overview of functions provided#

// typedefs

typedef float spc_;
typedef double rpc_;
typedef int ipc_;

// structs

struct rqs_control_type;
struct rqs_history_type;
struct rqs_inform_type;
struct rqs_time_type;

// global functions

void rqs_initialize(void **data, struct rqs_control_type* control, ipc_ *status);
void rqs_read_specfile(struct rqs_control_type* control, const char specfile[]);

void rqs_import(
    struct rqs_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    const char H_type[],
    ipc_ H_ne,
    const ipc_ H_row[],
    const ipc_ H_col[],
    const ipc_ H_ptr[]
);

void rqs_import_m(
    void **data,
    ipc_ *status,
    ipc_ n,
    const char M_type[],
    ipc_ M_ne,
    const ipc_ M_row[],
    const ipc_ M_col[],
    const ipc_ M_ptr[]
);

void rqs_import_a(
    void **data,
    ipc_ *status,
    ipc_ m,
    const char A_type[],
    ipc_ A_ne,
    const ipc_ A_row[],
    const ipc_ A_col[],
    const ipc_ A_ptr[]
);

void rqs_reset_control(
    struct rqs_control_type* control,
    void **data,
    ipc_ *status
);

void rqs_solve_problem(
    void **data,
    ipc_ *status,
    ipc_ n,
    const rpc_ power,
    const rpc_ weight,
    const rpc_ f,
    const rpc_ c[],
    ipc_ H_ne,
    const rpc_ H_val[],
    rpc_ x[],
    ipc_ M_ne,
    const rpc_ M_val[],
    ipc_ m,
    ipc_ A_ne,
    const rpc_ A_val[],
    rpc_ y[]
);

void rqs_information(void **data, struct rqs_inform_type* inform, ipc_ *status);

void rqs_terminate(
    void **data,
    struct rqs_control_type* control,
    struct rqs_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 and structure names#

The function and structure names described below are appropriate for the default real working precision (double) and integer word length (int32_t). To use the functions and structures with different precisions and integer word lengths, an additional suffix must be added to their names (and the arguments set accordingly). The appropriate suffices are:

_s for single precision (float) reals and standard 32-bit (int32_t) integers;

_q for quadruple precision (__real128) reals (if supported) and standard 32-bit (int32_t) integers;

_64 for standard precision (double) reals and 64-bit (int64_t) integers;

_s_64 for single precision (float) reals and 64-bit (int64_t) integers; and

_q_64 for quadruple precision (__real128) reals (if supported) and 64-bit (int64_t) integers.

Thus a call to rqs_initialize below will instead be

void rqs_initialize_s_64(void **data, struct rqs_control_type_s_64* control,
                         int64_t *status)

if single precision (float) reals and 64-bit (int64_t) integers are required. Thus it is possible to call functions for this package with more that one precision and/or integer word length at same time. An example is provided for the package expo, and the obvious modifications apply equally here.

function calls#

void rqs_initialize(void **data, struct rqs_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 rqs_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 rqs_read_specfile(struct rqs_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/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 struct containing control information (see rqs_control_type)
specfile	is a character string containing the name of the specification file

void rqs_import(
    struct rqs_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    const char H_type[],
    ipc_ H_ne,
    const ipc_ H_row[],
    const ipc_ H_col[],
    const ipc_ H_ptr[]
)

Import problem data into internal storage prior to solution.

Parameters:

control	is a struct whose members provide control paramters for the remaining prcedures (see rqs_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 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 ipc_, that holds the number of rows (and columns) of H.
H_type	is a one-dimensional array of type char 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 ipc_, 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 ipc_, 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 NULL.
H_col	is a one-dimensional array of size H_ne and type ipc_, 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 NULL.
H_ptr	is a one-dimensional array of size n+1 and type ipc_, 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 NULL.

void rqs_import_m(
    void **data,
    ipc_ *status,
    ipc_ n,
    const char M_type[],
    ipc_ M_ne,
    const ipc_ M_row[],
    const ipc_ M_col[],
    const ipc_ 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 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 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 ipc_, that holds the number of rows (and columns) of M.
M_type	is a one-dimensional array of type char 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 ipc_, 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 ipc_, 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 NULL.
M_col	is a one-dimensional array of size M_ne and type ipc_, 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 NULL.
M_ptr	is a one-dimensional array of size n+1 and type ipc_, 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 NULL.

void rqs_import_a(
    void **data,
    ipc_ *status,
    ipc_ m,
    const char A_type[],
    ipc_ A_ne,
    const ipc_ A_row[],
    const ipc_ A_col[],
    const ipc_ 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 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 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 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 char 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 ipc_, 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 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 n+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.

void rqs_reset_control(
    struct rqs_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 rqs_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 rqs_solve_problem(
    void **data,
    ipc_ *status,
    ipc_ n,
    const rpc_ power,
    const rpc_ weight,
    const rpc_ f,
    const rpc_ c[],
    ipc_ H_ne,
    const rpc_ H_val[],
    rpc_ x[],
    ipc_ M_ne,
    const rpc_ M_val[],
    ipc_ m,
    ipc_ A_ne,
    const rpc_ A_val[],
    rpc_ y[]
)

Solve the regularised quadratic problem.

Parameters:

data	holds private internal data
status	is a scalar variable of type ipc_, 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 ipc_, that holds the number of variables.
power	is a scalar of type rpc_, that holds the order of regularisation, $p$, used. power must be no smaller than 2.
weight	is a scalar of type rpc_, that holds the regularisation weight, $\sigma$, used. weight must be strictly positive.
c	is a one-dimensional array of size n and type rpc_, that holds the linear term $c$ of the objective function. The j-th component of c, j = 0, … , n-1, contains $c_j$.
f	is a scalar of type rpc_, that holds the constant term $f$ of the objective function.
H_ne	is a scalar variable of type ipc_, 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 rpc_, 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 rpc_, that holds the values $x$ of the optimization variables. The j-th component of x, j = 0, … , n-1, contains $x_j$.
M_ne	is a scalar variable of type ipc_, 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 rpc_, 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 NULL, M will be taken to be the identity matrix.
m	is a scalar variable of type ipc_, that holds the number of general linear constraints, if any. m must be non-negative.
A_ne	is a scalar variable of type ipc_, 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 rpc_, 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 NULL, no constraints will be enforced.
y	is a one-dimensional array of size m and type rpc_, 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 = 0, … , m-1, contains $y_i$.

void rqs_information(void **data, struct rqs_inform_type* inform, ipc_ *status)

Provides output information

Parameters:

data

holds private internal data

inform

is a struct containing output information (see rqs_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 rqs_terminate(
    void **data,
    struct rqs_control_type* control,
    struct rqs_inform_type* inform
)

Deallocate all internal private storage

Parameters:

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