GALAHAD SEC package

purpose

The sec package builds and updates dense BFGS and SR1 secant approximations to a Hessian so that the approximation \(B\) satisfies the secant condition \(B s = y\) for given vectors \(s\) and \(y\).

Currently only the options and inform dictionaries are exposed; these are provided and used by other GALAHAD packages with Python interfaces. Please contact us if you would like full functionality!

See Section 4 of $GALAHAD/doc/sec.pdf for a brief description of the method employed and other details.

callable functions

overview of functions provided

// namespaces

namespace conf;

// typedefs

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

// structs

struct sec_control_type;
struct sec_inform_type;

// global functions

void sec_initialize(struct sec_control_type* control, ipc_ *status);
void sec_information(void **data, struct sec_inform_type* inform, ipc_ *status);

void sec_terminate(
    void **data,
    struct sec_control_type* control,
    struct sec_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 sec_initialize below will instead be

void sec_initialize_s_64(void **data, struct sec_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 sec_initialize(struct sec_control_type* control, ipc_ *status)

Set default control values and initialize private data

Parameters:

control	is a struct containing control information (see sec_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 sec_information(void **data, struct sec_inform_type* inform, ipc_ *status)

Provides output information

Parameters:

data	holds private internal data
inform	is a struct containing output information (see sec_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 sec_terminate(
    void **data,
    struct sec_control_type* control,
    struct sec_inform_type* inform
)

Deallocate all internal private storage

Parameters:

data	holds private internal data
control	is a struct containing control information (see sec_control_type)
inform	is a struct containing output information (see sec_inform_type)

available structures

sec_control_type structure

#include <galahad_sec.h>

struct sec_control_type {
    // fields

    bool f_indexing;
    ipc_ error;
    ipc_ out;
    ipc_ print_level;
    rpc_ h_initial;
    rpc_ update_skip_tol;
    char prefix[31];
};

detailed documentation

control derived type as a C struct

components

bool f_indexing

use C or Fortran sparse matrix indexing

ipc_ error

error and warning diagnostics occur on stream error

ipc_ out

general output occurs on stream out

ipc_ print_level

the level of output required. <= 0 gives no output, >= 1 warning message

rpc_ h_initial

the initial Hessian approximation will be h_initial \* \(I\)

rpc_ update_skip_tol

an update is skipped if the resulting matrix would have grown too much; specifically it is skipped when y^T s / y^T y <= update_skip_tol.

char prefix[31]

all output lines will be prefixed by .prefix(2:LEN(TRIM(.prefix))-1) where .prefix contains the required string enclosed in quotes, e.g. “string” or ‘string’

sec_inform_type structure

#include <galahad_sec.h>

struct sec_inform_type {
    // fields

    ipc_ status;
};

detailed documentation

inform derived type as a C struct

components

ipc_ status

return status. Possible valuesa are:

• 0

  successful return

• -85

  an update is inappropriate and has been skipped

Index