overview of functions provided#

// typedefs

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

// structs

struct dps_control_type;
struct dps_inform_type;
struct dps_time_type;

// global functions

void dps_initialize(void **data, struct dps_control_type* control, ipc_ *status);
void dps_read_specfile(struct dps_control_type* control, const char specfile[]);

void dps_import(
    struct dps_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    const char H_type[],
    ipc_ ne,
    const ipc_ H_row[],
    const ipc_ H_col[],
    const ipc_ H_ptr[]
);

void dps_reset_control(
    struct dps_control_type* control,
    void **data,
    ipc_ *status
);

void dps_solve_tr_problem(
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ ne,
    rpc_ H_val[],
    rpc_ c[],
    rpc_ f,
    rpc_ radius,
    rpc_ x[]
);

void dps_solve_rq_problem(
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ ne,
    rpc_ H_val[],
    rpc_ c[],
    rpc_ f,
    rpc_ power,
    rpc_ weight,
    rpc_ x[]
);

void dps_resolve_tr_problem(
    void **data,
    ipc_ *status,
    ipc_ n,
    rpc_ c[],
    rpc_ f,
    rpc_ radius,
    rpc_ x[]
);

void dps_resolve_rq_problem(
    void **data,
    ipc_ *status,
    ipc_ n,
    rpc_ c[],
    rpc_ f,
    rpc_ power,
    rpc_ weight,
    rpc_ x[]
);

void dps_information(void **data, struct dps_inform_type* inform, ipc_ *status);

void dps_terminate(
    void **data,
    struct dps_control_type* control,
    struct dps_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 dps_initialize below will instead be

void dps_initialize_s_64(void **data, struct dps_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 dps_initialize(void **data, struct dps_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 dps_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 dps_read_specfile(struct dps_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/dps/DPS.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/dps.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 dps_control_type)
specfile	is a character string containing the name of the specification file

void dps_import(
    struct dps_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    const char H_type[],
    ipc_ 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 dps_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: 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’ or ‘sparse_by_rows’ has been violated.
n	is a scalar variable of type ipc_, that holds the number of variables
H_type	is a one-dimensional array of type char that specifies the symmetric storage scheme used for the Hessian. It should be one of ‘coordinate’, ‘sparse_by_rows’ or ‘dense’; lower or upper case variants are allowed
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 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 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 dps_reset_control(
    struct dps_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 dps_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:

1. The import was successful, and the package is ready for the solve phase

void dps_solve_tr_problem(
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ ne,
    rpc_ H_val[],
    rpc_ c[],
    rpc_ f,
    rpc_ radius,
    rpc_ x[]
)

Find the global minimizer of the trust-region problem (1).

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 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 restriction n > 0 or requirement that type contains its relevant string ‘dense’, ‘coordinate’ or ‘sparse_by_rows’ 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. -16 The problem is so ill-conditioned that further progress is impossible. -40 An error has occured when building the preconditioner.
n	is a scalar variable of type ipc_, that holds the number of variables
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 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.
c	is a one-dimensional array of size n and type rpc_, that holds the linear term $c$ in the objective function. The j-th component of c, j = 0, … , n-1, contains $c_j$.
f	is a scalar variable pointer of type rpc_, that holds the value of the holds the constant term $f$ in the objective function.
radius	is a scalar variable pointer of type rpc_, that holds the value of the trust-region radius, $\Delta > 0$.
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 $x_j$.

void dps_solve_rq_problem(
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ ne,
    rpc_ H_val[],
    rpc_ c[],
    rpc_ f,
    rpc_ power,
    rpc_ weight,
    rpc_ x[]
)

Find the global minimizer of the regularized-quadartic problem (2).

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 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 restriction n > 0 or requirement that type contains its relevant string ‘dense’, ‘coordinate’ or ‘sparse_by_rows’ 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. -16 The problem is so ill-conditioned that further progress is impossible. -40 An error has occured when building the preconditioner.
n	is a scalar variable of type ipc_, that holds the number of variables
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 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.
c	is a one-dimensional array of size n and type rpc_, that holds the linear term $c$ in the objective function. The j-th component of c, j = 0, … , n-1, contains $c_j$.
f	is a scalar variable pointer of type rpc_, that holds the value of the holds the constant term $f$ in the objective function.
weight	is a scalar variable pointer of type rpc_, that holds the value of the regularization weight, $\sigma > 0$.
power	is a scalar variable pointer of type rpc_, that holds the value of the regularization power, $p \geq 2$.
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 $x_j$.

void dps_resolve_tr_problem(
    void **data,
    ipc_ *status,
    ipc_ n,
    rpc_ c[],
    rpc_ f,
    rpc_ radius,
    rpc_ x[]
)

Find the global minimizer of the trust-region problem (1) if some non-matrix components have changed since a call to dps_solve_tr_problem.

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 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 restriction n > 0 or requirement that type contains its relevant string ‘dense’, ‘coordinate’ or ‘sparse_by_rows’ has been violated. -16 The problem is so ill-conditioned that further progress is impossible.
n	is a scalar variable of type ipc_, that holds the number of variables
c	is a one-dimensional array of size n and type rpc_, that holds the linear term $c$ in the objective function. The j-th component of c, j = 0, … , n-1, contains $c_j$.
f	is a scalar variable pointer of type rpc_, that holds the value of the constant term $f$ in the objective function.
radius	is a scalar variable pointer of type rpc_, that holds the value of the trust-region radius, $\Delta > 0$.
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 $x_j$.

void dps_resolve_rq_problem(
    void **data,
    ipc_ *status,
    ipc_ n,
    rpc_ c[],
    rpc_ f,
    rpc_ power,
    rpc_ weight,
    rpc_ x[]
)

Find the global minimizer of the regularized-quadartic problem (2) if some non-matrix components have changed since a call to dps_solve_rq_problem.

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 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. -16 The problem is so ill-conditioned that further progress is impossible.
n	is a scalar variable of type ipc_, that holds the number of variables
c	is a one-dimensional array of size n and type rpc_, that holds the linear term $c$ in the objective function. The j-th component of c, j = 0, … , n-1, contains $c_j$.
f	is a scalar variable pointer of type rpc_, that holds the value of the holds the constant term $f$ in the objective function.
weight	is a scalar variable pointer of type rpc_, that holds the value of the regularization weight, $\sigma > 0$.
power	is a scalar variable pointer of type rpc_, that holds the value of the regularization power, $p \geq 2$.
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 $x_j$.

void dps_information(void **data, struct dps_inform_type* inform, ipc_ *status)

Provides output information

Parameters:

data

holds private internal data

inform

is a struct containing output information (see dps_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 dps_terminate(
    void **data,
    struct dps_control_type* control,
    struct dps_inform_type* inform
)

Deallocate all internal private storage

Parameters:

data	holds private internal data
control	is a struct containing control information (see dps_control_type)
inform	is a struct containing output information (see dps_inform_type)