callable functions

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

    function llsr_import(T, control, data, status, m, n,
                         A_type, A_ne, A_row, A_col, A_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 llsr_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: 1 The import was successful, and the package is ready for the solve phase -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 type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’, ‘diagonal’ or ‘absent’ has been violated.
m	is a scalar variable of type Int32 that holds the number of residuals, i.e., the number of rows of \(A\). m must be positive.
n	is a scalar variable of type Int32 that holds the number of variables, i.e., the number of columns of \(A\). n must be positive.
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 llsr_import_scaling(T, control, data, status, n,
                                 S_type, S_ne, S_row, S_col, S_ptr)

Import the scaling matrix \(S\) into internal storage prior to solution. Thus must have been preceeded by a call to llsr_import.

Parameters:

control	is a structure whose members provide control parameters for the remaining procedures (see llsr_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: 1 The import was successful, and the package is ready for the solve phase -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 type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’ or ‘diagonal’ has been violated.
n	is a scalar variable of type Int32 that holds the number of variables, i.e., the number of rows and columns of \(S\). n must be positive.
S_type	is a one-dimensional array of type Vararg{Cchar} that specifies the symmetric storage scheme used for the matrix \(S\). It should be one of ‘coordinate’, ‘sparse_by_rows’, ‘dense’ or ‘diagonal’; lower or upper case variants are allowed.
S_ne	is a scalar variable of type Int32 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 Int32 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 Int32 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 (scaled) 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 Int32 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 llsr_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 llsr_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: The import was successful, and the package is ready for the solve phase

    function llsr_solve_problem(T, data, status, m, n, power, weight,
                                A_ne, A_val, b, x, S_ne, S_val)

Solve the regularization-region 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. 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 or A_type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’ or ‘diagonal’ has been violated. -9 The analysis phase of the factorization failed; the return status from the factorization package is given in the component inform.factor_status -10 The factorization failed; the return status from the factorization package is given in the component inform.factor_status. -11 The solution of a set of linear equations using factors from the factorization package failed; the return status from the factorization package is given in the component inform.factor_status. -15 The matrix \(S\) does not appear to be strictly diagonally dominant. -16 The problem is so ill-conditioned that further progress is impossible. -17 The step is too small to make further impact.
m	is a scalar variable of type Int32 that holds the number of residuals
n	is a scalar variable of type Int32 that holds the number of variables
power	is a scalar of type T that holds the regularization power, \(p\), used. power must be greater than or equal to two.
weight	is a scalar of type T that holds the regularization power, \(\sigma\), used. weight must be strictly positive
A_ne	is a scalar variable of type Int32 that holds the number of entries in the observation 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 observation matrix \(A\) in any of the available storage schemes.
b	is a one-dimensional array of size m and type T that holds the values \(b\) of observations. The i-th component of b, i = 1, … , m, contains \(b_i\).
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 Int32 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 \(S\) in any of the available storage schemes. If S_val is C_NULL, \(S\) will be taken to be the identity matrix.

    function llsr_information(T, data, inform, status)

Provides output information

Parameters:

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

Deallocate all internal private storage

Parameters:

data	holds private internal data
control	is a structure containing control information (see llsr_control_type)
inform	is a structure containing output information (see llsr_inform_type)