i, j, a.At(i, j) - (u[i - rowStart].Conjugate()*scale)); |
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} |
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} |
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} |
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} |
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} |
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} |
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@ -227,17 +226,6 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization |
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/// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>X</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<Complex32> input, Matrix<Complex32> result) |
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public override void Solve(Matrix<Complex32> input, Matrix<Complex32> result) |
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{ |
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{ |
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// Check for proper arguments.
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if (input == null) |
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{ |
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throw new ArgumentNullException("input"); |
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} |
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if (result == null) |
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{ |
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throw new ArgumentNullException("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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// 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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if (input.ColumnCount != result.ColumnCount) |
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{ |
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{ |
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@ -245,13 +233,13 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization |
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} |
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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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// 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 (MatrixR.RowCount != input.RowCount) |
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if (FullR.RowCount != input.RowCount) |
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{ |
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{ |
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throw new ArgumentException(Resources.ArgumentMatrixSameRowDimension); |
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throw new ArgumentException(Resources.ArgumentMatrixSameRowDimension); |
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} |
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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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// The solution X row dimension is equal to the column dimension of A
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if (MatrixR.ColumnCount != result.RowCount) |
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if (FullR.ColumnCount != result.RowCount) |
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{ |
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{ |
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throw new ArgumentException(Resources.ArgumentMatrixSameColumnDimension); |
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throw new ArgumentException(Resources.ArgumentMatrixSameColumnDimension); |
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} |
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} |
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@ -259,20 +247,20 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization |
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var inputCopy = input.Clone(); |
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var inputCopy = input.Clone(); |
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// Compute Y = transpose(Q)*B
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// Compute Y = transpose(Q)*B
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var column = new Complex32[MatrixR.RowCount]; |
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var column = new Complex32[FullR.RowCount]; |
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for (var j = 0; j < input.ColumnCount; j++) |
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for (var j = 0; j < input.ColumnCount; j++) |
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{ |
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{ |
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for (var k = 0; k < MatrixR.RowCount; k++) |
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for (var k = 0; k < FullR.RowCount; k++) |
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{ |
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{ |
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column[k] = inputCopy.At(k, j); |
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column[k] = inputCopy.At(k, j); |
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} |
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} |
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for (var i = 0; i < MatrixR.RowCount; i++) |
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for (var i = 0; i < FullR.RowCount; i++) |
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{ |
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{ |
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var s = Complex32.Zero; |
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var s = Complex32.Zero; |
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for (var k = 0; k < MatrixR.RowCount; k++) |
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for (var k = 0; k < FullR.RowCount; k++) |
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{ |
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{ |
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s += Q.At(k, i).Conjugate() * column[k]; |
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s += Q.At(k, i).Conjugate()*column[k]; |
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} |
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} |
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inputCopy.At(i, j, s); |
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inputCopy.At(i, j, s); |
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@ -280,23 +268,23 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization |
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} |
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} |
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// Solve R*X = Y;
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// Solve R*X = Y;
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for (var k = MatrixR.ColumnCount - 1; k >= 0; k--) |
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for (var k = FullR.ColumnCount - 1; k >= 0; k--) |
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{ |
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{ |
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for (var j = 0; j < input.ColumnCount; j++) |
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for (var j = 0; j < input.ColumnCount; j++) |
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{ |
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{ |
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inputCopy.At(k, j, inputCopy.At(k, j) / MatrixR.At(k, k)); |
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inputCopy.At(k, j, inputCopy.At(k, j)/FullR.At(k, k)); |
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} |
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} |
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for (var i = 0; i < k; i++) |
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for (var i = 0; i < k; i++) |
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{ |
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{ |
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for (var j = 0; j < input.ColumnCount; j++) |
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for (var j = 0; j < input.ColumnCount; j++) |
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{ |
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{ |
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inputCopy.At(i, j, inputCopy.At(i, j) - (inputCopy.At(k, j) * MatrixR.At(i, k))); |
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inputCopy.At(i, j, inputCopy.At(i, j) - (inputCopy.At(k, j)*FullR.At(i, k))); |
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} |
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} |
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} |
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} |
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} |
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} |
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for (var i = 0; i < MatrixR.ColumnCount; i++) |
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for (var i = 0; i < FullR.ColumnCount; i++) |
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{ |
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{ |
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for (var j = 0; j < inputCopy.ColumnCount; j++) |
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for (var j = 0; j < inputCopy.ColumnCount; j++) |
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{ |
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{ |
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@ -312,60 +300,50 @@ namespace MathNet.Numerics.LinearAlgebra.Complex32.Factorization |
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/// <param name="result">The left hand side <see cref="Matrix{T}"/>, <b>x</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<Complex32> input, Vector<Complex32> result) |
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public override void Solve(Vector<Complex32> input, Vector<Complex32> result) |
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{ |
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{ |
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if (input == null) |
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{ |
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throw new ArgumentNullException("input"); |
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} |
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if (result == null) |
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{ |
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throw new ArgumentNullException("result"); |
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} |
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// Ax=b where A is an m x n matrix
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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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// Check that b is a column vector with m entries
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if (MatrixR.RowCount != input.Count) |
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if (FullR.RowCount != input.Count) |
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{ |
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{ |
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throw new ArgumentException(Resources.ArgumentVectorsSameLength); |
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throw new ArgumentException(Resources.ArgumentVectorsSameLength); |
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} |
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} |
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// Check that x is a column vector with n entries
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// Check that x is a column vector with n entries
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if (MatrixR.ColumnCount != result.Count) |
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if (FullR.ColumnCount != result.Count) |
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{ |
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{ |
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throw Matrix.DimensionsDontMatch<ArgumentException>(MatrixR, result); |
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throw Matrix.DimensionsDontMatch<ArgumentException>(FullR, result); |
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} |
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} |
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var inputCopy = input.Clone(); |
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var inputCopy = input.Clone(); |
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// Compute Y = transpose(Q)*B
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// Compute Y = transpose(Q)*B
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var column = new Complex32[MatrixR.RowCount]; |
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var column = new Complex32[FullR.RowCount]; |
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for (var k = 0; k < MatrixR.RowCount; k++) |
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for (var k = 0; k < FullR.RowCount; k++) |
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{ |
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{ |
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column[k] = inputCopy[k]; |
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column[k] = inputCopy[k]; |
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} |
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} |
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for (var i = 0; i < MatrixR.RowCount; i++) |
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for (var i = 0; i < FullR.RowCount; i++) |
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{ |
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{ |
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var s = Complex32.Zero; |
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var s = Complex32.Zero; |
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for (var k = 0; k < MatrixR.RowCount; k++) |
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for (var k = 0; k < FullR.RowCount; k++) |
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{ |
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{ |
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s += Q.At(k, i).Conjugate() * column[k]; |
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s += Q.At(k, i).Conjugate()*column[k]; |
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} |
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} |
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inputCopy[i] = s; |
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inputCopy[i] = s; |
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} |
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} |
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// Solve R*X = Y;
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// Solve R*X = Y;
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for (var k = MatrixR.ColumnCount - 1; k >= 0; k--) |
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for (var k = FullR.ColumnCount - 1; k >= 0; k--) |
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{ |
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{ |
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inputCopy[k] /= MatrixR.At(k, k); |
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inputCopy[k] /= FullR.At(k, k); |
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for (var i = 0; i < k; i++) |
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for (var i = 0; i < k; i++) |
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{ |
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{ |
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inputCopy[i] -= inputCopy[k] * MatrixR.At(i, k); |
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inputCopy[i] -= inputCopy[k]*FullR.At(i, k); |
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} |
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} |
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} |
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} |
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for (var i = 0; i < MatrixR.ColumnCount; i++) |
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for (var i = 0; i < FullR.ColumnCount; i++) |
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{ |
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|
{ |
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result[i] = inputCopy[i]; |
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result[i] = inputCopy[i]; |
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} |
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} |
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Christoph Ruegg
13 years ago