static int
pcholesky_decomp (const int copy_uplo, gsl_matrix * A, gsl_permutation * p)
{
const size_t N = A->size1;
if (N != A->size2)
{
GSL_ERROR("LDLT decomposition requires square matrix", GSL_ENOTSQR);
}
else if (p->size != N)
{
GSL_ERROR ("permutation length must match matrix size", GSL_EBADLEN);
}
else
{
gsl_vector_view diag = gsl_matrix_diagonal(A);
size_t k;
if (copy_uplo)
{
/* save a copy of A in upper triangle (for later rcond calculation) */
gsl_matrix_transpose_tricpy('L', 0, A, A);
}
gsl_permutation_init(p);
for (k = 0; k < N; ++k)
{
gsl_vector_view w;
size_t j;
/* compute j = max_idx { A_kk, ..., A_nn } */
w = gsl_vector_subvector(&diag.vector, k, N - k);
j = gsl_vector_max_index(&w.vector) + k;
gsl_permutation_swap(p, k, j);
cholesky_swap_rowcol(A, k, j);
if (k < N - 1)
{
double alpha = gsl_matrix_get(A, k, k);
double alphainv = 1.0 / alpha;
/* v = A(k+1:n, k) */
gsl_vector_view v = gsl_matrix_subcolumn(A, k, k + 1, N - k - 1);
/* m = A(k+1:n, k+1:n) */
gsl_matrix_view m = gsl_matrix_submatrix(A, k + 1, k + 1, N - k - 1, N - k - 1);
/* m = m - v v^T / alpha */
gsl_blas_dsyr(CblasLower, -alphainv, &v.vector, &m.matrix);
/* v = v / alpha */
gsl_vector_scale(&v.vector, alphainv);
}
}
return GSL_SUCCESS;
}
}
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;
}
// f = -log(det(X))
void prox_neg_log_det(gsl_matrix *X, const double rho)
{
int n = X->size1;
gsl_vector *d = gsl_vector_alloc(n);
gsl_matrix *V = gsl_matrix_alloc(n,n);
gsl_eigen_symmv_workspace *w = gsl_eigen_symmv_alloc(n);
gsl_eigen_symmv(X, d, V, w);
gsl_eigen_symmv_free(w);
int i;
double d_i;
gsl_matrix_set_zero(X);
for (i = 0; i < n; i++) {
d_i = gsl_vector_get(d, i);
d_i = (d_i + sqrt(pow(d_i,2) + 4*rho))/(2*rho);
gsl_vector_set(d, i, d_i);
gsl_vector_view V_i = gsl_matrix_column(V, i);
gsl_blas_dsyr(CblasLower, d_i, &V_i.vector, X);
}
gsl_vector_free(d);
gsl_matrix_free(V);
}
// f = I(X >= 0)
void project_sdc(gsl_matrix *X)
{
int n = X->size1;
gsl_vector *d = gsl_vector_alloc(n);
gsl_matrix *V = gsl_matrix_alloc(n,n);
gsl_eigen_symmv_workspace *w = gsl_eigen_symmv_alloc(n);
gsl_eigen_symmv(X, d, V, w);
gsl_eigen_symmv_free(w);
int i;
double d_i;
gsl_matrix_set_zero(X);
for (i = 0; i < n; i++) {
d_i = gsl_vector_get(d, i);
if (d_i > 0) {
gsl_vector_view V_i = gsl_matrix_column(V, i);
gsl_blas_dsyr(CblasLower, d_i, &V_i.vector, X);
}
}
gsl_vector_free(d);
gsl_matrix_free(V);
}
/**
* C++ version of gsl_blas_dsyr().
* @param Uplo Upper or lower triangular
* @param alpha A constant
* @param X A vector
* @param A A matrix
* @return Error code on failure
*/
int dsyr( CBLAS_UPLO_t Uplo, double alpha, vector const& X, matrix& A ){
return gsl_blas_dsyr( Uplo, alpha, X.get(), A.get() ); }