static int
test_COD_lssolve2(gsl_rng * r)
{
int s = 0;
gsl_matrix *m;
gsl_vector *b;
size_t M, N;
const double lambda = 2.3;
M = 100;
N = 50;
m = gsl_matrix_alloc(M, N);
b = gsl_vector_alloc(M);
create_rank_matrix(26, m, r);
create_random_vector(b, r);
test_COD_lssolve2_eps(lambda, m, b, 1.0e2 * M * GSL_DBL_EPSILON, "COD_lssolve2 rank 26");
gsl_matrix_free(m);
gsl_vector_free(b);
M = 500;
N = 450;
m = gsl_matrix_alloc(M, N);
b = gsl_vector_alloc(M);
create_rank_matrix(278, m, r);
create_random_vector(b, r);
test_COD_lssolve2_eps(lambda, m, b, 1.0e4 * M * GSL_DBL_EPSILON, "COD_lssolve2 rank 278");
gsl_matrix_free(m);
gsl_vector_free(b);
return s;
}
static void
test_random(const size_t N, const gsl_rng *r, const int compress)
{
const gsl_splinalg_itersolve_type *T = gsl_splinalg_itersolve_gmres;
const double tol = 1.0e-8;
int status;
gsl_spmatrix *A = create_random_sparse(N, N, 0.3, r);
gsl_spmatrix *B;
gsl_vector *b = gsl_vector_alloc(N);
gsl_vector *x = gsl_vector_calloc(N);
/* these random matrices require all N iterations to converge */
gsl_splinalg_itersolve *w = gsl_splinalg_itersolve_alloc(T, N, N);
const char *desc = gsl_splinalg_itersolve_name(w);
create_random_vector(b, r);
if (compress)
B = gsl_spmatrix_compcol(A);
else
B = A;
status = gsl_splinalg_itersolve_iterate(B, b, tol, x, w);
gsl_test(status, "%s random status s=%d N=%zu", desc, status, N);
/* check that the residual satisfies ||r|| <= tol*||b|| */
{
gsl_vector *res = gsl_vector_alloc(N);
double normr, normb;
gsl_vector_memcpy(res, b);
gsl_spblas_dgemv(CblasNoTrans, -1.0, A, x, 1.0, res);
normr = gsl_blas_dnrm2(res);
normb = gsl_blas_dnrm2(b);
status = (normr <= tol*normb) != 1;
gsl_test(status, "%s random residual N=%zu normr=%.12e normb=%.12e",
desc, N, normr, normb);
gsl_vector_free(res);
}
gsl_spmatrix_free(A);
gsl_vector_free(b);
gsl_vector_free(x);
gsl_splinalg_itersolve_free(w);
if (compress)
gsl_spmatrix_free(B);
} /* test_random() */
/* create a matrix of a given rank */
static int
create_rank_matrix(const size_t rank, gsl_matrix * m, gsl_rng * r)
{
const size_t M = m->size1;
const size_t N = m->size2;
size_t i;
gsl_vector *u = gsl_vector_alloc(M);
gsl_vector *v = gsl_vector_alloc(N);
gsl_matrix_set_zero(m);
/* add several rank-1 matrices together */
for (i = 0; i < rank; ++i)
{
create_random_vector(u, r);
create_random_vector(v, r);
gsl_blas_dger(1.0, u, v, m);
}
gsl_vector_free(u);
gsl_vector_free(v);
return GSL_SUCCESS;
}
int main(){
printf("Let's test some linear algebra functions....\n\n");
// create a random nxn matrix for later use
matrix_t A = create_random_matrix(DIM,DIM);
printf("New Random Matrix A:\n");
print_matrix(A);
// also create random vector
vector_t b = create_random_vector(DIM);
printf("\nNew Random Vector b:\n");
print_vector(b);
// do an LUP decomposition on A
matrix_t L,U,P;
LUP_decomposition(A,&L,&U,&P);
printf("\nL:\n");
print_matrix(L);
printf("U:\n");
print_matrix(U);
printf("P:\n");
print_matrix(P);
// do a QR decomposition on A
matrix_t Q,R;
QR_decomposition(A,&Q,&R);
printf("\nQR Decomposition of A\n");
printf("Q:\n");
print_matrix(Q);
printf("R:\n");
print_matrix(R);
// get determinant of A
float det = matrix_determinant(A);
printf("\nDeterminant of A : %8.4f\n", det);
// get an inverse for A
matrix_t Ainv = invert_matrix(A);
if(A.initialized != 1) return -1;
printf("\nAinverse\n");
print_matrix(Ainv);
// multiply A times A inverse
matrix_t AA = multiply_matrices(A,Ainv);
if(AA.initialized!=1) return -1;
printf("\nA * Ainverse:\n");
print_matrix(AA);
// solve a square linear system
vector_t x = lin_system_solve(A, b);
printf("\nGaussian Elimination solution x to the equation Ax=b:\n");
print_vector(x);
// now do again but with qr decomposition method
vector_t xqr = lin_system_solve_qr(A, b);
printf("\nQR solution x to the equation Ax=b:\n");
print_vector(xqr);
// If b are the coefficients of a polynomial, get the coefficients of the
// new polynomial b^2
vector_t bb = poly_power(b,2);
printf("\nCoefficients of polynomial b times itself\n");
print_vector(bb);
// clean up all the allocated memory. This isn't strictly necessary since
// we are already at the end of the program, but good practice to do.
destroy_matrix(&A);
destroy_matrix(&AA);
destroy_vector(&b);
destroy_vector(&bb);
destroy_vector(&x);
destroy_vector(&xqr);
destroy_matrix(&Q);
destroy_matrix(&R);
printf("DONE\n");
return 0;
}
