Cholesky.cc 3.37 KB
 Peter Gottschling committed Feb 15, 2008 1 2 3 4 ``````#include "Cholesky.h" bool Cholesky::factorization(Matrix *A, Vector *p) { `````` Thomas Witkowski committed Apr 29, 2009 5 `````` FUNCNAME("Cholesky::factorization()"); `````` Peter Gottschling committed Feb 15, 2008 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 `````` int n = A->getNumRows(); // Checking memory for vector P of diagonal elements of factorization. static Vector *pT = NULL; if (p) { if (p->getSize() != n) p->resize(n); } else { if (pT) { if (pT->getSize() != n) pT->resize(n); } else pT = NEW Vector(n); p = pT; } // Constructs the Cholesky factorization A = L*L, with L lower triangular. // Only the upper triangle need be given; it is not modified. // The Cholesky factor L is stored in the lower triangle of A, except for // its diagonal which is stored in P. int i, j, k; double sum; for (i=0; i=0; k--) sum -= (*A)[i][k] * (*A)[j][k]; if (i==j) { if (sum<=0) { MSG("Matrix is (numerically) not positive definite!\n"); MSG("Cholesky decomposition does not work; choose another method for solving the system.\n"); return false; } (*p)[i] = sqrt(sum); } else (*A)[j][i] = sum / (*p)[i]; } } return true; } bool Cholesky::solve(Matrix *A, Vector *b, Vector *x, Vector *p) { FUNCNAME("Cholesky::solve"); bool success = true; int n = b->getSize(); TEST_EXIT(n == A->getNumRows()) ("Dimensions of matrix and vector do not match!\n"); // Checking memory for solution vector X. if (x && (x->getSize() != n)) x->resize(n); if (!x) x = NEW Vector(n); // Checking vector P. static Vector *pT = NULL; if (!p || (p->getSize() != n)) { if (pT && pT->getSize() != n) DELETE pT; if (!pT) pT = NEW Vector(n); p = pT; success = factorization(A, p); } // Now solve the system by backsubstitution. int i, k; double sum; for (i=0; i=0; k--) sum -= (*A)[i][k] * (*x)[k]; (*x)[i] = sum / (*p)[i]; } for (i=n-1; i>=0; i--) // Solve L^T*X = Y. { for (sum=(*x)[i], k=i+1; k *A, Vector > *b, Vector > *x, Vector *p) { FUNCNAME("Cholesky::solve"); bool success = true; int n = b->getSize(); TEST_EXIT(n == A->getNumRows()) ("Dimensions of matrix and vector do not match!\n"); // Checking memory for solution vector X. if (x && (x->getSize() != n)) x->resize(n); if (!x) x = NEW Vector >(n); // Checking vector P. static Vector *pT = NULL; if (!p || (p->getSize() != n)) { pT = NEW Vector(n); p = pT; success = factorization(A, p); } // Now solve the system by backsubstitution. int i, k; WorldVector vec_sum; for (i=0; i=0; k--) vec_sum -= (*x)[k] * (*A)[i][k] ; (*x)[i] = vec_sum * (1.0/(*p)[i]); } for (i=n-1; i>=0; i--) // Solve L^T*X = Y. { for (vec_sum=(*x)[i], k=i+1; k