callable functions

    function rqs_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 rqs_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 rqs_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/rqs/RQS.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/rqs.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 rqs_control_type)
specfile	is a one-dimensional array of type Vararg{Cchar} that must give the name of the specification file

    function rqs_import(T, control, data, status, n,
                        H_type, H_ne, H_row, H_col, H_ptr)

Import problem data into internal storage prior to solution.

Parameters:

control	is a structure whose members provide control parameters for the remaining procedures (see rqs_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 and m > 0 or requirement that a type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’, diagonal’ or ‘identity’ has been violated.
n	is a scalar variable of type Int32 that holds the number of rows (and columns) of H.
H_type	is a one-dimensional array of type Vararg{Cchar} that specifies the symmetric storage scheme used for the Hessian, \(H\). It should be one of ‘coordinate’, ‘sparse_by_rows’, ‘dense’, or ‘diagonal’; 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 or diagonal 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.

    function rqs_import_m(T, data, status, n, M_type, M_ne, M_row, M_col, M_ptr)

Import data for the scaling matrix M into internal storage prior to solution.

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 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 and m > 0 or requirement that a type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’, diagonal’ or ‘identity’ has been violated.
n	is a scalar variable of type Int32 that holds the number of rows (and columns) of M.
M_type	is a one-dimensional array of type Vararg{Cchar} that specifies the symmetric storage scheme used for the scaling matrix, \(M\). It should be one of ‘coordinate’, ‘sparse_by_rows’, ‘dense’, or ‘diagonal’; lower or upper case variants are allowed.
M_ne	is a scalar variable of type Int32 that holds the number of entries in the lower triangular part of \(M\) in the sparse co-ordinate storage scheme. It need not be set for any of the other schemes.
M_row	is a one-dimensional array of size M_ne and type Int32 that holds the row indices of the lower triangular part of \(M\) 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.
M_col	is a one-dimensional array of size M_ne and type Int32 that holds the column indices of the lower triangular part of \(M\) in either the sparse co-ordinate, or the sparse row-wise storage scheme. It need not be set when the dense, diagonal or identity storage schemes are used, and in this case can be C_NULL.
M_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 \(M\), 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 rqs_import_a(T, data, status, m, A_type, A_ne, A_row, A_col, A_ptr)

Import data for the constraint matrix A into internal storage prior to solution.

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 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 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 Int32 that holds the number of general linear constraints, i.e., the number of rows of A, if any. m must be non-negative.
A_type	is a one-dimensional array of type Vararg{Cchar} that specifies the unsymmetric storage scheme used for the constraint Jacobian, \(A\) if any. 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 Int32 that holds the number of entries in \(A\), if used, 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.

    function rqs_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 rqs_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 rqs_solve_problem(T, data, status, n, power, weight, f, c,
                              H_ne, H_val, x, M_ne, M_val, m, A_ne, A_val, y)

Solve the regularised quadratic problem.

Parameters:

data	holds private internal data
status	is a scalar variable of type Int32 that gives the entry and exit status from the package. On initial entry, status must be set to 1. 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, power > 2, weight > 0 and m > 0 or requirement that a type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’, ‘diagonal’ or ‘identity’ has been violated. -9 The analysis phase of the factorization of the matrix (1) failed. -10 The factorization of the matrix (1) failed. -15 The matrix M appears not to be diagonally dominant. -16 The problem is so ill-conditioned that further progress is impossible. -18 Too many factorizations have been required. This may happen if control.max factorizations is too small, but may also be symptomatic of a badly scaled problem.
n	is a scalar variable of type Int32 that holds the number of variables.
power	is a scalar of type T that holds the order of regularisation, \(p\), used. power must be no smaller than 2.
weight	is a scalar of type T that holds the regularisation weight, \(\sigma\), used. weight must be strictly positive.
c	is a one-dimensional array of size n and type T that holds the linear term \(c\) of the objective function. The j-th component of c, j = 1, … , m, contains \(c_j\).
f	is a scalar of type T that holds the constant term \(f\) of the objective function.
H_ne	is a scalar variable of type Int32 that holds the number of entries in the lower triangular part of the Hessian 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 Hessian matrix \(H\) in any of the available storage schemes.
x	is a one-dimensional array of size n and type T that holds the values \(x\) of the optimization variables. The j-th component of x, j = 1, … , n, contains \(x_j\).
M_ne	is a scalar variable of type Int32 that holds the number of entries in the scaling matrix \(M\) if it not the identity matrix.
M_val	is a one-dimensional array of size M_ne and type T that holds the values of the entries of the scaling matrix \(M\), if it is not the identity matrix, in any of the available storage schemes. If M_val is C_NULL, M will be taken to be the identity matrix.
m	is a scalar variable of type Int32 that holds the number of general linear constraints, if any. m must be non-negative.
A_ne	is a scalar variable of type Int32 that holds the number of entries in the constraint Jacobian matrix \(A\) if used. A_ne must be non-negative.
A_val	is a one-dimensional array of size A_ne and type T that holds the values of the entries of the constraint Jacobian matrix \(A\), if used, in any of the available storage schemes. If A_val is C_NULL, no constraints will be enforced.
y	is a one-dimensional array of size m and type T that holds the values \(y\) of the Lagrange multipliers for the equality constraints \(A x = 0\) if used. The i-th component of y, i = 1, … , m, contains \(y_i\).

    function rqs_information(T, data, inform, status)

Provides output information

Parameters:

data	holds private internal data
inform	is a structure containing output information (see rqs_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 rqs_terminate(T, data, control, inform)

Deallocate all internal private storage

Parameters:

data	holds private internal data
control	is a structure containing control information (see rqs_control_type)
inform	is a structure containing output information (see rqs_inform_type)