overview of functions provided

// typedefs

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

// structs

struct blls_control_type;
struct blls_inform_type;
struct blls_time_type;

// function calls

void blls_initialize(
    void **data,
    struct blls_control_type* control,
    ipc_ *status
);

void blls_read_specfile(
    struct blls_control_type* control,
    const char specfile[]
);

void blls_import(
    struct blls_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 blls_import_without_a(
    struct blls_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ m
);

void blls_reset_control(
    struct blls_control_type* control,
    void **data,
    ipc_ *status
);

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

void blls_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 blls_information(void **data, struct blls_inform_type* inform, ipc_ *status);

void blls_terminate(
    void **data,
    struct blls_control_type* control,
    struct blls_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 blls_initialize(
    void **data,
    struct blls_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 blls_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 blls_read_specfile(
    struct blls_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/blls/BLLS.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/blls.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 blls_control_type)
specfile	is a character string containing the name of the specification file

void blls_import(
    struct blls_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ o,
    const char A_type[],
    ipc_ A_ne,
    const ipc_ A_row[],
    const ipc_ A_col[],
    ipc_ A_ptr_ne,
    const ipc_ A_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 blls_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 blls_import_without_a(
    struct blls_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 blls_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 blls_reset_control(
    struct blls_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 blls_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: The import was successful, and the package is ready for the solve phase

void blls_solve_given_a(
    void **data,
    void *userdata,
    ipc_ *status,
    ipc_ n,
    ipc_ o,
    ipc_ Ao_ne,
    const rpc_ Ao_val[],
    const rpc_ b[],
    const rpc_ x_l[],
    const rpc_ x_u[],
    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 bound-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 \(A_o\).
A_val	is a one-dimensional array of size A_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_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 \(x_j\).
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.
w	is an optional one-dimensional array of size o 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.
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 blls_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 blls_solve_reverse_a_prod re-entered with all other arguments unchanged. If the product cannot be formed, v need not be set, but blls_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 blls_solve_reverse_a_prod re-entered with all other arguments unchanged. If the product cannot be formed, v need not be set, but blls_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 blls_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 blls_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 blls_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 blls_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 blls_solve_reverse_a_prod re-entered with all other arguments unchanged. If the product cannot be formed, v need not be set, but blls_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 blls_solve_reverse_a_prod re-entered with all other arguments unchanged. If the product cannot be formed, v need not be set, but blls_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 blls_information(void **data, struct blls_inform_type* inform, ipc_ *status)

Provides output information

Parameters:

data	holds private internal data
inform	is a struct containing output information (see blls_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 blls_terminate(
    void **data,
    struct blls_control_type* control,
    struct blls_inform_type* inform
)

Deallocate all internal private storage

Parameters:

data	holds private internal data
control	is a struct containing control information (see blls_control_type)
inform	is a struct containing output information (see blls_inform_type)