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 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 Ao. 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 Ao 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 Ao 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 Ao 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 Ao. 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 Ao, 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 Ao, 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 Ao 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 Ao.

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 Ao 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 bi.

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 xj.

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 zj.

r

is a one-dimensional array of size o and type rpc_, that holds the values of the residuals r=Aoxb. The i-th component of r, i = 0, … , o-1, contains ri.

g

is a one-dimensional array of size n and type rpc_, that holds the values of the gradient g=ATc. The j-th component of g, j = 0, … , n-1, contains gj.

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 xj 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=P1v 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 Ao 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 Aov of the design matrix Ao with a given output vector v is required from the user. The vector v will be stored in v and the product Aov 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 AoTv of the transpose of the design matrix Ao with a given output vector v is required from the user. The vector v will be stored in v and the product AoTv 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 Aov of the design matrix Ao 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 Aov 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 Aov of the design matrix Ao 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 Aov 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 AoTv of the transpose of the design matrix Ao 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 AoTv 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 P1v 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 P1v 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 bi.

x_l

is a one-dimensional array of size n and type rpc_, that holds the lower bounds xl on the variables x. The j-th component of x_l, j = 0, … , n-1, contains xjl.

x_u

is a one-dimensional array of size n and type rpc_, that holds the upper bounds xl on the variables x. The j-th component of x_u, j = 0, … , n-1, contains xjl.

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 xj.

r

is a one-dimensional array of size m and type rpc_, that holds the values of the residuals r=Axb. The i-th component of r, i = 0, … , o-1, contains ri.

g

is a one-dimensional array of size n and type rpc_, that holds the values of the gradient g=ATWr. The j-th component of g, j = 0, … , n-1, contains gj.

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 zj.

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 xj 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)