[2806] | 1 | /*************************************************************************
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| 2 | Copyright (c) 2005-2007, Sergey Bochkanov (ALGLIB project).
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| 3 |
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| 4 | >>> SOURCE LICENSE >>>
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| 5 | This program is free software; you can redistribute it and/or modify
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| 6 | it under the terms of the GNU General Public License as published by
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| 7 | the Free Software Foundation (www.fsf.org); either version 2 of the
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| 8 | License, or (at your option) any later version.
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| 9 |
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| 10 | This program is distributed in the hope that it will be useful,
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| 11 | but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 12 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 13 | GNU General Public License for more details.
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| 14 |
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| 15 | A copy of the GNU General Public License is available at
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| 16 | http://www.fsf.org/licensing/licenses
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| 17 |
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| 18 | >>> END OF LICENSE >>>
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| 19 | *************************************************************************/
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| 20 |
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| 21 | using System;
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| 22 |
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| 23 | namespace alglib
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| 24 | {
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| 25 | public class inverseupdate
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| 26 | {
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| 27 | /*************************************************************************
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| 28 | Inverse matrix update by the Sherman-Morrison formula
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| 29 |
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| 30 | The algorithm updates matrix A^-1 when adding a number to an element
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| 31 | of matrix A.
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| 32 |
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| 33 | Input parameters:
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| 34 | InvA - inverse of matrix A.
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| 35 | Array whose indexes range within [0..N-1, 0..N-1].
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| 36 | N - size of matrix A.
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| 37 | UpdRow - row where the element to be updated is stored.
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| 38 | UpdColumn - column where the element to be updated is stored.
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| 39 | UpdVal - a number to be added to the element.
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| 40 |
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| 41 |
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| 42 | Output parameters:
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| 43 | InvA - inverse of modified matrix A.
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| 44 |
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| 45 | -- ALGLIB --
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| 46 | Copyright 2005 by Bochkanov Sergey
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| 47 | *************************************************************************/
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| 48 | public static void rmatrixinvupdatesimple(ref double[,] inva,
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| 49 | int n,
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| 50 | int updrow,
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| 51 | int updcolumn,
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| 52 | double updval)
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| 53 | {
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| 54 | double[] t1 = new double[0];
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| 55 | double[] t2 = new double[0];
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| 56 | int i = 0;
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| 57 | double lambda = 0;
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| 58 | double vt = 0;
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| 59 | int i_ = 0;
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| 60 |
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| 61 | System.Diagnostics.Debug.Assert(updrow>=0 & updrow<n, "RMatrixInvUpdateSimple: incorrect UpdRow!");
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| 62 | System.Diagnostics.Debug.Assert(updcolumn>=0 & updcolumn<n, "RMatrixInvUpdateSimple: incorrect UpdColumn!");
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| 63 | t1 = new double[n-1+1];
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| 64 | t2 = new double[n-1+1];
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| 65 |
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| 66 | //
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| 67 | // T1 = InvA * U
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| 68 | //
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| 69 | for(i_=0; i_<=n-1;i_++)
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| 70 | {
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| 71 | t1[i_] = inva[i_,updrow];
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| 72 | }
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| 73 |
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| 74 | //
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| 75 | // T2 = v*InvA
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| 76 | //
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| 77 | for(i_=0; i_<=n-1;i_++)
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| 78 | {
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| 79 | t2[i_] = inva[updcolumn,i_];
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| 80 | }
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| 81 |
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| 82 | //
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| 83 | // Lambda = v * InvA * U
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| 84 | //
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| 85 | lambda = updval*inva[updcolumn,updrow];
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| 86 |
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| 87 | //
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| 88 | // InvA = InvA - correction
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| 89 | //
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| 90 | for(i=0; i<=n-1; i++)
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| 91 | {
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| 92 | vt = updval*t1[i];
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| 93 | vt = vt/(1+lambda);
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| 94 | for(i_=0; i_<=n-1;i_++)
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| 95 | {
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| 96 | inva[i,i_] = inva[i,i_] - vt*t2[i_];
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| 97 | }
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| 98 | }
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| 99 | }
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| 100 |
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| 101 |
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| 102 | /*************************************************************************
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| 103 | Inverse matrix update by the Sherman-Morrison formula
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| 104 |
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| 105 | The algorithm updates matrix A^-1 when adding a vector to a row
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| 106 | of matrix A.
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| 107 |
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| 108 | Input parameters:
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| 109 | InvA - inverse of matrix A.
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| 110 | Array whose indexes range within [0..N-1, 0..N-1].
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| 111 | N - size of matrix A.
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| 112 | UpdRow - the row of A whose vector V was added.
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| 113 | 0 <= Row <= N-1
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| 114 | V - the vector to be added to a row.
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| 115 | Array whose index ranges within [0..N-1].
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| 116 |
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| 117 | Output parameters:
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| 118 | InvA - inverse of modified matrix A.
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| 119 |
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| 120 | -- ALGLIB --
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| 121 | Copyright 2005 by Bochkanov Sergey
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| 122 | *************************************************************************/
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| 123 | public static void rmatrixinvupdaterow(ref double[,] inva,
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| 124 | int n,
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| 125 | int updrow,
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| 126 | ref double[] v)
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| 127 | {
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| 128 | double[] t1 = new double[0];
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| 129 | double[] t2 = new double[0];
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| 130 | int i = 0;
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| 131 | int j = 0;
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| 132 | double lambda = 0;
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| 133 | double vt = 0;
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| 134 | int i_ = 0;
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| 135 |
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| 136 | t1 = new double[n-1+1];
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| 137 | t2 = new double[n-1+1];
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| 138 |
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| 139 | //
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| 140 | // T1 = InvA * U
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| 141 | //
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| 142 | for(i_=0; i_<=n-1;i_++)
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| 143 | {
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| 144 | t1[i_] = inva[i_,updrow];
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| 145 | }
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| 146 |
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| 147 | //
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| 148 | // T2 = v*InvA
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| 149 | // Lambda = v * InvA * U
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| 150 | //
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| 151 | for(j=0; j<=n-1; j++)
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| 152 | {
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| 153 | vt = 0.0;
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| 154 | for(i_=0; i_<=n-1;i_++)
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| 155 | {
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| 156 | vt += v[i_]*inva[i_,j];
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| 157 | }
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| 158 | t2[j] = vt;
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| 159 | }
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| 160 | lambda = t2[updrow];
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| 161 |
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| 162 | //
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| 163 | // InvA = InvA - correction
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| 164 | //
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| 165 | for(i=0; i<=n-1; i++)
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| 166 | {
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| 167 | vt = t1[i]/(1+lambda);
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| 168 | for(i_=0; i_<=n-1;i_++)
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| 169 | {
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| 170 | inva[i,i_] = inva[i,i_] - vt*t2[i_];
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| 171 | }
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| 172 | }
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| 173 | }
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| 174 |
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| 175 |
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| 176 | /*************************************************************************
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| 177 | Inverse matrix update by the Sherman-Morrison formula
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| 178 |
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| 179 | The algorithm updates matrix A^-1 when adding a vector to a column
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| 180 | of matrix A.
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| 181 |
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| 182 | Input parameters:
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| 183 | InvA - inverse of matrix A.
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| 184 | Array whose indexes range within [0..N-1, 0..N-1].
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| 185 | N - size of matrix A.
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| 186 | UpdColumn - the column of A whose vector U was added.
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| 187 | 0 <= UpdColumn <= N-1
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| 188 | U - the vector to be added to a column.
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| 189 | Array whose index ranges within [0..N-1].
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| 190 |
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| 191 | Output parameters:
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| 192 | InvA - inverse of modified matrix A.
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| 193 |
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| 194 | -- ALGLIB --
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| 195 | Copyright 2005 by Bochkanov Sergey
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| 196 | *************************************************************************/
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| 197 | public static void rmatrixinvupdatecolumn(ref double[,] inva,
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| 198 | int n,
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| 199 | int updcolumn,
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| 200 | ref double[] u)
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| 201 | {
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| 202 | double[] t1 = new double[0];
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| 203 | double[] t2 = new double[0];
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| 204 | int i = 0;
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| 205 | double lambda = 0;
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| 206 | double vt = 0;
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| 207 | int i_ = 0;
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| 208 |
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| 209 | t1 = new double[n-1+1];
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| 210 | t2 = new double[n-1+1];
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| 211 |
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| 212 | //
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| 213 | // T1 = InvA * U
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| 214 | // Lambda = v * InvA * U
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| 215 | //
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| 216 | for(i=0; i<=n-1; i++)
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| 217 | {
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| 218 | vt = 0.0;
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| 219 | for(i_=0; i_<=n-1;i_++)
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| 220 | {
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| 221 | vt += inva[i,i_]*u[i_];
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| 222 | }
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| 223 | t1[i] = vt;
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| 224 | }
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| 225 | lambda = t1[updcolumn];
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| 226 |
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| 227 | //
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| 228 | // T2 = v*InvA
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| 229 | //
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| 230 | for(i_=0; i_<=n-1;i_++)
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| 231 | {
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| 232 | t2[i_] = inva[updcolumn,i_];
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| 233 | }
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| 234 |
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| 235 | //
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| 236 | // InvA = InvA - correction
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| 237 | //
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| 238 | for(i=0; i<=n-1; i++)
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| 239 | {
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| 240 | vt = t1[i]/(1+lambda);
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| 241 | for(i_=0; i_<=n-1;i_++)
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| 242 | {
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| 243 | inva[i,i_] = inva[i,i_] - vt*t2[i_];
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| 244 | }
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| 245 | }
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| 246 | }
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| 247 |
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| 248 |
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| 249 | /*************************************************************************
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| 250 | Inverse matrix update by the Sherman-Morrison formula
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| 251 |
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| 252 | The algorithm computes the inverse of matrix A+u*v by using the given matrix
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| 253 | A^-1 and the vectors u and v.
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| 254 |
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| 255 | Input parameters:
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| 256 | InvA - inverse of matrix A.
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| 257 | Array whose indexes range within [0..N-1, 0..N-1].
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| 258 | N - size of matrix A.
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| 259 | U - the vector modifying the matrix.
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| 260 | Array whose index ranges within [0..N-1].
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| 261 | V - the vector modifying the matrix.
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| 262 | Array whose index ranges within [0..N-1].
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| 263 |
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| 264 | Output parameters:
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| 265 | InvA - inverse of matrix A + u*v'.
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| 266 |
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| 267 | -- ALGLIB --
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| 268 | Copyright 2005 by Bochkanov Sergey
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| 269 | *************************************************************************/
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| 270 | public static void rmatrixinvupdateuv(ref double[,] inva,
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| 271 | int n,
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| 272 | ref double[] u,
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| 273 | ref double[] v)
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| 274 | {
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| 275 | double[] t1 = new double[0];
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| 276 | double[] t2 = new double[0];
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| 277 | int i = 0;
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| 278 | int j = 0;
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| 279 | double lambda = 0;
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| 280 | double vt = 0;
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| 281 | int i_ = 0;
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| 282 |
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| 283 | t1 = new double[n-1+1];
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| 284 | t2 = new double[n-1+1];
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| 285 |
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| 286 | //
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| 287 | // T1 = InvA * U
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| 288 | // Lambda = v * T1
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| 289 | //
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| 290 | for(i=0; i<=n-1; i++)
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| 291 | {
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| 292 | vt = 0.0;
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| 293 | for(i_=0; i_<=n-1;i_++)
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| 294 | {
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| 295 | vt += inva[i,i_]*u[i_];
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| 296 | }
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| 297 | t1[i] = vt;
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| 298 | }
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| 299 | lambda = 0.0;
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| 300 | for(i_=0; i_<=n-1;i_++)
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| 301 | {
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| 302 | lambda += v[i_]*t1[i_];
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| 303 | }
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| 304 |
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| 305 | //
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| 306 | // T2 = v*InvA
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| 307 | //
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| 308 | for(j=0; j<=n-1; j++)
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| 309 | {
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| 310 | vt = 0.0;
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| 311 | for(i_=0; i_<=n-1;i_++)
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| 312 | {
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| 313 | vt += v[i_]*inva[i_,j];
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| 314 | }
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| 315 | t2[j] = vt;
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| 316 | }
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| 317 |
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| 318 | //
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| 319 | // InvA = InvA - correction
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| 320 | //
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| 321 | for(i=0; i<=n-1; i++)
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| 322 | {
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| 323 | vt = t1[i]/(1+lambda);
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| 324 | for(i_=0; i_<=n-1;i_++)
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| 325 | {
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| 326 | inva[i,i_] = inva[i,i_] - vt*t2[i_];
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| 327 | }
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| 328 | }
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| 329 | }
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| 330 |
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| 331 |
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| 332 | public static void shermanmorrisonsimpleupdate(ref double[,] inva,
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| 333 | int n,
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| 334 | int updrow,
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| 335 | int updcolumn,
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| 336 | double updval)
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| 337 | {
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| 338 | double[] t1 = new double[0];
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| 339 | double[] t2 = new double[0];
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| 340 | int i = 0;
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| 341 | double lambda = 0;
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| 342 | double vt = 0;
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| 343 | int i_ = 0;
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| 344 |
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| 345 | t1 = new double[n+1];
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| 346 | t2 = new double[n+1];
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| 347 |
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| 348 | //
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| 349 | // T1 = InvA * U
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| 350 | //
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| 351 | for(i_=1; i_<=n;i_++)
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| 352 | {
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| 353 | t1[i_] = inva[i_,updrow];
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| 354 | }
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| 355 |
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| 356 | //
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| 357 | // T2 = v*InvA
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| 358 | //
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| 359 | for(i_=1; i_<=n;i_++)
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| 360 | {
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| 361 | t2[i_] = inva[updcolumn,i_];
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| 362 | }
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| 363 |
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| 364 | //
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| 365 | // Lambda = v * InvA * U
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| 366 | //
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| 367 | lambda = updval*inva[updcolumn,updrow];
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| 368 |
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| 369 | //
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| 370 | // InvA = InvA - correction
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| 371 | //
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| 372 | for(i=1; i<=n; i++)
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| 373 | {
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| 374 | vt = updval*t1[i];
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| 375 | vt = vt/(1+lambda);
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| 376 | for(i_=1; i_<=n;i_++)
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| 377 | {
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| 378 | inva[i,i_] = inva[i,i_] - vt*t2[i_];
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| 379 | }
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| 380 | }
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| 381 | }
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| 382 |
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| 383 |
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| 384 | public static void shermanmorrisonupdaterow(ref double[,] inva,
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| 385 | int n,
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| 386 | int updrow,
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| 387 | ref double[] v)
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| 388 | {
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| 389 | double[] t1 = new double[0];
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| 390 | double[] t2 = new double[0];
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| 391 | int i = 0;
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| 392 | int j = 0;
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| 393 | double lambda = 0;
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| 394 | double vt = 0;
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| 395 | int i_ = 0;
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| 396 |
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| 397 | t1 = new double[n+1];
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| 398 | t2 = new double[n+1];
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| 399 |
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| 400 | //
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| 401 | // T1 = InvA * U
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| 402 | //
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| 403 | for(i_=1; i_<=n;i_++)
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| 404 | {
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| 405 | t1[i_] = inva[i_,updrow];
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| 406 | }
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| 407 |
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| 408 | //
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| 409 | // T2 = v*InvA
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| 410 | // Lambda = v * InvA * U
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| 411 | //
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| 412 | for(j=1; j<=n; j++)
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| 413 | {
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| 414 | vt = 0.0;
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| 415 | for(i_=1; i_<=n;i_++)
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| 416 | {
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| 417 | vt += v[i_]*inva[i_,j];
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| 418 | }
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| 419 | t2[j] = vt;
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| 420 | }
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| 421 | lambda = t2[updrow];
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| 422 |
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| 423 | //
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| 424 | // InvA = InvA - correction
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| 425 | //
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| 426 | for(i=1; i<=n; i++)
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| 427 | {
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| 428 | vt = t1[i]/(1+lambda);
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| 429 | for(i_=1; i_<=n;i_++)
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| 430 | {
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| 431 | inva[i,i_] = inva[i,i_] - vt*t2[i_];
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| 432 | }
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| 433 | }
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| 434 | }
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| 435 |
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| 436 |
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| 437 | public static void shermanmorrisonupdatecolumn(ref double[,] inva,
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| 438 | int n,
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| 439 | int updcolumn,
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| 440 | ref double[] u)
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| 441 | {
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| 442 | double[] t1 = new double[0];
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| 443 | double[] t2 = new double[0];
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| 444 | int i = 0;
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| 445 | double lambda = 0;
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| 446 | double vt = 0;
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| 447 | int i_ = 0;
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| 448 |
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| 449 | t1 = new double[n+1];
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| 450 | t2 = new double[n+1];
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| 451 |
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| 452 | //
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| 453 | // T1 = InvA * U
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| 454 | // Lambda = v * InvA * U
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| 455 | //
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| 456 | for(i=1; i<=n; i++)
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| 457 | {
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| 458 | vt = 0.0;
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| 459 | for(i_=1; i_<=n;i_++)
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| 460 | {
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| 461 | vt += inva[i,i_]*u[i_];
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| 462 | }
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| 463 | t1[i] = vt;
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| 464 | }
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| 465 | lambda = t1[updcolumn];
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| 466 |
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| 467 | //
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| 468 | // T2 = v*InvA
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| 469 | //
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| 470 | for(i_=1; i_<=n;i_++)
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| 471 | {
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| 472 | t2[i_] = inva[updcolumn,i_];
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| 473 | }
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| 474 |
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| 475 | //
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| 476 | // InvA = InvA - correction
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| 477 | //
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| 478 | for(i=1; i<=n; i++)
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| 479 | {
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| 480 | vt = t1[i]/(1+lambda);
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| 481 | for(i_=1; i_<=n;i_++)
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| 482 | {
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| 483 | inva[i,i_] = inva[i,i_] - vt*t2[i_];
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| 484 | }
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| 485 | }
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| 486 | }
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| 487 |
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| 488 |
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| 489 | public static void shermanmorrisonupdateuv(ref double[,] inva,
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| 490 | int n,
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| 491 | ref double[] u,
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| 492 | ref double[] v)
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| 493 | {
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| 494 | double[] t1 = new double[0];
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| 495 | double[] t2 = new double[0];
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| 496 | int i = 0;
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| 497 | int j = 0;
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| 498 | double lambda = 0;
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| 499 | double vt = 0;
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| 500 | int i_ = 0;
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| 501 |
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| 502 | t1 = new double[n+1];
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| 503 | t2 = new double[n+1];
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| 504 |
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| 505 | //
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| 506 | // T1 = InvA * U
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| 507 | // Lambda = v * T1
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| 508 | //
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| 509 | for(i=1; i<=n; i++)
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| 510 | {
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| 511 | vt = 0.0;
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| 512 | for(i_=1; i_<=n;i_++)
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| 513 | {
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| 514 | vt += inva[i,i_]*u[i_];
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| 515 | }
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| 516 | t1[i] = vt;
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| 517 | }
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| 518 | lambda = 0.0;
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| 519 | for(i_=1; i_<=n;i_++)
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| 520 | {
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| 521 | lambda += v[i_]*t1[i_];
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| 522 | }
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| 523 |
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| 524 | //
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| 525 | // T2 = v*InvA
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| 526 | //
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| 527 | for(j=1; j<=n; j++)
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| 528 | {
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| 529 | vt = 0.0;
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| 530 | for(i_=1; i_<=n;i_++)
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| 531 | {
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| 532 | vt += v[i_]*inva[i_,j];
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| 533 | }
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| 534 | t2[j] = vt;
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| 535 | }
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| 536 |
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| 537 | //
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| 538 | // InvA = InvA - correction
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| 539 | //
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| 540 | for(i=1; i<=n; i++)
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| 541 | {
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| 542 | vt = t1[i]/(1+lambda);
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| 543 | for(i_=1; i_<=n;i_++)
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| 544 | {
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| 545 | inva[i,i_] = inva[i,i_] - vt*t2[i_];
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| 546 | }
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| 547 | }
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| 548 | }
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| 549 | }
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| 550 | }
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