overview of functions provided#

// typedefs

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

// structs

struct qpb_control_type;
struct qpb_inform_type;
struct qpb_time_type;

// function calls

void qpb_initialize(void **data, struct qpb_control_type* control, ipc_ *status);
void qpb_read_specfile(struct qpb_control_type* control, const char specfile[]);

void qpb_import(
    struct qpb_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ m,
    const char H_type[],
    ipc_ H_ne,
    const ipc_ H_row[],
    const ipc_ H_col[],
    const ipc_ H_ptr[],
    const char A_type[],
    ipc_ A_ne,
    const ipc_ A_row[],
    const ipc_ A_col[],
    const ipc_ A_ptr[]
);

void qpb_reset_control(
    struct qpb_control_type* control,
    void **data,
    ipc_ *status
);

void qpb_solve_qp(
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ m,
    ipc_ h_ne,
    const rpc_ H_val[],
    const rpc_ g[],
    const rpc_ f,
    ipc_ a_ne,
    const rpc_ A_val[],
    const rpc_ c_l[],
    const rpc_ c_u[],
    const rpc_ x_l[],
    const rpc_ x_u[],
    rpc_ x[],
    rpc_ c[],
    rpc_ y[],
    rpc_ z[],
    ipc_ x_stat[],
    ipc_ c_stat[]
);

void qpb_information(void **data, struct qpb_inform_type* inform, ipc_ *status);

void qpb_terminate(
    void **data,
    struct qpb_control_type* control,
    struct qpb_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 qpb_initialize(void **data, struct qpb_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 qpb_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 qpb_read_specfile(struct qpb_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/qpb/QPB.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/qpb.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 qpb_control_type)

specfile

is a character string containing the name of the specification file

void qpb_import(
    struct qpb_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ m,
    const char H_type[],
    ipc_ H_ne,
    const ipc_ H_row[],
    const ipc_ H_col[],
    const ipc_ H_ptr[],
    const char A_type[],
    ipc_ A_ne,
    const ipc_ A_row[],
    const ipc_ A_col[],
    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 qpb_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:

  • 0

    The import 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 or m > 0 or requirement that a type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’, ‘diagonal’, ‘scaled_identity’, ‘identity’, ‘zero’ or ‘none’ has been violated.

  • -23

    An entry from the strict upper triangle of H has been specified.

n

is a scalar variable of type ipc_, that holds the number of variables.

m

is a scalar variable of type ipc_, that holds the number of general linear constraints.

H_type

is a one-dimensional array of type char that specifies the symmetric storage scheme used for the Hessian, H. It should be one of ‘coordinate’, ‘sparse_by_rows’, ‘dense’, ‘diagonal’, ‘scaled_identity’, ‘identity’, ‘zero’ or ‘none’, the latter pair if H=0; lower or upper case variants are allowed.

H_ne

is a scalar variable of type ipc_, that holds the number of entries in the lower triangular part of H in the sparse co-ordinate storage scheme. It need not be set for any of the other schemes.

H_row

is a one-dimensional array of size H_ne and type ipc_, that holds the row indices of the lower triangular part of H in the sparse co-ordinate storage scheme. It need not be set for any of the other three schemes, and in this case can be NULL.

H_col

is a one-dimensional array of size H_ne and type ipc_, that holds the column indices of the lower triangular part of H in either the sparse co-ordinate, or the sparse row-wise storage scheme. It need not be set when the dense, diagonal or (scaled) identity storage schemes are used, and in this case can be NULL.

H_ptr

is a one-dimensional array of size n+1 and type ipc_, that holds the starting position of each row of the lower triangular part of H, as well as the total number of entries, in the sparse row-wise storage scheme. It need not be set when the other schemes are used, and in this case can be NULL.

A_type

is a one-dimensional array of type char that specifies the unsymmetric storage scheme used for the constraint Jacobian, A. It should be one of ‘coordinate’, ‘sparse_by_rows’ or ‘dense; lower or upper case variants are allowed.

A_ne

is a scalar variable of type ipc_, that holds the number of entries in A in the sparse co-ordinate storage scheme. It need not be set for any of the other schemes.

A_row

is a one-dimensional array of size A_ne and type ipc_, that holds the row indices of A in the sparse co-ordinate storage scheme. It need not be set for any of the other schemes, and in this case can be NULL.

A_col

is a one-dimensional array of size A_ne and type ipc_, that holds the column indices of A in either the sparse co-ordinate, or the sparse row-wise storage scheme. It need not be set when the dense or diagonal storage schemes are used, and in this case can be NULL.

A_ptr

is a one-dimensional array of size n+1 and type ipc_, that holds the starting position of each row of A, as well as the total number of entries, in the sparse row-wise storage scheme. It need not be set when the other schemes are used, and in this case can be NULL.

void qpb_reset_control(
    struct qpb_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 qpb_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:

  • 0

    The import was successful.

void qpb_solve_qp(
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ m,
    ipc_ h_ne,
    const rpc_ H_val[],
    const rpc_ g[],
    const rpc_ f,
    ipc_ a_ne,
    const rpc_ A_val[],
    const rpc_ c_l[],
    const rpc_ c_u[],
    const rpc_ x_l[],
    const rpc_ x_u[],
    rpc_ x[],
    rpc_ c[],
    rpc_ y[],
    rpc_ z[],
    ipc_ x_stat[],
    ipc_ c_stat[]
)

Solve the quadratic program when the Hessian H is available.

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 restrictions n > 0 and m > 0 or requirement that a type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’, ‘diagonal’, ‘scaled_identity’, ‘identity’, ‘zero’ or ‘none’ has been violated.

  • -5

    The simple-bound constraints are inconsistent.

  • -7

    The constraints appear to have no feasible point.

  • -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.

  • -16

    The problem is so ill-conditioned that further progress is impossible.

  • -17

    The step is too small to make further impact.

  • -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.

  • -23

    An entry from the strict upper triangle of H has been specified.

n

is a scalar variable of type ipc_, that holds the number of variables

m

is a scalar variable of type ipc_, that holds the number of general linear constraints.

h_ne

is a scalar variable of type ipc_, that holds the number of entries in the lower triangular part of the Hessian matrix H.

H_val

is a one-dimensional array of size h_ne and type rpc_, that holds the values of the entries of the lower triangular part of the Hessian matrix H in any of the available storage schemes.

g

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

f

is a scalar of type rpc_, that holds the constant term f of the objective function.

a_ne

is a scalar variable of type ipc_, that holds the number of entries in the constraint Jacobian matrix A.

A_val

is a one-dimensional array of size a_ne and type rpc_, that holds the values of the entries of the constraint Jacobian matrix A in any of the available storage schemes.

c_l

is a one-dimensional array of size m and type rpc_, that holds the lower bounds cl on the constraints Ax. The i-th component of c_l, i = 0, … , m-1, contains cil.

c_u

is a one-dimensional array of size m and type rpc_, that holds the upper bounds cl on the constraints Ax. The i-th component of c_u, i = 0, … , m-1, contains ciu.

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.

c

is a one-dimensional array of size m and type rpc_, that holds the residual c(x). The i-th component of c, j = 0, … , n-1, contains cj(x).

y

is a one-dimensional array of size n and type rpc_, that holds the values y of the Lagrange multipliers for the general linear constraints. The j-th component of y, j = 0, … , n-1, contains yj.

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.

c_stat

is a one-dimensional array of size m and type ipc_, that gives the optimal status of the general linear constraints. If c_stat(i) is negative, the constraint value aiTx 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.

void qpb_information(void **data, struct qpb_inform_type* inform, ipc_ *status)

Provides output information

Parameters:

data

holds private internal data

inform

is a struct containing output information (see qpb_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 qpb_terminate(
    void **data,
    struct qpb_control_type* control,
    struct qpb_inform_type* inform
)

Deallocate all internal private storage

Parameters:

data

holds private internal data

control

is a struct containing control information (see qpb_control_type)

inform

is a struct containing output information (see qpb_inform_type)