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 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 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 \(g_j\).

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 \(c^l\) on the constraints \(A x\). The i-th component of c_l, i = 0, … , m-1, contains \(c^l_i\).

c_u

is a one-dimensional array of size m and type rpc_, that holds the upper bounds \(c^l\) on the constraints \(A x\). The i-th component of c_u, i = 0, … , m-1, contains \(c^u_i\).

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 \(x_j\).

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 \(c_j(x)\).

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 \(y_j\).

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.

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 \(a_i^Tx\) 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)