static gsl_spmatrix * create_random_sparse(const size_t M, const size_t N, const double density, const gsl_rng *r) { size_t nnzwanted = (size_t) floor(M * N * GSL_MIN(density, 1.0)); gsl_spmatrix *m = gsl_spmatrix_alloc_nzmax(M, N, nnzwanted, GSL_SPMATRIX_TRIPLET); size_t i; /* set diagonal entries to try to ensure non-singularity */ for (i = 0; i < GSL_MIN(M, N); ++i) { double x = gsl_rng_uniform(r); gsl_spmatrix_set(m, i, i, x); } while (gsl_spmatrix_nnz(m) < nnzwanted) { /* generate a random row and column */ size_t i = gsl_rng_uniform(r) * M; size_t j = gsl_rng_uniform(r) * N; /* generate random m_{ij} and add it */ double x = gsl_rng_uniform(r); gsl_spmatrix_set(m, i, j, x); } return m; } /* create_random_sparse() */
int main() { gsl_spmatrix *A = gsl_spmatrix_alloc(5, 4); /* triplet format */ gsl_spmatrix *C; size_t i, j; /* build the sparse matrix */ gsl_spmatrix_set(A, 0, 2, 3.1); gsl_spmatrix_set(A, 0, 3, 4.6); gsl_spmatrix_set(A, 1, 0, 1.0); gsl_spmatrix_set(A, 1, 2, 7.2); gsl_spmatrix_set(A, 3, 0, 2.1); gsl_spmatrix_set(A, 3, 1, 2.9); gsl_spmatrix_set(A, 3, 3, 8.5); gsl_spmatrix_set(A, 4, 0, 4.1); printf("printing all matrix elements:\n"); for (i = 0; i < 5; ++i) for (j = 0; j < 4; ++j) printf("A(%zu,%zu) = %g\n", i, j, gsl_spmatrix_get(A, i, j)); /* print out elements in triplet format */ printf("matrix in triplet format (i,j,Aij):\n"); for (i = 0; i < A->nz; ++i) printf("(%zu, %zu, %.1f)\n", A->i[i], A->p[i], A->data[i]); /* convert to compressed column format */ C = gsl_spmatrix_compcol(A); printf("matrix in compressed column format:\n"); printf("i = [ "); for (i = 0; i < C->nz; ++i) printf("%zu, ", C->i[i]); printf("]\n"); printf("p = [ "); for (i = 0; i < C->size2 + 1; ++i) printf("%zu, ", C->p[i]); printf("]\n"); printf("d = [ "); for (i = 0; i < C->nz; ++i) printf("%g, ", C->data[i]); printf("]\n"); gsl_spmatrix_free(A); gsl_spmatrix_free(C); return 0; }
static gsl_spmatrix * create_random_sparse(const size_t M, const size_t N, const double density, const gsl_rng *r) { gsl_spmatrix *m = gsl_spmatrix_alloc(M, N); size_t nnzwanted = (size_t) round(M * N * GSL_MIN(density, 1.0)); size_t n = 0; size_t i; /* set diagonal entries to try to ensure non-singularity */ for (i = 0; i < GSL_MIN(M, N); ++i) { double x = gsl_rng_uniform(r); gsl_spmatrix_set(m, i, i, x); ++n; } while (n <= nnzwanted) { /* generate a random row and column */ size_t i = gsl_rng_uniform(r) * M; size_t j = gsl_rng_uniform(r) * N; double x; /* check if this position is already filled */ if (gsl_spmatrix_get(m, i, j) != 0.0) continue; /* generate random m_{ij} and add it */ x = gsl_rng_uniform(r); gsl_spmatrix_set(m, i, j, x); ++n; } return m; } /* create_random_sparse() */
static gsl_spmatrix * create_random_sparse(const size_t M, const size_t N, const double density, const gsl_rng *r) { size_t nnzwanted = (size_t) floor(M * N * GSL_MIN(density, 1.0)); gsl_spmatrix *m = gsl_spmatrix_alloc_nzmax(M, N, nnzwanted, GSL_SPMATRIX_TRIPLET); while (gsl_spmatrix_nnz(m) < nnzwanted) { /* generate a random row and column */ size_t i = gsl_rng_uniform(r) * M; size_t j = gsl_rng_uniform(r) * N; /* generate random m_{ij} and add it */ double x = gsl_rng_uniform(r); gsl_spmatrix_set(m, i, j, x, 0); } return m; } /* create_random_sparse() */
static gsl_spmatrix * create_random_sparse_int(const size_t M, const size_t N, const double density, const gsl_rng *r) { const double lower = 1.0; const double upper = 10.0; size_t nnzwanted = (size_t) floor(M * N * GSL_MIN(density, 1.0)); gsl_spmatrix *m = gsl_spmatrix_alloc_nzmax(M, N, nnzwanted, GSL_SPMATRIX_TRIPLET); while (gsl_spmatrix_nnz(m) < nnzwanted) { /* generate a random row and column */ size_t i = gsl_rng_uniform(r) * M; size_t j = gsl_rng_uniform(r) * N; /* generate random m_{ij} and add it */ int x = (int) (gsl_rng_uniform(r) * (upper - lower) + lower); gsl_spmatrix_set(m, i, j, (double) x); } return m; }
int penalty_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x, const gsl_vector * u, void * params, gsl_vector * v, gsl_matrix * JTJ) { struct model_params *par = (struct model_params *) params; const size_t p = x->size; size_t j; /* store 2*x in last row of J */ for (j = 0; j < p; ++j) { double xj = gsl_vector_get(x, j); gsl_spmatrix_set(par->J, p, j, 2.0 * xj); } /* compute v = op(J) u */ if (v) gsl_spblas_dgemv(TransJ, 1.0, par->J, u, 0.0, v); if (JTJ) { gsl_vector_view diag = gsl_matrix_diagonal(JTJ); /* compute J^T J = [ alpha*I_p + 4 x x^T ] */ gsl_matrix_set_zero(JTJ); /* store 4 x x^T in lower half of JTJ */ gsl_blas_dsyr(CblasLower, 4.0, x, JTJ); /* add alpha to diag(JTJ) */ gsl_vector_add_constant(&diag.vector, par->alpha); } return GSL_SUCCESS; }
static void test_toeplitz(const size_t N, const double a, const double b, const double c) { int status; const double tol = 1.0e-10; const size_t max_iter = 10; const gsl_splinalg_itersolve_type *T = gsl_splinalg_itersolve_gmres; const char *desc; gsl_spmatrix *A; gsl_vector *rhs, *x; gsl_splinalg_itersolve *w; size_t i, iter = 0; if (N <= 1) return; A = gsl_spmatrix_alloc(N ,N); rhs = gsl_vector_alloc(N); x = gsl_vector_calloc(N); w = gsl_splinalg_itersolve_alloc(T, N, 0); desc = gsl_splinalg_itersolve_name(w); /* first row */ gsl_spmatrix_set(A, 0, 0, b); gsl_spmatrix_set(A, 0, 1, c); /* interior rows */ for (i = 1; i < N - 1; ++i) { gsl_spmatrix_set(A, i, i - 1, a); gsl_spmatrix_set(A, i, i, b); gsl_spmatrix_set(A, i, i + 1, c); } /* last row */ gsl_spmatrix_set(A, N - 1, N - 2, a); gsl_spmatrix_set(A, N - 1, N - 1, b); /* set rhs vector */ gsl_vector_set_all(rhs, 1.0); /* solve the system */ do { status = gsl_splinalg_itersolve_iterate(A, rhs, tol, x, w); } while (status == GSL_CONTINUE && ++iter < max_iter); gsl_test(status, "%s toeplitz status s=%d N=%zu a=%f b=%f c=%f", desc, status, N, a, b, c); /* check that the residual satisfies ||r|| <= tol*||b|| */ { gsl_vector *r = gsl_vector_alloc(N); double normr, normb; gsl_vector_memcpy(r, rhs); gsl_spblas_dgemv(CblasNoTrans, -1.0, A, x, 1.0, r); normr = gsl_blas_dnrm2(r); normb = gsl_blas_dnrm2(rhs); status = (normr <= tol*normb) != 1; gsl_test(status, "%s toeplitz residual N=%zu a=%f b=%f c=%f normr=%.12e normb=%.12e", desc, N, a, b, c, normr, normb); gsl_vector_free(r); } gsl_vector_free(x); gsl_vector_free(rhs); gsl_spmatrix_free(A); gsl_splinalg_itersolve_free(w); } /* test_toeplitz() */
/* test_poisson() Solve u''(x) = -pi^2 sin(pi*x), u(x) = sin(pi*x) epsrel is the relative error threshold with the exact solution */ static void test_poisson(const size_t N, const double epsrel, const int compress) { const gsl_splinalg_itersolve_type *T = gsl_splinalg_itersolve_gmres; const size_t n = N - 2; /* subtract 2 to exclude boundaries */ const double h = 1.0 / (N - 1.0); /* grid spacing */ const double tol = 1.0e-9; const size_t max_iter = 10; size_t iter = 0; gsl_spmatrix *A = gsl_spmatrix_alloc(n ,n); /* triplet format */ gsl_spmatrix *B; gsl_vector *b = gsl_vector_alloc(n); /* right hand side vector */ gsl_vector *u = gsl_vector_calloc(n); /* solution vector, u0 = 0 */ gsl_splinalg_itersolve *w = gsl_splinalg_itersolve_alloc(T, n, 0); const char *desc = gsl_splinalg_itersolve_name(w); size_t i; int status; /* construct the sparse matrix for the finite difference equation */ /* first row of matrix */ gsl_spmatrix_set(A, 0, 0, -2.0); gsl_spmatrix_set(A, 0, 1, 1.0); /* loop over interior grid points */ for (i = 1; i < n - 1; ++i) { gsl_spmatrix_set(A, i, i + 1, 1.0); gsl_spmatrix_set(A, i, i, -2.0); gsl_spmatrix_set(A, i, i - 1, 1.0); } /* last row of matrix */ gsl_spmatrix_set(A, n - 1, n - 1, -2.0); gsl_spmatrix_set(A, n - 1, n - 2, 1.0); /* scale by h^2 */ gsl_spmatrix_scale(A, 1.0 / (h * h)); /* construct right hand side vector */ for (i = 0; i < n; ++i) { double xi = (i + 1) * h; double bi = -M_PI * M_PI * sin(M_PI * xi); gsl_vector_set(b, i, bi); } if (compress) B = gsl_spmatrix_compcol(A); else B = A; /* solve the system */ do { status = gsl_splinalg_itersolve_iterate(B, b, tol, u, w); } while (status == GSL_CONTINUE && ++iter < max_iter); gsl_test(status, "%s poisson status s=%d N=%zu", desc, status, N); /* check solution against analytic */ for (i = 0; i < n; ++i) { double xi = (i + 1) * h; double u_gsl = gsl_vector_get(u, i); double u_exact = sin(M_PI * xi); gsl_test_rel(u_gsl, u_exact, epsrel, "%s poisson N=%zu i=%zu", desc, N, i); } /* check that the residual satisfies ||r|| <= tol*||b|| */ { gsl_vector *r = gsl_vector_alloc(n); double normr, normb; gsl_vector_memcpy(r, b); gsl_spblas_dgemv(CblasNoTrans, -1.0, A, u, 1.0, r); normr = gsl_blas_dnrm2(r); normb = gsl_blas_dnrm2(b); status = (normr <= tol*normb) != 1; gsl_test(status, "%s poisson residual N=%zu normr=%.12e normb=%.12e", desc, N, normr, normb); gsl_vector_free(r); } gsl_splinalg_itersolve_free(w); gsl_spmatrix_free(A); gsl_vector_free(b); gsl_vector_free(u); if (compress) gsl_spmatrix_free(B); } /* test_poisson() */
int main() { const size_t N = 100; /* number of grid points */ const size_t n = N - 2; /* subtract 2 to exclude boundaries */ const double h = 1.0 / (N - 1.0); /* grid spacing */ gsl_spmatrix *A = gsl_spmatrix_alloc(n ,n); /* triplet format */ gsl_spmatrix *C; /* compressed format */ gsl_vector *f = gsl_vector_alloc(n); /* right hand side vector */ gsl_vector *u = gsl_vector_alloc(n); /* solution vector */ size_t i; /* construct the sparse matrix for the finite difference equation */ /* construct first row */ gsl_spmatrix_set(A, 0, 0, -2.0); gsl_spmatrix_set(A, 0, 1, 1.0); /* construct rows [1:n-2] */ for (i = 1; i < n - 1; ++i) { gsl_spmatrix_set(A, i, i + 1, 1.0); gsl_spmatrix_set(A, i, i, -2.0); gsl_spmatrix_set(A, i, i - 1, 1.0); } /* construct last row */ gsl_spmatrix_set(A, n - 1, n - 1, -2.0); gsl_spmatrix_set(A, n - 1, n - 2, 1.0); /* scale by h^2 */ gsl_spmatrix_scale(A, 1.0 / (h * h)); /* construct right hand side vector */ for (i = 0; i < n; ++i) { double xi = (i + 1) * h; double fi = -M_PI * M_PI * sin(M_PI * xi); gsl_vector_set(f, i, fi); } /* convert to compressed column format */ C = gsl_spmatrix_ccs(A); /* now solve the system with the GMRES iterative solver */ { const double tol = 1.0e-6; /* solution relative tolerance */ const size_t max_iter = 10; /* maximum iterations */ const gsl_splinalg_itersolve_type *T = gsl_splinalg_itersolve_gmres; gsl_splinalg_itersolve *work = gsl_splinalg_itersolve_alloc(T, n, 0); size_t iter = 0; double residual; int status; /* initial guess u = 0 */ gsl_vector_set_zero(u); /* solve the system A u = f */ do { status = gsl_splinalg_itersolve_iterate(C, f, tol, u, work); /* print out residual norm ||A*u - f|| */ residual = gsl_splinalg_itersolve_normr(work); fprintf(stderr, "iter "F_ZU" residual = %.12e\n", iter, residual); if (status == GSL_SUCCESS) fprintf(stderr, "Converged\n"); } while (status == GSL_CONTINUE && ++iter < max_iter); /* output solution */ for (i = 0; i < n; ++i) { double xi = (i + 1) * h; double u_exact = sin(M_PI * xi); double u_gsl = gsl_vector_get(u, i); printf("%f %.12e %.12e\n", xi, u_gsl, u_exact); } gsl_splinalg_itersolve_free(work); } gsl_spmatrix_free(A); gsl_spmatrix_free(C); gsl_vector_free(f); gsl_vector_free(u); return 0; } /* main() */
static void test_getset(const size_t M, const size_t N, const gsl_rng *r) { int status; size_t i, j; /* test triplet versions of _get and _set */ { size_t k = 0; gsl_spmatrix *m = gsl_spmatrix_alloc(M, N); status = 0; for (i = 0; i < M; ++i) { for (j = 0; j < N; ++j) { double x = (double) ++k; double y; gsl_spmatrix_set(m, i, j, x, 0); y = gsl_spmatrix_get(m, i, j); if (x != y) status = 1; } } gsl_test(status, "test_getset: M=%zu N=%zu _get != _set", M, N); /* test setting an element to 0 */ gsl_spmatrix_set(m, 0, 0, 1.0, 0); gsl_spmatrix_set(m, 0, 0, 0.0, 0); status = gsl_spmatrix_get(m, 0, 0) != 0.0; gsl_test(status, "test_getset: M=%zu N=%zu m(0,0) = %f", M, N, gsl_spmatrix_get(m, 0, 0)); /* test gsl_spmatrix_set_zero() */ gsl_spmatrix_set(m, 0, 0, 1.0, 0); gsl_spmatrix_set_zero(m); status = gsl_spmatrix_get(m, 0, 0) != 0.0; gsl_test(status, "test_getset: M=%zu N=%zu set_zero m(0,0) = %f", M, N, gsl_spmatrix_get(m, 0, 0)); /* resassemble matrix to ensure nz is calculated correctly */ k = 0; for (i = 0; i < M; ++i) { for (j = 0; j < N; ++j) { double x = (double) ++k; gsl_spmatrix_set(m, i, j, x, 0); } } status = gsl_spmatrix_nnz(m) != M * N; gsl_test(status, "test_getset: M=%zu N=%zu set_zero nz = %zu", M, N, gsl_spmatrix_nnz(m)); gsl_spmatrix_free(m); } /* test duplicate values are handled correctly */ { size_t min = GSL_MIN(M, N); size_t expected_nnz = min; size_t nnz; size_t k = 0; gsl_spmatrix *m = gsl_spmatrix_alloc(M, N); status = 0; for (i = 0; i < min; ++i) { for (j = 0; j < 5; ++j) { double x = (double) ++k; double y; gsl_spmatrix_set(m, i, i, x, 0); y = gsl_spmatrix_get(m, i, i); if (x != y) status = 1; } } gsl_test(status, "test_getset: duplicate test M=%zu N=%zu _get != _set", M, N); nnz = gsl_spmatrix_nnz(m); status = nnz != expected_nnz; gsl_test(status, "test_getset: duplicate test M=%zu N=%zu nnz=%zu, expected=%zu", M, N, nnz, expected_nnz); gsl_spmatrix_free(m); } /* test compressed version of gsl_spmatrix_get() */ { gsl_spmatrix *T = create_random_sparse(M, N, 0.3, r); gsl_spmatrix *C = gsl_spmatrix_compress(T, GSL_SPMATRIX_CCS); gsl_spmatrix *CR = gsl_spmatrix_compress(T, GSL_SPMATRIX_CRS); status = 0; for (i = 0; i < M; ++i) { for (j = 0; j < N; ++j) { double Tij = gsl_spmatrix_get(T, i, j); double Cij = gsl_spmatrix_get(C, i, j); if (Tij != Cij) status = 1; } } gsl_test(status, "test_getset: M=%zu N=%zu compressed column _get", M, N); status = 0; for (i = 0; i < M; ++i) { for (j = 0; j < N; ++j) { double Tij = gsl_spmatrix_get(T, i, j); double Cij = gsl_spmatrix_get(CR, i, j); if (Tij != Cij) status = 1; } } gsl_test(status, "test_getset: M=%zu N=%zu compressed row _get", M, N); gsl_spmatrix_free(T); gsl_spmatrix_free(C); gsl_spmatrix_free(CR); } } /* test_getset() */
static void test_getset(const size_t M, const size_t N, const double density, const gsl_rng *r) { int status; size_t i, j; /* test triplet versions of _get and _set */ { const double val = 0.75; size_t k = 0; gsl_spmatrix *m = gsl_spmatrix_alloc(M, N); status = 0; for (i = 0; i < M; ++i) { for (j = 0; j < N; ++j) { double x = (double) ++k; double y; gsl_spmatrix_set(m, i, j, x); y = gsl_spmatrix_get(m, i, j); if (x != y) status = 1; } } gsl_test(status, "test_getset: M="F_ZU" N="F_ZU" _get != _set", M, N); /* test setting an element to 0 */ gsl_spmatrix_set(m, 0, 0, 1.0); gsl_spmatrix_set(m, 0, 0, 0.0); status = gsl_spmatrix_get(m, 0, 0) != 0.0; gsl_test(status, "test_getset: M="F_ZU" N="F_ZU" m(0,0) = %f", M, N, gsl_spmatrix_get(m, 0, 0)); /* test gsl_spmatrix_set_zero() */ gsl_spmatrix_set(m, 0, 0, 1.0); gsl_spmatrix_set_zero(m); status = gsl_spmatrix_get(m, 0, 0) != 0.0; gsl_test(status, "test_getset: M="F_ZU" N="F_ZU" set_zero m(0,0) = %f", M, N, gsl_spmatrix_get(m, 0, 0)); /* resassemble matrix to ensure nz is calculated correctly */ k = 0; for (i = 0; i < M; ++i) { for (j = 0; j < N; ++j) { double x = (double) ++k; gsl_spmatrix_set(m, i, j, x); } } status = gsl_spmatrix_nnz(m) != M * N; gsl_test(status, "test_getset: M="F_ZU" N="F_ZU" set_zero nz = "F_ZU, M, N, gsl_spmatrix_nnz(m)); /* test gsl_spmatrix_ptr() */ status = 0; for (i = 0; i < M; ++i) { for (j = 0; j < N; ++j) { double mij = gsl_spmatrix_get(m, i, j); double *ptr = gsl_spmatrix_ptr(m, i, j); *ptr += val; if (gsl_spmatrix_get(m, i, j) != mij + val) status = 2; } } gsl_test(status == 2, "test_getset: M="F_ZU" N="F_ZU" triplet ptr", M, N); gsl_spmatrix_free(m); } /* test duplicate values are handled correctly */ { size_t min = GSL_MIN(M, N); size_t expected_nnz = min; size_t nnz; size_t k = 0; gsl_spmatrix *m = gsl_spmatrix_alloc(M, N); status = 0; for (i = 0; i < min; ++i) { for (j = 0; j < 5; ++j) { double x = (double) ++k; double y; gsl_spmatrix_set(m, i, i, x); y = gsl_spmatrix_get(m, i, i); if (x != y) status = 1; } } gsl_test(status, "test_getset: duplicate test M="F_ZU" N="F_ZU" _get != _set", M, N); nnz = gsl_spmatrix_nnz(m); status = nnz != expected_nnz; gsl_test(status, "test_getset: duplicate test M="F_ZU" N="F_ZU" nnz="F_ZU", expected="F_ZU, M, N, nnz, expected_nnz); gsl_spmatrix_free(m); } /* test CCS version of gsl_spmatrix_get() */ { const double val = 0.75; gsl_spmatrix *T = create_random_sparse(M, N, density, r); gsl_spmatrix *C = gsl_spmatrix_ccs(T); status = 0; for (i = 0; i < M; ++i) { for (j = 0; j < N; ++j) { double Tij = gsl_spmatrix_get(T, i, j); double Cij = gsl_spmatrix_get(C, i, j); double *ptr = gsl_spmatrix_ptr(C, i, j); if (Tij != Cij) status = 1; if (ptr) { *ptr += val; Cij = gsl_spmatrix_get(C, i, j); if (Tij + val != Cij) status = 2; } } } gsl_test(status == 1, "test_getset: M="F_ZU" N="F_ZU" CCS get", M, N); gsl_test(status == 2, "test_getset: M="F_ZU" N="F_ZU" CCS ptr", M, N); gsl_spmatrix_free(T); gsl_spmatrix_free(C); } /* test CRS version of gsl_spmatrix_get() */ { const double val = 0.75; gsl_spmatrix *T = create_random_sparse(M, N, density, r); gsl_spmatrix *C = gsl_spmatrix_crs(T); status = 0; for (i = 0; i < M; ++i) { for (j = 0; j < N; ++j) { double Tij = gsl_spmatrix_get(T, i, j); double Cij = gsl_spmatrix_get(C, i, j); double *ptr = gsl_spmatrix_ptr(C, i, j); if (Tij != Cij) status = 1; if (ptr) { *ptr += val; Cij = gsl_spmatrix_get(C, i, j); if (Tij + val != Cij) status = 2; } } } gsl_test(status == 1, "test_getset: M="F_ZU" N="F_ZU" CRS get", M, N); gsl_test(status == 2, "test_getset: M="F_ZU" N="F_ZU" CRS ptr", M, N); gsl_spmatrix_free(T); gsl_spmatrix_free(C); } } /* test_getset() */
int main (void) { const size_t p = 2000; const size_t n = p + 1; gsl_vector *f = gsl_vector_alloc(n); gsl_vector *x = gsl_vector_alloc(p); /* allocate sparse Jacobian matrix with 2*p non-zero elements in triplet format */ gsl_spmatrix *J = gsl_spmatrix_alloc_nzmax(n, p, 2 * p, GSL_SPMATRIX_TRIPLET); gsl_multilarge_nlinear_fdf fdf; gsl_multilarge_nlinear_parameters fdf_params = gsl_multilarge_nlinear_default_parameters(); struct model_params params; size_t i; params.alpha = 1.0e-5; params.J = J; /* define function to be minimized */ fdf.f = penalty_f; fdf.df = penalty_df; fdf.fvv = penalty_fvv; fdf.n = n; fdf.p = p; fdf.params = ¶ms; for (i = 0; i < p; ++i) { /* starting point */ gsl_vector_set(x, i, i + 1.0); /* store sqrt(alpha)*I_p in upper p-by-p block of J */ gsl_spmatrix_set(J, i, i, sqrt(params.alpha)); } fprintf(stderr, "%-25s %-4s %-4s %-5s %-6s %-4s %-10s %-10s %-7s %-11s %-10s\n", "Method", "NITER", "NFEV", "NJUEV", "NJTJEV", "NAEV", "Init Cost", "Final cost", "cond(J)", "Final |x|^2", "Time (s)"); fdf_params.scale = gsl_multilarge_nlinear_scale_levenberg; fdf_params.trs = gsl_multilarge_nlinear_trs_lm; solve_system(x, &fdf, &fdf_params); fdf_params.trs = gsl_multilarge_nlinear_trs_lmaccel; solve_system(x, &fdf, &fdf_params); fdf_params.trs = gsl_multilarge_nlinear_trs_dogleg; solve_system(x, &fdf, &fdf_params); fdf_params.trs = gsl_multilarge_nlinear_trs_ddogleg; solve_system(x, &fdf, &fdf_params); fdf_params.trs = gsl_multilarge_nlinear_trs_cgst; solve_system(x, &fdf, &fdf_params); gsl_vector_free(f); gsl_vector_free(x); gsl_spmatrix_free(J); return 0; }