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 SINGLE.

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 \(A_o\). 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)