callable functions#

    function bqp_initialize(T, INT, data, control, status)

Set default control values and initialize private data

Parameters:

data

holds private internal data

control

is a structure containing control information (see bqp_control_type)

status

is a scalar variable of type INT that gives the exit status from the package. Possible values are (currently):

  • 0

    The initialization was successful.

    function bqp_read_specfile(T, INT, control, 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/bqp/BQP.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/bqp.pdf for a list of how these keywords relate to the components of the control structure.

Parameters:

control

is a structure containing control information (see bqp_control_type)

specfile

is a one-dimensional array of type Vararg{Cchar} that must give the name of the specification file

    function bqp_import(T, INT, control, data, status, n, H_type, ne,
                        H_row, H_col, H_ptr)

Import problem data into internal storage prior to solution.

Parameters:

control

is a structure whose members provide control parameters for the remaining procedures (see bqp_control_type)

data

holds private internal data

status

is a scalar variable of type INT 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 requirement that type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’ or ‘diagonal’ has been violated.

n

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

H_type

is a one-dimensional array of type Vararg{Cchar} that specifies the symmetric storage scheme used for the Hessian. It should be one of ‘coordinate’, ‘sparse_by_rows’, ‘dense’, ‘diagonal’ or ‘absent’, the latter if access to the Hessian is via matrix-vector products; lower or upper case variants are allowed.

ne

is a scalar variable of type INT 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 three schemes.

H_row

is a one-dimensional array of size ne and type INT 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 C_NULL

H_col

is a one-dimensional array of size ne and type INT 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 or diagonal storage schemes are used, and in this case can be C_NULL

H_ptr

is a one-dimensional array of size n+1 and type INT 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 C_NULL

    function bqp_import_without_h(T, INT, control, data, status, n)

Import problem data into internal storage prior to solution.

Parameters:

control

is a structure whose members provide control parameters for the remaining procedures (see bqp_control_type)

data

holds private internal data

status

is a scalar variable of type INT 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 has been violated.

n

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

    function bqp_reset_control(T, INT, control, data, status)

Reset control parameters after import if required.

Parameters:

control

is a structure whose members provide control parameters for the remaining procedures (see bqp_control_type)

data

holds private internal data

status

is a scalar variable of type INT 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

    function bqp_solve_given_h(T, INT, data, status, n, h_ne, H_val, g, f,
                               x_l, x_u, x, z, x_stat)

Solve the bound-constrained quadratic program when the Hessian H is available.

Parameters:

data

holds private internal data

status

is a scalar variable of type INT 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 restriction n > 0 or requirement that a type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’ or ‘diagonal’ 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.

  • -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.

  • -20

    The Hessian matrix H appears to be indefinite. specified.

  • -23

    An entry from the strict upper triangle of H has been

n

is a scalar variable of type INT that holds the number of variables

h_ne

is a scalar variable of type INT 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 T 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 T that holds the linear term g of the objective function. The j-th component of g, j = 1, … , n, contains gj.

f

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

x_l

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

x_u

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

x

is a one-dimensional array of size n and type T that holds the values x of the optimization variables. The j-th component of x, j = 1, … , n, contains xj.

z

is a one-dimensional array of size n and type T that holds the values z of the dual variables. The j-th component of z, j = 1, … , n, contains zj.

x_stat

is a one-dimensional array of size n and type INT 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.

    function bqp_solve_reverse_h_prod(T, INT, data, status, n, g, f,
                                      x_l, x_u, x, z, x_stat, v,
                                      prod, nz_v, nz_v_start,
                                      nz_v_end, nz_prod, nz_prod_end)

Solve the bound-constrained quadratic program when the products of the Hessian H with specified vectors may be computed by the calling program.

Parameters:

data

holds private internal data

status

is a scalar variable of type INT 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 ‘dense’, ‘coordinate’, ‘sparse_by_rows’ or ‘diagonal’ 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.

  • -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.

  • -20

    The Hessian matrix H appears to be indefinite. specified.

  • -23

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

  • 2

    The product Hv of the Hessian H with a given output vector v is required from the user. The vector v will be stored in v and the product Hv must be returned in prod, and bqp_solve_reverse_h_prod re-entered with all other arguments unchanged.

  • 3

    The product Hv of the Hessian H with a given output vector v is required from the user. Only components nz_v[nz_v_start-1:nz_v_end-1] of the vector v stored in v are nonzero. The resulting product Hv must be placed in prod, and bqp_solve_reverse_h_prod re-entered with all other arguments unchanged.

  • 4

    The product Hv of the Hessian H with a given output vector v is required from the user. Only components nz_v[nz_v_start-1:nz_v_end-1] of the vector v stored in v are nonzero. The resulting nonzeros in the product Hv must be placed in their appropriate comnponents of prod, while a list of indices of the nonzeros placed in nz_prod[0 : nz_prod_end-1]. bqp_solve_reverse_h_prod should then be re-entered with all other arguments unchanged. Typically v will be very sparse (i.e., nz_p_end-nz_p_start will be small).

n

is a scalar variable of type INT that holds the number of variables

g

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

f

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

x_l

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

x_u

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

x

is a one-dimensional array of size n and type T that holds the values x of the optimization variables. The j-th component of x, j = 1, … , n, contains xj.

z

is a one-dimensional array of size n and type T that holds the values z of the dual variables. The j-th component of z, j = 1, … , n, contains zj.

x_stat

is a one-dimensional array of size n and type INT 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 T that is used for reverse communication (see status=2-4 above for details)

prod

is a one-dimensional array of size n and type T 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 INT that is used for reverse communication (see status=3-4 above for details)

nz_v_start

is a scalar of type INT that is used for reverse communication (see status=3-4 above for details)

nz_v_end

is a scalar of type INT that is used for reverse communication (see status=3-4 above for details)

nz_prod

is a one-dimensional array of size n and type INT that is used for reverse communication (see status=4 above for details)

nz_prod_end

is a scalar of type INT that is used for reverse communication (see status=4 above for details)

    function bqp_information(T, INT, data, inform, status)

Provides output information

Parameters:

data

holds private internal data

inform

is a structure containing output information (see bqp_inform_type)

status

is a scalar variable of type INT that gives the exit status from the package. Possible values are (currently):

  • 0

    The values were recorded successfully

    function bqp_terminate(T, INT, data, control, inform)

Deallocate all internal private storage

Parameters:

data

holds private internal data

control

is a structure containing control information (see bqp_control_type)

inform

is a structure containing output information (see bqp_inform_type)