Coordinates
hlib_coord_t	hlib_coord_import (const size_t n, const unsigned int dim, double *coord, const double period, int *info)
size_t	hlib_coord_ncoord (const hlib_coord_t coord, int *info)
unsigned int	hlib_coord_dim (const hlib_coord_t coord, int *info)
double *	hlib_coord_get (const hlib_coord_t coord, const size_t i, int *info)
double *	hlib_coord_bbmin (const hlib_coord_t coord, const size_t i, int *info)
double *	hlib_coord_bbmax (const hlib_coord_t coord, const size_t i, int *info)
int	hlib_coord_has_bbox (const hlib_coord_t coord, int *info)
void	hlib_coord_set_period (hlib_coord_t coord, const double period[], int *info)
void	hlib_coord_get_period (hlib_coord_t coord, double period[], int *info)
void	hlib_coord_free (hlib_coord_t coord, int *info)
size_t	hlib_coord_bytesize (const hlib_coord_t coord, int *info)
void	hlib_coord_print_vrml (const hlib_coord_t coord, const char filename, int info)

Admissibility condition
hlib_admcond_t	hlib_admcond_geom (const hlib_adm_t crit, const double eta, int *info)
hlib_admcond_t	hlib_admcond_geom_period (const hlib_adm_t crit, const double eta, const double period, const unsigned int dim, int info)
hlib_admcond_t	hlib_admcond_alg (const hlib_adm_t crit, const double eta, const hlib_matrix_t S, const hlib_permutation_t row_perm, const hlib_permutation_t col_perm, int *info)
void	hlib_admcond_free (const hlib_admcond_t ac, int *info)

Clusters
Nodes and sub trees in a cluster tree.
int	hlib_cl_first (const hlib_cluster_t cl, int *info)
int	hlib_cl_last (const hlib_cluster_t cl, int *info)
size_t	hlib_cl_size (const hlib_cluster_t cl, int *info)
size_t	hlib_cl_nsons (const hlib_cluster_t cl, int *info)
hlib_cluster_t	hlib_cl_son (const hlib_cluster_t cl, const unsigned int i, int *info)
int	hlib_cl_is_leaf (const hlib_cluster_t cl, int *info)
size_t	hlib_cl_nnodes (const hlib_cluster_t cl, int *info)
size_t	hlib_cl_depth (const hlib_cluster_t cl, int *info)
hlib_cluster_t	hlib_cl_copy (const hlib_cluster_t cl, int *info)
void	hlib_cl_free (hlib_cluster_t cl, int *info)
size_t	hlib_cl_bytesize (const hlib_cluster_t cl, int *info)
void	hlib_cl_print_ps (const hlib_cluster_t cl, const char filename, int info)

Cluster Trees
Root of a cluster tree with stored index permutations.
hlib_clustertree_t	hlib_clt_build_bsp (const hlib_coord_t coord, const hlib_bsp_t bsptype, const unsigned int nmin, int *info)
hlib_clustertree_t	hlib_clt_build_bsp_nd (const hlib_coord_t coord, const hlib_matrix_t S, const hlib_bsp_t bsptype, const unsigned int nmin, int *info)
hlib_clustertree_t	hlib_clt_build_bsp_part (const hlib_coord_t coord, const unsigned int partition, const int eq_depth, const hlib_bsp_t bsptype, const unsigned int nmin, int info)
hlib_clustertree_t	hlib_clt_build_alg (const hlib_matrix_t S, const unsigned int nmin, int *info)
hlib_clustertree_t	hlib_clt_build_alg_nd (const hlib_matrix_t S, const unsigned int nmin, int *info)
hlib_clustertree_t	hlib_clt_build_alg_part (const hlib_matrix_t S, const unsigned int partition, const unsigned int nmin, int info)
hlib_cluster_t	hlib_clt_root (hlib_clustertree_t ct, int *info)
hlib_permutation_t	hlib_clt_perm_i2e (hlib_clustertree_t ct, int *info)
hlib_permutation_t	hlib_clt_perm_e2i (hlib_clustertree_t ct, int *info)
void	hlib_clt_free (hlib_clustertree_t ct, int *info)
size_t	hlib_clt_bytesize (const hlib_clustertree_t ct, int *info)
size_t	hlib_clt_nnodes (const hlib_clustertree_t ct, int *info)
size_t	hlib_clt_depth (const hlib_clustertree_t ct, int *info)
void	hlib_clt_print_ps (const hlib_clustertree_t ct, const char filename, int info)

Block Clusters
Nodes and sub trees of block cluster trees.
hlib_blockcluster_t	hlib_bc_parent (const hlib_blockcluster_t bc, int *info)
size_t	hlib_bc_nsons (const hlib_blockcluster_t bc, int *info)
hlib_blockcluster_t	hlib_bc_son (const hlib_blockcluster_t bc, const unsigned int i, const unsigned int j, int *info)
int	hlib_bc_is_leaf (const hlib_blockcluster_t bc, int *info)
int	hlib_bc_is_adm (const hlib_blockcluster_t bc, int *info)
size_t	hlib_bc_nnodes (const hlib_blockcluster_t bc, int *info)
size_t	hlib_bc_depth (const hlib_blockcluster_t bc, int *info)
hlib_cluster_t	hlib_bc_rowcl (const hlib_blockcluster_t bc, int *info)
hlib_cluster_t	hlib_bc_colcl (const hlib_blockcluster_t bc, int *info)
hlib_blockcluster_t	hlib_bc_copy (const hlib_blockcluster_t bc, int *info)
void	hlib_bc_free (hlib_blockcluster_t bc, int *info)
size_t	hlib_bc_bytesize (const hlib_blockcluster_t bc, int *info)
int	hlib_bc_csp (const hlib_blockcluster_t bc, int *info)
void	hlib_bc_print_ps (const hlib_blockcluster_t bc, const char filename, int info)

Block Cluster Trees
Root of block cluster trees with access to index permutations.
hlib_blockclustertree_t	hlib_bct_build (const hlib_clustertree_t rowct, const hlib_clustertree_t colct, const hlib_admcond_t ac, int *info)
size_t	hlib_bct_nnodes (const hlib_blockclustertree_t bct, int *info)
size_t	hlib_bct_depth (const hlib_blockclustertree_t bct, int *info)
hlib_clustertree_t	hlib_bct_rowct (const hlib_blockclustertree_t bct, int *info)
hlib_clustertree_t	hlib_bct_colct (const hlib_blockclustertree_t bct, int *info)
void	hlib_bct_free (hlib_blockclustertree_t bct, int *info)
size_t	hlib_bct_bytesize (const hlib_blockclustertree_t bct, int *info)
void	hlib_bct_distribute_block (hlib_blockclustertree_t bct, const unsigned int p, const unsigned int min_lvl, const int symmetric, int *info)
int	hlib_bct_csp (const hlib_blockclustertree_t bct, int *info)
void	hlib_bct_print_ps (const hlib_blockclustertree_t bct, const char filename, int info)

Vectors
size_t	hlib_vector_size (const hlib_vector_t v, int *info)
hlib_vector_t	hlib_vector_copy (const hlib_vector_t v, int *info)
size_t	hlib_vector_bytesize (const hlib_vector_t v, int *info)
void	hlib_vector_free (hlib_vector_t v, int *info)
hlib_real_t	hlib_vector_entry_get (const hlib_vector_t x, const size_t i, int *info)
hlib_complex_t	hlib_vector_centry_get (const hlib_vector_t x, const size_t i, int *info)
void	hlib_vector_entry_set (const hlib_vector_t x, const size_t i, const hlib_real_t f, int *info)
void	hlib_vector_centry_set (const hlib_vector_t x, const size_t i, const hlib_complex_t f, int *info)
hlib_vector_t	hlib_vector_build (const size_t size, int *info)
hlib_vector_t	hlib_vector_cbuild (const size_t size, int *info)
void	hlib_vector_import (hlib_vector_t v, const hlib_real_t arr, int info)
void	hlib_vector_cimport (hlib_vector_t v, const hlib_complex_t arr, int info)
void	hlib_vector_export (const hlib_vector_t v, hlib_real_t arr, int info)
void	hlib_vector_cexport (const hlib_vector_t v, hlib_complex_t arr, int info)
void	hlib_vector_fill (hlib_vector_t x, const hlib_real_t f, int *info)
void	hlib_vector_cfill (hlib_vector_t x, const hlib_complex_t f, int *info)
void	hlib_vector_fill_rand (hlib_vector_t x, int *info)
void	hlib_vector_assign (hlib_vector_t y, const hlib_vector_t x, int *info)
void	hlib_vector_scale (hlib_vector_t x, const hlib_real_t f, int *info)
void	hlib_vector_cscale (hlib_vector_t x, const hlib_complex_t f, int *info)
void	hlib_vector_axpy (const hlib_real_t alpha, const hlib_vector_t x, hlib_vector_t y, int *info)
void	hlib_vector_caxpy (const hlib_complex_t alpha, const hlib_vector_t x, hlib_vector_t y, int *info)
hlib_complex_t	hlib_vector_dot (const hlib_vector_t x, const hlib_vector_t y, int *info)
hlib_real_t	hlib_vector_norm2 (const hlib_vector_t x, int *info)
hlib_real_t	hlib_vector_norm_inf (const hlib_vector_t x, int *info)
hlib_vector_t	hlib_vector_restrict_re (const hlib_vector_t v, int *info)
hlib_vector_t	hlib_vector_restrict_im (const hlib_vector_t v, int *info)
void	hlib_vector_fft (const hlib_vector_t v, int *info)
void	hlib_vector_ifft (const hlib_vector_t v, int *info)

Matrices
size_t	hlib_matrix_rows (const hlib_matrix_t A, int *info)
size_t	hlib_matrix_cols (const hlib_matrix_t A, int *info)
hlib_matrix_t	hlib_matrix_copy (const hlib_matrix_t A, int *info)
hlib_matrix_t	hlib_matrix_copy_acc (const hlib_matrix_t A, const hlib_acc_t acc, const int coarsen, int *info)
void	hlib_matrix_copyto (const hlib_matrix_t A, hlib_matrix_t B, int *info)
void	hlib_matrix_copyto_acc (const hlib_matrix_t A, hlib_matrix_t B, const hlib_acc_t acc, const int coarsen, int *info)
hlib_matrix_t	hlib_matrix_copy_blockdiag (const hlib_matrix_t A, const unsigned int lvl, int *info)
hlib_matrix_t	hlib_matrix_copy_blockdiag_acc (const hlib_matrix_t A, const unsigned int lvl, const hlib_acc_t acc, int *info)
hlib_matrix_t	hlib_matrix_copy_nearfield (const hlib_matrix_t A, const int without_rk, int *info)
size_t	hlib_matrix_bytesize (const hlib_matrix_t A, int *info)
void	hlib_matrix_free (hlib_matrix_t A, int *info)
int	hlib_matrix_is_sym (const hlib_matrix_t A, int *info)
int	hlib_matrix_is_herm (const hlib_matrix_t A, int *info)
int	hlib_matrix_is_complex (const hlib_matrix_t A, int *info)
void	hlib_matrix_to_real (const hlib_matrix_t A, const int force, int *info)
void	hlib_matrix_to_complex (const hlib_matrix_t A, const int force, int *info)
hlib_real_t	hlib_matrix_entry_get (const hlib_matrix_t A, const size_t i, const size_t j, int *info)
hlib_complex_t	hlib_matrix_centry_get (const hlib_matrix_t A, const size_t i, const size_t j, int *info)
hlib_vector_t	hlib_matrix_row_vector (const hlib_matrix_t A, int *info)
hlib_vector_t	hlib_matrix_col_vector (const hlib_matrix_t A, int *info)
hlib_matrix_t	hlib_matrix_import_crs (const size_t rows, const size_t cols, const size_t nnz, const int rowind, const int colind, const hlib_real_t coeffs, const int sym, int info)
hlib_matrix_t	hlib_matrix_import_ccrs (const size_t rows, const size_t cols, const size_t nnz, const int rowind, const int colind, const hlib_complex_t coeffs, const int sym, int info)
hlib_matrix_t	hlib_matrix_import_dense (const size_t rows, const size_t cols, const hlib_real_t D, const int sym, int info)
hlib_matrix_t	hlib_matrix_import_cdense (const size_t rows, const size_t cols, const hlib_complex_t D, const int sym, int info)
hlib_matrix_t	hlib_matrix_build_sparse (const hlib_blockclustertree_t bct, const hlib_matrix_t S, const hlib_acc_t acc, int *info)
hlib_matrix_t	hlib_matrix_build_dense (const hlib_blockclustertree_t bct, const hlib_matrix_t D, const hlib_lrapx_t lrapx, const hlib_acc_t acc, int *info)
hlib_matrix_t	hlib_matrix_build_coeff (const hlib_blockclustertree_t bct, const hlib_coeff_t f, void arg, const hlib_lrapx_t lrapx, const hlib_acc_t acc, const int sym, int info)
hlib_matrix_t	hlib_matrix_build_ccoeff (const hlib_blockclustertree_t bct, const hlib_ccoeff_t f, void arg, const hlib_lrapx_t lrapx, const hlib_acc_t acc, const int sym, int info)
hlib_matrix_t	hlib_matrix_build_identity (const hlib_blockclustertree_t bct, int *info)
hlib_matrix_t	hlib_matrix_assemble_block (const size_t brows, const size_t bcols, hlib_matrix_t submat, const int copy, int info)
void	hlib_matrix_print_ps (const hlib_matrix_t A, const char filename, const int options, int info)

Algebra
void	hlib_matrix_mulvec (const hlib_real_t alpha, const hlib_matrix_t A, const hlib_vector_t x, const hlib_real_t beta, hlib_vector_t y, const hlib_matop_t matop, int *info)
void	hlib_matrix_cmulvec (const hlib_complex_t alpha, const hlib_matrix_t A, const hlib_vector_t x, const hlib_complex_t beta, hlib_vector_t y, const hlib_matop_t matop, int *info)
void	hlib_matrix_transpose (const hlib_matrix_t A, int *info)
void	hlib_matrix_conjugate (const hlib_matrix_t A, int *info)
void	hlib_matrix_scale (const hlib_real_t f, const hlib_matrix_t A, int *info)
void	hlib_matrix_cscale (const hlib_complex_t f, const hlib_matrix_t A, int *info)
void	hlib_matrix_add (const hlib_real_t alpha, const hlib_matrix_t A, const hlib_real_t beta, hlib_matrix_t B, const hlib_acc_t acc, int *info)
void	hlib_matrix_cadd (const hlib_complex_t alpha, const hlib_matrix_t A, const hlib_complex_t beta, hlib_matrix_t B, const hlib_acc_t acc, int *info)
void	hlib_matrix_mul (const hlib_real_t alpha, const hlib_matop_t matop_A, const hlib_matrix_t A, const hlib_matop_t matop_B, const hlib_matrix_t B, const hlib_real_t beta, hlib_matrix_t C, const hlib_acc_t acc, int *info)
void	hlib_matrix_cmul (const hlib_complex_t alpha, const hlib_matop_t matop_A, const hlib_matrix_t A, const hlib_matop_t matop_B, const hlib_matrix_t B, const hlib_complex_t beta, hlib_matrix_t C, const hlib_acc_t acc, int *info)
hlib_matrix_t	hlib_matrix_inv (hlib_matrix_t A, const hlib_acc_t acc, int *info)
hlib_vector_t	hlib_matrix_inv_diag (hlib_matrix_t A, const hlib_acc_t acc, int *info)
hlib_matrix_t	hlib_matrix_factorise (hlib_matrix_t A, const hlib_acc_t acc, int *info)
hlib_matrix_t	hlib_matrix_factorise_inv (hlib_matrix_t A, const hlib_acc_t acc, int *info)
hlib_matrix_t	hlib_matrix_lu (hlib_matrix_t A, const hlib_acc_t acc, int *info)
hlib_matrix_t	hlib_matrix_ldl (hlib_matrix_t A, const hlib_acc_t acc, int *info)
hlib_matrix_t	hlib_matrix_ll (hlib_matrix_t A, const hlib_acc_t acc, int *info)
void	hlib_matrix_solve_lower_left (const hlib_matrix_t L, hlib_matrix_t A, const hlib_acc_t acc, const int pointwise, const int unit_diag, int *info)
void	hlib_matrix_solve_lower_right (hlib_matrix_t A, const hlib_matrix_t L, const hlib_matop_t op_L, const hlib_acc_t acc, const int pointwise, const int unit_diag, int *info)
void	hlib_matrix_solve_upper_right (hlib_matrix_t A, const hlib_matrix_t U, const hlib_acc_t acc, const int pointwise, const int unit_diag, int *info)
void	hlib_matrix_solve_diag_left (const hlib_matrix_t D, const hlib_matop_t op_D, hlib_matrix_t A, const hlib_acc_t acc, const int pointwise, int *info)
void	hlib_matrix_solve_diag_right (hlib_matrix_t A, const hlib_matrix_t D, const hlib_matop_t op_D, const hlib_acc_t acc, const int pointwise, int *info)
hlib_real_t	hlib_matrix_norm_frobenius (const hlib_matrix_t A, int *info)
hlib_real_t	hlib_matrix_norm_frobenius_diff (const hlib_matrix_t A, const hlib_matrix_t B, int *info)
hlib_real_t	hlib_matrix_norm_spectral (const hlib_matrix_t A, int *info)
hlib_real_t	hlib_matrix_norm_spectral_inv (const hlib_matrix_t A, int *info)
hlib_real_t	hlib_matrix_norm_spectral_diff (const hlib_matrix_t A, const hlib_matrix_t B, int *info)
hlib_real_t	hlib_matrix_norm_inv_approx (const hlib_matrix_t A, const hlib_matrix_t B, int *info)

Solver
hlib_solver_t	hlib_solver_auto (int *info)
hlib_solver_t	hlib_solver_richardson (int *info)
hlib_solver_t	hlib_solver_cg (int *info)
hlib_solver_t	hlib_solver_bicgstab (int *info)
hlib_solver_t	hlib_solver_minres (int *info)
hlib_solver_t	hlib_solver_gmres (const int restart, int *info)
void	hlib_solver_solve (const hlib_solver_t solver, const hlib_matrix_t A, hlib_vector_t x, const hlib_vector_t b, const hlib_matrix_t W, hlib_solve_info_t solve_info, int info)
void	hlib_solver_stopcrit (hlib_solver_t solver, const int maxit, const hlib_real_t abs_red, const hlib_real_t rel_red, int *info)
void	hlib_solver_free (hlib_solver_t solver, int *info)

Input/Output
hlib_matrix_t	hlib_hformat_load_matrix (const char filename, int info)
hlib_vector_t	hlib_hformat_load_vector (const char filename, int info)
void	hlib_hformat_save_matrix (const hlib_matrix_t A, const char filename, int info)
void	hlib_hformat_save_vector (const hlib_vector_t v, const char filename, int info)
hlib_coord_t	hlib_hformat_load_coord (const char filename, int info)
void	hlib_hformat_save_coord (const hlib_coord_t coord, const char filename, int info)
hlib_matrix_t	hlib_samg_load_matrix (const char filename, int info)
void	hlib_samg_save_matrix (const hlib_matrix_t A, const char filename, int info)
hlib_vector_t	hlib_samg_load_vector (const char filename, int info)
void	hlib_samg_save_vector (const hlib_vector_t x, const char filename, int info)
void	hlib_samg_save_coord (const hlib_coord_t coord, const char filename, int info)
hlib_coord_t	hlib_samg_load_coord (const char filename, int info)
hlib_matrix_t	hlib_matlab_load_matrix (const char filename, const char matname, int *info)
void	hlib_matlab_save_matrix (const hlib_matrix_t M, const char filename, const char matname, int *info)
hlib_vector_t	hlib_matlab_load_vector (const char filename, const char vecname, int *info)
void	hlib_matlab_save_vector (const hlib_vector_t v, const char filename, const char vecname, int *info)
hlib_matrix_t	hlib_pltmg_load_matrix (const char filename, int info)
hlib_matrix_t	hlib_hb_load_matrix (const char filename, int info)
void	hlib_hb_save_matrix (const hlib_matrix_t M, const char filename, int info)
hlib_matrix_t	hlib_mm_load_matrix (const char filename, int info)
hlib_matrix_t	hlib_load_matrix (const char filename, int info)
hlib_vector_t	hlib_load_vector (const char filename, int info)
hlib_coord_t	hlib_load_coord (const char filename, int info)

Accuracy Management
hlib_acc_t	hlib_acc_fixed_eps (const hlib_real_t eps)
hlib_acc_t	hlib_acc_fixed_rank (const unsigned int k)
hlib_acc_t	hlib_acc_blocked (const hlib_acc_t *blockacc)

Misc.
double	hlib_walltime ()
double	hlib_cputime ()
void	hlib_set_n_min (const unsigned int n)
void	hlib_set_verbosity (const unsigned int verb)
void	hlib_set_abs_eps (const hlib_real_t eps)
void	hlib_set_coarsening (const int build, const int arith)
void	hlib_set_recompress (const int recompress)
void	hlib_set_diag_scale (const int scale)
void	hlib_set_nthreads (const unsigned int p)
void	hlib_set_progress_cb (hlib_progressfn_t fn, void *arg)
void	hlib_set_error_fn (const hlib_errorfn_t errorfn)
void	hlib_set_warning_fn (const hlib_errorfn_t warnfn)
unsigned int	hlib_major_version ()
unsigned int	hlib_minor_version ()

Functions for hlib_complex_t
hlib_complex_t	hlib_complex (const double re, const double im)
hlib_complex_t	hlib_cmplx_add (const hlib_complex_t a, const hlib_complex_t b)
hlib_complex_t	hlib_cmplx_sub (const hlib_complex_t a, const hlib_complex_t b)
hlib_complex_t	hlib_cmplx_mul (const hlib_complex_t a, const hlib_complex_t b)
hlib_complex_t	hlib_cmplx_div (const hlib_complex_t a, const hlib_complex_t b)
hlib_complex_t	hlib_cmplx_conj (const hlib_complex_t a)
hlib_real_t	hlib_cmplx_abs (const hlib_complex_t a)
hlib_complex_t	hlib_cmplx_sqrt (const hlib_complex_t a)
hlib_complex_t	hlib_cmplx_exp (const hlib_complex_t a)

Detailed Description

This modules defines functions for the usage of 𝓗𝖫𝖨𝖡𝗉𝗋𝗈 in C programs instead of C++.

To include all standard 𝓗-matrix related functions add

#include <hlib-c.h>

to your source files. For using BEM functions in C, you also have to add

#include <hlib-c-bem.h>

Function Documentation

hlib_acc_t hlib_acc_blocked ( const hlib_acc_t * blockacc )

return accuracy object with blockwise accuracy defined by array blockacc of dimension blockrows × blockcolumns corresponding to first partitioning level; the array must be stored column wise

hlib_acc_t hlib_acc_fixed_eps ( const hlib_real_t eps )

return accuracy object with fixed accuracy eps

hlib_acc_t hlib_acc_fixed_rank ( const unsigned int k )

return accuracy object with fixed rank k

hlib_admcond_t hlib_admcond_alg	(	const hlib_adm_t	crit,
		const double	eta,
		const hlib_matrix_t	S,
		const hlib_permutation_t	row_perm,
		const hlib_permutation_t	col_perm,
		int *	info
	)

create admissibility condition based on algebraic connectivity in S

row_perm and col_perm define the (optional) mapping between internal to external ordering for row and column index sets, respectively (see hlib_ct_perm_i2e); set to NULL if not present

void hlib_admcond_free	(	const hlib_admcond_t	ac,
		int *	info
	)

free admissibility condition

hlib_admcond_t hlib_admcond_geom	(	const hlib_adm_t	crit,
		const double	eta,
		int *	info
	)

create admissibility condition based on geometrical data

hlib_admcond_t hlib_admcond_geom_period	(	const hlib_adm_t	crit,
		const double	eta,
		const double *	period,
		const unsigned int	dim,
		int *	info
	)

create admissibility condition based on geometrical data with additional periodicity in geometry defined by vector period

period must have same dimension dim as coordinates used for constructing cluster trees

size_t hlib_bc_bytesize	(	const hlib_blockcluster_t	bc,
		int *	info
	)

return size of memory in bytes used by block cluster

hlib_cluster_t hlib_bc_colcl	(	const hlib_blockcluster_t	bc,
		int *	info
	)

return column cluster of given block cluster

hlib_blockcluster_t hlib_bc_copy	(	const hlib_blockcluster_t	bc,
		int *	info
	)

return copy of sub tree defined by bc

int hlib_bc_csp	(	const hlib_blockcluster_t	bc,
		int *	info
	)

compute sparsity constant of block cluster tree

size_t hlib_bc_depth	(	const hlib_blockcluster_t	bc,
		int *	info
	)

return depth of block cluster

void hlib_bc_free	(	hlib_blockcluster_t	bc,
		int *	info
	)

free resources coupled with block cluster tree bct

int hlib_bc_is_adm	(	const hlib_blockcluster_t	bc,
		int *	info
	)

return 1 if block cluster is admissible and 0 otherwise

int hlib_bc_is_leaf	(	const hlib_blockcluster_t	bc,
		int *	info
	)

return 1 if block cluster is leaf and 0 otherwise

size_t hlib_bc_nnodes	(	const hlib_blockcluster_t	bc,
		int *	info
	)

return number of nodes in block cluster

size_t hlib_bc_nsons	(	const hlib_blockcluster_t	bc,
		int *	info
	)

return total number of sons of block cluster bc

hlib_blockcluster_t hlib_bc_parent	(	const hlib_blockcluster_t	bc,
		int *	info
	)

return parent block cluster of block cluster bc

void hlib_bc_print_ps	(	const hlib_blockcluster_t	bc,
		const char *	filename,
		int *	info
	)

print block cluster tree in PostScript format to file filename

hlib_cluster_t hlib_bc_rowcl	(	const hlib_blockcluster_t	bc,
		int *	info
	)

return row cluster of given block cluster

hlib_blockcluster_t hlib_bc_son	(	const hlib_blockcluster_t	bc,
		const unsigned int	i,
		const unsigned int	j,
		int *	info
	)

return son (i,j) of block cluster bc

the indices i and j are with respect to the numbering in the row and column cluster trees

hlib_blockclustertree_t hlib_bct_build	(	const hlib_clustertree_t	rowct,
		const hlib_clustertree_t	colct,
		const hlib_admcond_t	ac,
		int *	info
	)

build block cluster tree over given row and column clusters using admissibility condition ac

size_t hlib_bct_bytesize	(	const hlib_blockclustertree_t	bct,
		int *	info
	)

return size of memory in bytes used by block cluster

hlib_clustertree_t hlib_bct_colct	(	const hlib_blockclustertree_t	bct,
		int *	info
	)

return column cluster tree of given block cluster tree

int hlib_bct_csp	(	const hlib_blockclustertree_t	bct,
		int *	info
	)

compute sparsity constant of block cluster tree

size_t hlib_bct_depth	(	const hlib_blockclustertree_t	bct,
		int *	info
	)

return depth of block cluster tree

void hlib_bct_distribute_block	(	hlib_blockclustertree_t	bct,
		const unsigned int	p,
		const unsigned int	min_lvl,
		const int	symmetric,
		int *	info
	)

distribute block cluster tree onto p processors based on block-wise partition with unique processor per block

assuming compatible structure of bct
min_lvl controls minimal level for blocks in bct to schedule
if symmetric ≠ 0, the scheduling is performed for the lower left part and mirrored to the upper right part (for symmetric/hermitian matrices)

void hlib_bct_free	(	hlib_blockclustertree_t	bct,
		int *	info
	)

free resources coupled with cluster tree ct

size_t hlib_bct_nnodes	(	const hlib_blockclustertree_t	bct,
		int *	info
	)

return number of nodes in block cluster tree

void hlib_bct_print_ps	(	const hlib_blockclustertree_t	bct,
		const char *	filename,
		int *	info
	)

print block cluster tree in PostScript format to file filename

hlib_clustertree_t hlib_bct_rowct	(	const hlib_blockclustertree_t	bct,
		int *	info
	)

return row cluster tree of given block cluster tree

size_t hlib_cl_bytesize	(	const hlib_cluster_t	cl,
		int *	info
	)

return size of memory in bytes used by cluster

hlib_cluster_t hlib_cl_copy	(	const hlib_cluster_t	cl,
		int *	info
	)

return copy of sub tree defined by cl

size_t hlib_cl_depth	(	const hlib_cluster_t	cl,
		int *	info
	)

return depth of cluster tree

int hlib_cl_first	(	const hlib_cluster_t	cl,
		int *	info
	)

return first index in index set

void hlib_cl_free	(	hlib_cluster_t	cl,
		int *	info
	)

free resources coupled with cluster cl

int hlib_cl_is_leaf	(	const hlib_cluster_t	cl,
		int *	info
	)

return 1 if cluster is leaf and 0 otherwise

int hlib_cl_last	(	const hlib_cluster_t	cl,
		int *	info
	)

return last index in index set

size_t hlib_cl_nnodes	(	const hlib_cluster_t	cl,
		int *	info
	)

return number of nodes in cluster tree

size_t hlib_cl_nsons	(	const hlib_cluster_t	cl,
		int *	info
	)

return number of sons of cluster

void hlib_cl_print_ps	(	const hlib_cluster_t	cl,
		const char *	filename,
		int *	info
	)

print cluster tree in PostScript format to file filename

size_t hlib_cl_size	(	const hlib_cluster_t	cl,
		int *	info
	)

return size of index set

hlib_cluster_t hlib_cl_son	(	const hlib_cluster_t	cl,
		const unsigned int	i,
		int *	info
	)

return i'th son of cluster cl

hlib_clustertree_t hlib_clt_build_alg	(	const hlib_matrix_t	S,
		const unsigned int	nmin,
		int *	info
	)

build clustertree via algebraic clustering based on given sparse matrix S

hlib_clustertree_t hlib_clt_build_alg_nd	(	const hlib_matrix_t	S,
		const unsigned int	nmin,
		int *	info
	)

build clustertree via algebraic clustering with nested dissection based on given sparse matrix S

hlib_clustertree_t hlib_clt_build_alg_part	(	const hlib_matrix_t	S,
		const unsigned int *	partition,
		const unsigned int	nmin,
		int *	info
	)

build clustertree via algebraic clustering and use a predefined partition for first step

partition must have size "rows(S)" and contain ids ∈ [0,k-1], where k is the total number of partitions
index "i" will go into group partition[i]

hlib_clustertree_t hlib_clt_build_bsp	(	const hlib_coord_t	coord,
		const hlib_bsp_t	bsptype,
		const unsigned int	nmin,
		int *	info
	)

build cluster tree using binary space partitioning

optional periodicity of the coordinates defined by period, e.g. vector containing stride in all spatial dimensions or NULL if not defined

hlib_clustertree_t hlib_clt_build_bsp_nd	(	const hlib_coord_t	coord,
		const hlib_matrix_t	S,
		const hlib_bsp_t	bsptype,
		const unsigned int	nmin,
		int *	info
	)

build cluster tree using binary space partitioning and nested dissection based on given sparse matrix S

for period see HLIBPF(clt_build_bsp)

hlib_clustertree_t hlib_clt_build_bsp_part	(	const hlib_coord_t	coord,
		const unsigned int *	partition,
		const int	eq_depth,
		const hlib_bsp_t	bsptype,
		const unsigned int	nmin,
		int *	info
	)

build cluster tree using binary space partitioning but use a predefined partition for first step, e.g. first divide indices into groups defined by partition and apply BSP on these sets

partition must have size "size(coord)" and contain ids ∈ [0,k-1], where k is the total number of partitions
index "i" will go into group partition[i]
if eq_depth ≠ 0, the depth of subsequent sub trees (for each partition) is adjusted according to depth of previous sub trees

size_t hlib_clt_bytesize	(	const hlib_clustertree_t	ct,
		int *	info
	)

return size of memory in bytes used by cluster

size_t hlib_clt_depth	(	const hlib_clustertree_t	ct,
		int *	info
	)

return depth of cluster tree

void hlib_clt_free	(	hlib_clustertree_t	ct,
		int *	info
	)

free resources coupled with cluster tree ct

size_t hlib_clt_nnodes	(	const hlib_clustertree_t	ct,
		int *	info
	)

return number of nodes in cluster tree

hlib_permutation_t hlib_clt_perm_e2i	(	hlib_clustertree_t	ct,
		int *	info
	)

return mapping from external to internal (in cluster tree) ordering

hlib_permutation_t hlib_clt_perm_i2e	(	hlib_clustertree_t	ct,
		int *	info
	)

return mapping from internal (in cluster tree) to external ordering

void hlib_clt_print_ps	(	const hlib_clustertree_t	ct,
		const char *	filename,
		int *	info
	)

print cluster tree in PostScript format to file filename

hlib_cluster_t hlib_clt_root	(	hlib_clustertree_t	ct,
		int *	info
	)

return root node in cluster tree

hlib_real_t hlib_cmplx_abs ( const hlib_complex_t a )

return absolute value

hlib_complex_t hlib_cmplx_add	(	const hlib_complex_t	a,
		const hlib_complex_t	b
	)

conversion to/from C99 complex if available standard mathematical operators

hlib_complex_t hlib_cmplx_conj ( const hlib_complex_t a )

return conjugate value

hlib_complex_t hlib_cmplx_exp ( const hlib_complex_t a )

exponential function e^a

hlib_complex_t hlib_cmplx_sqrt ( const hlib_complex_t a )

return square root

hlib_complex_t hlib_complex	(	const double	re,
		const double	im
	)

construct hlib_complex_t variable

double* hlib_coord_bbmax	(	const hlib_coord_t	coord,
		const size_t	i,
		int *	info
	)

return pointer too coordinate of i'th maximal bounding box

double* hlib_coord_bbmin	(	const hlib_coord_t	coord,
		const size_t	i,
		int *	info
	)

return pointer too coordinate of i'th minimal bounding box

size_t hlib_coord_bytesize	(	const hlib_coord_t	coord,
		int *	info
	)

return size of memory in bytes used by coordinates

unsigned int hlib_coord_dim	(	const hlib_coord_t	coord,
		int *	info
	)

return dimension of coordinates in given coordinate set coord

void hlib_coord_free	(	hlib_coord_t	coord,
		int *	info
	)

free resources coupled with coordinates

if "HLIBPF(coord_import)" was used to create coord, the memory occupied by coordinate array will not be freed

double* hlib_coord_get	(	const hlib_coord_t	coord,
		const size_t	i,
		int *	info
	)

return pointer too coordinate i in given coordinate set coord

the returned value points to an array of size dim(coord)
to pointer is no copy, so all changes to the data are direct changes to the coordinates

void hlib_coord_get_period	(	hlib_coord_t	coord,
		double	period[],
		int *	info
	)

store periodicity vector in period

period must have the same dimensions as the coordinates

int hlib_coord_has_bbox	(	const hlib_coord_t	coord,
		int *	info
	)

return 1, if coordinate set has bounding box info and 0 otherwise

hlib_coord_t hlib_coord_import	(	const size_t	n,
		const unsigned int	dim,
		double **	coord,
		const double *	period,
		int *	info
	)

import given coordinates into HLIBpro

any later changes to coord will also change coordinate set
optional periodicity of the coordinates defined by period, e.g. vector containing stride in all spatial dimensions or NULL if not defined

size_t hlib_coord_ncoord	(	const hlib_coord_t	coord,
		int *	info
	)

return number of coordinates in given coordinate set coord

void hlib_coord_print_vrml	(	const hlib_coord_t	coord,
		const char *	filename,
		int *	info
	)

print coordinates in VRML format to file filename

void hlib_coord_set_period	(	hlib_coord_t	coord,
		const double	period[],
		int *	info
	)

set perdiodicity of coordinates to period

period must have the same dimensions as the coordinates

double hlib_cputime ( )

return execution time of program in seconds

hlib_matrix_t hlib_hb_load_matrix	(	const char *	filename,
		int *	info
	)

read matrix from file filename

void hlib_hb_save_matrix	(	const hlib_matrix_t	M,
		const char *	filename,
		int *	info
	)

save matrix M to file filename

hlib_coord_t hlib_hformat_load_coord	(	const char *	filename,
		int *	info
	)

read coordinates from file filename

hlib_matrix_t hlib_hformat_load_matrix	(	const char *	filename,
		int *	info
	)

read matrix from file filename

hlib_vector_t hlib_hformat_load_vector	(	const char *	filename,
		int *	info
	)

read vector from file filename

void hlib_hformat_save_coord	(	const hlib_coord_t	coord,
		const char *	filename,
		int *	info
	)

save coordinates to file filename

void hlib_hformat_save_matrix	(	const hlib_matrix_t	A,
		const char *	filename,
		int *	info
	)

save matrix A to file filename

void hlib_hformat_save_vector	(	const hlib_vector_t	v,
		const char *	filename,
		int *	info
	)

save vector v to file filename

hlib_coord_t hlib_load_coord	(	const char *	filename,
		int *	info
	)

read coordinates from file filename

hlib_matrix_t hlib_load_matrix	(	const char *	filename,
		int *	info
	)

read matrix from file filename

hlib_vector_t hlib_load_vector	(	const char *	filename,
		int *	info
	)

read vector from file filename

unsigned int hlib_major_version ( )

return major version number of 𝓗𝖫𝖨𝖡𝗉𝗋𝗈

hlib_matrix_t hlib_matlab_load_matrix	(	const char *	filename,
		const char *	matname,
		int *	info
	)

read matrix named matname in Matlab V7 format from file filename; if matname == NULL or matname == "", the first matrix in filename will be read

hlib_vector_t hlib_matlab_load_vector	(	const char *	filename,
		const char *	vecname,
		int *	info
	)

read vector named vname from file filename in Matlab V7 format

void hlib_matlab_save_matrix	(	const hlib_matrix_t	M,
		const char *	filename,
		const char *	matname,
		int *	info
	)

save matrix M named matname in Matlab V7 format to file filename

void hlib_matlab_save_vector	(	const hlib_vector_t	v,
		const char *	filename,
		const char *	vecname,
		int *	info
	)

save vector named vname to file filename in Matlab V7 format

void hlib_matrix_add	(	const hlib_real_t	alpha,
		const hlib_matrix_t	A,
		const hlib_real_t	beta,
		hlib_matrix_t	B,
		const hlib_acc_t	acc,
		int *	info
	)

compute B := alpha A + beta B with block-wise precision acc

hlib_matrix_t hlib_matrix_assemble_block	(	const size_t	brows,
		const size_t	bcols,
		hlib_matrix_t *	submat,
		const int	copy,
		int *	info
	)

assemble brows × bcols block matrix out of sub blocks submat

sub matrices have to be stored column wise in submat
if copy is non-zero, sub matrices are copied, otherwise used directly in new block matrix
index sets of sub matrices are adjusted to be consistent in new block matrix
if sub matrices are H-matrices, permutations from internal to external ordering (and vice versa) are also adjusted

hlib_matrix_t hlib_matrix_build_ccoeff	(	const hlib_blockclustertree_t	bct,
		const hlib_ccoeff_t	f,
		void *	arg,
		const hlib_lrapx_t	lrapx,
		const hlib_acc_t	acc,
		const int	sym,
		int *	info
	)

build H-matrix over block cluster tree bct of precision acc out of dense matrix given by a matrix coefficient function f by using a low-rank approximation for admissible blocks

hlib_matrix_t hlib_matrix_build_coeff	(	const hlib_blockclustertree_t	bct,
		const hlib_coeff_t	f,
		void *	arg,
		const hlib_lrapx_t	lrapx,
		const hlib_acc_t	acc,
		const int	sym,
		int *	info
	)

build H-matrix over block cluster tree bct of precision acc out of dense matrix given by a matrix coefficient function f by using a low-rank approximation for admissible blocks

hlib_matrix_t hlib_matrix_build_dense	(	const hlib_blockclustertree_t	bct,
		const hlib_matrix_t	D,
		const hlib_lrapx_t	lrapx,
		const hlib_acc_t	acc,
		int *	info
	)

build H-matrix over block cluster tree bct with contents defined by given dense matrix D with low-rank approximation method lrapx and block-wise accuracy acc

hlib_matrix_t hlib_matrix_build_identity	(	const hlib_blockclustertree_t	bct,
		int *	info
	)

build H-matrix over block cluster tree bct representing identity

hlib_matrix_t hlib_matrix_build_sparse	(	const hlib_blockclustertree_t	bct,
		const hlib_matrix_t	S,
		const hlib_acc_t	acc,
		int *	info
	)

build H-matrix over block cluster tree bct with contents defined by given sparse matrix S

size_t hlib_matrix_bytesize	(	const hlib_matrix_t	A,
		int *	info
	)

return size of matrix in bytes

void hlib_matrix_cadd	(	const hlib_complex_t	alpha,
		const hlib_matrix_t	A,
		const hlib_complex_t	beta,
		hlib_matrix_t	B,
		const hlib_acc_t	acc,
		int *	info
	)

compute B := alpha A + beta B with block-wise precision acc

hlib_complex_t hlib_matrix_centry_get	(	const hlib_matrix_t	A,
		const size_t	i,
		const size_t	j,
		int *	info
	)

get single entry at position (i,j) in matrix A

void hlib_matrix_cmul	(	const hlib_complex_t	alpha,
		const hlib_matop_t	matop_A,
		const hlib_matrix_t	A,
		const hlib_matop_t	matop_B,
		const hlib_matrix_t	B,
		const hlib_complex_t	beta,
		hlib_matrix_t	C,
		const hlib_acc_t	acc,
		int *	info
	)

compute C := alpha op(A) op(B) + beta C with block-wise precision acc

void hlib_matrix_cmulvec	(	const hlib_complex_t	alpha,
		const hlib_matrix_t	A,
		const hlib_vector_t	x,
		const hlib_complex_t	beta,
		hlib_vector_t	y,
		const hlib_matop_t	matop,
		int *	info
	)

compute y := alpha op(A) x + beta y, where op(A) is either A, A^T or A^H

hlib_vector_t hlib_matrix_col_vector	(	const hlib_matrix_t	A,
		int *	info
	)

create vectors matching the column indexsets of matrix A

size_t hlib_matrix_cols	(	const hlib_matrix_t	A,
		int *	info
	)

return number of columns of matrix

void hlib_matrix_conjugate	(	const hlib_matrix_t	A,
		int *	info
	)

conjugate matrix A

hlib_matrix_t hlib_matrix_copy	(	const hlib_matrix_t	A,
		int *	info
	)

return copy of matrix A

hlib_matrix_t hlib_matrix_copy_acc	(	const hlib_matrix_t	A,
		const hlib_acc_t	acc,
		const int	coarsen,
		int *	info
	)

return copy of matrix A with accuracy acc; if coarsen != 0, copy is coarsend

hlib_matrix_t hlib_matrix_copy_blockdiag	(	const hlib_matrix_t	A,
		const unsigned int	lvl,
		int *	info
	)

copy blockdiagonal part of first lvl levels of matrix

hlib_matrix_t hlib_matrix_copy_blockdiag_acc	(	const hlib_matrix_t	A,
		const unsigned int	lvl,
		const hlib_acc_t	acc,
		int *	info
	)

copy blockdiagonal part of first lvl levels of matrix with given accuracy acc

hlib_matrix_t hlib_matrix_copy_nearfield	(	const hlib_matrix_t	A,
		const int	without_rk,
		int *	info
	)

copy nearfield part of matrix

if without_rk is non-zero, low-rank matrices will be skipped, otherwise set to rank 0

void hlib_matrix_copyto	(	const hlib_matrix_t	A,
		hlib_matrix_t	B,
		int *	info
	)

copy matrix A to B

void hlib_matrix_copyto_acc	(	const hlib_matrix_t	A,
		hlib_matrix_t	B,
		const hlib_acc_t	acc,
		const int	coarsen,
		int *	info
	)

copy matrix A to B with accuracy acc; if coarsen != 0, B is coarsend

void hlib_matrix_cscale	(	const hlib_complex_t	f,
		const hlib_matrix_t	A,
		int *	info
	)

scale matrix A by factor f

hlib_real_t hlib_matrix_entry_get	(	const hlib_matrix_t	A,
		const size_t	i,
		const size_t	j,
		int *	info
	)

get single entry at position (i,j) in matrix A

hlib_matrix_t hlib_matrix_factorise	(	hlib_matrix_t	A,
		const hlib_acc_t	acc,
		int *	info
	)

factorise matrix A up to block-wise precision acc

depending on form of A, e.g. if unsymmetric, symmetric or hermitian, an appropriate factorisation method is chosen
A will be overwritten by the factors
the return value is a matrix which can be used to evaluate the factorisation, e.g. for matrix-vector mult. (this is not possible with A after factorisation as it holds just the data, albeit, it is still needed)

hlib_matrix_t hlib_matrix_factorise_inv	(	hlib_matrix_t	A,
		const hlib_acc_t	acc,
		int *	info
	)

same as hlib_matrix_factorise but return matrix object for evaluation of inverse of A.

void hlib_matrix_free	(	hlib_matrix_t	A,
		int *	info
	)

free resources coupled with matrix A

hlib_matrix_t hlib_matrix_import_ccrs	(	const size_t	rows,
		const size_t	cols,
		const size_t	nnz,
		const int *	rowind,
		const int *	colind,
		const hlib_complex_t *	coeffs,
		const int	sym,
		int *	info
	)

import given complex sparse matrix in CRS format into internal sparse matrix format

hlib_matrix_t hlib_matrix_import_cdense	(	const size_t	rows,
		const size_t	cols,
		const hlib_complex_t *	D,
		const int	sym,
		int *	info
	)

import given complex dense matrix in column major format into internal dense matrix format

hlib_matrix_t hlib_matrix_import_crs	(	const size_t	rows,
		const size_t	cols,
		const size_t	nnz,
		const int *	rowind,
		const int *	colind,
		const hlib_real_t *	coeffs,
		const int	sym,
		int *	info
	)

import given real sparse matrix in CRS format into internal sparse matrix format

hlib_matrix_t hlib_matrix_import_dense	(	const size_t	rows,
		const size_t	cols,
		const hlib_real_t *	D,
		const int	sym,
		int *	info
	)

import given real dense matrix in column major format into internal dense matrix format

hlib_matrix_t hlib_matrix_inv	(	hlib_matrix_t	A,
		const hlib_acc_t	acc,
		int *	info
	)

compute inverse of A with block-wise precision acc; A will be overwritten with A^-1 upon exit

the return value is either A, or a new representation for the inverse of A (A is still needed then)

hlib_vector_t hlib_matrix_inv_diag	(	hlib_matrix_t	A,
		const hlib_acc_t	acc,
		int *	info
	)

compute diagonal of inverse of A with local accuracy acc

A will be overwritten during computation

int hlib_matrix_is_complex	(	const hlib_matrix_t	A,
		int *	info
	)

return 1 if matrix A is complex valued and 0 otherwise

int hlib_matrix_is_herm	(	const hlib_matrix_t	A,
		int *	info
	)

return 1 if matrix A is hermitian, e.g. A = A^H

int hlib_matrix_is_sym	(	const hlib_matrix_t	A,
		int *	info
	)

return 1 if matrix A is symmetric, e.g. A = A^T

hlib_matrix_t hlib_matrix_ldl	(	hlib_matrix_t	A,
		const hlib_acc_t	acc,
		int *	info
	)

LDL factorisation of matrix A up to block-wise precision acc

A will be overwritten by L*D*L^T, which only allows matrix vector mult.
in case of hermitian matrices, LDL^H is computed
for return value see "hlib_matrix_lu"

hlib_matrix_t hlib_matrix_ll	(	hlib_matrix_t	A,
		const hlib_acc_t	acc,
		int *	info
	)

Cholesky factorisation of matrix A up to block-wise precision acc

A will be overwritten by L*L^T, which only allows matrix vector mult.
in case of hermitian matrices, L*L^H is computed
for return value see "hlib_matrix_lu"

hlib_matrix_t hlib_matrix_lu	(	hlib_matrix_t	A,
		const hlib_acc_t	acc,
		int *	info
	)

LU factorise matrix A up to block-wise precision acc

A will be overwritten by L*U, which only allows matrix vector mult.
the return value is a matrix which can be used to evaluate LU, e.g. for matrix-vector multiplication (this is not possible with A after factorisation as it holds just the data, albeit, it is still needed)

void hlib_matrix_mul	(	const hlib_real_t	alpha,
		const hlib_matop_t	matop_A,
		const hlib_matrix_t	A,
		const hlib_matop_t	matop_B,
		const hlib_matrix_t	B,
		const hlib_real_t	beta,
		hlib_matrix_t	C,
		const hlib_acc_t	acc,
		int *	info
	)

compute C := alpha op(A) op(B) + beta C with block-wise precision acc

void hlib_matrix_mulvec	(	const hlib_real_t	alpha,
		const hlib_matrix_t	A,
		const hlib_vector_t	x,
		const hlib_real_t	beta,
		hlib_vector_t	y,
		const hlib_matop_t	matop,
		int *	info
	)

compute y := alpha op(A) x + beta y, where op(A) is either A or A^T

hlib_real_t hlib_matrix_norm_frobenius	(	const hlib_matrix_t	A,
		int *	info
	)

compute Frobenius norm of matrix

hlib_real_t hlib_matrix_norm_frobenius_diff	(	const hlib_matrix_t	A,
		const hlib_matrix_t	B,
		int *	info
	)

compute Frobenius norm of A-B

hlib_real_t hlib_matrix_norm_inv_approx	(	const hlib_matrix_t	A,
		const hlib_matrix_t	B,
		int *	info
	)

compute inversion error |I-BA|_2, where B is supposed to be A^-1

hlib_real_t hlib_matrix_norm_spectral	(	const hlib_matrix_t	A,
		int *	info
	)

compute spectral norm of matrix

hlib_real_t hlib_matrix_norm_spectral_diff	(	const hlib_matrix_t	A,
		const hlib_matrix_t	B,
		int *	info
	)

compute relative spectral norm of A-B, e.g. |A-B|_2/|A|_2

hlib_real_t hlib_matrix_norm_spectral_inv	(	const hlib_matrix_t	A,
		int *	info
	)

compute spectral norm of inverse matrix

void hlib_matrix_print_ps	(	const hlib_matrix_t	A,
		const char *	filename,
		const int	options,
		int *	info
	)

print matrix A in postscript format to file filename

hlib_vector_t hlib_matrix_row_vector	(	const hlib_matrix_t	A,
		int *	info
	)

create vectors matching the row indexsets of matrix A

size_t hlib_matrix_rows	(	const hlib_matrix_t	A,
		int *	info
	)

return number of rows of matrix

void hlib_matrix_scale	(	const hlib_real_t	f,
		const hlib_matrix_t	A,
		int *	info
	)

scale matrix A by factor f

void hlib_matrix_solve_diag_left	(	const hlib_matrix_t	D,
		const hlib_matop_t	op_D,
		hlib_matrix_t	A,
		const hlib_acc_t	acc,
		const int	pointwise,
		int *	info
	)

solve op(D) B = A with diagonal D and known A

B will overwrite A
if pointwise is true, evaluation is performed pointwise, otherwise blockwise, e.g. diagonal leaf matrices are considered full and not diagonal

void hlib_matrix_solve_diag_right	(	hlib_matrix_t	A,
		const hlib_matrix_t	D,
		const hlib_matop_t	op_D,
		const hlib_acc_t	acc,
		const int	pointwise,
		int *	info
	)

solve B op(D) = A with diagonal D and known A

B will overwrite A
if pointwise is true, evaluation is performed pointwise, otherwise blockwise, e.g. diagonal leaf matrices are considered full and not diagonal

void hlib_matrix_solve_lower_left	(	const hlib_matrix_t	L,
		hlib_matrix_t	A,
		const hlib_acc_t	acc,
		const int	pointwise,
		const int	unit_diag,
		int *	info
	)

solve L B = A with lower triangular L and known A

B will overwrite A
if pointwise is true, evaluation is performed pointwise, otherwise blockwise, e.g. diagonal leaf matrices are considered full and not triangular
if unit_diag is true, the pointwise/blockwise diagonal is considered to be the identity

void hlib_matrix_solve_lower_right	(	hlib_matrix_t	A,
		const hlib_matrix_t	L,
		const hlib_matop_t	op_L,
		const hlib_acc_t	acc,
		const int	pointwise,
		const int	unit_diag,
		int *	info
	)

solve B op(L) = A with lower triangular L and known A

B will overwrite A
if pointwise is true, evaluation is performed pointwise, otherwise blockwise, e.g. diagonal leaf matrices are considered full and not triangular
if unit_diag is true, the pointwise/blockwise diagonal is considered to be the identity

void hlib_matrix_solve_upper_right	(	hlib_matrix_t	A,
		const hlib_matrix_t	U,
		const hlib_acc_t	acc,
		const int	pointwise,
		const int	unit_diag,
		int *	info
	)

solve B U = A with upper triangular U and known A

B will overwrite A
if pointwise is true, evaluation is performed pointwise, otherwise blockwise, e.g. diagonal leaf matrices are considered full and not triangular
if unit_diag is true, the pointwise/blockwise diagonal is considered to be the identity

void hlib_matrix_to_complex	(	const hlib_matrix_t	A,
		const int	force,
		int *	info
	)

switch matrix to complex value; if force is 1, the conversion is performed independent of the current state (applies to block matrices)

void hlib_matrix_to_real	(	const hlib_matrix_t	A,
		const int	force,
		int *	info
	)

switch matrix to real value (if possible); if force is 1, the conversion is performed independent of the current state (applies to block matrices)

void hlib_matrix_transpose	(	const hlib_matrix_t	A,
		int *	info
	)

transpose matrix A

unsigned int hlib_minor_version ( )

return minor version number of 𝓗𝖫𝖨𝖡𝗉𝗋𝗈

hlib_matrix_t hlib_mm_load_matrix	(	const char *	filename,
		int *	info
	)

read matrix from file filename

hlib_matrix_t hlib_pltmg_load_matrix	(	const char *	filename,
		int *	info
	)

read matrix from file filename

hlib_coord_t hlib_samg_load_coord	(	const char *	filename,
		int *	info
	)

read coordinates from file filename

hlib_matrix_t hlib_samg_load_matrix	(	const char *	filename,
		int *	info
	)

read matrix A from file "\a filename" in SAMG format

expecting format definition in basename(filename)>.frm

hlib_vector_t hlib_samg_load_vector	(	const char *	filename,
		int *	info
	)

read vector from file filename in SAMG format

expecting format definition in basename(filename)>.frm

void hlib_samg_save_coord	(	const hlib_coord_t	coord,
		const char *	filename,
		int *	info
	)

write coordinates coord to file filename

void hlib_samg_save_matrix	(	const hlib_matrix_t	A,
		const char *	filename,
		int *	info
	)

save matrix A to file "\a filename" in SAMG format

also writing format definition to basename(filename)>.frm

void hlib_samg_save_vector	(	const hlib_vector_t	x,
		const char *	filename,
		int *	info
	)

save vector to file filename in SAMG format

void hlib_set_abs_eps ( const hlib_real_t eps )

define minimal boundary for singular values, e.g. not smaller

void hlib_set_coarsening	(	const int	build,
		const int	arith
	)

enable (1) or disable (0) coarsening during H-matrix building and arithmetic (default: build=1, arith=0)

void hlib_set_diag_scale ( const int scale )

enable (1) or disable (0) diagonal scaling during LU, etc. (default: off)

void hlib_set_error_fn ( const hlib_errorfn_t errorfn )

set call back function in case of an error

void hlib_set_n_min ( const unsigned int n )

set maximal leaf size in cluster trees to n

void hlib_set_nthreads ( const unsigned int p )

set maximal number of threads to use in H arithmetic

void hlib_set_progress_cb	(	hlib_progressfn_t	fn,
		void *	arg
	)

set callback function for progress information if fn == NULL, HLIBpro uses default progress output

void hlib_set_recompress ( const int recompress )

enable (1) or disable (0) recompression during H-matrix building (default: on)

void hlib_set_verbosity ( const unsigned int verb )

define verbosity of HLib

void hlib_set_warning_fn ( const hlib_errorfn_t warnfn )

set call back function in case of a warning

hlib_solver_t hlib_solver_auto ( int * info )

create automatic solver

hlib_solver_t hlib_solver_bicgstab ( int * info )

create BiCG-Stab solver

hlib_solver_t hlib_solver_cg ( int * info )

create CG solver

void hlib_solver_free	(	hlib_solver_t	solver,
		int *	info
	)

free solver

hlib_solver_t hlib_solver_gmres	(	const int	restart,
		int *	info
	)

create GMRES solver with restart after restart steps

hlib_solver_t hlib_solver_minres ( int * info )

create MINRES solver

hlib_solver_t hlib_solver_richardson ( int * info )

create Richardson solver

void hlib_solver_solve	(	const hlib_solver_t	solver,
		const hlib_matrix_t	A,
		hlib_vector_t	x,
		const hlib_vector_t	b,
		const hlib_matrix_t	W,
		hlib_solve_info_t *	solve_info,
		int *	info
	)

solve A x = b using solver with optional preconditioning, e.g. W A x = W b if W != NULL; information about the solving process is stored in solve_info

void hlib_solver_stopcrit	(	hlib_solver_t	solver,
		const int	maxit,
		const hlib_real_t	abs_red,
		const hlib_real_t	rel_red,
		int *	info
	)

set stopping criterion for solver

maxit : maximal number of iterations
abs_red : iterate until ||residual||_2 reaches abs_red
rel_red : iterate until ||residual||_2 reaches rel_red * ||start-res.||_2
in case of a preconditioner r = W(Ax - b), e.g. the preconditioned res.

void hlib_vector_assign	(	hlib_vector_t	y,
		const hlib_vector_t	x,
		int *	info
	)

copy content of vector x to vector y x and y have to be of equal type

void hlib_vector_axpy	(	const hlib_real_t	alpha,
		const hlib_vector_t	x,
		hlib_vector_t	y,
		int *	info
	)

compute y := y + a x

hlib_vector_t hlib_vector_build	(	const size_t	size,
		int *	info
	)

create scalar vectors of size size initialised with 0

size_t hlib_vector_bytesize	(	const hlib_vector_t	v,
		int *	info
	)

return size of matrix in bytes

void hlib_vector_caxpy	(	const hlib_complex_t	alpha,
		const hlib_vector_t	x,
		hlib_vector_t	y,
		int *	info
	)

compute y := y + a x

hlib_vector_t hlib_vector_cbuild	(	const size_t	size,
		int *	info
	)

create scalar vectors of size size initialised with 0

hlib_complex_t hlib_vector_centry_get	(	const hlib_vector_t	x,
		const size_t	i,
		int *	info
	)

get single entry at position i in vector x

void hlib_vector_centry_set	(	const hlib_vector_t	x,
		const size_t	i,
		const hlib_complex_t	f,
		int *	info
	)

set single entry at position i in vector x

void hlib_vector_cexport	(	const hlib_vector_t	v,
		hlib_complex_t *	arr,
		int *	info
	)

copy data from vector v into given C arrays

arr has to be of size hlib_vector_size( v )

void hlib_vector_cfill	(	hlib_vector_t	x,
		const hlib_complex_t	f,
		int *	info
	)

fill vector x with constant value f

void hlib_vector_cimport	(	hlib_vector_t	v,
		const hlib_complex_t *	arr,
		int *	info
	)

copy data from C array arr into vector v

arr has to be of size hlib_vector_size( v )

hlib_vector_t hlib_vector_copy	(	const hlib_vector_t	v,
		int *	info
	)

copy vectormatrix

void hlib_vector_cscale	(	hlib_vector_t	x,
		const hlib_complex_t	f,
		int *	info
	)

scale vector x by f

hlib_complex_t hlib_vector_dot	(	const hlib_vector_t	x,
		const hlib_vector_t	y,
		int *	info
	)

compute dot product <x,y> = x^H * y

hlib_real_t hlib_vector_entry_get	(	const hlib_vector_t	x,
		const size_t	i,
		int *	info
	)

get single entry at position i in vector x

void hlib_vector_entry_set	(	const hlib_vector_t	x,
		const size_t	i,
		const hlib_real_t	f,
		int *	info
	)

set single entry at position i in vector x

void hlib_vector_export	(	const hlib_vector_t	v,
		hlib_real_t *	arr,
		int *	info
	)

copy data from vector v into given C arrays

arr has to be of size hlib_vector_size( v )

void hlib_vector_fft	(	const hlib_vector_t	v,
		int *	info
	)

compute FFT of vector v inplace

void hlib_vector_fill	(	hlib_vector_t	x,
		const hlib_real_t	f,
		int *	info
	)

fill vector x with constant value f

void hlib_vector_fill_rand	(	hlib_vector_t	x,
		int *	info
	)

fill vector x with random values

void hlib_vector_free	(	hlib_vector_t	v,
		int *	info
	)

free resources coupled with vector v

void hlib_vector_ifft	(	const hlib_vector_t	v,
		int *	info
	)

compute inverse FFT of vector v inplace

void hlib_vector_import	(	hlib_vector_t	v,
		const hlib_real_t *	arr,
		int *	info
	)

copy data from C array arr into vector v

arr has to be of size hlib_vector_size( v )

hlib_real_t hlib_vector_norm2	(	const hlib_vector_t	x,
		int *	info
	)

compute euklidean norm of x

hlib_real_t hlib_vector_norm_inf	(	const hlib_vector_t	x,
		int *	info
	)

compute infinity norm of x

hlib_vector_t hlib_vector_restrict_im	(	const hlib_vector_t	v,
		int *	info
	)

return vector containing only imaginary parts * of the entries of the given vector

hlib_vector_t hlib_vector_restrict_re	(	const hlib_vector_t	v,
		int *	info
	)

return vector containing only real parts * of the entries of the given vector

void hlib_vector_scale	(	hlib_vector_t	x,
		const hlib_real_t	f,
		int *	info
	)

scale vector x by f

size_t hlib_vector_size	(	const hlib_vector_t	v,
		int *	info
	)

return size of vectors

double hlib_walltime ( )

return current walltime in seconds

Coordinates

Admissibility condition

Clusters

Cluster Trees

Block Clusters

Block Cluster Trees

Vectors

Matrices

Algebra

Solver

Input/Output

Accuracy Management

Misc.

Functions for hlib_complex_t

Detailed Description

Function Documentation