| 1 | /*************************************************************************
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| 2 | Copyright (c) 1992-2007 The University of Tennessee. All rights reserved.
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| 3 |
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| 4 | Contributors:
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| 5 | * Sergey Bochkanov (ALGLIB project). Translation from FORTRAN to
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| 6 | pseudocode.
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| 7 |
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| 8 | See subroutines comments for additional copyrights.
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| 9 |
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| 10 | >>> SOURCE LICENSE >>>
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| 11 | This program is free software; you can redistribute it and/or modify
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| 12 | it under the terms of the GNU General Public License as published by
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| 13 | the Free Software Foundation (www.fsf.org); either version 2 of the
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| 14 | License, or (at your option) any later version.
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| 15 |
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| 16 | This program is distributed in the hope that it will be useful,
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| 17 | but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 18 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 19 | GNU General Public License for more details.
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| 20 |
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| 21 | A copy of the GNU General Public License is available at
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| 22 | http://www.fsf.org/licensing/licenses
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| 23 |
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| 24 | >>> END OF LICENSE >>>
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| 25 | *************************************************************************/
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| 26 |
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| 27 | using System;
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| 28 |
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| 29 | namespace alglib
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| 30 | {
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| 31 | public class srcond
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| 32 | {
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| 33 | /*************************************************************************
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| 34 | Condition number estimate of a symmetric matrix
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| 35 |
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| 36 | The algorithm calculates a lower bound of the condition number. In this
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| 37 | case, the algorithm does not return a lower bound of the condition number,
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| 38 | but an inverse number (to avoid an overflow in case of a singular matrix).
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| 39 |
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| 40 | It should be noted that 1-norm and inf-norm condition numbers of symmetric
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| 41 | matrices are equal, so the algorithm doesn't take into account the
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| 42 | differences between these types of norms.
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| 43 |
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| 44 | Input parameters:
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| 45 | A - symmetric definite matrix which is given by its upper or
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| 46 | lower triangle depending on IsUpper.
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| 47 | Array with elements [0..N-1, 0..N-1].
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| 48 | N - size of matrix A.
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| 49 | IsUpper - storage format.
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| 50 |
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| 51 | Result:
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| 52 | 1/LowerBound(cond(A))
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| 53 | *************************************************************************/
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| 54 | public static double smatrixrcond(ref double[,] a,
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| 55 | int n,
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| 56 | bool isupper)
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| 57 | {
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| 58 | double result = 0;
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| 59 | int i = 0;
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| 60 | int j = 0;
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| 61 | double[,] a1 = new double[0,0];
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| 62 |
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| 63 | a1 = new double[n+1, n+1];
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| 64 | for(i=1; i<=n; i++)
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| 65 | {
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| 66 | if( isupper )
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| 67 | {
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| 68 | for(j=i; j<=n; j++)
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| 69 | {
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| 70 | a1[i,j] = a[i-1,j-1];
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| 71 | }
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| 72 | }
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| 73 | else
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| 74 | {
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| 75 | for(j=1; j<=i; j++)
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| 76 | {
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| 77 | a1[i,j] = a[i-1,j-1];
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| 78 | }
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| 79 | }
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| 80 | }
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| 81 | result = rcondsymmetric(a1, n, isupper);
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| 82 | return result;
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| 83 | }
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| 84 |
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| 85 |
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| 86 | /*************************************************************************
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| 87 | Condition number estimate of a matrix given by LDLT-decomposition
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| 88 |
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| 89 | The algorithm calculates a lower bound of the condition number. In this
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| 90 | case, the algorithm does not return a lower bound of the condition number,
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| 91 | but an inverse number (to avoid an overflow in case of a singular matrix).
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| 92 |
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| 93 | It should be noted that 1-norm and inf-norm condition numbers of symmetric
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| 94 | matrices are equal, so the algorithm doesn't take into account the
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| 95 | differences between these types of norms.
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| 96 |
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| 97 | Input parameters:
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| 98 | L - LDLT-decomposition of matrix A given by the upper or lower
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| 99 | triangle depending on IsUpper.
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| 100 | Output of SMatrixLDLT subroutine.
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| 101 | Pivots - table of permutations which were made during LDLT-decomposition,
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| 102 | Output of SMatrixLDLT subroutine.
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| 103 | N - size of matrix A.
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| 104 | IsUpper - storage format.
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| 105 |
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| 106 | Result:
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| 107 | 1/LowerBound(cond(A))
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| 108 | *************************************************************************/
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| 109 | public static double smatrixldltrcond(ref double[,] l,
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| 110 | ref int[] pivots,
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| 111 | int n,
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| 112 | bool isupper)
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| 113 | {
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| 114 | double result = 0;
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| 115 | int i = 0;
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| 116 | int j = 0;
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| 117 | double[,] l1 = new double[0,0];
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| 118 | int[] p1 = new int[0];
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| 119 |
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| 120 | l1 = new double[n+1, n+1];
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| 121 | for(i=1; i<=n; i++)
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| 122 | {
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| 123 | if( isupper )
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| 124 | {
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| 125 | for(j=i; j<=n; j++)
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| 126 | {
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| 127 | l1[i,j] = l[i-1,j-1];
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| 128 | }
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| 129 | }
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| 130 | else
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| 131 | {
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| 132 | for(j=1; j<=i; j++)
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| 133 | {
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| 134 | l1[i,j] = l[i-1,j-1];
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| 135 | }
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| 136 | }
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| 137 | }
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| 138 | p1 = new int[n+1];
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| 139 | for(i=1; i<=n; i++)
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| 140 | {
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| 141 | if( pivots[i-1]>=0 )
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| 142 | {
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| 143 | p1[i] = pivots[i-1]+1;
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| 144 | }
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| 145 | else
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| 146 | {
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| 147 | p1[i] = -(pivots[i-1]+n+1);
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| 148 | }
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| 149 | }
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| 150 | result = rcondldlt(ref l1, ref p1, n, isupper);
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| 151 | return result;
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| 152 | }
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| 153 |
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| 154 |
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| 155 | public static double rcondsymmetric(double[,] a,
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| 156 | int n,
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| 157 | bool isupper)
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| 158 | {
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| 159 | double result = 0;
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| 160 | int i = 0;
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| 161 | int j = 0;
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| 162 | int im = 0;
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| 163 | int jm = 0;
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| 164 | double v = 0;
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| 165 | double nrm = 0;
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| 166 | int[] pivots = new int[0];
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| 167 |
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| 168 | a = (double[,])a.Clone();
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| 169 |
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| 170 | nrm = 0;
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| 171 | for(j=1; j<=n; j++)
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| 172 | {
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| 173 | v = 0;
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| 174 | for(i=1; i<=n; i++)
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| 175 | {
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| 176 | im = i;
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| 177 | jm = j;
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| 178 | if( isupper & j<i )
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| 179 | {
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| 180 | im = j;
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| 181 | jm = i;
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| 182 | }
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| 183 | if( !isupper & j>i )
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| 184 | {
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| 185 | im = j;
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| 186 | jm = i;
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| 187 | }
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| 188 | v = v+Math.Abs(a[im,jm]);
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| 189 | }
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| 190 | nrm = Math.Max(nrm, v);
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| 191 | }
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| 192 | ldlt.ldltdecomposition(ref a, n, isupper, ref pivots);
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| 193 | internalldltrcond(ref a, ref pivots, n, isupper, true, nrm, ref v);
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| 194 | result = v;
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| 195 | return result;
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| 196 | }
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| 197 |
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| 198 |
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| 199 | public static double rcondldlt(ref double[,] l,
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| 200 | ref int[] pivots,
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| 201 | int n,
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| 202 | bool isupper)
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| 203 | {
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| 204 | double result = 0;
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| 205 | double v = 0;
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| 206 |
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| 207 | internalldltrcond(ref l, ref pivots, n, isupper, false, 0, ref v);
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| 208 | result = v;
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| 209 | return result;
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| 210 | }
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| 211 |
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| 212 |
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| 213 | public static void internalldltrcond(ref double[,] l,
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| 214 | ref int[] pivots,
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| 215 | int n,
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| 216 | bool isupper,
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| 217 | bool isnormprovided,
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| 218 | double anorm,
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| 219 | ref double rcond)
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| 220 | {
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| 221 | int i = 0;
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| 222 | int ix = 0;
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| 223 | int kase = 0;
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| 224 | int k = 0;
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| 225 | int km1 = 0;
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| 226 | int km2 = 0;
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| 227 | int kp1 = 0;
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| 228 | int kp2 = 0;
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| 229 | double ainvnm = 0;
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| 230 | double[] work0 = new double[0];
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| 231 | double[] work1 = new double[0];
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| 232 | double[] work2 = new double[0];
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| 233 | int[] iwork = new int[0];
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| 234 | double v = 0;
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| 235 | int i_ = 0;
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| 236 |
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| 237 | System.Diagnostics.Debug.Assert(n>=0);
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| 238 |
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| 239 | //
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| 240 | // Check that the diagonal matrix D is nonsingular.
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| 241 | //
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| 242 | rcond = 0;
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| 243 | if( isupper )
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| 244 | {
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| 245 | for(i=n; i>=1; i--)
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| 246 | {
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| 247 | if( pivots[i]>0 & (double)(l[i,i])==(double)(0) )
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| 248 | {
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| 249 | return;
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| 250 | }
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| 251 | }
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| 252 | }
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| 253 | else
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| 254 | {
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| 255 | for(i=1; i<=n; i++)
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| 256 | {
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| 257 | if( pivots[i]>0 & (double)(l[i,i])==(double)(0) )
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| 258 | {
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| 259 | return;
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| 260 | }
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| 261 | }
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| 262 | }
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| 263 |
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| 264 | //
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| 265 | // Estimate the norm of A.
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| 266 | //
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| 267 | if( !isnormprovided )
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| 268 | {
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| 269 | kase = 0;
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| 270 | anorm = 0;
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| 271 | while( true )
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| 272 | {
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| 273 | estnorm.iterativeestimate1norm(n, ref work1, ref work0, ref iwork, ref anorm, ref kase);
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| 274 | if( kase==0 )
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| 275 | {
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| 276 | break;
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| 277 | }
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| 278 | if( isupper )
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| 279 | {
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| 280 |
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| 281 | //
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| 282 | // Multiply by U'
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| 283 | //
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| 284 | k = n;
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| 285 | while( k>=1 )
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| 286 | {
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| 287 | if( pivots[k]>0 )
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| 288 | {
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| 289 |
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| 290 | //
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| 291 | // P(k)
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| 292 | //
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| 293 | v = work0[k];
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| 294 | work0[k] = work0[pivots[k]];
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| 295 | work0[pivots[k]] = v;
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| 296 |
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| 297 | //
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| 298 | // U(k)
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| 299 | //
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| 300 | km1 = k-1;
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| 301 | v = 0.0;
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| 302 | for(i_=1; i_<=km1;i_++)
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| 303 | {
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| 304 | v += work0[i_]*l[i_,k];
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| 305 | }
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| 306 | work0[k] = work0[k]+v;
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| 307 |
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| 308 | //
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| 309 | // Next k
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| 310 | //
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| 311 | k = k-1;
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| 312 | }
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| 313 | else
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| 314 | {
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| 315 |
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| 316 | //
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| 317 | // P(k)
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| 318 | //
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| 319 | v = work0[k-1];
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| 320 | work0[k-1] = work0[-pivots[k-1]];
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| 321 | work0[-pivots[k-1]] = v;
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| 322 |
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| 323 | //
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| 324 | // U(k)
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| 325 | //
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| 326 | km1 = k-1;
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| 327 | km2 = k-2;
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| 328 | v = 0.0;
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| 329 | for(i_=1; i_<=km2;i_++)
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| 330 | {
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| 331 | v += work0[i_]*l[i_,km1];
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| 332 | }
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| 333 | work0[km1] = work0[km1]+v;
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| 334 | v = 0.0;
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| 335 | for(i_=1; i_<=km2;i_++)
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| 336 | {
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| 337 | v += work0[i_]*l[i_,k];
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| 338 | }
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| 339 | work0[k] = work0[k]+v;
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| 340 |
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| 341 | //
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| 342 | // Next k
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| 343 | //
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| 344 | k = k-2;
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| 345 | }
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| 346 | }
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| 347 |
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| 348 | //
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| 349 | // Multiply by D
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| 350 | //
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| 351 | k = n;
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| 352 | while( k>=1 )
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| 353 | {
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| 354 | if( pivots[k]>0 )
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| 355 | {
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| 356 | work0[k] = work0[k]*l[k,k];
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| 357 | k = k-1;
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| 358 | }
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| 359 | else
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| 360 | {
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| 361 | v = work0[k-1];
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| 362 | work0[k-1] = l[k-1,k-1]*work0[k-1]+l[k-1,k]*work0[k];
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| 363 | work0[k] = l[k-1,k]*v+l[k,k]*work0[k];
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| 364 | k = k-2;
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| 365 | }
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| 366 | }
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| 367 |
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| 368 | //
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| 369 | // Multiply by U
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| 370 | //
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| 371 | k = 1;
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| 372 | while( k<=n )
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| 373 | {
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| 374 | if( pivots[k]>0 )
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| 375 | {
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| 376 |
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| 377 | //
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| 378 | // U(k)
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| 379 | //
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| 380 | km1 = k-1;
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| 381 | v = work0[k];
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| 382 | for(i_=1; i_<=km1;i_++)
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| 383 | {
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| 384 | work0[i_] = work0[i_] + v*l[i_,k];
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| 385 | }
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| 386 |
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| 387 | //
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| 388 | // P(k)
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| 389 | //
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| 390 | v = work0[k];
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| 391 | work0[k] = work0[pivots[k]];
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| 392 | work0[pivots[k]] = v;
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| 393 |
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| 394 | //
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| 395 | // Next k
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| 396 | //
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| 397 | k = k+1;
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| 398 | }
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| 399 | else
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| 400 | {
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| 401 |
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| 402 | //
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| 403 | // U(k)
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| 404 | //
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| 405 | km1 = k-1;
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| 406 | kp1 = k+1;
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| 407 | v = work0[k];
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| 408 | for(i_=1; i_<=km1;i_++)
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| 409 | {
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| 410 | work0[i_] = work0[i_] + v*l[i_,k];
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| 411 | }
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| 412 | v = work0[kp1];
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| 413 | for(i_=1; i_<=km1;i_++)
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| 414 | {
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| 415 | work0[i_] = work0[i_] + v*l[i_,kp1];
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| 416 | }
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| 417 |
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| 418 | //
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| 419 | // P(k)
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| 420 | //
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| 421 | v = work0[k];
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| 422 | work0[k] = work0[-pivots[k]];
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| 423 | work0[-pivots[k]] = v;
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| 424 |
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| 425 | //
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| 426 | // Next k
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| 427 | //
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| 428 | k = k+2;
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| 429 | }
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| 430 | }
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| 431 | }
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| 432 | else
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| 433 | {
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| 434 |
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| 435 | //
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| 436 | // Multiply by L'
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| 437 | //
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| 438 | k = 1;
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| 439 | while( k<=n )
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| 440 | {
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| 441 | if( pivots[k]>0 )
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| 442 | {
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| 443 |
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| 444 | //
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| 445 | // P(k)
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| 446 | //
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| 447 | v = work0[k];
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| 448 | work0[k] = work0[pivots[k]];
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| 449 | work0[pivots[k]] = v;
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| 450 |
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| 451 | //
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| 452 | // L(k)
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| 453 | //
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| 454 | kp1 = k+1;
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| 455 | v = 0.0;
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| 456 | for(i_=kp1; i_<=n;i_++)
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| 457 | {
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| 458 | v += work0[i_]*l[i_,k];
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| 459 | }
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| 460 | work0[k] = work0[k]+v;
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| 461 |
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| 462 | //
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| 463 | // Next k
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| 464 | //
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| 465 | k = k+1;
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| 466 | }
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| 467 | else
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| 468 | {
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| 469 |
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| 470 | //
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| 471 | // P(k)
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| 472 | //
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| 473 | v = work0[k+1];
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| 474 | work0[k+1] = work0[-pivots[k+1]];
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| 475 | work0[-pivots[k+1]] = v;
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| 476 |
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| 477 | //
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| 478 | // L(k)
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| 479 | //
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| 480 | kp1 = k+1;
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| 481 | kp2 = k+2;
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| 482 | v = 0.0;
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| 483 | for(i_=kp2; i_<=n;i_++)
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| 484 | {
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| 485 | v += work0[i_]*l[i_,k];
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| 486 | }
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| 487 | work0[k] = work0[k]+v;
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| 488 | v = 0.0;
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| 489 | for(i_=kp2; i_<=n;i_++)
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| 490 | {
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| 491 | v += work0[i_]*l[i_,kp1];
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| 492 | }
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| 493 | work0[kp1] = work0[kp1]+v;
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| 494 |
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| 495 | //
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| 496 | // Next k
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| 497 | //
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| 498 | k = k+2;
|
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| 499 | }
|
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| 500 | }
|
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| 501 |
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| 502 | //
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| 503 | // Multiply by D
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| 504 | //
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| 505 | k = n;
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| 506 | while( k>=1 )
|
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| 507 | {
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| 508 | if( pivots[k]>0 )
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| 509 | {
|
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| 510 | work0[k] = work0[k]*l[k,k];
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| 511 | k = k-1;
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| 512 | }
|
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| 513 | else
|
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| 514 | {
|
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| 515 | v = work0[k-1];
|
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| 516 | work0[k-1] = l[k-1,k-1]*work0[k-1]+l[k,k-1]*work0[k];
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| 517 | work0[k] = l[k,k-1]*v+l[k,k]*work0[k];
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| 518 | k = k-2;
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| 519 | }
|
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| 520 | }
|
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| 521 |
|
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| 522 | //
|
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| 523 | // Multiply by L
|
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| 524 | //
|
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| 525 | k = n;
|
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| 526 | while( k>=1 )
|
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| 527 | {
|
|---|
| 528 | if( pivots[k]>0 )
|
|---|
| 529 | {
|
|---|
| 530 |
|
|---|
| 531 | //
|
|---|
| 532 | // L(k)
|
|---|
| 533 | //
|
|---|
| 534 | kp1 = k+1;
|
|---|
| 535 | v = work0[k];
|
|---|
| 536 | for(i_=kp1; i_<=n;i_++)
|
|---|
| 537 | {
|
|---|
| 538 | work0[i_] = work0[i_] + v*l[i_,k];
|
|---|
| 539 | }
|
|---|
| 540 |
|
|---|
| 541 | //
|
|---|
| 542 | // P(k)
|
|---|
| 543 | //
|
|---|
| 544 | v = work0[k];
|
|---|
| 545 | work0[k] = work0[pivots[k]];
|
|---|
| 546 | work0[pivots[k]] = v;
|
|---|
| 547 |
|
|---|
| 548 | //
|
|---|
| 549 | // Next k
|
|---|
| 550 | //
|
|---|
| 551 | k = k-1;
|
|---|
| 552 | }
|
|---|
| 553 | else
|
|---|
| 554 | {
|
|---|
| 555 |
|
|---|
| 556 | //
|
|---|
| 557 | // L(k)
|
|---|
| 558 | //
|
|---|
| 559 | kp1 = k+1;
|
|---|
| 560 | km1 = k-1;
|
|---|
| 561 | v = work0[k];
|
|---|
| 562 | for(i_=kp1; i_<=n;i_++)
|
|---|
| 563 | {
|
|---|
| 564 | work0[i_] = work0[i_] + v*l[i_,k];
|
|---|
| 565 | }
|
|---|
| 566 | v = work0[km1];
|
|---|
| 567 | for(i_=kp1; i_<=n;i_++)
|
|---|
| 568 | {
|
|---|
| 569 | work0[i_] = work0[i_] + v*l[i_,km1];
|
|---|
| 570 | }
|
|---|
| 571 |
|
|---|
| 572 | //
|
|---|
| 573 | // P(k)
|
|---|
| 574 | //
|
|---|
| 575 | v = work0[k];
|
|---|
| 576 | work0[k] = work0[-pivots[k]];
|
|---|
| 577 | work0[-pivots[k]] = v;
|
|---|
| 578 |
|
|---|
| 579 | //
|
|---|
| 580 | // Next k
|
|---|
| 581 | //
|
|---|
| 582 | k = k-2;
|
|---|
| 583 | }
|
|---|
| 584 | }
|
|---|
| 585 | }
|
|---|
| 586 | }
|
|---|
| 587 | }
|
|---|
| 588 |
|
|---|
| 589 | //
|
|---|
| 590 | // Quick return if possible
|
|---|
| 591 | //
|
|---|
| 592 | rcond = 0;
|
|---|
| 593 | if( n==0 )
|
|---|
| 594 | {
|
|---|
| 595 | rcond = 1;
|
|---|
| 596 | return;
|
|---|
| 597 | }
|
|---|
| 598 | if( (double)(anorm)==(double)(0) )
|
|---|
| 599 | {
|
|---|
| 600 | return;
|
|---|
| 601 | }
|
|---|
| 602 |
|
|---|
| 603 | //
|
|---|
| 604 | // Estimate the 1-norm of inv(A).
|
|---|
| 605 | //
|
|---|
| 606 | kase = 0;
|
|---|
| 607 | while( true )
|
|---|
| 608 | {
|
|---|
| 609 | estnorm.iterativeestimate1norm(n, ref work1, ref work0, ref iwork, ref ainvnm, ref kase);
|
|---|
| 610 | if( kase==0 )
|
|---|
| 611 | {
|
|---|
| 612 | break;
|
|---|
| 613 | }
|
|---|
| 614 | ssolve.solvesystemldlt(ref l, ref pivots, work0, n, isupper, ref work2);
|
|---|
| 615 | for(i_=1; i_<=n;i_++)
|
|---|
| 616 | {
|
|---|
| 617 | work0[i_] = work2[i_];
|
|---|
| 618 | }
|
|---|
| 619 | }
|
|---|
| 620 |
|
|---|
| 621 | //
|
|---|
| 622 | // Compute the estimate of the reciprocal condition number.
|
|---|
| 623 | //
|
|---|
| 624 | if( (double)(ainvnm)!=(double)(0) )
|
|---|
| 625 | {
|
|---|
| 626 | v = 1/ainvnm;
|
|---|
| 627 | rcond = v/anorm;
|
|---|
| 628 | }
|
|---|
| 629 | }
|
|---|
| 630 | }
|
|---|
| 631 | }
|
|---|
