Last Update: Oct. 4, 2007
/***********************************************/ /* T.Kouya's GSL sample program collection */ /* Solving Linear System of Equations */ /* LU decomposition */ /* Written by Tomonori Kouya */ /* */ /* Version 0.01: 2007-10-02 */ /***********************************************/ #include <stdio.h> #include <gsl/gsl_math.h> #include <gsl/gsl_blas.h> #include <gsl/gsl_vector.h> #include <gsl/gsl_matrix.h> #include <gsl/gsl_linalg.h> /* Dimension of Matrix and Vectors */ #define DIM 5 int main(void) { int i, j, lotkin_signum, frank_signum; gsl_matrix *lotkin_a, *frank_a; gsl_vector *x, *lotkin_b, *frank_b, *lotkin_x, *frank_x; gsl_permutation *lotkin_perm, *frank_perm; /* allocate a, x, b */ lotkin_a = gsl_matrix_alloc(DIM, DIM); frank_a = gsl_matrix_alloc(DIM, DIM); x = gsl_vector_alloc(DIM); lotkin_b = gsl_vector_alloc(DIM); frank_b = gsl_vector_alloc(DIM); lotkin_x = gsl_vector_alloc(DIM); frank_x = gsl_vector_alloc(DIM); /* set x = [1 2 ... DIM] */ for(i = 0; i < DIM; i++) gsl_vector_set(x, i, (double)i); /* set Lotkin matrix */ /* a_ij = 1 (i = 1) or 1/(i+j-1) (i != 1) */ for(i = 0; i < DIM; i++) gsl_matrix_set(lotkin_a, 0, i, 1.0); for(i = 1; i < DIM; i++) for(j = 0; j < DIM; j++) gsl_matrix_set(lotkin_a, i, j, 1.0 / (double)(i + j + 1)); /* set Frank matrix */ /* a_ij = DIM - min(i,j) + 1 */ for(i = 0; i < DIM; i++) for(j = 0; j < DIM; j++) gsl_matrix_set(frank_a, i, j, (double)DIM - (double)GSL_MAX(i, j) ); /* Print matrix */ printf("Lotkin Matrix(DIM = %d)\n", DIM); for(i = 0; i < DIM; i++) { printf("%3d: ", i); for(j = 0; j < DIM; j++) printf("%g ", gsl_matrix_get(lotkin_a, i, j)); printf("\n"); } printf("\n"); printf("Frank Matrix(DIM = %d)\n", DIM); for(i = 0; i < DIM; i++) { printf("%3d: ", i); for(j = 0; j < DIM; j++) printf("%g ", gsl_matrix_get(frank_a, i, j)); printf("\n"); } printf("\n"); /* b = A * x */ gsl_blas_dgemv(CblasNoTrans, 1.0, lotkin_a, x, 0.0, lotkin_b); gsl_blas_dgemv(CblasNoTrans, 1.0, frank_a, x, 0.0, frank_b); /* LU decomposition and forward&backward substition */ lotkin_perm = gsl_permutation_alloc(DIM); gsl_linalg_LU_decomp(lotkin_a, lotkin_perm, &lotkin_signum); gsl_linalg_LU_solve(lotkin_a, lotkin_perm, lotkin_b, lotkin_x); gsl_permutation_free(lotkin_perm); frank_perm = gsl_permutation_alloc(DIM); gsl_linalg_LU_decomp(frank_a, frank_perm, &frank_signum); gsl_linalg_LU_solve(frank_a, frank_perm, frank_b, frank_x); gsl_permutation_free(frank_perm); /* print */ printf("index Lotkin Frank True\n"); for(i = 0; i < DIM; i++) printf("%3d %25.17e %25.17e %25.17e\n", i, gsl_vector_get(lotkin_x, i), gsl_vector_get(frank_x, i), gsl_vector_get(x, i)); /* free a, x, b */ gsl_matrix_free(lotkin_a); gsl_matrix_free(frank_a); gsl_vector_free(x); gsl_vector_free(lotkin_b); gsl_vector_free(frank_b); gsl_vector_free(lotkin_x); gsl_vector_free(frank_x); return 0; }
$ ./linear_system Lotkin Matrix(DIM = 5) 0: 1 1 1 1 1 1: 0.5 0.333333 0.25 0.2 0.166667 2: 0.333333 0.25 0.2 0.166667 0.142857 3: 0.25 0.2 0.166667 0.142857 0.125 4: 0.2 0.166667 0.142857 0.125 0.111111 Frank Matrix(DIM = 5) 0: 5 4 3 2 1 1: 4 4 3 2 1 2: 3 3 3 2 1 3: 2 2 2 2 1 4: 1 1 1 1 1 index Lotkin Frank True 0 -2.82440737464639824e-13 -1.42108547152020045e-15 0.00000000000000000e+00 1 1.00000000000282596e+00 1.00000000000000355e+00 1.00000000000000000e+00 2 1.99999999999155187e+00 1.99999999999999645e+00 2.00000000000000000e+00 3 3.00000000000982148e+00 3.00000000000000178e+00 3.00000000000000000e+00 4 3.99999999999608313e+00 4.00000000000000000e+00 4.00000000000000000e+00