callable functions

    function nrek_initialize(T, INT, 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 nrek_control_type)
status	is a scalar variable of type INT that gives the exit status from the package. Possible values are (currently): 0 The initialization was successful.

    function nrek_read_specfile(T, INT, 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/nrek/NREK.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/nrek.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 nrek_control_type)
specfile	is a one-dimensional array of type Vararg{Cchar} that must give the name of the specification file

    function nrek_import(T, INT, 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 nrek_control_type)
data	holds private internal data
status	is a scalar variable of type INT 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 restriction n > 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 INT 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’, ‘diagonal’, ‘scaled_identity’, ‘identity’, ‘zero’ or ‘none’; lower or upper case variants are allowed.
H_ne	is a scalar variable of type INT 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 INT 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 INT 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 INT 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 nrek_import_s(T, INT, data, status, n, S_type, S_ne, S_row, S_col, S_ptr)

Import data for the scaling matrix \(S\) into internal storage prior to solution.

Parameters:

data	holds private internal data
status	is a scalar variable of type INT 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 restriction n > 0 or requirement that a type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’, diagonal’ or ‘coordinate’, ‘sparse_by_rows’, diagonal’, ‘scaled_identity’, or ‘identity’ has been violated.
n	is a scalar variable of type INT that holds the number of rows (and columns) of \(S\).
S_type	is a one-dimensional array of type Vararg{Cchar} that specifies the symmetric storage scheme used for the scaling matrix, \(S\). It should be one of ‘coordinate’, ‘sparse_by_rows’, ‘dense’, ‘diagonal’, ‘scaled_identity’ or ‘identity’; lower or upper case variants are allowed.
S_ne	is a scalar variable of type INT that holds the number of entries in the lower triangular part of \(S\) in the sparse co-ordinate storage scheme. It need not be set for any of the other schemes.
S_row	is a one-dimensional array of size S_ne and type INT that holds the row indices of the lower triangular part of \(S\) 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.
S_col	is a one-dimensional array of size S_ne and type INT that holds the column indices of the lower triangular part of \(S\) 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.
S_ptr	is a one-dimensional array of size n+1 and type INT that holds the starting position of each row of the lower triangular part of \(S\), 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 nrek_reset_control(T, INT, 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 nrek_control_type)
data	holds private internal data
status	is a scalar variable of type INT that gives the exit status from the package. Possible values are: 0 The import was successful.

    function nrek_solve_problem(T, INT, data, status, n, H_ne, H_val, c,
                                power, weight, x, S_ne, S_val)

Solve the norm-regularization subproblem.

Parameters:

data	holds private internal data
status	is a scalar variable of type INT 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 or weight > 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 The analysis phase of the factorization of the matrix \(H\) or \(S\) failed. -10 The factorization of the matrix \(H\) or \(S\) failed. -11 A solve involving the matrix \(H\) or \(S\) failed. -15 The matrix \(S\) appears not to be diagonally dominant. -16 The problem is so ill-conditioned that further progress is impossible. -18 Too many iterations have been required. This may happen if control.eks max is too small, but may also be symptomatic of a badly scaled problem. -31 A resolve call has been made before an initial call (see control.new_weight and control.new_values). -38 An error occurred in a call to an LAPACK subroutine.
n	is a scalar variable of type INT that holds the number of variables
H_ne	is a scalar variable of type INT 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.
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 \(c_j\).
power	is a scalar of type T that holds the regularization power, \(p\), used. power must be strictly larger than two
weight	is a scalar of type T that holds the regularization weight, \(\Delta\), used. weight must be strictly positive
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 \(x_j\).
S_ne	is a scalar variable of type INT that holds the number of entries in the scaling matrix \(S\) if it not the identity matrix.
S_val	is a one-dimensional array of size S_ne and type T that holds the values of the entries of the scaling matrix \(S\), if it is not the identity matrix, in any of the available storage schemes. If S_val is C_NULL, \(S\) will be taken to be the identity matrix.

    function nrek_information(T, INT, data, inform, status)

Provides output information

Parameters:

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

    function nrek_terminate(T, INT, data, control, inform)

Deallocate all internal private storage

Parameters:

data	holds private internal data
control	is a structure containing control information (see nrek_control_type)
inform	is a structure containing output information (see nrek_inform_type)