// <copyright file="NudaLinearAlgebraProvider.Complex.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) 2009-2015 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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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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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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#if NATIVE
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using System;
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using System.Security;
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using IStation.Numerics.Providers.Common.Cuda;
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using Complex = System.Numerics.Complex;
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namespace IStation.Numerics.Providers.LinearAlgebra.Cuda
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{
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/// <summary>
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/// NVidia's CUDA Toolkit linear algebra provider.
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/// </summary>
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internal partial class CudaLinearAlgebraProvider
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{
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/// <summary>
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/// Computes the dot product of x and y.
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/// </summary>
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/// <param name="x">The vector x.</param>
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/// <param name="y">The vector y.</param>
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/// <returns>The dot product of x and y.</returns>
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/// <remarks>This is equivalent to the DOT BLAS routine.</remarks>
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[SecuritySafeCritical]
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public override Complex DotProduct(Complex[] x, Complex[] y)
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{
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if (y == null)
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{
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throw new ArgumentNullException(nameof(y));
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}
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if (x == null)
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{
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throw new ArgumentNullException(nameof(x));
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}
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if (x.Length != y.Length)
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{
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throw new ArgumentException("The array arguments must have the same length.");
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}
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return SafeNativeMethods.z_dot_product(_blasHandle, x.Length, x, y);
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}
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/// <summary>
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/// Adds a scaled vector to another: <c>result = y + alpha*x</c>.
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/// </summary>
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/// <param name="y">The vector to update.</param>
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/// <param name="alpha">The value to scale <paramref name="x"/> by.</param>
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/// <param name="x">The vector to add to <paramref name="y"/>.</param>
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/// <param name="result">The result of the addition.</param>
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/// <remarks>This is similar to the AXPY BLAS routine.</remarks>
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[SecuritySafeCritical]
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public override void AddVectorToScaledVector(Complex[] y, Complex alpha, Complex[] x, Complex[] result)
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{
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if (y == null)
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{
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throw new ArgumentNullException(nameof(y));
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}
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if (x == null)
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{
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throw new ArgumentNullException(nameof(x));
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}
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if (y.Length != x.Length)
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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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if (!ReferenceEquals(y, result))
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{
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Array.Copy(y, 0, result, 0, y.Length);
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}
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if (alpha == Complex.Zero)
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{
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return;
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}
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SafeNativeMethods.z_axpy(_blasHandle, y.Length, alpha, x, result);
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}
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/// <summary>
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/// Scales an array. Can be used to scale a vector and a matrix.
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/// </summary>
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/// <param name="alpha">The scalar.</param>
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/// <param name="x">The values to scale.</param>
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/// <param name="result">This result of the scaling.</param>
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/// <remarks>This is similar to the SCAL BLAS routine.</remarks>
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[SecuritySafeCritical]
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public override void ScaleArray(Complex alpha, Complex[] x, Complex[] result)
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{
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if (x == null)
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{
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throw new ArgumentNullException(nameof(x));
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}
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if (!ReferenceEquals(x, result))
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{
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Array.Copy(x, 0, result, 0, x.Length);
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}
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if (alpha == Complex.One)
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{
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return;
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}
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SafeNativeMethods.z_scale(_blasHandle, x.Length, alpha, result);
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}
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/// <summary>
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/// Multiples two matrices. <c>result = x * y</c>
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/// </summary>
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/// <param name="x">The x matrix.</param>
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/// <param name="rowsX">The number of rows in the x matrix.</param>
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/// <param name="columnsX">The number of columns in the x matrix.</param>
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/// <param name="y">The y matrix.</param>
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/// <param name="rowsY">The number of rows in the y matrix.</param>
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/// <param name="columnsY">The number of columns in the y matrix.</param>
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/// <param name="result">Where to store the result of the multiplication.</param>
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/// <remarks>This is a simplified version of the BLAS GEMM routine with alpha
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/// set to Complex.One and beta set to Complex.Zero, and x and y are not transposed.</remarks>
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public override void MatrixMultiply(Complex[] x, int rowsX, int columnsX, Complex[] y, int rowsY, int columnsY, Complex[] result)
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{
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MatrixMultiplyWithUpdate(Transpose.DontTranspose, Transpose.DontTranspose, Complex.One, x, rowsX, columnsX, y, rowsY, columnsY, Complex.Zero, result);
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}
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/// <summary>
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/// Multiplies two matrices and updates another with the result. <c>c = alpha*op(a)*op(b) + beta*c</c>
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/// </summary>
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/// <param name="transposeA">How to transpose the <paramref name="a"/> matrix.</param>
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/// <param name="transposeB">How to transpose the <paramref name="b"/> matrix.</param>
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/// <param name="alpha">The value to scale <paramref name="a"/> matrix.</param>
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/// <param name="a">The a matrix.</param>
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/// <param name="rowsA">The number of rows in the <paramref name="a"/> matrix.</param>
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/// <param name="columnsA">The number of columns in the <paramref name="a"/> matrix.</param>
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/// <param name="b">The b matrix</param>
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/// <param name="rowsB">The number of rows in the <paramref name="b"/> matrix.</param>
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/// <param name="columnsB">The number of columns in the <paramref name="b"/> matrix.</param>
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/// <param name="beta">The value to scale the <paramref name="c"/> matrix.</param>
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/// <param name="c">The c matrix.</param>
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[SecuritySafeCritical]
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public override void MatrixMultiplyWithUpdate(Transpose transposeA, Transpose transposeB, Complex alpha, Complex[] a, int rowsA, int columnsA, Complex[] b, int rowsB, int columnsB, Complex beta, Complex[] c)
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{
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if (a == null)
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{
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throw new ArgumentNullException(nameof(a));
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}
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if (b == null)
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{
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throw new ArgumentNullException(nameof(b));
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}
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if (c == null)
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{
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throw new ArgumentNullException(nameof(c));
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}
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var m = transposeA == Transpose.DontTranspose ? rowsA : columnsA;
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var n = transposeB == Transpose.DontTranspose ? columnsB : rowsB;
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var k = transposeA == Transpose.DontTranspose ? columnsA : rowsA;
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var l = transposeB == Transpose.DontTranspose ? rowsB : columnsB;
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if (c.Length != m*n)
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{
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throw new ArgumentException("Matrix dimensions must agree.");
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}
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if (k != l)
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{
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throw new ArgumentException("Matrix dimensions must agree.");
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}
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SafeNativeMethods.z_matrix_multiply(_blasHandle, transposeA.ToCUDA(), transposeB.ToCUDA(), m, n, k, alpha, a, b, beta, c);
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}
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/// <summary>
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/// Computes the LUP factorization of A. P*A = L*U.
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/// </summary>
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/// <param name="data">An <paramref name="order"/> by <paramref name="order"/> matrix. The matrix is overwritten with the
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/// the LU factorization on exit. The lower triangular factor L is stored in under the diagonal of <paramref name="data"/> (the diagonal is always Complex.One
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/// for the L factor). The upper triangular factor U is stored on and above the diagonal of <paramref name="data"/>.</param>
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/// <param name="order">The order of the square matrix <paramref name="data"/>.</param>
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/// <param name="ipiv">On exit, it contains the pivot indices. The size of the array must be <paramref name="order"/>.</param>
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/// <remarks>This is equivalent to the GETRF LAPACK routine.</remarks>
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[SecuritySafeCritical]
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public override void LUFactor(Complex[] data, int order, int[] ipiv)
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{
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if (data == null)
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{
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throw new ArgumentNullException(nameof(data));
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}
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if (ipiv == null)
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{
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throw new ArgumentNullException(nameof(ipiv));
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}
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if (data.Length != order*order)
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(data));
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}
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if (ipiv.Length != order)
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(ipiv));
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}
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Solver(SafeNativeMethods.z_lu_factor(_solverHandle, order, data, ipiv));
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}
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/// <summary>
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/// Computes the inverse of matrix using LU factorization.
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/// </summary>
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/// <param name="a">The N by N matrix to invert. Contains the inverse On exit.</param>
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/// <param name="order">The order of the square matrix <paramref name="a"/>.</param>
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/// <remarks>This is equivalent to the GETRF and GETRI LAPACK routines.</remarks>
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[SecuritySafeCritical]
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public override void LUInverse(Complex[] a, int order)
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{
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if (a == null)
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{
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throw new ArgumentNullException(nameof(a));
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}
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if (a.Length != order*order)
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(a));
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}
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Solver(SafeNativeMethods.z_lu_inverse(_solverHandle, _blasHandle, order, a));
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}
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/// <summary>
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/// Computes the inverse of a previously factored matrix.
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/// </summary>
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/// <param name="a">The LU factored N by N matrix. Contains the inverse On exit.</param>
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/// <param name="order">The order of the square matrix <paramref name="a"/>.</param>
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/// <param name="ipiv">The pivot indices of <paramref name="a"/>.</param>
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/// <remarks>This is equivalent to the GETRI LAPACK routine.</remarks>
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[SecuritySafeCritical]
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public override void LUInverseFactored(Complex[] a, int order, int[] ipiv)
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{
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if (a == null)
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{
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throw new ArgumentNullException(nameof(a));
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}
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if (ipiv == null)
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{
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throw new ArgumentNullException(nameof(ipiv));
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}
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if (a.Length != order*order)
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(a));
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}
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if (ipiv.Length != order)
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(ipiv));
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}
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BLAS(SafeNativeMethods.z_lu_inverse_factored(_blasHandle, order, a, ipiv));
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}
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/// <summary>
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/// Solves A*X=B for X using LU factorization.
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/// </summary>
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/// <param name="columnsOfB">The number of columns of B.</param>
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/// <param name="a">The square matrix A.</param>
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/// <param name="order">The order of the square matrix <paramref name="a"/>.</param>
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/// <param name="b">On entry the B matrix; on exit the X matrix.</param>
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/// <remarks>This is equivalent to the GETRF and GETRS LAPACK routines.</remarks>
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[SecuritySafeCritical]
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public override void LUSolve(int columnsOfB, Complex[] a, int order, Complex[] b)
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{
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if (a == null)
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{
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throw new ArgumentNullException(nameof(a));
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}
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if (a.Length != order*order)
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(a));
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}
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if (b.Length != columnsOfB*order)
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(b));
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}
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if (ReferenceEquals(a, b))
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{
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throw new ArgumentException("Arguments must be different objects.");
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}
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Solver(SafeNativeMethods.z_lu_solve(_solverHandle, order, columnsOfB, a, b));
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}
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/// <summary>
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/// Solves A*X=B for X using a previously factored A matrix.
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/// </summary>
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/// <param name="columnsOfB">The number of columns of B.</param>
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/// <param name="a">The factored A matrix.</param>
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/// <param name="order">The order of the square matrix <paramref name="a"/>.</param>
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/// <param name="ipiv">The pivot indices of <paramref name="a"/>.</param>
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/// <param name="b">On entry the B matrix; on exit the X matrix.</param>
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/// <remarks>This is equivalent to the GETRS LAPACK routine.</remarks>
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[SecuritySafeCritical]
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public override void LUSolveFactored(int columnsOfB, Complex[] a, int order, int[] ipiv, Complex[] b)
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{
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if (a == null)
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{
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throw new ArgumentNullException(nameof(a));
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}
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if (ipiv == null)
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{
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throw new ArgumentNullException(nameof(ipiv));
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}
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if (a.Length != order*order)
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(a));
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}
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if (ipiv.Length != order)
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(ipiv));
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}
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if (b.Length != columnsOfB*order)
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(b));
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}
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if (ReferenceEquals(a, b))
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{
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throw new ArgumentException("Arguments must be different objects.");
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}
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Solver(SafeNativeMethods.z_lu_solve_factored(_solverHandle, order, columnsOfB, a, ipiv, b));
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}
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/// <summary>
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/// Computes the Cholesky factorization of A.
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/// </summary>
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/// <param name="a">On entry, a square, positive definite matrix. On exit, the matrix is overwritten with the
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/// the Cholesky factorization.</param>
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/// <param name="order">The number of rows or columns in the matrix.</param>
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/// <remarks>This is equivalent to the POTRF LAPACK routine.</remarks>
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[SecuritySafeCritical]
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public override void CholeskyFactor(Complex[] a, int order)
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{
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if (a == null)
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{
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throw new ArgumentNullException(nameof(a));
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}
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if (order < 1)
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{
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throw new ArgumentException("Value must be positive.", nameof(order));
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}
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if (a.Length != order*order)
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(a));
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}
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Solver(SafeNativeMethods.z_cholesky_factor(_solverHandle, order, a));
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}
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/// <summary>
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/// Solves A*X=B for X using Cholesky factorization.
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/// </summary>
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/// <param name="a">The square, positive definite matrix A.</param>
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/// <param name="orderA">The number of rows and columns in A.</param>
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/// <param name="b">On entry the B matrix; on exit the X matrix.</param>
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/// <param name="columnsB">The number of columns in the B matrix.</param>
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/// <remarks>This is equivalent to the POTRF add POTRS LAPACK routines.
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/// </remarks>
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[SecuritySafeCritical]
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public override void CholeskySolve(Complex[] a, int orderA, Complex[] b, int columnsB)
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{
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if (a == null)
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{
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throw new ArgumentNullException(nameof(a));
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}
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if (b == null)
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{
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throw new ArgumentNullException(nameof(b));
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}
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if (b.Length != orderA*columnsB)
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(b));
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}
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if (ReferenceEquals(a, b))
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{
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throw new ArgumentException("Arguments must be different objects.");
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}
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Solver(SafeNativeMethods.z_cholesky_solve(_solverHandle, orderA, columnsB, a, b));
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}
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/// <summary>
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/// Solves A*X=B for X using a previously factored A matrix.
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/// </summary>
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/// <param name="a">The square, positive definite matrix A.</param>
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/// <param name="orderA">The number of rows and columns in A.</param>
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/// <param name="b">On entry the B matrix; on exit the X matrix.</param>
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/// <param name="columnsB">The number of columns in the B matrix.</param>
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/// <remarks>This is equivalent to the POTRS LAPACK routine.</remarks>
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[SecuritySafeCritical]
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public override void CholeskySolveFactored(Complex[] a, int orderA, Complex[] b, int columnsB)
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{
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if (a == null)
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{
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throw new ArgumentNullException(nameof(a));
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}
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if (b == null)
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{
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throw new ArgumentNullException(nameof(b));
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}
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if (b.Length != orderA*columnsB)
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(b));
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}
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if (ReferenceEquals(a, b))
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{
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throw new ArgumentException("Arguments must be different objects.");
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}
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Solver(SafeNativeMethods.z_cholesky_solve_factored(_solverHandle, orderA, columnsB, a, b));
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}
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/// <summary>
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/// Solves A*X=B for X using the singular value decomposition of A.
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/// </summary>
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/// <param name="a">On entry, the M by N matrix to decompose.</param>
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/// <param name="rowsA">The number of rows in the A matrix.</param>
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/// <param name="columnsA">The number of columns in the A matrix.</param>
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/// <param name="b">The B matrix.</param>
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/// <param name="columnsB">The number of columns of B.</param>
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/// <param name="x">On exit, the solution matrix.</param>
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public override void SvdSolve(Complex[] a, int rowsA, int columnsA, Complex[] b, int columnsB, Complex[] x)
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{
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if (a == null)
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{
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throw new ArgumentNullException(nameof(a));
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}
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if (b == null)
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{
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throw new ArgumentNullException(nameof(b));
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}
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if (x == null)
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{
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throw new ArgumentNullException(nameof(x));
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}
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if (b.Length != rowsA*columnsB)
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(b));
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}
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if (x.Length != columnsA*columnsB)
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(b));
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}
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var s = new Complex[Math.Min(rowsA, columnsA)];
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var u = new Complex[rowsA*rowsA];
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var vt = new Complex[columnsA*columnsA];
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var clone = new Complex[a.Length];
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a.Copy(clone);
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SingularValueDecomposition(true, clone, rowsA, columnsA, s, u, vt);
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SvdSolveFactored(rowsA, columnsA, s, u, vt, b, columnsB, x);
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}
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/// <summary>
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/// Computes the singular value decomposition of A.
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/// </summary>
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/// <param name="computeVectors">Compute the singular U and VT vectors or not.</param>
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/// <param name="a">On entry, the M by N matrix to decompose. On exit, A may be overwritten.</param>
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/// <param name="rowsA">The number of rows in the A matrix.</param>
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/// <param name="columnsA">The number of columns in the A matrix.</param>
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/// <param name="s">The singular values of A in ascending value.</param>
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/// <param name="u">If <paramref name="computeVectors"/> is <c>true</c>, on exit U contains the left
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/// singular vectors.</param>
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/// <param name="vt">If <paramref name="computeVectors"/> is <c>true</c>, on exit VT contains the transposed
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/// right singular vectors.</param>
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/// <remarks>This is equivalent to the GESVD LAPACK routine.</remarks>
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[SecuritySafeCritical]
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public override void SingularValueDecomposition(bool computeVectors, Complex[] a, int rowsA, int columnsA, Complex[] s, Complex[] u, Complex[] vt)
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{
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if (a == null)
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{
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throw new ArgumentNullException(nameof(a));
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}
|
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if (s == null)
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{
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throw new ArgumentNullException(nameof(s));
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}
|
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if (u == null)
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{
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throw new ArgumentNullException(nameof(u));
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}
|
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if (vt == null)
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{
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throw new ArgumentNullException(nameof(vt));
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}
|
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if (u.Length != rowsA*rowsA)
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(u));
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}
|
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if (vt.Length != columnsA*columnsA)
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(vt));
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}
|
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if (s.Length != Math.Min(rowsA, columnsA))
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{
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throw new ArgumentException("The array arguments must have the same length.", nameof(s));
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}
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if (columnsA > rowsA || !computeVectors) // see remarks http://docs.nvidia.com/cuda/cusolver/index.html#cuds-lt-t-gt-gesvd
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base.SingularValueDecomposition(computeVectors, a, rowsA, columnsA, s, u, vt);
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else Solver(SafeNativeMethods.z_svd_factor(_solverHandle, computeVectors, rowsA, columnsA, a, s, u, vt));
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}
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}
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}
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#endif
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