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;
}
