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 SINGLE.

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 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)