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 \(A\).

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

matrix storage#

The unsymmetric \(m\) by \(n\) matrix \(A\) may be presented and stored in a variety of convenient input formats.

Dense storage format: The matrix \(A\) is stored as a compact dense matrix by rows, that is, the values of the entries of each row in turn are stored in order within an appropriate real one-dimensional array. In this case, component \(n \ast i + j\) of the storage array A_val will hold the value \(A_{ij}\) for \(0 \leq i \leq m-1\), \(0 \leq j \leq n-1\). The string A_type = ‘dense’ should be specified.

Sparse co-ordinate storage format: Only the nonzero entries of the matrices are stored. For the \(l\)-th entry, \(0 \leq l \leq ne-1\), of \(A\), its row index i, column index j and value \(A_{ij}\), \(0 \leq i \leq m-1\), \(0 \leq j \leq n-1\), are stored as the \(l\)-th components of the integer arrays A_row and A_col and real array A_val, respectively, while the number of nonzeros is recorded as A_ne = \(ne\). The string A_type = ‘coordinate’should be specified.

Sparse row-wise storage format: Again only the nonzero entries are stored, but this time they are ordered so that those in row i appear directly before those in row i+1. For the i-th row of \(A\) the i-th component of the integer array A_ptr holds the position of the first entry in this row, while A_ptr(m) holds the total number of entries. The column indices j, \(0 \leq j \leq n-1\), and values \(A_{ij}\) of the nonzero entries in the i-th row are stored in components l = A_ptr(i), \(\ldots\), A_ptr(i+1)-1, \(0 \leq i \leq m-1,\) of the integer array A_col, and real array A_val, respectively. For sparse matrices, this scheme almost always requires less storage than its predecessor. The string A_type = ‘sparse_by_rows’ should be specified.

Sparse column-wise storage format: Once again only the nonzero entries are stored, but this time they are ordered so that those in column j appear directly before those in column j+1. For the j-th column of \(A\) the j-th component of the integer array A_ptr holds the position of the first entry in this column, while A_ptr(n) holds the total number of entries. The row indices i, \(0 \leq i \leq m-1\), and values \(A_{ij}\) of the nonzero entries in the j-th columns are stored in components l = A_ptr(j), \(\ldots\), A_ptr(j+1)-1, \(0 \leq j \leq n-1\), of the integer array A_row, and real array A_val, respectively. As before, for sparse matrices, this scheme almost always requires less storage than the co-ordinate format. The string A_type = ‘sparse_by_columns’ should be specified.

The symmetric \(n\) by \(n\) Schur complement matrix \(S\) may be returned in a couple of formats. But now crucially symmetry is exploited by only storing values from the lower triangular part (i.e, those entries that lie on or below the leading diagonal).

Sparse co-ordinate storage format: Only the nonzero entries of the matrices are stored. For the \(l\)-th entry, \(0 \leq l \leq ne-1\), of \(S\), its row index i, column index j and value \(S_{ij}\), \(0 \leq j \leq i \leq n-1\), are stored as the \(l\)-th components of the integer arrays S_row and S_col and real array S_val, respectively, while the number of nonzeros is recorded as S_ne = \(ne\). Note that only the entries in the lower triangle will be returned.

Sparse row-wise storage format: Again only the nonzero entries are stored, but this time they are ordered so that those in row i appear directly before those in row i+1. For the i-th row of \(S\) the i-th component of the integer array S_ptr holds the position of the first entry in this row, while S_ptr(n) holds the total number of entries. The column indices j, \(0 \leq j \leq i\), and values \(S_{ij}\) of the entries in the i-th row are stored in components l = S_ptr(i), …, S_ptr(i+1)-1, \(0 \leq i \leq n-1,\) of the integer array S_col, and real array S_val, respectively. Note that as before only the entries in the lower triangle will be stored. For sparse matrices, this scheme almost always requires less storage than its predecessor.

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 \(A\) and \(S\).

  • bsc_reset_control (optional) - possibly change control parameters if a sequence of problems are being solved

  • bsc_form_s - 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_read_specfile(struct bsc_control_type* control, const char specfile[]);
void bsc_import(
    struct bsc_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ m,
    ipc_ n,
    const char A_type[],
    ipc_ A_ne,
    const ipc_ A_row[],
    const ipc_ A_col[],
    const ipc_ A_ptr[],
    ipc_ S_ne
);

void bsc_reset_control(
    struct bsc_control_type* control,
    void **data,
    ipc_ *status
);

void bsc_form_s(
    void **data,
    ipc_ *status,
    ipc_ m,
    ipc_ n,
    ipc_ A_ne,
    const rpc_ A_val[],
    ipc_ S_ne,
    ipc_ S_row[],
    ipc_ S_col[],
    ipc_ S_ptr[],
    ipc_ S_val[],
    const rpc_ D[]
);
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 REAL_32 or (if supported) to __real128 using the variable REAL_128.

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_read_specfile(struct bsc_control_type* control, const char specfile[])

Read the content of a specification file, and assign values associated with given keywords to the corresponding control parameters. An in-depth discussion of specification files is available, and a detailed list of keywords with associated default values is provided in $GALAHAD/src/bsc/BSC.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/bsc.pdf for a list of how these keywords relate to the components of the control structure.

Parameters:

control

is a struct containing control information (see bsc_control_type)

specfile

is a character string containing the name of the specification file

void bsc_import(
    struct bsc_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ m,
    ipc_ n,
    const char A_type[],
    ipc_ A_ne,
    const ipc_ A_row[],
    const ipc_ A_col[],
    const ipc_ A_ptr[],
    ipc_ S_ne
)

Import data into internal storage prior to solution and set up structure of \(S\),

Parameters:

control

is a struct whose members provide control paramters for the remaining prcedures (see bsc_control_type)

data

holds private internal data

status

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

  • 0

    The import was successful

  • -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.

m

is a scalar variable of type ipc_, that holds the number of rows of \(A\).

n

is a scalar variable of type ipc_, that holds the number of columns of \(A\).

A_type

is a one-dimensional array of type char that specifies the unsymmetric storage scheme used for the matrix \(A\). It should be one of ‘coordinate’, ‘sparse_by_rows’ or ‘dense; lower or upper case variants are allowed.

A_ne

is a scalar variable of type ipc_, that holds the number of entries in \(A\) in the sparse co-ordinate storage scheme. It need not be set for any of the other schemes.

A_row

is a one-dimensional array of size A_ne and type ipc_, that holds the row indices of \(A\) in the sparse co-ordinate storage scheme. It need not be set for any of the other schemes, and in this case can be NULL.

A_col

is a one-dimensional array of size A_ne and type ipc_, that holds the column indices of \(A\) in either the sparse co-ordinate, or the sparse row-wise storage scheme. It need not be set when the dense or diagonal storage schemes are used, and in this case can be NULL.

A_ptr

is a one-dimensional array of size m+1 and type ipc_, that holds the starting position of each row of \(A\), as well as the total number of entries, in the sparse row-wise storage scheme. It need not be set when the other schemes are used, and in this case can be NULL.

S_ne

is a scalar variable of type ipc_, that holds the number of entries required to hold \(S\) in the sparse co-ordinate storage scheme.

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

Reset control parameters after import if required.

Parameters:

control

is a struct whose members provide control paramters for the remaining prcedures (see bsc_control_type)

data

holds private internal data

status

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

  • 0

    The import was successful.

void bsc_form_s(
    void **data,
    ipc_ *status,
    ipc_ m,
    ipc_ n,
    ipc_ A_ne,
    const rpc_ A_val[],
    ipc_ S_ne,
    ipc_ S_row[],
    ipc_ S_col[],
    ipc_ S_ptr[],
    ipc_ S_val[],
    const rpc_ D[]
)

Form the Schur complement matrix, \(S\).

Parameters:

data

holds private internal data

status

is a scalar variable of type ipc_, that gives the entry and exit status from the package.

Possible exit values are:

  • 0

    The run was successful.

  • -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 and m > 0 or requirement that a type contains its relevant string ‘dense’, ‘coordinate’ or ‘sparse_by_rows’ has been violated.

m

is a scalar variable of type ipc_, that holds the number of rows of \(A\).

n

is a scalar variable of type ipc_, that holds the number of columns of \(A\).

A_ne

is a scalar variable of type ipc_, that holds the number of entries in \(A\).

A_val

is a one-dimensional array of size A_ne and type rpc_, that holds the values of the entries of the matrix \(A\) in any of the available storage schemes.

S_ne

is a scalar variable of type ipc_, that holds the number of entries in the lower traingle of \(S\) in the sparse co-ordinate storage scheme.

S_row

is a one-dimensional array of size S_ne and type ipc_, that gives the row indices the lower traingle of \(S\) in the sparse co-ordinate storage scheme.

S_col

is a one-dimensional array of size S_ne and type ipc_, that gives the column indices the lower traingle of \(S\) in either the sparse co-ordinate, or the sparse row-wise storage scheme.

S_ptr

is a one-dimensional array of size n+1 and type ipc_, that gives the starting position of each row the lower traingle of \(S\), as well as the total number of entries, in the sparse row-wise storage scheme.

S_val

is a one-dimensional array of size S_ne and type rpc_, that gives the values of the entries of the lower traingle of the matrix \(S\).

D

is a one-dimensional array of size n and type rpc_, that gives the values of the diagonal entries in \(D\). If \(D\) is the identity matrix, D can be NULL to save storage.

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

example calls#

This is an example of how to use the package to find the Schur complement from given data \(A\) and \(D\); the code is available in $GALAHAD/src/bsc/C/bsct.c . A variety of supported Hessian and constraint matrix storage formats are shown.

Notice that C-style indexing is used, and that this is flagged by setting control.f_indexing to false. The floating-point type rpc_ is set in galahad_precision.h to double by default, but to float if the preprocessor variable SINGLE is defined. Similarly, the integer type ipc_ from galahad_precision.h is set to int by default, but to int64_t if the preprocessor variable INTEGER_64 is defined.

/* bsct.c */
/* Full test for the BSC C interface using C sparse matrix indexing */

#include <stdio.h>
#include <math.h>
#include <string.h>
#include "galahad_precision.h"
#include "galahad_cfunctions.h"
#include "galahad_bsc.h"
#ifdef REAL_128
#include <quadmath.h>
#endif

int main(void) {

    // Derived types
    void *data;
    struct bsc_control_type control;
    struct bsc_inform_type inform;

    // Set problem data
    ipc_ m = 3; // row dimension of A
    ipc_ n = 4; // column dimension of A
    ipc_ A_ne = 6; // nonzeros in lower triangle of A
    ipc_ A_dense_ne = 12; // positions in lower triangle of A
    ipc_ A_row[] = {0, 0, 1, 1, 2, 2}; // row indices
    ipc_ A_col[] = {0, 1, 2, 3, 0, 3}; // column indices
    ipc_ A_ptr[] = {0, 2, 4, 6}; // row pointers
    rpc_ A_val[] = {1.0, 1.0, 1.0, 1.0, 1.0, 1.0}; // values
    rpc_ A_dense[] = {1.0, 1.0, 0.0, 0.0, 0.0, 0.0,
                      1.0, 1.0, 1.0, 0.0, 0.0, 1.0}; // dense values
    rpc_ D[] = {1.0, 2.0, 3.0, 4.0}; // diagonals of D

    // Set output storage
    char st = ' ';
    ipc_ status, S_ne;

    printf(" C sparse matrix indexing\n\n");

    printf(" basic tests of storage formats\n\n");

      for( ipc_ d=1; d <= 3; d++){

        // Initialize BSC
        bsc_initialize( &data, &control, &status );

        // Set user-defined control options
        control.f_indexing = false; // C sparse matrix indexing
        //control.print_level = 1;

        switch(d){
            case 1: // sparse co-ordinate storage
                st = 'C';
                bsc_import( &control, &data, &status, m, n,
                           "coordinate", A_ne, A_row, A_col, NULL, &S_ne );
                break;
            case 2: // sparse by rows
                st = 'R';
                bsc_import( &control, &data, &status, m, n,
                            "sparse_by_rows", A_ne, NULL, A_col, A_ptr, &S_ne );
                break;
            case 3: // dense
                st = 'D';
                bsc_import( &control, &data, &status, m, n,
                            "dense", A_dense_ne, NULL, NULL, NULL, &S_ne );
                break;
            }

        ipc_ S_row[S_ne], S_col[S_ne], S_ptr[m+1];
        rpc_ S_val[S_ne];

        for( ipc_ ptr=0; ptr <= 1; ptr++){

          if(ptr == 0){
            switch(d){
                case 3: // dense
                    bsc_form_s( &data, &status, m, n, A_dense_ne, A_dense,
                                S_ne, S_row, S_col, NULL, S_val, NULL );
                    break;
                default:
                    bsc_form_s( &data, &status, m, n, A_ne, A_val,
                                S_ne, S_row, S_col, NULL, S_val, NULL );
                }
          } else {
            switch(d){
                case 3: // dense
                    bsc_form_s( &data, &status, m, n, A_dense_ne, A_dense,
                                S_ne, S_row, S_col, S_ptr, S_val, D );
                    break;
                default:
                    bsc_form_s( &data, &status, m, n, A_ne, A_val,
                                S_ne, S_row, S_col, S_ptr, S_val, D );
                }
          }

          bsc_information( &data, &inform, &status );

          if(inform.status == 0){
#ifdef REAL_128
            printf(" format %c: status = %1" i_ipc_ "\n", st, inform.status);
#else
            printf(" format %c: status = %1" i_ipc_ "\n", st, inform.status);
#endif
          }else{
              printf(" format %c: BSC_solve exit status = %1" i_ipc_ "\n",
                     st, inform.status);
          }

          printf("S_row: ");
          for( ipc_ i = 0; i < S_ne; i++) printf("%1" i_ipc_ " ", S_row[i]);
          printf("\n");
          printf("S_col: ");
          for( ipc_ i = 0; i < S_ne; i++) printf("%1" i_ipc_ " ", S_col[i]);
          printf("\n");
          printf("S_val: ");
#ifdef REAL_128
          for( ipc_ i = 0; i < S_ne; i++) printf("%.2f ", (double)S_val[i]);
#else
          for( ipc_ i = 0; i < S_ne; i++) printf("%.2f ", S_val[i]);
#endif
          printf("\n");
          if(ptr == 1){
            printf("S_ptr: ");
            for( ipc_ i = 0; i < m + 1; i++) printf("%1" i_ipc_ " ", S_ptr[i]);
            printf("\n");
          }
        }

        // Delete internal workspace
        bsc_terminate( &data, &control, &inform );
    }
    printf("Tests complete\n");
}

This is the same example, but now fortran-style indexing is used; the code is available in $GALAHAD/src/bsc/C/bsctf.c .

/* bsctf.c */
/* Full test for the BSC C interface using Fortran sparse matrix indexing */

#include <stdio.h>
#include <math.h>
#include <string.h>
#include "galahad_precision.h"
#include "galahad_cfunctions.h"
#include "galahad_bsc.h"
#ifdef REAL_128
#include <quadmath.h>
#endif

int main(void) {

    // Derived types
    void *data;
    struct bsc_control_type control;
    struct bsc_inform_type inform;

    // Set problem data
    ipc_ m = 3; // row dimension of A
    ipc_ n = 4; // column dimension of A
    ipc_ A_ne = 6; // nonzeros in lower triangle of A
    ipc_ A_dense_ne = 12; // positions in lower triangle of A
    ipc_ A_row[] = {1, 1, 2, 2, 3, 3}; // row indices
    ipc_ A_col[] = {1, 2, 3, 4, 1, 4}; // column indices
    ipc_ A_ptr[] = {1, 3, 5, 7}; // row pointers
    rpc_ A_val[] = {1.0, 1.0, 1.0, 1.0, 1.0, 1.0}; // values
    rpc_ A_dense[] = {1.0, 1.0, 0.0, 0.0, 0.0, 0.0,
                      1.0, 1.0, 1.0, 0.0, 0.0, 1.0}; // dense values
    rpc_ D[] = {1.0, 2.0, 3.0, 4.0}; // diagonals of D

    // Set output storage
    char st = ' ';
    ipc_ status, S_ne;

    printf(" Fortran sparse matrix indexing\n\n");

    printf(" basic tests of storage formats\n\n");

      for( ipc_ d=1; d <= 3; d++){

        // Initialize BSC
        bsc_initialize( &data, &control, &status );

        // Set user-defined control options
        control.f_indexing = true; // Fortran sparse matrix indexing
        //control.print_level = 1;

        switch(d){
            case 1: // sparse co-ordinate storage
                st = 'C';
                bsc_import( &control, &data, &status, m, n,
                           "coordinate", A_ne, A_row, A_col, NULL, &S_ne );
                break;
            case 2: // sparse by rows
                st = 'R';
                bsc_import( &control, &data, &status, m, n,
                            "sparse_by_rows", A_ne, NULL, A_col, A_ptr, &S_ne );
                break;
            case 3: // dense
                st = 'D';
                bsc_import( &control, &data, &status, m, n,
                            "dense", A_dense_ne, NULL, NULL, NULL, &S_ne );
                break;
            }

        ipc_ S_row[S_ne], S_col[S_ne], S_ptr[m+1];
        rpc_ S_val[S_ne];

        for( ipc_ ptr=0; ptr <= 1; ptr++){

          if(ptr == 0){
            switch(d){
                case 3: // dense
                    bsc_form_s( &data, &status, m, n, A_dense_ne, A_dense,
                                S_ne, S_row, S_col, NULL, S_val, NULL );
                    break;
                default:
                    bsc_form_s( &data, &status, m, n, A_ne, A_val,
                                S_ne, S_row, S_col, NULL, S_val, NULL );
                }
          } else {
            switch(d){
                case 3: // dense
                    bsc_form_s( &data, &status, m, n, A_dense_ne, A_dense,
                                S_ne, S_row, S_col, S_ptr, S_val, D );
                    break;
                default:
                    bsc_form_s( &data, &status, m, n, A_ne, A_val,
                                S_ne, S_row, S_col, S_ptr, S_val, D );
                }
          }

          bsc_information( &data, &inform, &status );

          if(inform.status == 0){
#ifdef REAL_128
            printf(" format %c: status = %1" i_ipc_ "\n", st, inform.status);
#else
            printf(" format %c: status = %1" i_ipc_ "\n", st, inform.status);
#endif
          }else{
              printf(" format %c: BSC_solve exit status = %1" i_ipc_ "\n",
                     st, inform.status);
          }

          printf("S_row: ");
          for( ipc_ i = 0; i < S_ne; i++) printf("%1" i_ipc_ " ", S_row[i]);
          printf("\n");
          printf("S_col: ");
          for( ipc_ i = 0; i < S_ne; i++) printf("%1" i_ipc_ " ", S_col[i]);
          printf("\n");
          printf("S_val: ");
#ifdef REAL_128
          for( ipc_ i = 0; i < S_ne; i++) printf("%.2f ", (double)S_val[i]);
#else
          for( ipc_ i = 0; i < S_ne; i++) printf("%.2f ", S_val[i]);
#endif
          printf("\n");
          if(ptr == 1){
            printf("S_ptr: ");
            for( ipc_ i = 0; i < m + 1; i++) printf("%1" i_ipc_ " ", S_ptr[i]);
            printf("\n");
          }
        }

        // Delete internal workspace
        bsc_terminate( &data, &control, &inform );
    }
    printf("Tests complete\n");
}