callable functions

    function sbls_initialize(T, data, control, status)

Set default control values and initialize private data

Parameters:

data	holds private internal data
control	is a structure containing control information (see sbls_control_type)
status	is a scalar variable of type Int32 that gives the exit status from the package. Possible values are (currently): 0 The initialization was successful.

    function sbls_read_specfile(T, control, 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/sbls/SBLS.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/sbls.pdf for a list of how these keywords relate to the components of the control structure.

Parameters:

control	is a structure containing control information (see sbls_control_type)
specfile	is a one-dimensional array of type Vararg{Cchar} that must give the name of the specification file

    function sbls_import(T, control, data, status, n, m,
                         H_type, H_ne, H_row, H_col, H_ptr,
                         A_type, A_ne, A_row, A_col, A_ptr,
                         C_type, C_ne, C_row, C_col, C_ptr)

Import structural matrix data into internal storage prior to solution.

Parameters:

control	is a structure whose members provide control parameters for the remaining procedures (see sbls_control_type)
data	holds private internal data
status	is a scalar variable of type Int32 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’, ‘sparse_by_rows’, ‘diagonal’, ‘scaled_identity’, ‘identity’, ‘zero’ or ‘none’ has been violated.
n	is a scalar variable of type Int32 that holds the number of rows in the symmetric matrix \(H\).
m	is a scalar variable of type Int32 that holds the number of rows in the symmetric matrix \(C\).
H_type	is a one-dimensional array of type Vararg{Cchar} that specifies the symmetric storage scheme used for the matrix \(H\). It should be one of ‘coordinate’, ‘sparse_by_rows’, ‘dense’, ‘diagonal’, ‘scaled_identity’, ‘identity’, ‘zero’ or ‘none’, the latter pair if \(H=0\); lower or upper case variants are allowed.
H_ne	is a scalar variable of type Int32 that holds the number of entries in the lower triangular part of \(H\) in the sparse co-ordinate storage scheme. It need not be set for any of the other schemes.
H_row	is a one-dimensional array of size H_ne and type Int32 that holds the row indices of the lower triangular part of \(H\) in the sparse co-ordinate storage scheme. It need not be set for any of the other three schemes, and in this case can be C_NULL.
H_col	is a one-dimensional array of size H_ne and type Int32 that holds the column indices of the lower triangular part of \(H\) in either the sparse co-ordinate, or the sparse row-wise storage scheme. It need not be set when the dense, diagonal or (scaled) identity storage schemes are used, and in this case can be C_NULL.
H_ptr	is a one-dimensional array of size n+1 and type Int32 that holds the starting position of each row of the lower triangular part of \(H\), 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 C_NULL.
A_type	is a one-dimensional array of type Vararg{Cchar} that specifies the unsymmetric storage scheme used for the matrix \(A\). It should be one of ‘coordinate’, ‘sparse_by_rows’, ‘dense’ or ‘absent’, the latter if access to the Jacobian is via matrix-vector products; lower or upper case variants are allowed.
A_ne	is a scalar variable of type Int32 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 Int32 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 C_NULL.
A_col	is a one-dimensional array of size A_ne and type Int32 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 C_NULL.
A_ptr	is a one-dimensional array of size n+1 and type Int32 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 C_NULL.
C_type	is a one-dimensional array of type Vararg{Cchar} that specifies the symmetric storage scheme used for the matrix \(C\). It should be one of ‘coordinate’, ‘sparse_by_rows’, ‘dense’, ‘diagonal’, ‘scaled_identity’, ‘identity’, ‘zero’ or ‘none’, the latter pair if \(C=0\); lower or upper case variants are allowed.
C_ne	is a scalar variable of type Int32 that holds the number of entries in the lower triangular part of \(C\) in the sparse co-ordinate storage scheme. It need not be set for any of the other schemes.
C_row	is a one-dimensional array of size C_ne and type Int32 that holds the row indices of the lower triangular part of \(C\) in the sparse co-ordinate storage scheme. It need not be set for any of the other three schemes, and in this case can be C_NULL.
C_col	is a one-dimensional array of size C_ne and type Int32 that holds the column indices of the lower triangular part of \(C\) in either the sparse co-ordinate, or the sparse row-wise storage scheme. It need not be set when the dense, diagonal or (scaled) identity storage schemes are used, and in this case can be C_NULL.
C_ptr	is a one-dimensional array of size n+1 and type Int32 that holds the starting position of each row of the lower triangular part of \(C\), 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 C_NULL.

    function sbls_reset_control(T, control, data, status)

Reset control parameters after import if required.

Parameters:

control	is a structure whose members provide control parameters for the remaining procedures (see sbls_control_type)
data	holds private internal data
status	is a scalar variable of type Int32 that gives the exit status from the package. Possible values are: 0 The import was successful.

    function sbls_factorize_matrix(T, data, status, n, h_ne, H_val,
                               a_ne, A_val, c_ne, C_val, D)

Form and factorize the block matrix

\[\begin{split}K_{G} = \begin{pmatrix}G & A^T \\ A & - C\end{pmatrix}\end{split}\]

for some appropriate matrix \(G\).

Parameters:

data	holds private internal data
status	is a scalar variable of type Int32 that gives the exit status from the package. Possible values are: 0 The factors were generated successfully. -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’, ‘sparse_by_rows’, ‘diagonal’, ‘scaled_identity’, ‘identity’, ‘zero’ or ‘none’ has been violated. -9 An error was reported by SLS analyse. The return status from SLS analyse is given in inform.sls_inform.status. See the documentation for the GALAHAD package SLS for further details. -10 An error was reported by SLS_factorize. The return status from SLS factorize is given in inform.sls_inform.status. See the documentation for the GALAHAD package SLS for further details. -13 An error was reported by ULS_factorize. The return status from ULS_factorize is given in inform.uls_factorize_status. See the documentation for the GALAHAD package ULS for further details. -15 The computed preconditioner \(K_G\) is singular and is thus unsuitable. -20 The computed preconditioner \(K_G\) has the wrong inertia and is thus unsuitable. -24 An error was reported by the GALAHAD package SORT_reorder_by_rows. The return status from SORT_reorder_by_rows is given in inform.sort_status. See the documentation for the GALAHAD package SORT for further details.
n	is a scalar variable of type Int32 that holds the number of rows in the symmetric matrix \(H\).
h_ne	is a scalar variable of type Int32 that holds the number of entries in the lower triangular part of the symmetric matrix \(H\).
H_val	is a one-dimensional array of size h_ne and type T that holds the values of the entries of the lower triangular part of the symmetric matrix \(H\) in any of the available storage schemes
a_ne	is a scalar variable of type Int32 that holds the number of entries in the unsymmetric matrix \(A\).
A_val	is a one-dimensional array of size a_ne and type T that holds the values of the entries of the unsymmetric matrix \(A\) in any of the available storage schemes.
c_ne	is a scalar variable of type Int32 that holds the number of entries in the lower triangular part of the symmetric matrix \(C\).
C_val	is a one-dimensional array of size c_ne and type T that holds the values of the entries of the lower triangular part of the symmetric matrix \(C\) in any of the available storage schemes
D	is a one-dimensional array of size n and type T that holds the values of the entries of the diagonal matrix \(D\) that is required if the user has specified control.preconditioner = 5. It need not be set otherwise.

    function sbls_solve_system(T, data, status, n, m, sol)

Solve the block linear system

\[\begin{split}\begin{pmatrix}G & A^T \\ A & - C\end{pmatrix} \begin{pmatrix}x \\ y\end{pmatrix} = \begin{pmatrix}a \\ b\end{pmatrix}.\end{split}\]

Parameters:

data	holds private internal data
status	is a scalar variable of type Int32 that gives the exit status from the package. Possible values are: 0 The required solution was obtained. -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. -11 An error was reported by SLS_solve. The return status from SLS solve is given in inform.sls_inform.status. See the documentation for the GALAHAD package SLS for further details. -14 An error was reported by ULS_solve. The return status from ULS_solve is given in inform.uls_solve_status. See the documentation for the GALAHAD package ULS for further details.
n	is a scalar variable of type Int32 that holds the number of entries in the vector \(a\).
m	is a scalar variable of type Int32 that holds the number of entries in the vector \(b\).
sol	is a one-dimensional array of size n + m and type T. on entry, its first n entries must hold the vector \(a\), and the following entries must hold the vector \(b\). On a successful exit, its first n entries contain the solution components \(x\), and the following entries contain the components \(y\).

    function sbls_information(T, data, inform, status)

Provides output information

Parameters:

data	holds private internal data
inform	is a structure containing output information (see sbls_inform_type)
status	is a scalar variable of type Int32 that gives the exit status from the package. Possible values are (currently): 0 The values were recorded successfully

    function sbls_terminate(T, data, control, inform)

Deallocate all internal private storage

Parameters:

data	holds private internal data
control	is a structure containing control information (see sbls_control_type)
inform	is a structure containing output information (see sbls_inform_type)