GALAHAD BSC package#

purpose#

The bsc package takes given matrices $A$ and (diagonal) $D$, and builds the Schur complement $S = A D A^T$ in sparse co-ordinate (and optionally sparse column) format(s). Full advantage is taken of any zero coefficients in the matrix $A$.

Currently only the options and inform dictionaries are exposed; these are provided and used by other GALAHAD packages with Python interfaces. Please contact us if you would like full functionality!

See Section 4 of $GALAHAD/doc/bsc.pdf for a brief description of the method employed and other details.

introduction to function calls#

To solve a given problem, functions from the bsc package must be called in the following order:

bsc_initialize - provide default control parameters and set up initial data structures
bsc_read_specfile (optional) - override control values by reading replacement values from a file
bsc_import - set up matrix data structures for $A$.
bsc_reset_control (optional) - possibly change control parameters if a sequence of problems are being solved
bsc_form - form the Schur complement $S$
bsc_information (optional) - recover information about the process
bsc_terminate - deallocate data structures

See the examples section for illustrations of use.

callable functions#

overview of functions provided#

// namespaces

namespace conf;

// typedefs

typedef float spc_;
typedef double rpc_;
typedef int ipc_;

// structs

struct bsc_control_type;
struct bsc_inform_type;

// global functions

void bsc_initialize(void **data, struct bsc_control_type* control, ipc_ *status);
void bsc_information(void **data, struct bsc_inform_type* inform, ipc_ *status);

void bsc_terminate(
    void **data,
    struct bsc_control_type* control,
    struct bsc_inform_type* inform
);

typedefs#

typedef float spc_

spc_ is real single precision

typedef double rpc_

rpc_ is the real working precision used, but may be changed to float by defining the preprocessor variable SINGLE.

typedef int ipc_

ipc_ is the default integer word length used, but may be changed to int64_t by defining the preprocessor variable INTEGER_64.

function calls#

void bsc_initialize(void **data, struct bsc_control_type* control, ipc_ *status)

Set default control values and initialize private data

Parameters:

data

holds private internal data

control

is a struct containing control information (see bsc_control_type)

status

is a scalar variable of type ipc_, that gives the exit status from the package. Possible values are (currently):

0
The initialization was successful.

void bsc_information(void **data, struct bsc_inform_type* inform, ipc_ *status)

Provides output information

Parameters:

data

holds private internal data

inform

is a struct containing output information (see bsc_inform_type)

status

is a scalar variable of type ipc_, that gives the exit status from the package. Possible values are (currently):

0
The values were recorded successfully

void bsc_terminate(
    void **data,
    struct bsc_control_type* control,
    struct bsc_inform_type* inform
)

Deallocate all internal private storage

Parameters:

data	holds private internal data
control	is a struct containing control information (see bsc_control_type)
inform	is a struct containing output information (see bsc_inform_type)

available structures#

bsc_control_type structure#

#include <galahad_bsc.h>

struct bsc_control_type {
    // fields

    bool f_indexing;
    ipc_ error;
    ipc_ out;
    ipc_ print_level;
    ipc_ max_col;
    ipc_ new_a;
    ipc_ extra_space_s;
    bool s_also_by_column;
    bool space_critical;
    bool deallocate_error_fatal;
    char prefix[31];
};

detailed documentation#

control derived type as a C struct

components#

bool f_indexing

use C or Fortran sparse matrix indexing

ipc_ error

error and warning diagnostics occur on stream error

ipc_ out

general output occurs on stream out

ipc_ print_level

the level of output required is specified by print_level

ipc_ max_col

maximum permitted number of nonzeros in a column of $A$; -ve means unlimit

ipc_ new_a

how much has $A$ changed since it was last accessed:

0 = not changed,
1 = values changed,
2 = structure changed
3 = structure changed but values not required

ipc_ extra_space_s

how much extra space is to be allocated in $S$ above that needed to hold the Schur complement

bool s_also_by_column

should s.ptr also be set to indicate the first entry in each column of $S$

bool space_critical

if .space_critical true, every effort will be made to use as little space as possible. This may result in longer computation time

bool deallocate_error_fatal

if .deallocate_error_fatal is true, any array/pointer deallocation error will terminate execution. Otherwise, computation will continue

char prefix[31]

all output lines will be prefixed by .prefix(2:LEN(TRIM(.prefix))-1) where .prefix contains the required string enclosed in quotes, e.g. “string” or ‘string’

bsc_inform_type structure#

#include <galahad_bsc.h>

struct bsc_inform_type {
    // fields

    ipc_ status;
    ipc_ alloc_status;
    char bad_alloc[81];
    ipc_ max_col_a;
    ipc_ exceeds_max_col;
    rpc_ time;
    rpc_ clock_time;
};

detailed documentation#

inform derived type as a C struct

components#

ipc_ status

the return status from the package. Possible values are:

0

The call was succcesful
-1

An allocation error occurred. A message indicating the offending array is written on unit control.error, and the returned allocation status and a string containing the name of the offending array are held in inform.alloc_status and inform.bad_alloc respectively.
-2

A deallocation error occurred. A message indicating the offending array is written on unit control.error and the returned allocation status and a string containing the name of the offending array are held in inform.alloc_status and inform.bad_alloc respectively.
-3

The restrictions n > 0 or m > 0 or requirement that a type contains its relevant string ‘dense’, ‘coordinate’ or ‘sparse_by_rows’ has been violated.

ipc_ alloc_status

the status of the last attempted allocation/deallocation

char bad_alloc[81]

the name of the array for which an allocation/deallocation error occurred.

ipc_ max_col_a

the maximum number of entries in a column of $A$

ipc_ exceeds_max_col

the number of columns of $A$ that have more than control.max_col entries

rpc_ time

the total CPU time spent in the package

rpc_ clock_time

the total clock time spent in the package

Index