[9102] | 1 | ///
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| 2 | /// This file is part of ILNumerics Community Edition.
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| 3 | ///
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| 4 | /// ILNumerics Community Edition - high performance computing for applications.
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| 5 | /// Copyright (C) 2006 - 2012 Haymo Kutschbach, http://ilnumerics.net
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| 6 | ///
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| 7 | /// ILNumerics Community Edition is free software: you can redistribute it and/or modify
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| 8 | /// it under the terms of the GNU General Public License version 3 as published by
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| 9 | /// the Free Software Foundation.
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| 10 | ///
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| 11 | /// ILNumerics Community Edition is distributed in the hope that it will be useful,
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| 12 | /// but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 13 | /// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 14 | /// GNU General Public License for more details.
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| 15 | ///
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| 16 | /// You should have received a copy of the GNU General Public License
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| 17 | /// along with ILNumerics Community Edition. See the file License.txt in the root
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| 18 | /// of your distribution package. If not, see <http://www.gnu.org/licenses/>.
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| 19 | ///
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| 20 | /// In addition this software uses the following components and/or licenses:
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| 21 | ///
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| 22 | /// =================================================================================
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| 23 | /// The Open Toolkit Library License
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| 24 | ///
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| 25 | /// Copyright (c) 2006 - 2009 the Open Toolkit library.
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| 26 | ///
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| 27 | /// Permission is hereby granted, free of charge, to any person obtaining a copy
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| 28 | /// of this software and associated documentation files (the "Software"), to deal
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| 29 | /// in the Software without restriction, including without limitation the rights to
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| 30 | /// use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
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| 31 | /// the Software, and to permit persons to whom the Software is furnished to do
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| 32 | /// so, subject to the following conditions:
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| 33 | ///
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| 34 | /// The above copyright notice and this permission notice shall be included in all
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| 35 | /// copies or substantial portions of the Software.
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| 36 | ///
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| 37 | /// =================================================================================
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| 38 | ///
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| 39 |
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| 40 | #pragma warning disable 1591
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| 41 |
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| 42 | using System;
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| 43 | using System.Collections.Generic;
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| 44 | using System.Text;
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| 45 |
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| 46 | namespace ILNumerics.Native {
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| 47 | /// <summary>
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| 48 | /// Interface to all LAPACK/BLAS functions available
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| 49 | /// </summary>
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| 50 | /// <remarks>Each native module must implement this interface explicitly. Calls
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| 51 | /// to native functions are made virtual by calling functions of this interface.
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| 52 | /// Therefore the user can transparently call any function regardless of the
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| 53 | /// plattform the assymbly (currently) runs on. The native modules implementing
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| 54 | /// this interface take care of the details of implementation.
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| 55 | /// <para>Usually users of the library will not have to handle with this interface.
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| 56 | /// Its functions will be used from inside built in functions and are therefore wrapped
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| 57 | /// (mainly from inside <see cref="ILNumerics.ILMath">ILNumerics.ILMath</see>).</para>
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| 58 | /// <para>Every LAPACK/BLAS function is explicitly implemented for any type supported.
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| 59 | /// e.g. IILLapack includes four functions doing general matrix multiply: dgemm, zgemm, cgemm and sgemm -
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| 60 | /// for all four floating point datatypes supported from the LAPACK package.</para>
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| 61 | /// <para>LAPACK is an open source linear algebra functions package optimized for
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| 62 | /// use together with highly natively optimized BLAS functions. A LAPACK guide is
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| 63 | /// available in the internet: <see href="http://www.netlib.org/lapack">www.netlib.org</see>.</para>
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| 64 | /// </remarks>
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| 65 | [System.Security.SuppressUnmanagedCodeSecurity]
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| 66 | public interface IILLapack {
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| 67 |
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| 68 | #region ?GEMM
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| 69 |
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| 70 | /// <summary>
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| 71 | /// Wrapper implementiation for ATLAS GeneralMatrixMultiply
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| 72 | /// </summary>
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| 73 | /// <param name="TransA">Transposition state for matrix A: one of the constants in enum CBlas_Transpose</param>
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| 74 | /// <param name="TransB">Transposition state for matrix B: one of the constants in enum CBlas_Transpose</param>
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| 75 | /// <param name="M">Number of rows in A</param>
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| 76 | /// <param name="N">Number of columns in B</param>
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| 77 | /// <param name="K">Number of columns in A and number of rows in B</param>
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| 78 | /// <param name="alpha">multiplicationi factor for A</param>
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| 79 | /// <param name="A">pointer to array A</param>
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| 80 | /// <param name="lda">distance between first elements of each column for column based orientation or
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| 81 | /// distance between first elements of each row for row based orientation for matrix A</param>
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| 82 | /// <param name="B">pointer to array B</param>
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| 83 | /// <param name="ldb">distance between first elements of each column for column based orientation or
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| 84 | /// distance between first elements of each row for row based orientation for matrix B</param>
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| 85 | /// <param name="beta">multiplication faktor for matrix B</param>
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| 86 | /// <param name="C">pointer to predefined array C of neccessary length</param>
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| 87 | /// <param name="ldc">distance between first elements of each column for column based orientation or
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| 88 | /// distance between first elements of each row for row based orientation for matrix C</param>
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| 89 | /// <remarks>All parameters except C are readonly. Only elements of matrix C will be altered. C must be a predefined
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| 90 | /// continous array of size MxN</remarks>
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| 91 | void dgemm (char TransA, char TransB, int M, int N, int K,
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| 92 | double alpha, IntPtr A, int lda,
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| 93 | IntPtr B, int ldb,
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| 94 | double beta, double [] C, int ldc);
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| 95 |
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| 96 | /// <summary>
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| 97 | /// Wrapper implementiation for ATLAS GeneralMatrixMultiply
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| 98 | /// </summary>
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| 99 | /// <param name="TransA">Transposition state for matrix A: one of the constants in enum CBlas_Transpose</param>
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| 100 | /// <param name="TransB">Transposition state for matrix B: one of the constants in enum CBlas_Transpose</param>
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| 101 | /// <param name="M">Number of rows in A</param>
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| 102 | /// <param name="N">Number of columns in B</param>
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| 103 | /// <param name="K">Number of columns in A and number of rows in B</param>
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| 104 | /// <param name="alpha">multiplicationi factor for A</param>
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| 105 | /// <param name="A">pointer to array A</param>
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| 106 | /// <param name="lda">distance between first elements of each column for column based orientation or
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| 107 | /// distance between first elements of each row for row based orientation for matrix A</param>
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| 108 | /// <param name="B">pointer to array B</param>
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| 109 | /// <param name="ldb">distance between first elements of each column for column based orientation or
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| 110 | /// distance between first elements of each row for row based orientation for matrix B</param>
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| 111 | /// <param name="beta">multiplication faktor for matrix B</param>
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| 112 | /// <param name="C">pointer to predefined array C of neccessary length</param>
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| 113 | /// <param name="ldc">distance between first elements of each column for column based orientation or
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| 114 | /// distance between first elements of each row for row based orientation for matrix C</param>
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| 115 | /// <remarks>All parameters except C are readonly. Only elements of matrix C will be altered. C must be a predefined
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| 116 | /// continous array of size MxN</remarks>
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| 117 | void sgemm (char TransA, char TransB, int M, int N, int K,
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| 118 | float alpha, IntPtr A, int lda,
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| 119 | IntPtr B, int ldb,
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| 120 | float beta, float [] C, int ldc);
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| 121 |
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| 122 |
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| 123 | /// <summary>
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| 124 | /// Wrapper implementiation for ATLAS GeneralMatrixMultiply
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| 125 | /// </summary>
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| 126 | /// <param name="TransA">Transposition state for matrix A: one of the constants in enum CBlas_Transpose</param>
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| 127 | /// <param name="TransB">Transposition state for matrix B: one of the constants in enum CBlas_Transpose</param>
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| 128 | /// <param name="M">Number of rows in A</param>
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| 129 | /// <param name="N">Number of columns in B</param>
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| 130 | /// <param name="K">Number of columns in A and number of rows in B</param>
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| 131 | /// <param name="alpha">multiplicationi factor for A</param>
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| 132 | /// <param name="A">pointer to array A</param>
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| 133 | /// <param name="lda">distance between first elements of each column for column based orientation or
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| 134 | /// distance between first elements of each row for row based orientation for matrix A</param>
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| 135 | /// <param name="B">pointer to array B</param>
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| 136 | /// <param name="ldb">distance between first elements of each column for column based orientation or
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| 137 | /// distance between first elements of each row for row based orientation for matrix B</param>
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| 138 | /// <param name="beta">multiplication faktor for matrix B</param>
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| 139 | /// <param name="C">pointer to predefined array C of neccessary length</param>
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| 140 | /// <param name="ldc">distance between first elements of each column for column based orientation or
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| 141 | /// distance between first elements of each row for row based orientation for matrix C</param>
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| 142 | /// <remarks>All parameters except C are readonly. Only elements of matrix C will be altered. C must be a predefined
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| 143 | /// continous array of size MxN</remarks>
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| 144 | void cgemm (char TransA, char TransB, int M, int N, int K,
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| 145 | fcomplex alpha, IntPtr A, int lda,
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| 146 | IntPtr B, int ldb,
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| 147 | fcomplex beta, fcomplex [] C, int ldc);
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| 148 |
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| 149 |
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| 150 | /// <summary>
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| 151 | /// Wrapper implementiation for ATLAS GeneralMatrixMultiply
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| 152 | /// </summary>
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| 153 | /// <param name="TransA">Transposition state for matrix A: one of the constants in enum CBlas_Transpose</param>
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| 154 | /// <param name="TransB">Transposition state for matrix B: one of the constants in enum CBlas_Transpose</param>
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| 155 | /// <param name="M">Number of rows in A</param>
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| 156 | /// <param name="N">Number of columns in B</param>
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| 157 | /// <param name="K">Number of columns in A and number of rows in B</param>
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| 158 | /// <param name="alpha">multiplicationi factor for A</param>
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| 159 | /// <param name="A">pointer to array A</param>
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| 160 | /// <param name="lda">distance between first elements of each column for column based orientation or
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| 161 | /// distance between first elements of each row for row based orientation for matrix A</param>
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| 162 | /// <param name="B">pointer to array B</param>
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| 163 | /// <param name="ldb">distance between first elements of each column for column based orientation or
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| 164 | /// distance between first elements of each row for row based orientation for matrix B</param>
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| 165 | /// <param name="beta">multiplication faktor for matrix B</param>
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| 166 | /// <param name="C">pointer to predefined array C of neccessary length</param>
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| 167 | /// <param name="ldc">distance between first elements of each column for column based orientation or
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| 168 | /// distance between first elements of each row for row based orientation for matrix C</param>
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| 169 | /// <remarks>All parameters except C are readonly. Only elements of matrix C will be altered. C must be a predefined
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| 170 | /// continous array of size MxN</remarks>
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| 171 | void zgemm (char TransA, char TransB, int M, int N, int K,
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| 172 | complex alpha, IntPtr A, int lda,
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| 173 | IntPtr B, int ldb,
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| 174 | complex beta, complex [] C, int ldc);
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| 175 |
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| 176 | #endregion
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| 177 |
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| 178 | #region ?GESDD
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| 179 | /// <summary>
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| 180 | /// singular value decomposition, new version, more memory needed
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| 181 | /// </summary>
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| 182 | /// <param name="jobz">Specifies options for computing all or part of the matrix U
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| 183 | /// <list type="table">
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| 184 | /// <listheader>
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| 185 | /// <term>jobz value</term>
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| 186 | /// <description>... will result in:</description>
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| 187 | /// </listheader>
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| 188 | /// <item>
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| 189 | /// <term>A</term>
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| 190 | /// <description>all M columns of U and all N rows of V**T are
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| 191 | /// returned in the arrays U and VT</description>
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| 192 | /// </item>
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| 193 | /// <item> <term>S</term>
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| 194 | /// <description>the first min(M,N) columns of U and the first
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| 195 | /// min(M,N) rows of V**T are returned in the arrays U
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| 196 | /// and VT</description>
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| 197 | /// </item>
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| 198 | /// <item> <term>O</term>
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| 199 | /// <description>If M >= N, the first N columns of U are overwritten
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| 200 | /// on the array A and all rows of V**T are returned in
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| 201 | /// the array VT,
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| 202 | /// otherwise, all columns of U are returned in the
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| 203 | /// array U and the first M rows of V**T are overwritten
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| 204 | /// in the array VT</description>
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| 205 | /// </item>
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| 206 | /// <item> <term>N</term>
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| 207 | /// <description>no columns of U or rows of V**T are computed.</description>
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| 208 | /// </item>
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| 209 | /// </list>
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| 210 | /// </param>
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| 211 | /// <param name="m">The number of rows of the input matrix A. M greater or equal to 0.</param>
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| 212 | /// <param name="n">The number of columns of the input matrix A. N greater or equal to 0</param>
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| 213 | /// <param name="a">On entry, the M-by-N matrix A.
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| 214 | /// On exit, <list><item>
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| 215 | /// if JOBZ = 'O', A is overwritten with the first N columns
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| 216 | /// of U (the left singular vectors, stored
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| 217 | /// columnwise) if M >= N;
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| 218 | /// A is overwritten with the first M rows
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| 219 | /// of V**T (the right singular vectors, stored
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| 220 | /// rowwise) otherwise.</item>
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| 221 | /// <item>if JOBZ .ne. 'O', the contents of A are destroyed.</item></list></param>
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| 222 | /// <param name="lda">The leading dimension of the array A. LDA ge max(1,M).</param>
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| 223 | /// <param name="s">array, dimension (min(M,N)). The singular values of A, sorted so that S(i) ge S(i+1)</param>
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| 224 | /// <param name="u">array, dimension (LDU,UCOL)
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| 225 | /// UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
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| 226 | /// UCOL = min(M,N) if JOBZ = 'S'.
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| 227 | /// If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
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| 228 | /// orthogonal matrix U;
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| 229 | /// if JOBZ = 'S', U contains the first min(M,N) columns of U
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| 230 | /// (the left singular vectors, stored columnwise);
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| 231 | /// if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.</param>
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| 232 | /// <param name="ldu">The leading dimension of the array U. LDU >= 1; if
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| 233 | /// JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M</param>
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| 234 | /// <param name="vt">array, dimension (LDVT,N). If JOBZ = 'A' or JOBZ = 'O' and
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| 235 | /// M >= N, VT contains the N-by-N orthogonal matrix V**T; if JOBZ = 'S',
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| 236 | /// VT contains the first min(M,N) rows of V**T
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| 237 | /// (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N,
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| 238 | /// or JOBZ = 'N', VT is not referenced</param>
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| 239 | /// <param name="ldvt">The leading dimension of the array VT. LDVT > = 1;
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| 240 | /// if JOBZ = 'A' or JOBZ = 'O' and M > = N, LDVT >= N;
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| 241 | /// if JOBZ = 'S', LDVT > min(M,N).</param>
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| 242 | /// <param name="info">
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| 243 | /// <list>
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| 244 | /// <item> 0: successful exit.</item>
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| 245 | /// <item> <![CDATA[< 0]]> : if INFO = -i, the i-th argument had an illegal value.</item>
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| 246 | /// <item> <![CDATA[> 0]]> : ?BGSDD did not converge, updating process failed.</item>
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| 247 | /// </list>
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| 248 | /// </param>
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| 249 | /// <remarks>(From the lapack manual):DGESDD computes the singular value decomposition (SVD) of a real
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| 250 | ///M-by-N matrix A, optionally computing the left and right singular
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| 251 | ///vectors. If singular vectors are desired, it uses a
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| 252 | ///divide-and-conquer algorithm.
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| 253 | ///The SVD is written
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| 254 | /// <code>A = U * SIGMA * transpose(V)</code>
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| 255 | ///where SIGMA is an M-by-N matrix which is zero except for its
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| 256 | ///min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
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| 257 | ///V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA
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| 258 | ///are the singular values of A; they are real and non-negative, and
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| 259 | ///are returned in descending order. The first min(m,n) columns of
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| 260 | ///U and V are the left and right singular vectors of A.
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| 261 | ///Note that the routine returns VT = V**T, not V.
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| 262 | ///The divide and conquer algorithm makes very mild assumptions about
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| 263 | ///floating point arithmetic. It will work on machines with a guard
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| 264 | ///digit in add/subtract, or on those binary machines without guard
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| 265 | ///digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
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| 266 | ///Cray-2. It could conceivably fail on hexadecimal or decimal machines
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| 267 | ///without guard digits, but we know of none.</remarks>
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| 268 | void dgesdd (char jobz, int m, int n,
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| 269 | double [] a, int lda, double [] s,
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| 270 | double [] u, int ldu, double [] vt,
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| 271 | int ldvt, //double [] work, int lwork,
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| 272 | // int [] iwork,
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| 273 | ref int info);
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| 274 |
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| 275 | /// <summary>
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| 276 | /// singular value decomposition, new version, more memory needed
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| 277 | /// </summary>
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| 278 | /// <param name="jobz">Specifies options for computing all or part of the matrix U
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| 279 | /// <list type="table">
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| 280 | /// <listheader>
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| 281 | /// <term>jobz value</term>
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| 282 | /// <description>... will result in:</description>
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| 283 | /// </listheader>
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| 284 | /// <item>
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| 285 | /// <term>A</term>
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| 286 | /// <description>all M columns of U and all N rows of V**T are
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| 287 | /// returned in the arrays U and VT</description>
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| 288 | /// </item>
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| 289 | /// <item> <term>S</term>
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| 290 | /// <description>the first min(M,N) columns of U and the first
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| 291 | /// min(M,N) rows of V**T are returned in the arrays U
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| 292 | /// and VT</description>
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| 293 | /// </item>
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| 294 | /// <item> <term>O</term>
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| 295 | /// <description>If M >= N, the first N columns of U are overwritten
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| 296 | /// on the array A and all rows of V**T are returned in
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| 297 | /// the array VT,
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| 298 | /// otherwise, all columns of U are returned in the
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| 299 | /// array U and the first M rows of V**T are overwritten
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| 300 | /// in the array VT</description>
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| 301 | /// </item>
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| 302 | /// <item> <term>N</term>
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| 303 | /// <description>no columns of U or rows of V**T are computed.</description>
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| 304 | /// </item>
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| 305 | /// </list>
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| 306 | /// </param>
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| 307 | /// <param name="m">The number of rows of the input matrix A. M greater or equal to 0.</param>
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| 308 | /// <param name="n">The number of columns of the input matrix A. N greater or equal to 0</param>
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| 309 | /// <param name="a">On entry, the M-by-N matrix A.
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| 310 | /// On exit, <list><item>
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| 311 | /// if JOBZ = 'O', A is overwritten with the first N columns
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| 312 | /// of U (the left singular vectors, stored
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| 313 | /// columnwise) if M >= N;
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| 314 | /// A is overwritten with the first M rows
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| 315 | /// of V**T (the right singular vectors, stored
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| 316 | /// rowwise) otherwise.</item>
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| 317 | /// <item>if JOBZ .ne. 'O', the contents of A are destroyed.</item></list></param>
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| 318 | /// <param name="lda">The leading dimension of the array A. LDA ge max(1,M).</param>
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| 319 | /// <param name="s">array, dimension (min(M,N)). The singular values of A, sorted so that S(i) ge S(i+1)</param>
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| 320 | /// <param name="u">array, dimension (LDU,UCOL)
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| 321 | /// UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
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| 322 | /// UCOL = min(M,N) if JOBZ = 'S'.
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| 323 | /// If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
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| 324 | /// orthogonal matrix U;
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| 325 | /// if JOBZ = 'S', U contains the first min(M,N) columns of U
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| 326 | /// (the left singular vectors, stored columnwise);
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| 327 | /// if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.</param>
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| 328 | /// <param name="ldu">The leading dimension of the array U. LDU >= 1; if
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| 329 | /// JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M</param>
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| 330 | /// <param name="vt">array, dimension (LDVT,N). If JOBZ = 'A' or JOBZ = 'O' and
|
---|
| 331 | /// M >= N, VT contains the N-by-N orthogonal matrix V**T; if JOBZ = 'S',
|
---|
| 332 | /// VT contains the first min(M,N) rows of V**T
|
---|
| 333 | /// (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N,
|
---|
| 334 | /// or JOBZ = 'N', VT is not referenced</param>
|
---|
| 335 | /// <param name="ldvt">The leading dimension of the array VT. LDVT > = 1;
|
---|
| 336 | /// if JOBZ = 'A' or JOBZ = 'O' and M > = N, LDVT >= N;
|
---|
| 337 | /// if JOBZ = 'S', LDVT > min(M,N).</param>
|
---|
| 338 | /// <param name="info">
|
---|
| 339 | /// <list>
|
---|
| 340 | /// <item> 0: successful exit.</item>
|
---|
| 341 | /// <item> <![CDATA[< 0]]> : if INFO = -i, the i-th argument had an illegal value.</item>
|
---|
| 342 | /// <item> <![CDATA[> 0]]> : ?BGSDD did not converge, updating process failed.</item>
|
---|
| 343 | /// </list>
|
---|
| 344 | /// </param>
|
---|
| 345 | /// <remarks>(From the lapack manual):DGESDD computes the singular value decomposition (SVD) of a real
|
---|
| 346 | ///M-by-N matrix A, optionally computing the left and right singular
|
---|
| 347 | ///vectors. If singular vectors are desired, it uses a
|
---|
| 348 | ///divide-and-conquer algorithm.
|
---|
| 349 | ///The SVD is written
|
---|
| 350 | /// <code>A = U * SIGMA * transpose(V)</code>
|
---|
| 351 | ///where SIGMA is an M-by-N matrix which is zero except for its
|
---|
| 352 | ///min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
|
---|
| 353 | ///V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA
|
---|
| 354 | ///are the singular values of A; they are real and non-negative, and
|
---|
| 355 | ///are returned in descending order. The first min(m,n) columns of
|
---|
| 356 | ///U and V are the left and right singular vectors of A.
|
---|
| 357 | ///Note that the routine returns VT = V**T, not V.
|
---|
| 358 | ///The divide and conquer algorithm makes very mild assumptions about
|
---|
| 359 | ///floating point arithmetic. It will work on machines with a guard
|
---|
| 360 | ///digit in add/subtract, or on those binary machines without guard
|
---|
| 361 | ///digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
|
---|
| 362 | ///Cray-2. It could conceivably fail on hexadecimal or decimal machines
|
---|
| 363 | ///without guard digits, but we know of none.</remarks>
|
---|
| 364 | void sgesdd (char jobz, int m, int n,
|
---|
| 365 | float [] a, int lda, float [] s,
|
---|
| 366 | float [] u, int ldu, float [] vt,
|
---|
| 367 | int ldvt, //double [] work, int lwork,
|
---|
| 368 | // int [] iwork,
|
---|
| 369 | ref int info);
|
---|
| 370 |
|
---|
| 371 | /// <summary>
|
---|
| 372 | /// singular value decomposition, new version, more memory needed
|
---|
| 373 | /// </summary>
|
---|
| 374 | /// <param name="jobz">Specifies options for computing all or part of the matrix U
|
---|
| 375 | /// <list type="table">
|
---|
| 376 | /// <listheader>
|
---|
| 377 | /// <term>jobz value</term>
|
---|
| 378 | /// <description>... will result in:</description>
|
---|
| 379 | /// </listheader>
|
---|
| 380 | /// <item>
|
---|
| 381 | /// <term>A</term>
|
---|
| 382 | /// <description>all M columns of U and all N rows of V**T are
|
---|
| 383 | /// returned in the arrays U and VT</description>
|
---|
| 384 | /// </item>
|
---|
| 385 | /// <item> <term>S</term>
|
---|
| 386 | /// <description>the first min(M,N) columns of U and the first
|
---|
| 387 | /// min(M,N) rows of V**T are returned in the arrays U
|
---|
| 388 | /// and VT</description>
|
---|
| 389 | /// </item>
|
---|
| 390 | /// <item> <term>O</term>
|
---|
| 391 | /// <description>If M >= N, the first N columns of U are overwritten
|
---|
| 392 | /// on the array A and all rows of V**T are returned in
|
---|
| 393 | /// the array VT,
|
---|
| 394 | /// otherwise, all columns of U are returned in the
|
---|
| 395 | /// array U and the first M rows of V**T are overwritten
|
---|
| 396 | /// in the array VT</description>
|
---|
| 397 | /// </item>
|
---|
| 398 | /// <item> <term>N</term>
|
---|
| 399 | /// <description>no columns of U or rows of V**T are computed.</description>
|
---|
| 400 | /// </item>
|
---|
| 401 | /// </list>
|
---|
| 402 | /// </param>
|
---|
| 403 | /// <param name="m">The number of rows of the input matrix A. M greater or equal to 0.</param>
|
---|
| 404 | /// <param name="n">The number of columns of the input matrix A. N greater or equal to 0</param>
|
---|
| 405 | /// <param name="a">On entry, the M-by-N matrix A.
|
---|
| 406 | /// On exit, <list><item>
|
---|
| 407 | /// if JOBZ = 'O', A is overwritten with the first N columns
|
---|
| 408 | /// of U (the left singular vectors, stored
|
---|
| 409 | /// columnwise) if M >= N;
|
---|
| 410 | /// A is overwritten with the first M rows
|
---|
| 411 | /// of V**T (the right singular vectors, stored
|
---|
| 412 | /// rowwise) otherwise.</item>
|
---|
| 413 | /// <item>if JOBZ .ne. 'O', the contents of A are destroyed.</item></list></param>
|
---|
| 414 | /// <param name="lda">The leading dimension of the array A. LDA ge max(1,M).</param>
|
---|
| 415 | /// <param name="s">array, dimension (min(M,N)). The singular values of A, sorted so that S(i) ge S(i+1)</param>
|
---|
| 416 | /// <param name="u">array, dimension (LDU,UCOL)
|
---|
| 417 | /// UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
|
---|
| 418 | /// UCOL = min(M,N) if JOBZ = 'S'.
|
---|
| 419 | /// If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
|
---|
| 420 | /// orthogonal matrix U;
|
---|
| 421 | /// if JOBZ = 'S', U contains the first min(M,N) columns of U
|
---|
| 422 | /// (the left singular vectors, stored columnwise);
|
---|
| 423 | /// if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.</param>
|
---|
| 424 | /// <param name="ldu">The leading dimension of the array U. LDU >= 1; if
|
---|
| 425 | /// JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M</param>
|
---|
| 426 | /// <param name="vt">array, dimension (LDVT,N). If JOBZ = 'A' or JOBZ = 'O' and
|
---|
| 427 | /// M >= N, VT contains the N-by-N orthogonal matrix V**T; if JOBZ = 'S',
|
---|
| 428 | /// VT contains the first min(M,N) rows of V**T
|
---|
| 429 | /// (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N,
|
---|
| 430 | /// or JOBZ = 'N', VT is not referenced</param>
|
---|
| 431 | /// <param name="ldvt">The leading dimension of the array VT. LDVT > = 1;
|
---|
| 432 | /// if JOBZ = 'A' or JOBZ = 'O' and M > = N, LDVT >= N;
|
---|
| 433 | /// if JOBZ = 'S', LDVT > min(M,N).</param>
|
---|
| 434 | /// <param name="info">
|
---|
| 435 | /// <list>
|
---|
| 436 | /// <item> 0: successful exit.</item>
|
---|
| 437 | /// <item> <![CDATA[< 0]]> : if INFO = -i, the i-th argument had an illegal value.</item>
|
---|
| 438 | /// <item> <![CDATA[> 0]]> : ?BGSDD did not converge, updating process failed.</item>
|
---|
| 439 | /// </list>
|
---|
| 440 | /// </param>
|
---|
| 441 | /// <remarks>(From the lapack manual):DGESDD computes the singular value decomposition (SVD) of a real
|
---|
| 442 | ///M-by-N matrix A, optionally computing the left and right singular
|
---|
| 443 | ///vectors. If singular vectors are desired, it uses a
|
---|
| 444 | ///divide-and-conquer algorithm.
|
---|
| 445 | ///The SVD is written
|
---|
| 446 | /// <code>A = U * SIGMA * transpose(V)</code>
|
---|
| 447 | ///where SIGMA is an M-by-N matrix which is zero except for its
|
---|
| 448 | ///min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
|
---|
| 449 | ///V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA
|
---|
| 450 | ///are the singular values of A; they are real and non-negative, and
|
---|
| 451 | ///are returned in descending order. The first min(m,n) columns of
|
---|
| 452 | ///U and V are the left and right singular vectors of A.
|
---|
| 453 | ///Note that the routine returns VT = V**T, not V.
|
---|
| 454 | ///The divide and conquer algorithm makes very mild assumptions about
|
---|
| 455 | ///floating point arithmetic. It will work on machines with a guard
|
---|
| 456 | ///digit in add/subtract, or on those binary machines without guard
|
---|
| 457 | ///digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
|
---|
| 458 | ///Cray-2. It could conceivably fail on hexadecimal or decimal machines
|
---|
| 459 | ///without guard digits, but we know of none.</remarks>
|
---|
| 460 | void cgesdd (char jobz, int m, int n,
|
---|
| 461 | fcomplex [] a, int lda, float [] s,
|
---|
| 462 | fcomplex [] u, int ldu, fcomplex [] vt,
|
---|
| 463 | int ldvt, //double [] work, int lwork,
|
---|
| 464 | // int [] iwork,
|
---|
| 465 | ref int info);
|
---|
| 466 |
|
---|
| 467 | /// <summary>
|
---|
| 468 | /// singular value decomposition, new version, more memory needed
|
---|
| 469 | /// </summary>
|
---|
| 470 | /// <param name="jobz">Specifies options for computing all or part of the matrix U
|
---|
| 471 | /// <list type="table">
|
---|
| 472 | /// <listheader>
|
---|
| 473 | /// <term>jobz value</term>
|
---|
| 474 | /// <description>... will result in:</description>
|
---|
| 475 | /// </listheader>
|
---|
| 476 | /// <item>
|
---|
| 477 | /// <term>A</term>
|
---|
| 478 | /// <description>all M columns of U and all N rows of V**T are
|
---|
| 479 | /// returned in the arrays U and VT</description>
|
---|
| 480 | /// </item>
|
---|
| 481 | /// <item> <term>S</term>
|
---|
| 482 | /// <description>the first min(M,N) columns of U and the first
|
---|
| 483 | /// min(M,N) rows of V**T are returned in the arrays U
|
---|
| 484 | /// and VT</description>
|
---|
| 485 | /// </item>
|
---|
| 486 | /// <item> <term>O</term>
|
---|
| 487 | /// <description>If M >= N, the first N columns of U are overwritten
|
---|
| 488 | /// on the array A and all rows of V**T are returned in
|
---|
| 489 | /// the array VT,
|
---|
| 490 | /// otherwise, all columns of U are returned in the
|
---|
| 491 | /// array U and the first M rows of V**T are overwritten
|
---|
| 492 | /// in the array VT</description>
|
---|
| 493 | /// </item>
|
---|
| 494 | /// <item> <term>N</term>
|
---|
| 495 | /// <description>no columns of U or rows of V**T are computed.</description>
|
---|
| 496 | /// </item>
|
---|
| 497 | /// </list>
|
---|
| 498 | /// </param>
|
---|
| 499 | /// <param name="m">The number of rows of the input matrix A. M greater or equal to 0.</param>
|
---|
| 500 | /// <param name="n">The number of columns of the input matrix A. N greater or equal to 0</param>
|
---|
| 501 | /// <param name="a">On entry, the M-by-N matrix A.
|
---|
| 502 | /// On exit, <list><item>
|
---|
| 503 | /// if JOBZ = 'O', A is overwritten with the first N columns
|
---|
| 504 | /// of U (the left singular vectors, stored
|
---|
| 505 | /// columnwise) if M >= N;
|
---|
| 506 | /// A is overwritten with the first M rows
|
---|
| 507 | /// of V**T (the right singular vectors, stored
|
---|
| 508 | /// rowwise) otherwise.</item>
|
---|
| 509 | /// <item>if JOBZ .ne. 'O', the contents of A are destroyed.</item></list></param>
|
---|
| 510 | /// <param name="lda">The leading dimension of the array A. LDA ge max(1,M).</param>
|
---|
| 511 | /// <param name="s">array, dimension (min(M,N)). The singular values of A, sorted so that S(i) ge S(i+1)</param>
|
---|
| 512 | /// <param name="u">array, dimension (LDU,UCOL)
|
---|
| 513 | /// UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
|
---|
| 514 | /// UCOL = min(M,N) if JOBZ = 'S'.
|
---|
| 515 | /// If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
|
---|
| 516 | /// orthogonal matrix U;
|
---|
| 517 | /// if JOBZ = 'S', U contains the first min(M,N) columns of U
|
---|
| 518 | /// (the left singular vectors, stored columnwise);
|
---|
| 519 | /// if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.</param>
|
---|
| 520 | /// <param name="ldu">The leading dimension of the array U. LDU >= 1; if
|
---|
| 521 | /// JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M</param>
|
---|
| 522 | /// <param name="vt">array, dimension (LDVT,N). If JOBZ = 'A' or JOBZ = 'O' and
|
---|
| 523 | /// M >= N, VT contains the N-by-N orthogonal matrix V**T; if JOBZ = 'S',
|
---|
| 524 | /// VT contains the first min(M,N) rows of V**T
|
---|
| 525 | /// (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N,
|
---|
| 526 | /// or JOBZ = 'N', VT is not referenced</param>
|
---|
| 527 | /// <param name="ldvt">The leading dimension of the array VT. LDVT > = 1;
|
---|
| 528 | /// if JOBZ = 'A' or JOBZ = 'O' and M > = N, LDVT >= N;
|
---|
| 529 | /// if JOBZ = 'S', LDVT > min(M,N).</param>
|
---|
| 530 | /// <param name="info">
|
---|
| 531 | /// <list>
|
---|
| 532 | /// <item> 0: successful exit.</item>
|
---|
| 533 | /// <item> <![CDATA[< 0]]> : if INFO = -i, the i-th argument had an illegal value.</item>
|
---|
| 534 | /// <item> <![CDATA[> 0]]> : ?BGSDD did not converge, updating process failed.</item>
|
---|
| 535 | /// </list>
|
---|
| 536 | /// </param>
|
---|
| 537 | /// <remarks>(From the lapack manual):DGESDD computes the singular value decomposition (SVD) of a real
|
---|
| 538 | ///M-by-N matrix A, optionally computing the left and right singular
|
---|
| 539 | ///vectors. If singular vectors are desired, it uses a
|
---|
| 540 | ///divide-and-conquer algorithm.
|
---|
| 541 | ///The SVD is written
|
---|
| 542 | /// <code>A = U * SIGMA * transpose(V)</code>
|
---|
| 543 | ///where SIGMA is an M-by-N matrix which is zero except for its
|
---|
| 544 | ///min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
|
---|
| 545 | ///V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA
|
---|
| 546 | ///are the singular values of A; they are real and non-negative, and
|
---|
| 547 | ///are returned in descending order. The first min(m,n) columns of
|
---|
| 548 | ///U and V are the left and right singular vectors of A.
|
---|
| 549 | ///Note that the routine returns VT = V**T, not V.
|
---|
| 550 | ///The divide and conquer algorithm makes very mild assumptions about
|
---|
| 551 | ///floating point arithmetic. It will work on machines with a guard
|
---|
| 552 | ///digit in add/subtract, or on those binary machines without guard
|
---|
| 553 | ///digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
|
---|
| 554 | ///Cray-2. It could conceivably fail on hexadecimal or decimal machines
|
---|
| 555 | ///without guard digits, but we know of none.</remarks>
|
---|
| 556 | void zgesdd (char jobz, int m, int n,
|
---|
| 557 | complex [] a, int lda, double [] s,
|
---|
| 558 | complex [] u, int ldu, complex [] vt,
|
---|
| 559 | int ldvt, //double [] work, int lwork,
|
---|
| 560 | // int [] iwork,
|
---|
| 561 | ref int info);
|
---|
| 562 |
|
---|
| 563 | #endregion
|
---|
| 564 |
|
---|
| 565 | #region ?GESVD
|
---|
| 566 | /// <summary>
|
---|
| 567 | /// singular value decomposition, older version, less memory needed
|
---|
| 568 | /// </summary>
|
---|
| 569 | /// <param name="jobz">Specifies options for computing all or part of the matrix U
|
---|
| 570 | /// <list type="bullet"><item>= 'A': all M columns of U and all N rows of V**T are
|
---|
| 571 | ///returned in the arrays U and VT</item>
|
---|
| 572 | /// <item> = 'S': the first min(M,N) columns of U and the first
|
---|
| 573 | /// min(M,N) rows of V**T are returned in the arrays U
|
---|
| 574 | /// and VT</item>
|
---|
| 575 | /// <item> = 'O': If M >= N, the first N columns of U are overwritten
|
---|
| 576 | /// on the array A and all rows of V**T are returned in
|
---|
| 577 | /// the array VT. Otherwise, all columns of U are returned in the
|
---|
| 578 | /// array U and the first M rows of V**T are overwritten
|
---|
| 579 | /// in the array VT</item>
|
---|
| 580 | /// <item> = 'N': no columns of U or rows of V**T are computed.</item>
|
---|
| 581 | /// </list>
|
---|
| 582 | /// </param>
|
---|
| 583 | /// <param name="m">The number of rows of the input matrix A. M greater or equal to 0.</param>
|
---|
| 584 | /// <param name="n">The number of columns of the input matrix A. N greater or equal to 0</param>
|
---|
| 585 | /// <param name="a">On entry, the M-by-N matrix A.
|
---|
| 586 | /// On exit, <list><item>
|
---|
| 587 | /// if JOBZ = 'O', A is overwritten with the first N columns
|
---|
| 588 | /// of U (the left singular vectors, stored
|
---|
| 589 | /// columnwise) if M >= N;
|
---|
| 590 | /// A is overwritten with the first M rows
|
---|
| 591 | /// of V**T (the right singular vectors, stored
|
---|
| 592 | /// rowwise) otherwise.</item>
|
---|
| 593 | /// <item>if JOBZ .ne. 'O', the contents of A are destroyed.</item></list></param>
|
---|
| 594 | /// <param name="lda">The leading dimension of the array A. LDA ge max(1,M).</param>
|
---|
| 595 | /// <param name="s">array, dimension (min(M,N)). The singular values of A, sorted so that S(i) ge S(i+1)</param>
|
---|
| 596 | /// <param name="u">array, dimension (LDU,UCOL)
|
---|
| 597 | /// UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
|
---|
| 598 | /// UCOL = min(M,N) if JOBZ = 'S'.
|
---|
| 599 | /// If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
|
---|
| 600 | /// orthogonal matrix U;
|
---|
| 601 | /// if JOBZ = 'S', U contains the first min(M,N) columns of U
|
---|
| 602 | /// (the left singular vectors, stored columnwise);
|
---|
| 603 | /// if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.</param>
|
---|
| 604 | /// <param name="ldu">The leading dimension of the array U. LDU >= 1; if
|
---|
| 605 | /// JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M</param>
|
---|
| 606 | /// <param name="vt">array, dimension (LDVT,N). If JOBZ = 'A' or JOBZ = 'O' and
|
---|
| 607 | /// M >= N, VT contains the N-by-N orthogonal matrix V**T; if JOBZ = 'S',
|
---|
| 608 | /// VT contains the first min(M,N) rows of V**T
|
---|
| 609 | /// (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N,
|
---|
| 610 | /// or JOBZ = 'N', VT is not referenced</param>
|
---|
| 611 | /// <param name="ldvt">The leading dimension of the array VT. LDVT > = 1;
|
---|
| 612 | /// if JOBZ = 'A' or JOBZ = 'O' and M > = N, LDVT >= N;
|
---|
| 613 | /// if JOBZ = 'S', LDVT > min(M,N).</param>
|
---|
| 614 | /// <param name="info">
|
---|
| 615 | /// <list>
|
---|
| 616 | /// <item> 0: successful exit.</item>
|
---|
| 617 | /// <item> lower 0: if INFO = -i, the i-th argument had an illegal value.</item>
|
---|
| 618 | /// <item> greater 0: DBDSDC did not converge, updating process failed.</item>
|
---|
| 619 | /// </list>
|
---|
| 620 | /// </param>
|
---|
| 621 | /// <remarks>(From the lapack manual):DGESDD computes the singular value decomposition (SVD) of a real
|
---|
| 622 | ///M-by-N matrix A, optionally computing the left and right singular
|
---|
| 623 | ///vectors. If singular vectors are desired, it uses a
|
---|
| 624 | ///divide-and-conquer algorithm.
|
---|
| 625 | ///The SVD is written
|
---|
| 626 | /// <br>A = U * SIGMA * transpose(V)</br>
|
---|
| 627 | ///where SIGMA is an M-by-N matrix which is zero except for its
|
---|
| 628 | ///min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
|
---|
| 629 | ///V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA
|
---|
| 630 | ///are the singular values of A; they are real and non-negative, and
|
---|
| 631 | ///are returned in descending order. The first min(m,n) columns of
|
---|
| 632 | ///U and V are the left and right singular vectors of A.
|
---|
| 633 | ///Note that the routine returns VT = V**T, not V.
|
---|
| 634 | ///The divide and conquer algorithm makes very mild assumptions about
|
---|
| 635 | ///floating point arithmetic. It will work on machines with a guard
|
---|
| 636 | ///digit in add/subtract, or on those binary machines without guard
|
---|
| 637 | ///digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
|
---|
| 638 | ///Cray-2. It could conceivably fail on hexadecimal or decimal machines
|
---|
| 639 | ///without guard digits, but we know of none.</remarks>
|
---|
| 640 | void dgesvd (char jobz, int m, int n, double [] a, int lda,
|
---|
| 641 | double [] s, double [] u, int ldu,
|
---|
| 642 | double [] vt, int ldvt, ref int info);
|
---|
| 643 |
|
---|
| 644 | /// <summary>
|
---|
| 645 | /// singular value decomposition, older version, less memory needed
|
---|
| 646 | /// </summary>
|
---|
| 647 | /// <param name="jobz">Specifies options for computing all or part of the matrix U
|
---|
| 648 | /// <list type="bullet"><item>= 'A': all M columns of U and all N rows of V**T are
|
---|
| 649 | ///returned in the arrays U and VT</item>
|
---|
| 650 | /// <item> = 'S': the first min(M,N) columns of U and the first
|
---|
| 651 | /// min(M,N) rows of V**T are returned in the arrays U
|
---|
| 652 | /// and VT</item>
|
---|
| 653 | /// <item> = 'O': If M >= N, the first N columns of U are overwritten
|
---|
| 654 | /// on the array A and all rows of V**T are returned in
|
---|
| 655 | /// the array VT. Otherwise, all columns of U are returned in the
|
---|
| 656 | /// array U and the first M rows of V**T are overwritten
|
---|
| 657 | /// in the array VT</item>
|
---|
| 658 | /// <item> = 'N': no columns of U or rows of V**T are computed.</item>
|
---|
| 659 | /// </list>
|
---|
| 660 | /// </param>
|
---|
| 661 | /// <param name="m">The number of rows of the input matrix A. M greater or equal to 0.</param>
|
---|
| 662 | /// <param name="n">The number of columns of the input matrix A. N greater or equal to 0</param>
|
---|
| 663 | /// <param name="a">On entry, the M-by-N matrix A.
|
---|
| 664 | /// On exit, <list><item>
|
---|
| 665 | /// if JOBZ = 'O', A is overwritten with the first N columns
|
---|
| 666 | /// of U (the left singular vectors, stored
|
---|
| 667 | /// columnwise) if M >= N;
|
---|
| 668 | /// A is overwritten with the first M rows
|
---|
| 669 | /// of V**T (the right singular vectors, stored
|
---|
| 670 | /// rowwise) otherwise.</item>
|
---|
| 671 | /// <item>if JOBZ .ne. 'O', the contents of A are destroyed.</item></list></param>
|
---|
| 672 | /// <param name="lda">The leading dimension of the array A. LDA ge max(1,M).</param>
|
---|
| 673 | /// <param name="s">array, dimension (min(M,N)). The singular values of A, sorted so that S(i) ge S(i+1)</param>
|
---|
| 674 | /// <param name="u">array, dimension (LDU,UCOL)
|
---|
| 675 | /// UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
|
---|
| 676 | /// UCOL = min(M,N) if JOBZ = 'S'.
|
---|
| 677 | /// If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
|
---|
| 678 | /// orthogonal matrix U;
|
---|
| 679 | /// if JOBZ = 'S', U contains the first min(M,N) columns of U
|
---|
| 680 | /// (the left singular vectors, stored columnwise);
|
---|
| 681 | /// if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.</param>
|
---|
| 682 | /// <param name="ldu">The leading dimension of the array U. LDU >= 1; if
|
---|
| 683 | /// JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M</param>
|
---|
| 684 | /// <param name="vt">array, dimension (LDVT,N). If JOBZ = 'A' or JOBZ = 'O' and
|
---|
| 685 | /// M >= N, VT contains the N-by-N orthogonal matrix V**T; if JOBZ = 'S',
|
---|
| 686 | /// VT contains the first min(M,N) rows of V**T
|
---|
| 687 | /// (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N,
|
---|
| 688 | /// or JOBZ = 'N', VT is not referenced</param>
|
---|
| 689 | /// <param name="ldvt">The leading dimension of the array VT. LDVT > = 1;
|
---|
| 690 | /// if JOBZ = 'A' or JOBZ = 'O' and M > = N, LDVT >= N;
|
---|
| 691 | /// if JOBZ = 'S', LDVT > min(M,N).</param>
|
---|
| 692 | /// <param name="info">
|
---|
| 693 | /// <list>
|
---|
| 694 | /// <item> 0: successful exit.</item>
|
---|
| 695 | /// <item> lower 0: if INFO = -i, the i-th argument had an illegal value.</item>
|
---|
| 696 | /// <item> greater 0: DBDSDC did not converge, updating process failed.</item>
|
---|
| 697 | /// </list>
|
---|
| 698 | /// </param>
|
---|
| 699 | /// <remarks>(From the lapack manual):DGESDD computes the singular value decomposition (SVD) of a real
|
---|
| 700 | ///M-by-N matrix A, optionally computing the left and right singular
|
---|
| 701 | ///vectors. If singular vectors are desired, it uses a
|
---|
| 702 | ///divide-and-conquer algorithm.
|
---|
| 703 | ///The SVD is written
|
---|
| 704 | /// <br>A = U * SIGMA * transpose(V)</br>
|
---|
| 705 | ///where SIGMA is an M-by-N matrix which is zero except for its
|
---|
| 706 | ///min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
|
---|
| 707 | ///V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA
|
---|
| 708 | ///are the singular values of A; they are real and non-negative, and
|
---|
| 709 | ///are returned in descending order. The first min(m,n) columns of
|
---|
| 710 | ///U and V are the left and right singular vectors of A.
|
---|
| 711 | ///Note that the routine returns VT = V**T, not V.
|
---|
| 712 | ///The divide and conquer algorithm makes very mild assumptions about
|
---|
| 713 | ///floating point arithmetic. It will work on machines with a guard
|
---|
| 714 | ///digit in add/subtract, or on those binary machines without guard
|
---|
| 715 | ///digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
|
---|
| 716 | ///Cray-2. It could conceivably fail on hexadecimal or decimal machines
|
---|
| 717 | ///without guard digits, but we know of none.</remarks>
|
---|
| 718 | void sgesvd (char jobz, int m, int n, float [] a, int lda,
|
---|
| 719 | float [] s, float [] u, int ldu,
|
---|
| 720 | float [] vt, int ldvt, ref int info);
|
---|
| 721 |
|
---|
| 722 |
|
---|
| 723 | /// <summary>
|
---|
| 724 | /// singular value decomposition, older version, less memory needed
|
---|
| 725 | /// </summary>
|
---|
| 726 | /// <param name="jobz">Specifies options for computing all or part of the matrix U
|
---|
| 727 | /// <list type="bullet"><item>= 'A': all M columns of U and all N rows of V**T are
|
---|
| 728 | ///returned in the arrays U and VT</item>
|
---|
| 729 | /// <item> = 'S': the first min(M,N) columns of U and the first
|
---|
| 730 | /// min(M,N) rows of V**T are returned in the arrays U
|
---|
| 731 | /// and VT</item>
|
---|
| 732 | /// <item> = 'O': If M >= N, the first N columns of U are overwritten
|
---|
| 733 | /// on the array A and all rows of V**T are returned in
|
---|
| 734 | /// the array VT. Otherwise, all columns of U are returned in the
|
---|
| 735 | /// array U and the first M rows of V**T are overwritten
|
---|
| 736 | /// in the array VT</item>
|
---|
| 737 | /// <item> = 'N': no columns of U or rows of V**T are computed.</item>
|
---|
| 738 | /// </list>
|
---|
| 739 | /// </param>
|
---|
| 740 | /// <param name="m">The number of rows of the input matrix A. M greater or equal to 0.</param>
|
---|
| 741 | /// <param name="n">The number of columns of the input matrix A. N greater or equal to 0</param>
|
---|
| 742 | /// <param name="a">On entry, the M-by-N matrix A.
|
---|
| 743 | /// On exit, <list><item>
|
---|
| 744 | /// if JOBZ = 'O', A is overwritten with the first N columns
|
---|
| 745 | /// of U (the left singular vectors, stored
|
---|
| 746 | /// columnwise) if M >= N;
|
---|
| 747 | /// A is overwritten with the first M rows
|
---|
| 748 | /// of V**T (the right singular vectors, stored
|
---|
| 749 | /// rowwise) otherwise.</item>
|
---|
| 750 | /// <item>if JOBZ .ne. 'O', the contents of A are destroyed.</item></list></param>
|
---|
| 751 | /// <param name="lda">The leading dimension of the array A. LDA ge max(1,M).</param>
|
---|
| 752 | /// <param name="s">array, dimension (min(M,N)). The singular values of A, sorted so that S(i) ge S(i+1)</param>
|
---|
| 753 | /// <param name="u">array, dimension (LDU,UCOL)
|
---|
| 754 | /// UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
|
---|
| 755 | /// UCOL = min(M,N) if JOBZ = 'S'.
|
---|
| 756 | /// If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
|
---|
| 757 | /// orthogonal matrix U;
|
---|
| 758 | /// if JOBZ = 'S', U contains the first min(M,N) columns of U
|
---|
| 759 | /// (the left singular vectors, stored columnwise);
|
---|
| 760 | /// if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.</param>
|
---|
| 761 | /// <param name="ldu">The leading dimension of the array U. LDU >= 1; if
|
---|
| 762 | /// JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M</param>
|
---|
| 763 | /// <param name="vt">array, dimension (LDVT,N). If JOBZ = 'A' or JOBZ = 'O' and
|
---|
| 764 | /// M >= N, VT contains the N-by-N orthogonal matrix V**T; if JOBZ = 'S',
|
---|
| 765 | /// VT contains the first min(M,N) rows of V**T
|
---|
| 766 | /// (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N,
|
---|
| 767 | /// or JOBZ = 'N', VT is not referenced</param>
|
---|
| 768 | /// <param name="ldvt">The leading dimension of the array VT. LDVT > = 1;
|
---|
| 769 | /// if JOBZ = 'A' or JOBZ = 'O' and M > = N, LDVT >= N;
|
---|
| 770 | /// if JOBZ = 'S', LDVT > min(M,N).</param>
|
---|
| 771 | /// <param name="info">
|
---|
| 772 | /// <list>
|
---|
| 773 | /// <item> 0: successful exit.</item>
|
---|
| 774 | /// <item> lower 0: if INFO = -i, the i-th argument had an illegal value.</item>
|
---|
| 775 | /// <item> greater 0: DBDSDC did not converge, updating process failed.</item>
|
---|
| 776 | /// </list>
|
---|
| 777 | /// </param>
|
---|
| 778 | /// <remarks>(From the lapack manual):DGESDD computes the singular value decomposition (SVD) of a real
|
---|
| 779 | ///M-by-N matrix A, optionally computing the left and right singular
|
---|
| 780 | ///vectors. If singular vectors are desired, it uses a
|
---|
| 781 | ///divide-and-conquer algorithm.
|
---|
| 782 | ///The SVD is written
|
---|
| 783 | /// <br>A = U * SIGMA * transpose(V)</br>
|
---|
| 784 | ///where SIGMA is an M-by-N matrix which is zero except for its
|
---|
| 785 | ///min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
|
---|
| 786 | ///V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA
|
---|
| 787 | ///are the singular values of A; they are real and non-negative, and
|
---|
| 788 | ///are returned in descending order. The first min(m,n) columns of
|
---|
| 789 | ///U and V are the left and right singular vectors of A.
|
---|
| 790 | ///Note that the routine returns VT = V**T, not V.
|
---|
| 791 | ///The divide and conquer algorithm makes very mild assumptions about
|
---|
| 792 | ///floating point arithmetic. It will work on machines with a guard
|
---|
| 793 | ///digit in add/subtract, or on those binary machines without guard
|
---|
| 794 | ///digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
|
---|
| 795 | ///Cray-2. It could conceivably fail on hexadecimal or decimal machines
|
---|
| 796 | ///without guard digits, but we know of none.</remarks>
|
---|
| 797 | void cgesvd (char jobz, int m, int n, fcomplex [] a, int lda,
|
---|
| 798 | float [] s, fcomplex [] u, int ldu,
|
---|
| 799 | fcomplex [] vt, int ldvt, ref int info);
|
---|
| 800 |
|
---|
| 801 |
|
---|
| 802 | /// <summary>
|
---|
| 803 | /// singular value decomposition, older version, less memory needed
|
---|
| 804 | /// </summary>
|
---|
| 805 | /// <param name="jobz">Specifies options for computing all or part of the matrix U
|
---|
| 806 | /// <list type="bullet"><item>= 'A': all M columns of U and all N rows of V**T are
|
---|
| 807 | ///returned in the arrays U and VT</item>
|
---|
| 808 | /// <item> = 'S': the first min(M,N) columns of U and the first
|
---|
| 809 | /// min(M,N) rows of V**T are returned in the arrays U
|
---|
| 810 | /// and VT</item>
|
---|
| 811 | /// <item> = 'O': If M >= N, the first N columns of U are overwritten
|
---|
| 812 | /// on the array A and all rows of V**T are returned in
|
---|
| 813 | /// the array VT. Otherwise, all columns of U are returned in the
|
---|
| 814 | /// array U and the first M rows of V**T are overwritten
|
---|
| 815 | /// in the array VT</item>
|
---|
| 816 | /// <item> = 'N': no columns of U or rows of V**T are computed.</item>
|
---|
| 817 | /// </list>
|
---|
| 818 | /// </param>
|
---|
| 819 | /// <param name="m">The number of rows of the input matrix A. M greater or equal to 0.</param>
|
---|
| 820 | /// <param name="n">The number of columns of the input matrix A. N greater or equal to 0</param>
|
---|
| 821 | /// <param name="a">On entry, the M-by-N matrix A.
|
---|
| 822 | /// On exit, <list><item>
|
---|
| 823 | /// if JOBZ = 'O', A is overwritten with the first N columns
|
---|
| 824 | /// of U (the left singular vectors, stored
|
---|
| 825 | /// columnwise) if M >= N;
|
---|
| 826 | /// A is overwritten with the first M rows
|
---|
| 827 | /// of V**T (the right singular vectors, stored
|
---|
| 828 | /// rowwise) otherwise.</item>
|
---|
| 829 | /// <item>if JOBZ .ne. 'O', the contents of A are destroyed.</item></list></param>
|
---|
| 830 | /// <param name="lda">The leading dimension of the array A. LDA ge max(1,M).</param>
|
---|
| 831 | /// <param name="s">array, dimension (min(M,N)). The singular values of A, sorted so that S(i) ge S(i+1)</param>
|
---|
| 832 | /// <param name="u">array, dimension (LDU,UCOL)
|
---|
| 833 | /// UCOL = M if JOBZ = 'A' or JOBZ = 'O' and M < N;
|
---|
| 834 | /// UCOL = min(M,N) if JOBZ = 'S'.
|
---|
| 835 | /// If JOBZ = 'A' or JOBZ = 'O' and M < N, U contains the M-by-M
|
---|
| 836 | /// orthogonal matrix U;
|
---|
| 837 | /// if JOBZ = 'S', U contains the first min(M,N) columns of U
|
---|
| 838 | /// (the left singular vectors, stored columnwise);
|
---|
| 839 | /// if JOBZ = 'O' and M >= N, or JOBZ = 'N', U is not referenced.</param>
|
---|
| 840 | /// <param name="ldu">The leading dimension of the array U. LDU >= 1; if
|
---|
| 841 | /// JOBZ = 'S' or 'A' or JOBZ = 'O' and M < N, LDU >= M</param>
|
---|
| 842 | /// <param name="vt">array, dimension (LDVT,N). If JOBZ = 'A' or JOBZ = 'O' and
|
---|
| 843 | /// M >= N, VT contains the N-by-N orthogonal matrix V**T; if JOBZ = 'S',
|
---|
| 844 | /// VT contains the first min(M,N) rows of V**T
|
---|
| 845 | /// (the right singular vectors, stored rowwise); if JOBZ = 'O' and M < N,
|
---|
| 846 | /// or JOBZ = 'N', VT is not referenced</param>
|
---|
| 847 | /// <param name="ldvt">The leading dimension of the array VT. LDVT > = 1;
|
---|
| 848 | /// if JOBZ = 'A' or JOBZ = 'O' and M > = N, LDVT >= N;
|
---|
| 849 | /// if JOBZ = 'S', LDVT > min(M,N).</param>
|
---|
| 850 | /// <param name="info">
|
---|
| 851 | /// <list>
|
---|
| 852 | /// <item> 0: successful exit.</item>
|
---|
| 853 | /// <item> lower 0: if INFO = -i, the i-th argument had an illegal value.</item>
|
---|
| 854 | /// <item> greater 0: DBDSDC did not converge, updating process failed.</item>
|
---|
| 855 | /// </list>
|
---|
| 856 | /// </param>
|
---|
| 857 | /// <remarks>(From the lapack manual):DGESDD computes the singular value decomposition (SVD) of a real
|
---|
| 858 | ///M-by-N matrix A, optionally computing the left and right singular
|
---|
| 859 | ///vectors. If singular vectors are desired, it uses a
|
---|
| 860 | ///divide-and-conquer algorithm.
|
---|
| 861 | ///The SVD is written
|
---|
| 862 | /// <br>A = U * SIGMA * transpose(V)</br>
|
---|
| 863 | ///where SIGMA is an M-by-N matrix which is zero except for its
|
---|
| 864 | ///min(m,n) diagonal elements, U is an M-by-M orthogonal matrix, and
|
---|
| 865 | ///V is an N-by-N orthogonal matrix. The diagonal elements of SIGMA
|
---|
| 866 | ///are the singular values of A; they are real and non-negative, and
|
---|
| 867 | ///are returned in descending order. The first min(m,n) columns of
|
---|
| 868 | ///U and V are the left and right singular vectors of A.
|
---|
| 869 | ///Note that the routine returns VT = V**T, not V.
|
---|
| 870 | ///The divide and conquer algorithm makes very mild assumptions about
|
---|
| 871 | ///floating point arithmetic. It will work on machines with a guard
|
---|
| 872 | ///digit in add/subtract, or on those binary machines without guard
|
---|
| 873 | ///digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
|
---|
| 874 | ///Cray-2. It could conceivably fail on hexadecimal or decimal machines
|
---|
| 875 | ///without guard digits, but we know of none.</remarks>
|
---|
| 876 | void zgesvd (char jobz, int m, int n, complex [] a, int lda,
|
---|
| 877 | double [] s, complex [] u, int ldu,
|
---|
| 878 | complex [] vt, int ldvt, ref int info);
|
---|
| 879 | #endregion
|
---|
| 880 |
|
---|
| 881 | #region ?POTRF - cholesky factorization
|
---|
| 882 | /// <summary>
|
---|
| 883 | /// cholesky factorization
|
---|
| 884 | /// </summary>
|
---|
| 885 | void dpotrf (char uplo, int n, double [] A, int lda, ref int info);
|
---|
| 886 | /// <summary>
|
---|
| 887 | /// cholesky factorization
|
---|
| 888 | /// </summary>
|
---|
| 889 | void spotrf (char uplo, int n, float [] A, int lda, ref int info);
|
---|
| 890 |
|
---|
| 891 | /// <summary>
|
---|
| 892 | /// cholesky factorization
|
---|
| 893 | /// </summary>
|
---|
| 894 | void cpotrf (char uplo, int n, fcomplex [] A, int lda, ref int info);
|
---|
| 895 |
|
---|
| 896 | /// <summary>
|
---|
| 897 | /// cholesky factorization
|
---|
| 898 | /// </summary>
|
---|
| 899 | void zpotrf (char uplo, int n, complex [] A, int lda, ref int info);
|
---|
| 900 | #endregion
|
---|
| 901 |
|
---|
| 902 | #region ?POTRI - inverse via cholesky factorization
|
---|
| 903 | /// <summary>
|
---|
| 904 | /// matrix inverse via cholesky factorization (?potrf)
|
---|
| 905 | /// </summary>
|
---|
| 906 | void dpotri (char uplo, int n, double [] A, int lda,ref int info);
|
---|
| 907 | /// <summary>
|
---|
| 908 | /// matrix inverse via cholesky factorization (?potrf)
|
---|
| 909 | /// </summary>
|
---|
| 910 | void spotri (char uplo, int n, float [] A, int lda,ref int info);
|
---|
| 911 |
|
---|
| 912 | /// <summary>
|
---|
| 913 | /// matrix inverse via cholesky factorization (?potrf)
|
---|
| 914 | /// </summary>
|
---|
| 915 | void cpotri (char uplo, int n, fcomplex [] A, int lda,ref int info);
|
---|
| 916 |
|
---|
| 917 | /// <summary>
|
---|
| 918 | /// matrix inverse via cholesky factorization (?potrf)
|
---|
| 919 | /// </summary>
|
---|
| 920 | void zpotri (char uplo, int n, complex [] A, int lda,ref int info);
|
---|
| 921 |
|
---|
| 922 | #endregion
|
---|
| 923 |
|
---|
| 924 | #region ?POTRS - Solve via cholesky factors
|
---|
| 925 | /// <summary>
|
---|
| 926 | /// solve equation system via cholesky factorization (?potrs)
|
---|
| 927 | /// </summary>
|
---|
| 928 | void dpotrs (char uplo, int n, int nrhs, double [] A, int lda, double [] B, int ldb, ref int info);
|
---|
| 929 | /// <summary>
|
---|
| 930 | /// solve equation system via cholesky factorization (?potrs)
|
---|
| 931 | /// </summary>
|
---|
| 932 | void spotrs (char uplo, int n, int nrhs, float [] A, int lda, float [] B, int ldb, ref int info);
|
---|
| 933 | /// <summary>
|
---|
| 934 | /// solve equation system via cholesky factorization (?potrs)
|
---|
| 935 | /// </summary>
|
---|
| 936 | void cpotrs (char uplo, int n, int nrhs, fcomplex [] A, int lda, fcomplex [] B, int ldb, ref int info);
|
---|
| 937 | /// <summary>
|
---|
| 938 | /// solve equation system via cholesky factorization (?potrs)
|
---|
| 939 | /// </summary>
|
---|
| 940 | void zpotrs (char uplo, int n, int nrhs, complex [] A, int lda, complex [] B, int ldb, ref int info);
|
---|
| 941 | #endregion
|
---|
| 942 |
|
---|
| 943 | #region ?getrf - LU factorization
|
---|
| 944 | /// <summary>
|
---|
| 945 | /// LU factorization of general matrix
|
---|
| 946 | /// </summary>
|
---|
| 947 | void dgetrf (int M, int N, double [] A, int LDA, int [] IPIV, ref int info);
|
---|
| 948 | /// <summary>
|
---|
| 949 | /// LU factorization of general matrix
|
---|
| 950 | /// </summary>
|
---|
| 951 | void sgetrf (int M, int N, float [] A, int LDA, int [] IPIV, ref int info);
|
---|
| 952 |
|
---|
| 953 | /// <summary>
|
---|
| 954 | /// LU factorization of general matrix
|
---|
| 955 | /// </summary>
|
---|
| 956 | void cgetrf (int M, int N, fcomplex [] A, int LDA, int [] IPIV, ref int info);
|
---|
| 957 |
|
---|
| 958 | /// <summary>
|
---|
| 959 | /// LU factorization of general matrix
|
---|
| 960 | /// </summary>
|
---|
| 961 | void zgetrf (int M, int N, complex [] A, int LDA, int [] IPIV, ref int info);
|
---|
| 962 | #endregion
|
---|
| 963 |
|
---|
| 964 | #region ?getri - inverse via LU factorization
|
---|
| 965 | /// <summary>
|
---|
| 966 | /// inverse of a matrix via LU factorization
|
---|
| 967 | /// </summary>
|
---|
| 968 | void dgetri (int N, double [] A, int LDA, int [] IPIV, ref int info);
|
---|
| 969 | /// <summary>
|
---|
| 970 | /// inverse of a matrix via LU factorization
|
---|
| 971 | /// </summary>
|
---|
| 972 | void sgetri (int N, float [] A, int LDA, int [] IPIV, ref int info);
|
---|
| 973 |
|
---|
| 974 | /// <summary>
|
---|
| 975 | /// inverse of a matrix via LU factorization
|
---|
| 976 | /// </summary>
|
---|
| 977 | void cgetri (int N, fcomplex [] A, int LDA, int [] IPIV, ref int info);
|
---|
| 978 |
|
---|
| 979 | /// <summary>
|
---|
| 980 | /// inverse of a matrix via LU factorization
|
---|
| 981 | /// </summary>
|
---|
| 982 | void zgetri (int N, complex [] A, int LDA, int [] IPIV, ref int info);
|
---|
| 983 | #endregion
|
---|
| 984 |
|
---|
| 985 | #region ORGQR
|
---|
| 986 | /// <summary>
|
---|
| 987 | /// QR factor extraction
|
---|
| 988 | /// </summary>
|
---|
| 989 | void dorgqr (int M, int N, int K, double [] A, int lda, double [] tau, ref int info);
|
---|
| 990 | /// <summary>
|
---|
| 991 | /// QR factor extraction
|
---|
| 992 | /// </summary>
|
---|
| 993 | void sorgqr (int M, int N, int K, float [] A, int lda, float [] tau, ref int info);
|
---|
| 994 | /// <summary>
|
---|
| 995 | /// QR factor extraction
|
---|
| 996 | /// </summary>
|
---|
| 997 | void cungqr (int M, int N, int K, fcomplex [] A, int lda, fcomplex [] tau, ref int info);
|
---|
| 998 | /// <summary>
|
---|
| 999 | /// QR factor extraction
|
---|
| 1000 | /// </summary>
|
---|
| 1001 | void zungqr (int M, int N, int K, complex [] A, int lda, complex [] tau, ref int info);
|
---|
| 1002 | #endregion
|
---|
| 1003 |
|
---|
| 1004 | #region ?geqrf - QR factorization
|
---|
| 1005 | /// <summary>
|
---|
| 1006 | /// QR factorization
|
---|
| 1007 | /// </summary>
|
---|
| 1008 | void dgeqrf (int M, int N, double [] A, int lda, double [] tau, ref int info);
|
---|
| 1009 | /// <summary>
|
---|
| 1010 | /// QR factorization
|
---|
| 1011 | /// </summary>
|
---|
| 1012 | void sgeqrf (int M, int N, float [] A, int lda, float [] tau, ref int info);
|
---|
| 1013 | /// <summary>
|
---|
| 1014 | /// QR factorization
|
---|
| 1015 | /// </summary>
|
---|
| 1016 | void cgeqrf (int M, int N, fcomplex [] A, int lda, fcomplex [] tau, ref int info);
|
---|
| 1017 | /// <summary>
|
---|
| 1018 | /// QR factorization
|
---|
| 1019 | /// </summary>
|
---|
| 1020 | void zgeqrf (int M, int N, complex [] A, int lda, complex [] tau, ref int info);
|
---|
| 1021 | #endregion
|
---|
| 1022 |
|
---|
| 1023 | #region GEQP3
|
---|
| 1024 | /// <summary>
|
---|
| 1025 | /// QR factorisation with column pivoting
|
---|
| 1026 | /// </summary>
|
---|
| 1027 | void dgeqp3 (int M, int N, double [] A, int LDA, int [] JPVT, double [] tau, ref int info);
|
---|
| 1028 | /// <summary>
|
---|
| 1029 | /// QR factorisation with column pivoting
|
---|
| 1030 | /// </summary>
|
---|
| 1031 | void sgeqp3 (int M, int N, float [] A, int LDA, int [] JPVT, float [] tau, ref int info);
|
---|
| 1032 | /// <summary>
|
---|
| 1033 | /// QR factorisation with column pivoting
|
---|
| 1034 | /// </summary>
|
---|
| 1035 | void cgeqp3 (int M, int N, fcomplex [] A, int LDA, int [] JPVT, fcomplex [] tau, ref int info);
|
---|
| 1036 | /// <summary>
|
---|
| 1037 | /// QR factorisation with column pivoting
|
---|
| 1038 | /// </summary>
|
---|
| 1039 | void zgeqp3 (int M, int N, complex [] A, int LDA, int [] JPVT, complex [] tau, ref int info);
|
---|
| 1040 | #endregion
|
---|
| 1041 |
|
---|
| 1042 | #region ?ormqr - mmult of QR factorization result
|
---|
| 1043 | /// <summary>
|
---|
| 1044 | /// multipliation for general matrix with QR decomposition factor
|
---|
| 1045 | /// </summary>
|
---|
| 1046 | void dormqr (char side, char trans, int m, int n, int k, double [] A, int lda, double [] tau, double [] C, int LDC, ref int info);
|
---|
| 1047 | /// <summary>
|
---|
| 1048 | /// multipliation for general matrix with QR decomposition factor
|
---|
| 1049 | /// </summary>
|
---|
| 1050 | void sormqr (char side, char trans, int m, int n, int k, float [] A, int lda, float [] tau, float [] C, int LDC, ref int info);
|
---|
| 1051 |
|
---|
| 1052 | #endregion
|
---|
| 1053 |
|
---|
| 1054 | #region DTRTRS
|
---|
| 1055 | /// <summary>
|
---|
| 1056 | /// Solve triangular system of linear equations (forward-/ backward substitution)
|
---|
| 1057 | /// </summary>
|
---|
| 1058 | /// <param name="uplo">'U': A is upper triangular, 'L': A is lower triangular</param>
|
---|
| 1059 | /// <param name="transA">'N': A * X = B (No transpose); 'T': A**T * X = B (Transpose), 'T': A**T * X = B (Transpose)</param>
|
---|
| 1060 | /// <param name="diag">'N' arbitrary diagonal elements, 'U' unit diagonal</param>
|
---|
| 1061 | /// <param name="N">order of A</param>
|
---|
| 1062 | /// <param name="nrhs">number of right hand sides - columns of matrix B</param>
|
---|
| 1063 | /// <param name="A">square matrix A</param>
|
---|
| 1064 | /// <param name="LDA">spacing between columns for A</param>
|
---|
| 1065 | /// <param name="B">(input/output) on input: right hand side, on output: solution x </param>
|
---|
| 1066 | /// <param name="LDB">spacing between columns for B</param>
|
---|
| 1067 | /// <param name="info">(output) 0: success; < 0: illigal argument, > 0: A is sinular having a zero on the i-th diagonal element. No solution will be computed than. </param>
|
---|
| 1068 | void dtrtrs (char uplo, char transA, char diag, int N, int nrhs, IntPtr A, int LDA, IntPtr B, int LDB, ref int info);
|
---|
| 1069 | /// <summary>
|
---|
| 1070 | /// Solve triangular system of linear equations (forward-/ backward substitution)
|
---|
| 1071 | /// </summary>
|
---|
| 1072 | /// <param name="uplo">'U': A is upper triangular, 'L': A is lower triangular</param>
|
---|
| 1073 | /// <param name="transA">'N': A * X = B (No transpose); 'T': A**T * X = B (Transpose), 'T': A**T * X = B (Transpose)</param>
|
---|
| 1074 | /// <param name="diag">'N' arbitrary diagonal elements, 'U' unit diagonal</param>
|
---|
| 1075 | /// <param name="N">order of A</param>
|
---|
| 1076 | /// <param name="nrhs">number of right hand sides - columns of matrix B</param>
|
---|
| 1077 | /// <param name="A">square matrix A</param>
|
---|
| 1078 | /// <param name="LDA">spacing between columns for A</param>
|
---|
| 1079 | /// <param name="B">(input/output) on input: right hand side, on output: solution x </param>
|
---|
| 1080 | /// <param name="LDB">spacing between columns for B</param>
|
---|
| 1081 | /// <param name="info">(output) 0: success; < 0: illigal argument, > 0: A is sinular having a zero on the i-th diagonal element. No solution will be computed than. </param>
|
---|
| 1082 | void strtrs (char uplo, char transA, char diag, int N, int nrhs, IntPtr A, int LDA, IntPtr B, int LDB, ref int info);
|
---|
| 1083 | /// <summary>
|
---|
| 1084 | /// Solve triangular system of linear equations (forward-/ backward substitution)
|
---|
| 1085 | /// </summary>
|
---|
| 1086 | /// <param name="uplo">'U': A is upper triangular, 'L': A is lower triangular</param>
|
---|
| 1087 | /// <param name="transA">'N': A * X = B (No transpose); 'T': A**T * X = B (Transpose), 'T': A**T * X = B (Transpose)</param>
|
---|
| 1088 | /// <param name="diag">'N' arbitrary diagonal elements, 'U' unit diagonal</param>
|
---|
| 1089 | /// <param name="N">order of A</param>
|
---|
| 1090 | /// <param name="nrhs">number of right hand sides - columns of matrix B</param>
|
---|
| 1091 | /// <param name="A">square matrix A</param>
|
---|
| 1092 | /// <param name="LDA">spacing between columns for A</param>
|
---|
| 1093 | /// <param name="B">(input/output) on input: right hand side, on output: solution x </param>
|
---|
| 1094 | /// <param name="LDB">spacing between columns for B</param>
|
---|
| 1095 | /// <param name="info">(output) 0: success; < 0: illigal argument, > 0: A is sinular having a zero on the i-th diagonal element. No solution will be computed than. </param>
|
---|
| 1096 | void ctrtrs (char uplo, char transA, char diag, int N, int nrhs, IntPtr A, int LDA, IntPtr B, int LDB, ref int info);
|
---|
| 1097 | /// <summary>
|
---|
| 1098 | /// Solve triangular system of linear equations (forward-/ backward substitution)
|
---|
| 1099 | /// </summary>
|
---|
| 1100 | /// <param name="uplo">'U': A is upper triangular, 'L': A is lower triangular</param>
|
---|
| 1101 | /// <param name="transA">'N': A * X = B (No transpose); 'T': A**T * X = B (Transpose), 'T': A**T * X = B (Transpose)</param>
|
---|
| 1102 | /// <param name="diag">'N' arbitrary diagonal elements, 'U' unit diagonal</param>
|
---|
| 1103 | /// <param name="N">order of A</param>
|
---|
| 1104 | /// <param name="nrhs">number of right hand sides - columns of matrix B</param>
|
---|
| 1105 | /// <param name="A">square matrix A</param>
|
---|
| 1106 | /// <param name="LDA">spacing between columns for A</param>
|
---|
| 1107 | /// <param name="B">(input/output) on input: right hand side, on output: solution x </param>
|
---|
| 1108 | /// <param name="LDB">spacing between columns for B</param>
|
---|
| 1109 | /// <param name="info">(output) 0: success; < 0: illigal argument, > 0: A is sinular having a zero on the i-th diagonal element. No solution will be computed than. </param>
|
---|
| 1110 | void ztrtrs (char uplo, char transA, char diag, int N, int nrhs, IntPtr A, int LDA, IntPtr B, int LDB, ref int info);
|
---|
| 1111 | #endregion
|
---|
| 1112 |
|
---|
| 1113 | #region ?GETRS
|
---|
| 1114 | /// <summary>
|
---|
| 1115 | /// solve system of linear equations by triangular matrices
|
---|
| 1116 | /// </summary>
|
---|
| 1117 | /// <param name="trans">transpose before work?</param>
|
---|
| 1118 | /// <param name="N">number rows</param>
|
---|
| 1119 | /// <param name="NRHS">number right hand sides</param>
|
---|
| 1120 | /// <param name="A">matrix A</param>
|
---|
| 1121 | /// <param name="LDA">spacing between columns: A</param>
|
---|
| 1122 | /// <param name="IPIV">pivoting indices</param>
|
---|
| 1123 | /// <param name="B">matrix B</param>
|
---|
| 1124 | /// <param name="LDB">spacing between columns: B</param>
|
---|
| 1125 | /// <param name="info">success info</param>
|
---|
| 1126 | void dgetrs (char trans, int N, int NRHS, double [] A, int LDA, int [] IPIV, double [] B, int LDB, ref int info);
|
---|
| 1127 | /// <summary>
|
---|
| 1128 | /// solve system of linear equations by triangular matrices
|
---|
| 1129 | /// </summary>
|
---|
| 1130 | /// <param name="trans">transpose before work?</param>
|
---|
| 1131 | /// <param name="N">number rows</param>
|
---|
| 1132 | /// <param name="NRHS">number right hand sides</param>
|
---|
| 1133 | /// <param name="A">matrix A</param>
|
---|
| 1134 | /// <param name="LDA">spacing between columns: A</param>
|
---|
| 1135 | /// <param name="IPIV">pivoting indices</param>
|
---|
| 1136 | /// <param name="B">matrix B</param>
|
---|
| 1137 | /// <param name="LDB">spacing between columns: B</param>
|
---|
| 1138 | /// <param name="info">success info</param>
|
---|
| 1139 | void sgetrs (char trans, int N, int NRHS, float [] A, int LDA, int [] IPIV, float [] B, int LDB, ref int info);
|
---|
| 1140 | /// <summary>
|
---|
| 1141 | /// solve system of linear equations by triangular matrices
|
---|
| 1142 | /// </summary>
|
---|
| 1143 | /// <param name="trans">transpose before work?</param>
|
---|
| 1144 | /// <param name="N">number rows</param>
|
---|
| 1145 | /// <param name="NRHS">number right hand sides</param>
|
---|
| 1146 | /// <param name="A">matrix A</param>
|
---|
| 1147 | /// <param name="LDA">spacing between columns: A</param>
|
---|
| 1148 | /// <param name="IPIV">pivoting indices</param>
|
---|
| 1149 | /// <param name="B">matrix B</param>
|
---|
| 1150 | /// <param name="LDB">spacing between columns: B</param>
|
---|
| 1151 | /// <param name="info">success info</param>
|
---|
| 1152 | void cgetrs (char trans, int N, int NRHS, fcomplex [] A, int LDA, int [] IPIV, fcomplex [] B, int LDB, ref int info);
|
---|
| 1153 | /// <summary>
|
---|
| 1154 | /// solve system of linear equations by triangular matrices
|
---|
| 1155 | /// </summary>
|
---|
| 1156 | /// <param name="trans">transpose before work?</param>
|
---|
| 1157 | /// <param name="N">number rows</param>
|
---|
| 1158 | /// <param name="NRHS">number right hand sides</param>
|
---|
| 1159 | /// <param name="A">matrix A</param>
|
---|
| 1160 | /// <param name="LDA">spacing between columns: A</param>
|
---|
| 1161 | /// <param name="IPIV">pivoting indices</param>
|
---|
| 1162 | /// <param name="B">matrix B</param>
|
---|
| 1163 | /// <param name="LDB">spacing between columns: B</param>
|
---|
| 1164 | /// <param name="info">success info</param>
|
---|
| 1165 | void zgetrs (char trans, int N, int NRHS, complex [] A, int LDA, int [] IPIV, complex [] B, int LDB, ref int info);
|
---|
| 1166 | #endregion
|
---|
| 1167 |
|
---|
| 1168 | #region ?GELSD - least square solution, SVD - divide & conquer
|
---|
| 1169 | void dgelsd (int m, int n, int nrhs, double[] A, int lda, double[] B, int ldb, double[] S, double RCond, ref int rank, ref int info);
|
---|
| 1170 | void sgelsd (int m, int n, int nrhs, float[] A, int lda, float[] B, int ldb, float[] S, float RCond, ref int rank, ref int info);
|
---|
| 1171 | void cgelsd (int m, int n, int nrhs, fcomplex[] A, int lda, fcomplex[] B, int ldb, float[] S, float RCond, ref int rank, ref int info);
|
---|
| 1172 | void zgelsd (int m, int n, int nrhs, complex[] A, int lda, complex[] B, int ldb, double[] S, double RCond, ref int rank, ref int info);
|
---|
| 1173 | #endregion
|
---|
| 1174 |
|
---|
| 1175 | #region ?GELSY - least square solution, QRP
|
---|
| 1176 | void dgelsy (int m,int n,int nrhs, double[] A,int lda, double[] B,int ldb, int[] JPVT0, double RCond, ref int rank, ref int info);
|
---|
| 1177 | void sgelsy (int m,int n,int nrhs, float[] A,int lda, float[] B,int ldb, int[] JPVT0, float RCond, ref int rank, ref int info);
|
---|
| 1178 | void cgelsy (int m,int n,int nrhs, fcomplex[] A,int lda, fcomplex[] B,int ldb, int[] JPVT0, float RCond, ref int rank, ref int info);
|
---|
| 1179 | void zgelsy (int m,int n,int nrhs, complex[] A,int lda, complex[] B,int ldb, int[] JPVT0, double RCond, ref int rank, ref int info);
|
---|
| 1180 | #endregion
|
---|
| 1181 |
|
---|
| 1182 | #region ?GEEVX - eigenvectors & -values, nonsymmetric A
|
---|
| 1183 | void dgeevx (char balance, char jobvl, char jobvr, char sense, int n, double[] A, int lda, double[] wr, double[] wi, double[] vl, int ldvl, double[] vr, int ldvr, ref int ilo, ref int ihi, double[] scale, ref double abnrm, double[] rconde, double[] rcondv, ref int info);
|
---|
| 1184 | void sgeevx (char balance, char jobvl, char jobvr, char sense, int n, float[] A, int lda, float[] wr, float[] wi, float[] vl, int ldvl, float[] vr, int ldvr, ref int ilo, ref int ihi, float[] scale, ref float abnrm, float[] rconde, float[] rcondv, ref int info);
|
---|
| 1185 | void cgeevx (char balance, char jobvl, char jobvr, char sense, int n, fcomplex[] A, int lda, fcomplex[] w, fcomplex[] vl, int ldvl, fcomplex[] vr, int ldvr, ref int ilo, ref int ihi, float[] scale, ref float abnrm, float[] rconde, float[] rcondv, ref int info);
|
---|
| 1186 | void zgeevx (char balance, char jobvl, char jobvr, char sense, int n, complex[] A, int lda, complex[] w, complex[] vl, int ldvl, complex[] vr, int ldvr, ref int ilo, ref int ihi, double[] scale, ref double abnrm, double[] rconde, double[] rcondv, ref int info);
|
---|
| 1187 | #endregion
|
---|
| 1188 |
|
---|
| 1189 | #region ?GEEVR - eigenvectors & -values, symmetric/hermitian A
|
---|
| 1190 | void dsyevr (char jobz, char range, char uplo, int n, double [] A, int lda, double vl, double vu, int il, int iu, double abstol, ref int m, double[] w, double [] z, int ldz, int[] isuppz, ref int info);
|
---|
| 1191 | void ssyevr (char jobz, char range, char uplo, int n, float [] A, int lda, float vl, float vu, int il, int iu, float abstol, ref int m, float [] w, float [] z, int ldz, int[] isuppz, ref int info);
|
---|
| 1192 | void cheevr (char jobz, char range, char uplo, int n, fcomplex[] A, int lda, float vl, float vu, int il, int iu, float abstol, ref int m, float [] w, fcomplex[] z, int ldz, int[] isuppz, ref int info);
|
---|
| 1193 | void zheevr (char jobz, char range, char uplo, int n, complex [] A, int lda, double vl, double vu, int il, int iu, double abstol, ref int m, double[] w, complex [] z, int ldz, int[] isuppz, ref int info);
|
---|
| 1194 | #endregion
|
---|
| 1195 |
|
---|
| 1196 | #region ?SYGV - eigenvectors & -values, symmetric/hermitian A and B, pos.def.B
|
---|
| 1197 | void dsygv (int itype, char jobz, char uplo, int n, double [] A, int lda, double [] B, int ldb, double [] w, ref int info);
|
---|
| 1198 | void ssygv (int itype, char jobz, char uplo, int n, float [] A, int lda, float [] B, int ldb, float [] w, ref int info);
|
---|
| 1199 | void chegv (int itype, char jobz, char uplo, int n, fcomplex[] A, int lda, fcomplex[] B, int ldb, float [] w, ref int info);
|
---|
| 1200 | void zhegv (int itype, char jobz, char uplo, int n, complex [] A, int lda, complex [] B, int ldb, double [] w, ref int info);
|
---|
| 1201 | #endregion
|
---|
| 1202 |
|
---|
| 1203 | }
|
---|
| 1204 | }
|
---|