callable functions#

    function presolve_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 presolve_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 presolve_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/presolve/PRESOLVE.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/presolve.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 presolve_control_type)

specfile

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

 
    function presolve_import_problem(T, INT, control, data, status, n, m,
                                     H_type, H_ne, H_row, H_col, H_ptr,
                                     H_val,  g, f, A_type, A_ne, A_row,
                                     A_col, A_ptr, A_val, c_l, c_u,
                                     x_l, x_u, n_out, m_out, H_ne_out,
                                     A_ne_out)

Import the initial data, and apply the presolve algorithm to report crucial characteristics of the transformed variant

Parameters:

control

is a structure whose members provide control parameters for the remaining procedures (see presolve_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:

  • 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’ or ‘diagonal’ has been violated.

  • -23

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

n

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

m

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

H_type

is a one-dimensional array of type Vararg{Cchar} 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 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 schemes.

H_row

is a one-dimensional array of size H_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 H_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, diagonal or (scaled) identity 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.

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 \(g_j\).

f

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

A_type

is a one-dimensional array of type Vararg{Cchar} 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 INT 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 INT 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 C_NULL.

A_col

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

A_ptr

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

A_val

is a one-dimensional array of size a_ne and type T 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 T that holds the lower bounds \(c^l\) on the constraints \(A x\). The i-th component of c_l, i = 1, … , m, contains \(c^l_i\).

c_u

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

x_l

is a one-dimensional array of size n and type T that holds the lower bounds \(x^l\) on the variables \(x\). The j-th component of x_l, j = 1, … , n, contains \(x^l_j\).

x_u

is a one-dimensional array of size n and type T that holds the upper bounds \(x^l\) on the variables \(x\). The j-th component of x_u, j = 1, … , n, contains \(x^l_j\).

n_out

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

m_out

is a scalar variable of type INT that holds the number of general linear constraints in the transformed problem.

H_ne_out

is a scalar variable of type INT that holds the number of entries in the lower triangular part of \(H\) in the transformed problem.

A_ne_out

is a scalar variable of type INT that holds the number of entries in \(A\) in the transformed problem.

 
    function presolve_transform_problem(T, INT, data, status, n, m, H_ne, H_col,
                                        H_ptr, H_val, g, f, A_ne, A_col,
                                        A_ptr, A_val, c_l, c_u, x_l, x_u,
                                        y_l, y_u, z_l, z_u)

Apply the presolve algorithm to simplify the input problem, and output the transformed variant

Parameters:

data

holds private internal data

status

is a scalar variable of type INT 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 input values n, m, A_ne or H_ne do not agree with those output as necessary from presolve_import_problem.

n

is a scalar variable of type INT that holds the number of variables in the transformed problem. This must match the value n_out from the last call to presolve_import_problem.

m

is a scalar variable of type INT that holds the number of general linear constraints. This must match the value m_out from the last call to presolve_import_problem.

H_ne

is a scalar variable of type INT that holds the number of entries in the lower triangular part of the transformed \(H\). This must match the value H_ne_out from the last call to presolve_import_problem.

H_col

is a one-dimensional array of size H_ne and type INT that holds the column indices of the lower triangular part of the transformed \(H\) in the sparse row-wise storage scheme.

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 the transformed \(H\) in the sparse row-wise storage scheme.

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 the transformed Hessian matrix \(H\) in the sparse row-wise storage scheme.

g

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

f

is a scalar of type T that holds the transformed constant term \(f\) of the objective function.

A_ne

is a scalar variable of type INT that holds the number of entries in the transformed \(A\). This must match the value A_ne_out from the last call to presolve_import_problem.

A_col

is a one-dimensional array of size A_ne and type INT that holds the column indices of the transformed \(A\) in the sparse row-wise storage scheme.

A_ptr

is a one-dimensional array of size n+1 and type INT that holds the starting position of each row of the transformed \(A\), as well as the total number of entries, in the sparse row-wise storage scheme.

A_val

is a one-dimensional array of size a_ne and type T that holds the values of the entries of the transformed constraint Jacobian matrix \(A\) in the sparse row-wise storage scheme.

c_l

is a one-dimensional array of size m and type T that holds the transformed lower bounds \(c^l\) on the constraints \(A x\). The i-th component of c_l, i = 1, … , m, contains \(c^l_i\).

c_u

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

x_l

is a one-dimensional array of size n and type T that holds the transformed lower bounds \(x^l\) on the variables \(x\). The j-th component of x_l, j = 1, … , n, contains \(x^l_j\).

x_u

is a one-dimensional array of size n and type T that holds the transformed upper bounds \(x^l\) on the variables \(x\). The j-th component of x_u, j = 1, … , n, contains \(x^l_j\).

y_l

is a one-dimensional array of size m and type T that holds the implied lower bounds \(y^l\) on the transformed Lagrange multipliers \(y\). The i-th component of y_l, i = 1, … , m, contains \(y^l_i\).

y_u

is a one-dimensional array of size m and type T that holds the implied upper bounds \(y^u\) on the transformed Lagrange multipliers \(y\). The i-th component of y_u, i = 1, … , m, contains \(y^u_i\).

z_l

is a one-dimensional array of size m and type T that holds the implied lower bounds \(y^l\) on the transformed dual variables \(z\). The j-th component of z_l, j = 1, … , n, contains \(z^l_i\).

z_u

is a one-dimensional array of size m and type T that holds the implied upper bounds \(y^u\) on the transformed dual variables \(z\). The j-th component of z_u, j = 1, … , n, contains \(z^u_i\).

 
    function presolve_restore_solution(T, INT, data, status, n_in, m_in, x_in,
                                        c_in, y_in, z_in, n, m, x, c, y, z)

Given the solution (x_in,c_in,y_in,z_in) to the transformed problem, restore to recover the solution (x,c,y,z) to the original

Parameters:

data

holds private internal data

status

is a scalar variable of type INT 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 input values n, m, n_in and m_in do not agree with those input to and output as necessary from presolve_import_problem.

n_in

is a scalar variable of type INT that holds the number of variables in the transformed problem. This must match the value n_out from the last call to presolve_import_problem.

m_in

is a scalar variable of type INT that holds the number of general linear constraints. This must match the value m_out from the last call to presolve_import_problem.

x_in

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

c_in

is a one-dimensional array of size m and type T that holds the transformed residual \(c(x)\). The i-th component of c, j = 1, … , m, contains \(c_j(x)\).

y_in

is a one-dimensional array of size n_in and type T that holds the values \(y\) of the transformed Lagrange multipliers for the general linear constraints. The j-th component of y, j = 1, … , m, contains \(y_j\).

z_in

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

n

is a scalar variable of type INT that holds the number of variables in the transformed problem. This must match the value n as input to presolve_import_problem.

m

is a scalar variable of type INT that holds the number of general linear constraints. This must match the value m as input to presolve_import_problem.

x

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

c

is a one-dimensional array of size m and type T that holds the transformed residual \(c(x)\). The i-th component of c, j = 1, … , m, contains \(c_j(x)\).

y

is a one-dimensional array of size n and type T that holds the values \(y\) of the transformed Lagrange multipliers for the general linear constraints. The j-th component of y, j = 1, … , m, contains \(y_j\).

z

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

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

Provides output information

Parameters:

data

holds private internal data

inform

is a structure containing output information (see presolve_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 presolve_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 presolve_control_type)

inform

is a structure containing output information (see presolve_inform_type)