overview of functions provided#

// typedefs

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

// structs

struct sha_control_type;
struct sha_inform_type;

// function calls

void sha_initialize(void **data, struct sha_control_type* control, ipc_ *status);

void sha_read_specfile(struct sha_control_type* control, const char specfile[]);

void sha_analyse_matrix(
    struct sha_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ ne,
    const ipc_ row[],
    const ipc_ col[],
    ipc_ *m
);

void sha_recover_matrix(
    void **data,
    ipc_ *status,
    ipc_ ne,
    ipc_ m,
    ipc_ ls1,
    ipc_ ls2,
            const real_wp_ strans[][ls2],
            ipc_ ly1,
            ipc_ ly2,
            const real_wp_ ytrans[][ly2],
            real_wp_ val[],
            const ipc_ order[]
);


void sha_information(void **data, struct sha_inform_type* inform, ipc_ *status);

void sha_terminate(
    void **data,
    struct sha_control_type* control,
    struct sha_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 sha_initialize below will instead be

void sha_initialize_s_64(void **data, struct sha_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 sha_initialize(void **data, struct sha_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 sha_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 sha_read_specfile(struct sha_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/xxx/XXX.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/xxx.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 sha_control_type)

specfile

is a character string containing the name of the specification file

 
void sha_analyse_matrix(
    struct sha_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ ne,
    const ipc_ row[],
    const ipc_ col[],
    ipc_ *m
)

Analsyse the sparsity structure of \(H\) to generate information that will be used when estimating its values.

Parameters:

control

is a struct whose members provide control paramters for the remaining prcedures (see sha_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

    A restriction n > 0, ne \(\geq\) 0 or 0 \(\leq\) row[i] \(\leq\) col[i] \(\leq\) n has been violated.

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 upper triangular part of \(H\).

row

is a one-dimensional array of size ne and type ipc_, that holds the row indices of the upper triangular part of \(H\).

col

is a one-dimensional array of size ne and type ipc_, that holds the column indices of the upper triangular part of \(H\).

m

is a scalar variable of type ipc_, that gives the minimum number of \((s^{(k)},y^{(k)})\) pairs that will be needed to recover a good Hessian approximation.

 
void sha_recover_matrix(
    void **data,
    ipc_ *status,
            ipc_ ne,
            ipc_ m_available,
            ipc_ ls1,
            ipc_ ls2,
            const real_wp_ strans[][ls2],
            ipc_ ly1,
            ipc_ ly2,
            const real_wp_ ytrans[][ly2],
            real_wp_ val[],
            const ipc_ order[]
)

Estimate the nonzero entries of the Hessian \(H\) by component-wise secant approximation.

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 recovery was successful

  • 1

    Insufficient data pairs \((s_i,y_i)\) have been provided, as m is too small. The returned \(B\) is likely not fully accurate.

  • -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.

  • -31

    sha_recover_matrix has been called before sha_analyse_matrix.

ne

is a scalar variable of type ipc_, that holds the number of entries in the upper triangular part of \(H\).

m_available

is a scalar variable of type ipc_, that holds the number of differences provided. Ideally this will be as large as m as reported by sha_analyse_matrix, but better still there should be a further control.extra_differences to allow for unlikely singularities.

ls1

is a scalar variable of type ipc_, that holds the leading (first) dimension of the array strans.

ls2

is a scalar variable of type ipc_, that holds the trailing (second) dimension of the array strans.

strans

is a two-dimensional array of size [ls1][ls2] and type rpc_, that holds the values of the vectors \(\{s^{(k) T}\}\). Component [\(k\)][\(i\)] should hold \(s_i^{(k)}\).

ly1

is a scalar variable of type ipc_, that holds the leading (first) dimension of the array ytrans.

ly2

is a scalar variable of type ipc_, that holds the trailing (second) dimension of the array ytrans.

ytrans

is a two-dimensional array of size [ly1][ly2] and type rpc_, that holds the values of the vectors \(\{y^{(k) T}\}\). Component [\(k\)][\(i\)] should hold \(y_i^{(k)}\).

val

is a one-dimensional array of size ne and type rpc_, that holds the values of the entries of the upper triangular part of the symmetric matrix \(H\) in the sparse coordinate scheme.

order

is a one-dimensional array of size m and type ipc_, that holds the preferred order of access for the pairs \(\{(s^{(k)},y^{(k)})\}\). The \(k\)-th component of order specifies the row number of strans and ytrans that will be used as the \(k\)-th most favoured. order need not be set if the natural order, \(k, k = 1,...,\) m, is desired, and this case order should be NULL.

 
void sha_information(void **data, struct sha_inform_type* inform, ipc_ *status)

Provides output information

Parameters:

data

holds private internal data

inform

is a struct containing output information (see sha_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 sha_terminate(
    void **data,
    struct sha_control_type* control,
    struct sha_inform_type* inform
)

Deallocate all internal private storage

Parameters:

data

holds private internal data

control

is a struct containing control information (see sha_control_type)

inform

is a struct containing output information (see sha_inform_type)