| 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 lu
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| 32 | {
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| 33 | public const int lunb = 8;
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| 34 |
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| 35 |
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| 36 | /*************************************************************************
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| 37 | LU decomposition of a general matrix of size MxN
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| 38 |
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| 39 | The subroutine calculates the LU decomposition of a rectangular general
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| 40 | matrix with partial pivoting (with row permutations).
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| 41 |
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| 42 | Input parameters:
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| 43 | A - matrix A whose indexes range within [0..M-1, 0..N-1].
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| 44 | M - number of rows in matrix A.
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| 45 | N - number of columns in matrix A.
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| 46 |
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| 47 | Output parameters:
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| 48 | A - matrices L and U in compact form (see below).
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| 49 | Array whose indexes range within [0..M-1, 0..N-1].
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| 50 | Pivots - permutation matrix in compact form (see below).
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| 51 | Array whose index ranges within [0..Min(M-1,N-1)].
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| 52 |
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| 53 | Matrix A is represented as A = P * L * U, where P is a permutation matrix,
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| 54 | matrix L - lower triangular (or lower trapezoid, if M>N) matrix,
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| 55 | U - upper triangular (or upper trapezoid, if M<N) matrix.
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| 56 |
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| 57 | Let M be equal to 4 and N be equal to 3:
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| 58 |
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| 59 | ( 1 ) ( U11 U12 U13 )
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| 60 | A = P1 * P2 * P3 * ( L21 1 ) * ( U22 U23 )
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| 61 | ( L31 L32 1 ) ( U33 )
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| 62 | ( L41 L42 L43 )
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| 63 |
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| 64 | Matrix L has size MxMin(M,N), matrix U has size Min(M,N)xN, matrix P(i) is
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| 65 | a permutation of the identity matrix of size MxM with numbers I and Pivots[I].
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| 66 |
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| 67 | The algorithm returns array Pivots and the following matrix which replaces
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| 68 | matrix A and contains matrices L and U in compact form (the example applies
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| 69 | to M=4, N=3).
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| 70 |
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| 71 | ( U11 U12 U13 )
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| 72 | ( L21 U22 U23 )
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| 73 | ( L31 L32 U33 )
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| 74 | ( L41 L42 L43 )
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| 75 |
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| 76 | As we can see, the unit diagonal isn't stored.
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| 77 |
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| 78 | -- LAPACK routine (version 3.0) --
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| 79 | Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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| 80 | Courant Institute, Argonne National Lab, and Rice University
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| 81 | June 30, 1992
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| 82 | *************************************************************************/
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| 83 | public static void rmatrixlu(ref double[,] a,
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| 84 | int m,
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| 85 | int n,
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| 86 | ref int[] pivots)
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| 87 | {
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| 88 | double[,] b = new double[0,0];
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| 89 | double[] t = new double[0];
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| 90 | int[] bp = new int[0];
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| 91 | int minmn = 0;
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| 92 | int i = 0;
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| 93 | int ip = 0;
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| 94 | int j = 0;
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| 95 | int j1 = 0;
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| 96 | int j2 = 0;
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| 97 | int cb = 0;
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| 98 | int nb = 0;
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| 99 | double v = 0;
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| 100 | int i_ = 0;
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| 101 | int i1_ = 0;
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| 102 |
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| 103 | System.Diagnostics.Debug.Assert(lunb>=1, "RMatrixLU internal error");
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| 104 | nb = lunb;
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| 105 |
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| 106 | //
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| 107 | // Decide what to use - blocked or unblocked code
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| 108 | //
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| 109 | if( n<=1 | Math.Min(m, n)<=nb | nb==1 )
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| 110 | {
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| 111 |
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| 112 | //
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| 113 | // Unblocked code
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| 114 | //
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| 115 | rmatrixlu2(ref a, m, n, ref pivots);
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| 116 | }
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| 117 | else
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| 118 | {
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| 119 |
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| 120 | //
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| 121 | // Blocked code.
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| 122 | // First, prepare temporary matrix and indices
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| 123 | //
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| 124 | b = new double[m-1+1, nb-1+1];
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| 125 | t = new double[n-1+1];
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| 126 | pivots = new int[Math.Min(m, n)-1+1];
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| 127 | minmn = Math.Min(m, n);
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| 128 | j1 = 0;
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| 129 | j2 = Math.Min(minmn, nb)-1;
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| 130 |
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| 131 | //
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| 132 | // Main cycle
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| 133 | //
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| 134 | while( j1<minmn )
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| 135 | {
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| 136 | cb = j2-j1+1;
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| 137 |
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| 138 | //
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| 139 | // LU factorization of diagonal and subdiagonal blocks:
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| 140 | // 1. Copy columns J1..J2 of A to B
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| 141 | // 2. LU(B)
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| 142 | // 3. Copy result back to A
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| 143 | // 4. Copy pivots, apply pivots
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| 144 | //
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| 145 | for(i=j1; i<=m-1; i++)
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| 146 | {
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| 147 | i1_ = (j1) - (0);
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| 148 | for(i_=0; i_<=cb-1;i_++)
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| 149 | {
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| 150 | b[i-j1,i_] = a[i,i_+i1_];
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| 151 | }
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| 152 | }
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| 153 | rmatrixlu2(ref b, m-j1, cb, ref bp);
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| 154 | for(i=j1; i<=m-1; i++)
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| 155 | {
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| 156 | i1_ = (0) - (j1);
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| 157 | for(i_=j1; i_<=j2;i_++)
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| 158 | {
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| 159 | a[i,i_] = b[i-j1,i_+i1_];
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| 160 | }
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| 161 | }
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| 162 | for(i=0; i<=cb-1; i++)
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| 163 | {
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| 164 | ip = bp[i];
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| 165 | pivots[j1+i] = j1+ip;
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| 166 | if( bp[i]!=i )
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| 167 | {
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| 168 | if( j1!=0 )
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| 169 | {
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| 170 |
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| 171 | //
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| 172 | // Interchange columns 0:J1-1
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| 173 | //
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| 174 | for(i_=0; i_<=j1-1;i_++)
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| 175 | {
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| 176 | t[i_] = a[j1+i,i_];
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| 177 | }
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| 178 | for(i_=0; i_<=j1-1;i_++)
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| 179 | {
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| 180 | a[j1+i,i_] = a[j1+ip,i_];
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| 181 | }
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| 182 | for(i_=0; i_<=j1-1;i_++)
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| 183 | {
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| 184 | a[j1+ip,i_] = t[i_];
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| 185 | }
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| 186 | }
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| 187 | if( j2<n-1 )
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| 188 | {
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| 189 |
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| 190 | //
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| 191 | // Interchange the rest of the matrix, if needed
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| 192 | //
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| 193 | for(i_=j2+1; i_<=n-1;i_++)
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| 194 | {
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| 195 | t[i_] = a[j1+i,i_];
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| 196 | }
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| 197 | for(i_=j2+1; i_<=n-1;i_++)
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| 198 | {
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| 199 | a[j1+i,i_] = a[j1+ip,i_];
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| 200 | }
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| 201 | for(i_=j2+1; i_<=n-1;i_++)
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| 202 | {
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| 203 | a[j1+ip,i_] = t[i_];
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| 204 | }
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| 205 | }
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| 206 | }
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| 207 | }
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| 208 |
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| 209 | //
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| 210 | // Compute block row of U
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| 211 | //
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| 212 | if( j2<n-1 )
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| 213 | {
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| 214 | for(i=j1+1; i<=j2; i++)
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| 215 | {
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| 216 | for(j=j1; j<=i-1; j++)
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| 217 | {
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| 218 | v = a[i,j];
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| 219 | for(i_=j2+1; i_<=n-1;i_++)
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| 220 | {
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| 221 | a[i,i_] = a[i,i_] - v*a[j,i_];
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| 222 | }
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| 223 | }
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| 224 | }
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| 225 | }
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| 226 |
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| 227 | //
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| 228 | // Update trailing submatrix
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| 229 | //
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| 230 | if( j2<n-1 )
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| 231 | {
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| 232 | for(i=j2+1; i<=m-1; i++)
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| 233 | {
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| 234 | for(j=j1; j<=j2; j++)
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| 235 | {
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| 236 | v = a[i,j];
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| 237 | for(i_=j2+1; i_<=n-1;i_++)
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| 238 | {
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| 239 | a[i,i_] = a[i,i_] - v*a[j,i_];
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| 240 | }
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| 241 | }
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| 242 | }
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| 243 | }
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| 244 |
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| 245 | //
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| 246 | // Next step
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| 247 | //
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| 248 | j1 = j2+1;
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| 249 | j2 = Math.Min(minmn, j1+nb)-1;
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| 250 | }
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| 251 | }
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| 252 | }
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| 253 |
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| 254 |
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| 255 | public static void ludecomposition(ref double[,] a,
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| 256 | int m,
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| 257 | int n,
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| 258 | ref int[] pivots)
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| 259 | {
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| 260 | int i = 0;
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| 261 | int j = 0;
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| 262 | int jp = 0;
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| 263 | double[] t1 = new double[0];
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| 264 | double s = 0;
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| 265 | int i_ = 0;
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| 266 |
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| 267 | pivots = new int[Math.Min(m, n)+1];
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| 268 | t1 = new double[Math.Max(m, n)+1];
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| 269 | System.Diagnostics.Debug.Assert(m>=0 & n>=0, "Error in LUDecomposition: incorrect function arguments");
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| 270 |
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| 271 | //
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| 272 | // Quick return if possible
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| 273 | //
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| 274 | if( m==0 | n==0 )
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| 275 | {
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| 276 | return;
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| 277 | }
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| 278 | for(j=1; j<=Math.Min(m, n); j++)
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| 279 | {
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| 280 |
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| 281 | //
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| 282 | // Find pivot and test for singularity.
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| 283 | //
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| 284 | jp = j;
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| 285 | for(i=j+1; i<=m; i++)
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| 286 | {
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| 287 | if( (double)(Math.Abs(a[i,j]))>(double)(Math.Abs(a[jp,j])) )
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| 288 | {
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| 289 | jp = i;
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| 290 | }
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| 291 | }
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| 292 | pivots[j] = jp;
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| 293 | if( (double)(a[jp,j])!=(double)(0) )
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| 294 | {
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| 295 |
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| 296 | //
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| 297 | //Apply the interchange to rows
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| 298 | //
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| 299 | if( jp!=j )
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| 300 | {
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| 301 | for(i_=1; i_<=n;i_++)
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| 302 | {
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| 303 | t1[i_] = a[j,i_];
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| 304 | }
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| 305 | for(i_=1; i_<=n;i_++)
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| 306 | {
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| 307 | a[j,i_] = a[jp,i_];
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| 308 | }
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| 309 | for(i_=1; i_<=n;i_++)
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| 310 | {
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| 311 | a[jp,i_] = t1[i_];
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| 312 | }
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| 313 | }
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| 314 |
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| 315 | //
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| 316 | //Compute elements J+1:M of J-th column.
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| 317 | //
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| 318 | if( j<m )
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| 319 | {
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| 320 |
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| 321 | //
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| 322 | // CALL DSCAL( M-J, ONE / A( J, J ), A( J+1, J ), 1 )
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| 323 | //
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| 324 | jp = j+1;
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| 325 | s = 1/a[j,j];
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| 326 | for(i_=jp; i_<=m;i_++)
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| 327 | {
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| 328 | a[i_,j] = s*a[i_,j];
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| 329 | }
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| 330 | }
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| 331 | }
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| 332 | if( j<Math.Min(m, n) )
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| 333 | {
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| 334 |
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| 335 | //
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| 336 | //Update trailing submatrix.
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| 337 | //CALL DGER( M-J, N-J, -ONE, A( J+1, J ), 1, A( J, J+1 ), LDA,A( J+1, J+1 ), LDA )
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| 338 | //
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| 339 | jp = j+1;
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| 340 | for(i=j+1; i<=m; i++)
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| 341 | {
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| 342 | s = a[i,j];
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| 343 | for(i_=jp; i_<=n;i_++)
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| 344 | {
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| 345 | a[i,i_] = a[i,i_] - s*a[j,i_];
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| 346 | }
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| 347 | }
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| 348 | }
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| 349 | }
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| 350 | }
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| 351 |
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| 352 |
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| 353 | public static void ludecompositionunpacked(double[,] a,
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| 354 | int m,
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| 355 | int n,
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| 356 | ref double[,] l,
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| 357 | ref double[,] u,
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| 358 | ref int[] pivots)
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| 359 | {
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| 360 | int i = 0;
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| 361 | int j = 0;
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| 362 | int minmn = 0;
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| 363 |
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| 364 | a = (double[,])a.Clone();
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| 365 |
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| 366 | if( m==0 | n==0 )
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| 367 | {
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| 368 | return;
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| 369 | }
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| 370 | minmn = Math.Min(m, n);
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| 371 | l = new double[m+1, minmn+1];
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| 372 | u = new double[minmn+1, n+1];
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| 373 | ludecomposition(ref a, m, n, ref pivots);
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| 374 | for(i=1; i<=m; i++)
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| 375 | {
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| 376 | for(j=1; j<=minmn; j++)
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| 377 | {
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| 378 | if( j>i )
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| 379 | {
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| 380 | l[i,j] = 0;
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| 381 | }
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| 382 | if( j==i )
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| 383 | {
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| 384 | l[i,j] = 1;
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| 385 | }
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| 386 | if( j<i )
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| 387 | {
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| 388 | l[i,j] = a[i,j];
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| 389 | }
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| 390 | }
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| 391 | }
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| 392 | for(i=1; i<=minmn; i++)
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| 393 | {
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| 394 | for(j=1; j<=n; j++)
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| 395 | {
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| 396 | if( j<i )
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| 397 | {
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| 398 | u[i,j] = 0;
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| 399 | }
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| 400 | if( j>=i )
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| 401 | {
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| 402 | u[i,j] = a[i,j];
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| 403 | }
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| 404 | }
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| 405 | }
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| 406 | }
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| 407 |
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| 408 |
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| 409 | /*************************************************************************
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| 410 | Level 2 BLAS version of RMatrixLU
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| 411 |
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| 412 | -- LAPACK routine (version 3.0) --
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| 413 | Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
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| 414 | Courant Institute, Argonne National Lab, and Rice University
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| 415 | June 30, 1992
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| 416 | *************************************************************************/
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| 417 | private static void rmatrixlu2(ref double[,] a,
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| 418 | int m,
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| 419 | int n,
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| 420 | ref int[] pivots)
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| 421 | {
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| 422 | int i = 0;
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| 423 | int j = 0;
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| 424 | int jp = 0;
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| 425 | double[] t1 = new double[0];
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| 426 | double s = 0;
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| 427 | int i_ = 0;
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| 428 |
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| 429 | pivots = new int[Math.Min(m-1, n-1)+1];
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| 430 | t1 = new double[Math.Max(m-1, n-1)+1];
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| 431 | System.Diagnostics.Debug.Assert(m>=0 & n>=0, "Error in LUDecomposition: incorrect function arguments");
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| 432 |
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| 433 | //
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| 434 | // Quick return if possible
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| 435 | //
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| 436 | if( m==0 | n==0 )
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| 437 | {
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| 438 | return;
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| 439 | }
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| 440 | for(j=0; j<=Math.Min(m-1, n-1); j++)
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| 441 | {
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| 442 |
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| 443 | //
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| 444 | // Find pivot and test for singularity.
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| 445 | //
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| 446 | jp = j;
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| 447 | for(i=j+1; i<=m-1; i++)
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| 448 | {
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| 449 | if( (double)(Math.Abs(a[i,j]))>(double)(Math.Abs(a[jp,j])) )
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| 450 | {
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| 451 | jp = i;
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| 452 | }
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| 453 | }
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| 454 | pivots[j] = jp;
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| 455 | if( (double)(a[jp,j])!=(double)(0) )
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| 456 | {
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| 457 |
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| 458 | //
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| 459 | //Apply the interchange to rows
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| 460 | //
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| 461 | if( jp!=j )
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| 462 | {
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| 463 | for(i_=0; i_<=n-1;i_++)
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| 464 | {
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| 465 | t1[i_] = a[j,i_];
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| 466 | }
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| 467 | for(i_=0; i_<=n-1;i_++)
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| 468 | {
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| 469 | a[j,i_] = a[jp,i_];
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| 470 | }
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| 471 | for(i_=0; i_<=n-1;i_++)
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| 472 | {
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| 473 | a[jp,i_] = t1[i_];
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| 474 | }
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| 475 | }
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| 476 |
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| 477 | //
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| 478 | //Compute elements J+1:M of J-th column.
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| 479 | //
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| 480 | if( j<m )
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| 481 | {
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| 482 | jp = j+1;
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| 483 | s = 1/a[j,j];
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| 484 | for(i_=jp; i_<=m-1;i_++)
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| 485 | {
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| 486 | a[i_,j] = s*a[i_,j];
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| 487 | }
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| 488 | }
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| 489 | }
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| 490 | if( j<Math.Min(m, n)-1 )
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| 491 | {
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| 492 |
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| 493 | //
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| 494 | //Update trailing submatrix.
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| 495 | //
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| 496 | jp = j+1;
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| 497 | for(i=j+1; i<=m-1; i++)
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| 498 | {
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| 499 | s = a[i,j];
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| 500 | for(i_=jp; i_<=n-1;i_++)
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| 501 | {
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| 502 | a[i,i_] = a[i,i_] - s*a[j,i_];
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| 503 | }
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| 504 | }
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| 505 | }
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| 506 | }
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| 507 | }
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| 508 | }
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| 509 | }
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