overview of functions provided#

// typedefs

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

// structs

struct slls_control_type;
struct slls_inform_type;
struct slls_time_type;

// function calls

void slls_initialize(
    void **data,
    struct slls_control_type* control,
    ipc_ *status
);

void slls_read_specfile(
    struct slls_control_type* control,
    const char specfile[]
);

void slls_import(
    struct slls_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ o,
    const char A_type[],
    ipc_ Ao_ne,
    const ipc_ Ao_row[],
    const ipc_ Ao_col[],
    ipc_ Ao_ptr_ne,
    const ipc_ Ao_ptr[]
);

void slls_import_without_a(
    struct slls_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ m
);

void slls_reset_control(
    struct slls_control_type* control,
    void **data,
    ipc_ *status
);

void slls_solve_given_a(
    void **data,
    void *userdata,
    ipc_ *status,
    ipc_ n,
    ipc_ o,
    ipc_ Ao_ne,
    const rpc_ Ao_val[],
    const rpc_ b[],
    rpc_ x[],
    rpc_ z[],
    rpc_ r[],
    rpc_ g[],
    ipc_ x_stat[],
    const rpc_ w[],
    ipc_(*)(ipc_, const rpc_[], rpc_[], const void*) eval_prec
);

void slls_solve_reverse_a_prod(
    void **data,
    ipc_ *status,
    ipc_ *eval_status,
    ipc_ n,
    ipc_ o,
    const rpc_ b[],
    const rpc_ x_l[],
    const rpc_ x_u[],
    rpc_ x[],
    rpc_ z[],
    rpc_ r[],
    rpc_ g[],
    ipc_ x_stat[],
    rpc_ v[],
    const rpc_ p[],
    ipc_ nz_v[],
    ipc_ *nz_v_start,
    ipc_ *nz_v_end,
    const ipc_ nz_p[],
    ipc_ nz_p_end,
    const rpc_ w[]
);

void slls_information(void **data, struct slls_inform_type* inform, ipc_ *status);

void slls_terminate(
    void **data,
    struct slls_control_type* control,
    struct slls_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 slls_initialize below will instead be

void slls_initialize_s_64(void **data, struct slls_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 slls_initialize(
    void **data,
    struct slls_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 slls_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 slls_read_specfile(
    struct slls_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/slls/SLLS.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/slls.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 slls_control_type)
specfile	is a character string containing the name of the specification file

void slls_import(
    struct slls_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ o,
    const char Ao_type[],
    ipc_ Ao_ne,
    const ipc_ Ao_row[],
    const ipc_ Ao_col[],
    ipc_ Ao_ptr_ne,
    const ipc_ Ao_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 slls_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 restrictions n > 0, o > 0 or requirement that type contains its relevant string ‘coordinate’, ‘sparse_by_rows’, ‘sparse_by_columns’, ‘dense_by_rows’, or ‘dense_by_columns’; has been violated
n	is a scalar variable of type ipc_, that holds the number of variables.
o	is a scalar variable of type ipc_, that holds the number of residuals.
Ao_type	is a one-dimensional array of type char that specifies the symmetric storage scheme used for the design matrix $A_o$. It should be one of ‘coordinate’, ‘sparse_by_rows’, ‘sparse_by_columns’, ‘dense_by_rows’, or ‘dense_by_columns’; lower or upper case variants are allowed.
Ao_ne	is a scalar variable of type ipc_, that holds the number of entries in $A_o$ in the sparse co-ordinate storage scheme. It need not be set for any of the other schemes.
Ao_row	is a one-dimensional array of size Ao_ne and type ipc_, that holds the row indices of $A_o$ in the sparse co-ordinate or sparse column-wise storage scheme. It need not be set for any of the other schemes, and in this case can be NULL.
Ao_col	is a one-dimensional array of size Ao_ne and type ipc_, that holds the column indices of $A_o$ in either the sparse co-ordinate, or the sparse row-wise storage scheme. It need not be set for any of the other schemes, and in this case can be NULL.
Ao_ptr_ne	is a scalar variable of type ipc_, that holds the length of the pointer array if sparse row or column storage scheme is used for $A_o$. For the sparse row scheme, Ao_ptr_ne should be at least o+1, while for the sparse column scheme, it should be at least n+1, It need not be set when the other schemes are used.
Ao_ptr	is a one-dimensional array of size Ao_ptr_ne and type ipc_, that holds the starting position of each row of $A_o$, as well as the total number of entries, in the sparse row-wise storage scheme. By contrast, it holds the starting position of each column of $A_o$, as well as the total number of entries, in the sparse column-wise storage scheme. It need not be set when the other schemes are used, and in this case can be NULL.

void slls_import_without_a(
    struct slls_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ o
)

Import problem data into internal storage prior to solution.

Parameters:

control	is a struct whose members provide control paramters for the remaining prcedures (see slls_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 o > 0 has been violated
n	is a scalar variable of type ipc_, that holds the number of variables.
o	is a scalar variable of type ipc_, that holds the number of residuals.

void slls_reset_control(
    struct slls_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 slls_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 slls_solve_given_a(
    void **data,
    void *userdata,
    ipc_ *status,
    ipc_ n,
    ipc_ o,
    ipc_ Ao_ne,
    const rpc_ Ao_val[],
    const rpc_ b[],
    rpc_ x[],
    rpc_ z[],
    rpc_ r[],
    rpc_ g[],
    ipc_ x_stat[],
    const rpc_ w[],
    ipc_(*)(ipc_, const rpc_[], rpc_[], const void*) eval_prec
)

Solve the simplex-constrained linear least-squares problem when the design matrix $A_o$ is available.

Parameters:

data	holds private internal data
userdata	is a structure that allows data to be passed into the function and derivative evaluation programs.
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, o > 0 or requirement that a type contains its relevant string ‘coordinate’, ‘sparse_by_rows’, ‘sparse_by_columns’, ‘dense_by_rows’ or ‘dense_by_columns’ has been violated. -4 The simple-bound constraints are inconsistent. -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. -18 Too many iterations have been performed. This may happen if control.maxit is too small, but may also be symptomatic of a badly scaled problem. -19 The CPU time limit has been reached. This may happen if control.cpu_time_limit 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
o	is a scalar variable of type ipc_, that holds the number of residuals.
Ao_ne	is a scalar variable of type ipc_, that holds the number of entries in the design matrix $A_o$.
Ao_val	is a one-dimensional array of size Ao_ne and type rpc_, that holds the values of the entries in the design matrix $A_o$ in any of the available storage schemes.
b	is a one-dimensional array of size o and type rpc_, that holds the constant term $b$ in the residuals. The i-th component of b, i = 0, … , o-1, contains $b_i$.
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 $x_j$.
z	is a one-dimensional array of size n and type rpc_, that holds the values $z$ of the dual variables. The j-th component of z, j = 0, … , n-1, contains $z_j$.
r	is a one-dimensional array of size o and type rpc_, that holds the values of the residuals $r = A_o x - b$. The i-th component of r, i = 0, … , o-1, contains $r_i$.
g	is a one-dimensional array of size n and type rpc_, that holds the values of the gradient $g = A^T c$. The j-th component of g, j = 0, … , n-1, contains $g_j$.
x_stat	is a one-dimensional array of size n and type ipc_, that gives the optimal status of the problem variables. If x_stat(j) is negative, the variable $x_j$ most likely lies on its lower bound, if it is positive, it lies on its upper bound, and if it is zero, it lies between its bounds.
eval_prec	is an optional user-supplied function that may be NULL. If non-NULL, it must have the following signature: ipc_ eval_prec( ipc_ n, const rpc_ v[], rpc_ p[], const void *userdata ) The product $p = P^{-1} v$ involving the user’s preconditioner $P$ with the vector v = $v$, the result $p$ must be retured in p, and the function return value set to 0. If the evaluation is impossible, return should be set to a nonzero value. Data may be passed into `eval_prec` via the structure `userdata`.

void slls_solve_reverse_a_prod(
    void **data,
    ipc_ *status,
    ipc_ *eval_status,
    ipc_ n,
    ipc_ o,
    const rpc_ b[],
    const rpc_ x_l[],
    const rpc_ x_u[],
    rpc_ x[],
    rpc_ z[],
    rpc_ r[],
    rpc_ g[],
    ipc_ x_stat[],
    rpc_ v[],
    const rpc_ p[],
    ipc_ nz_v[],
    ipc_ *nz_v_start,
    ipc_ *nz_v_end,
    const ipc_ nz_p[],
    ipc_ nz_p_end,
    const rpc_ w[]
)

Solve the bound-constrained linear least-squares problem when the products of the Jacobian $A_o$ and its transpose with specified vectors may be computed by the calling program.

Parameters:

data	holds private internal data
status	is a scalar variable of type ipc_, that gives the entry and exit status from the package. 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 restriction n > 0 or requirement that a type contains its relevant string ‘coordinate’, ‘sparse_by_rows’, ‘sparse_by_columns’, ‘dense_by_rows’ or ‘dense_by_columns’ has been violated. -4 The simple-bound constraints are inconsistent. -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. -11 The solution of a set of linear equations using factors from the factorization package failed; the return status from the factorization package is given in the component inform.factor_status. -18 Too many iterations have been performed. This may happen if control.maxit is too small, but may also be symptomatic of a badly scaled problem. -19 The CPU time limit has been reached. This may happen if control.cpu_time_limit is too small, but may also be symptomatic of a badly scaled problem. 2 The product $A_ov$ of the design matrix $A_o$ with a given output vector $v$ is required from the user. The vector $v$ will be stored in v and the product $A_ov$ must be returned in p, status_eval should be set to 0, and slls_solve_reverse_a_prod re-entered with all other arguments unchanged. If the product cannot be formed, v need not be set, but slls_solve_reverse_a_prod should be re-entered with eval_status set to a nonzero value. 3 The product $A_o^Tv$ of the transpose of the design matrix $A_o$ with a given output vector $v$ is required from the user. The vector $v$ will be stored in v and the product $A_o^Tv$ must be returned in p, status_eval should be set to 0, and slls_solve_reverse_a_prod re-entered with all other arguments unchanged. If the product cannot be formed, v need not be set, but slls_solve_reverse_a_prod should be re-entered with eval_status set to a nonzero value. 4 The product $A_ov$ of the design matrix $A_o$ with a given sparse output vector $v$ is required from the user. The nonzero components of the vector $v$ will be stored as entries nz_in[nz_in_start-1:nz_in_end-1] of v and the product $A_ov$ must be returned in p, status_eval should be set to 0, and slls_solve_reverse_a_prod re-entered with all other arguments unchanged; The remaining components of v should be ignored. If the product cannot be formed, v need not be set, but slls_solve_reverse_a_prod should be re-entered with eval_status set to a nonzero value. 5 The nonzero components of the product $A_o v$ of the design matrix $A_o$ with a given sparse output vector $v$ is required from the user. The nonzero components of the vector $v$ will be stored as entries nz_in[nz_in_start-1:nz_in_end-1] of v; the remaining components of v should be ignored. The resulting nonzeros in the product $A_ov$ must be placed in their appropriate comnponents of p, while a list of indices of the nonzeros placed in nz_out[0 : nz_out_end-1] and the number of nonzeros recorded in nz_out_end. Additionally, status_eval should be set to 0, and slls_solve_reverse_a_prod re-entered with all other arguments unchanged. If the product cannot be formed, v, nz_out_end and nz_out need not be set, but slls_solve_reverse_a_prod should be re-entered with eval_status set to a nonzero value. 6 A subset of the product $A_o^T v$ of the transpose of the design matrix $A_o$ with a given output vector $v$ is required from the user. The vector $v$ will be stored in v and components nz_in[nz_in_start-1:nz_in_end-1] of the product $A_o^Tv$ must be returned in the relevant components of p (the remaining components should not be set), status_eval should be set to 0, and slls_solve_reverse_a_prod re-entered with all other arguments unchanged. If the product cannot be formed, v need not be set, but slls_solve_reverse_a_prod should be re-entered with eval_status set to a nonzero value. 7 The product $P^{-1}v$ of the inverse of the preconditioner $P$ with a given output vector $v$ is required from the user. The vector $v$ will be stored in v and the product $P^{-1} v$ must be returned in p, status_eval should be set to 0, and slls_solve_reverse_a_prod re-entered with all other arguments unchanged. If the product cannot be formed, v need not be set, but slls_solve_reverse_a_prod should be re-entered with eval_status set to a nonzero value. This value of status can only occur if the user has set control.preconditioner = 2.
eval_status	is a scalar variable of type ipc_, that is used to indicate if the matrix products can be provided (see `status` above)
n	is a scalar variable of type ipc_, that holds the number of variables
o	is a scalar variable of type ipc_, that holds the number of residuals.
b	is a one-dimensional array of size o and type rpc_, that holds the constant term $b$ in the residuals. The i-th component of b, i = 0, … , o-1, contains $b_i$.
x_l	is a one-dimensional array of size n and type rpc_, that holds the lower bounds $x^l$ on the variables $x$. The j-th component of x_l, j = 0, … , n-1, contains $x^l_j$.
x_u	is a one-dimensional array of size n and type rpc_, that holds the upper bounds $x^l$ on the variables $x$. The j-th component of x_u, j = 0, … , n-1, contains $x^l_j$.
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 $x_j$.
r	is a one-dimensional array of size m and type rpc_, that holds the values of the residuals $r = A x - b$. The i-th component of r, i = 0, … , o-1, contains $r_i$.
g	is a one-dimensional array of size n and type rpc_, that holds the values of the gradient $g = A^T W r$. The j-th component of g, j = 0, … , n-1, contains $g_j$.
z	is a one-dimensional array of size n and type rpc_, that holds the values $z$ of the dual variables. The j-th component of z, j = 0, … , n-1, contains $z_j$.
x_stat	is a one-dimensional array of size n and type ipc_, that gives the optimal status of the problem variables. If x_stat(j) is negative, the variable $x_j$ most likely lies on its lower bound, if it is positive, it lies on its upper bound, and if it is zero, it lies between its bounds.
v	is a one-dimensional array of size n and type rpc_, that is used for reverse communication (see status=2-4 above for details).
p	is a one-dimensional array of size n and type rpc_, that is used for reverse communication (see status=2-4 above for details).
nz_v	is a one-dimensional array of size n and type ipc_, that is used for reverse communication (see status=3-4 above for details).
nz_v_start	is a scalar of type ipc_, that is used for reverse communication (see status=3-4 above for details).
nz_v_end	is a scalar of type ipc_, that is used for reverse communication (see status=3-4 above for details).
nz_p	is a one-dimensional array of size n and type ipc_, that is used for reverse communication (see status=4 above for details).
nz_p_end	is a scalar of type ipc_, that is used for reverse communication (see status=4 above for details).
w	is an optional one-dimensional array of size m and type rpc_, that holds the values $w$ of the weights on the residuals in the least-squares objective function. It need not be set if the weights are all ones, and in this case can be NULL.

void slls_information(void **data, struct slls_inform_type* inform, ipc_ *status)

Provides output information

Parameters:

data

holds private internal data

inform

is a struct containing output information (see slls_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 slls_terminate(
    void **data,
    struct slls_control_type* control,
    struct slls_inform_type* inform
)

Deallocate all internal private storage

Parameters:

data	holds private internal data
control	is a struct containing control information (see slls_control_type)
inform	is a struct containing output information (see slls_inform_type)