overview of functions provided

// typedefs

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

// structs

struct l2rt_control_type;
struct l2rt_inform_type;

// global functions

void l2rt_initialize(
    void **data,
    struct l2rt_control_type* control,
    ipc_ *status
);

void l2rt_read_specfile(
    struct l2rt_control_type* control,
    const char specfile[]
);

void l2rt_import_control(
    struct l2rt_control_type* control,
    void **data,
    ipc_ *status
);

void l2rt_solve_problem(
    void **data,
    ipc_ *status,
    ipc_ m,
    ipc_ n,
    const rpc_ power,
    const rpc_ weight,
    const rpc_ shift,
    rpc_ x[],
    rpc_ u[],
    rpc_ v[]
);

void l2rt_information(void **data, struct l2rt_inform_type* inform, ipc_ *status);

void l2rt_terminate(
    void **data,
    struct l2rt_control_type* control,
    struct l2rt_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 l2rt_initialize below will instead be

void l2rt_initialize_s_64(void **data, struct l2rt_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 l2rt_initialize(
    void **data,
    struct l2rt_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 l2rt_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 l2rt_read_specfile(
    struct l2rt_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/l2rt/L2RT.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/l2rt.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 l2rt_control_type)
specfile	is a character string containing the name of the specification file

void l2rt_import_control(
    struct l2rt_control_type* control,
    void **data,
    ipc_ *status
)

Import control parameters prior to solution.

Parameters:

control	is a struct whose members provide control paramters for the remaining prcedures (see l2rt_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 (currently): 1 The import was successful, and the package is ready for the solve phase

void l2rt_solve_problem(
    void **data,
    ipc_ *status,
    ipc_ m,
    ipc_ n,
    const rpc_ power,
    const rpc_ weight,
    const rpc_ shift,
    rpc_ x[],
    rpc_ u[],
    rpc_ v[]
)

Solve the regularized-least-squares problem using reverse communication.

Parameters:

data	holds private internal data
status	is a scalar variable of type ipc_, that gives the entry and exit status from the package. This must be set to 1 on initial entry. Set u (below) to \(b\) for this entry. Possible exit values are: 0 the solution has been found 2 The user must perform the operation \[u := u + A v,\] n u := u + A v, \n and recall the function. The vectors \(u\) and \(v\) are available in the arrays u and v (below) respectively, and the result \(u\) must overwrite the content of u. No argument except u should be altered before recalling the function 3 The user must perform the operation \[v := v + A^T u,\] n v := v + A^T u, \n and recall the function. The vectors \(u\) and \(v\) are available in the arrays u and v (below) respectively, and the result \(v\) must overwrite the content of v. No argument except v should be altered before recalling the function 4 The user must reset u (below) to \(b\) are recall the function. No argument except u should be altered before recalling the function -1 an array allocation has failed -2 an array deallocation has failed -3 one or more of n, m, weight or shift violates allowed bounds -18 the iteration limit has been exceeded -25 status is negative on entry
m	is a scalar variable of type ipc_, that holds the number of equations (i.e., rows of \(A\)), \(m > 0\)
n	is a scalar variable of type ipc_, that holds the number of variables (i.e., columns of \(A\)), \(n > 0\)
power	is a scalar of type rpc_, that holds the regularization power, \(p \geq 2\)
weight	is a scalar of type rpc_, that holds the regularization weight, \(\sigma > 0\)
shift	is a scalar of type rpc_, that holds the shift, \(\mu\)
x	is a one-dimensional array of size n and type rpc_, that holds the solution \(x\). The j-th component of x, j = 0, … , n-1, contains \(x_j\).
u	is a one-dimensional array of size m and type rpc_, that should be used and reset appropriately when status = 1 to 5 as directed by status.
v	is a one-dimensional array of size n and type rpc_, that should be used and reset appropriately when status = 1 to 5 as directed by status.

void l2rt_information(void **data, struct l2rt_inform_type* inform, ipc_ *status)

Provides output information

Parameters:

data	holds private internal data
inform	is a struct containing output information (see l2rt_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 l2rt_terminate(
    void **data,
    struct l2rt_control_type* control,
    struct l2rt_inform_type* inform
)

Deallocate all internal private storage

Parameters:

data	holds private internal data
control	is a struct containing control information (see l2rt_control_type)
inform	is a struct containing output information (see l2rt_inform_type)