callable functions#

    function qpa_initialize(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 qpa_control_type)

status

is a scalar variable of type Int32 that gives the exit status from the package. Possible values are (currently):

0
The initialization was successful.

    function qpa_read_specfile(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/qpa/QPA.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/qpa.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 qpa_control_type)
specfile	is a one-dimensional array of type Vararg{Cchar} that must give the name of the specification file

    function qpa_import(control, data, status, n, m,
                        H_type, H_ne, H_row, H_col, H_ptr,
                        A_type, A_ne, A_row, A_col, A_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 qpa_control_type)
data	holds private internal data
status	is a scalar variable of type Int32 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 Int32 that holds the number of variables.
m	is a scalar variable of type Int32 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 Int32 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 Int32 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 Int32 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 Int32 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.
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 Int32 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 Int32 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 Int32 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 Int32 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.

    function qpa_reset_control(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 qpa_control_type)

data

holds private internal data

status

is a scalar variable of type Int32 that gives the exit status from the package. Possible values are:

0
The import was successful.

    function qpa_solve_qp(data, status, n, m, h_ne, H_val, g, f,
                          a_ne, A_val, c_l, c_u, x_l, x_u,
                          x, c, y, z, x_stat, c_stat)

Solve the quadratic program (2)-(4).

Parameters:

data	holds private internal data
status	is a scalar variable of type Int32 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. -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 Int32 that holds the number of variables
m	is a scalar variable of type Int32 that holds the number of general linear constraints.
h_ne	is a scalar variable of type Int32 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 $g_j$.
f	is a scalar of type T that holds the constant term $f$ of the objective function.
a_ne	is a scalar variable of type Int32 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 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 $x^l_j$.
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 $x_j$.
c	is a one-dimensional array of size m and type T that holds the 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 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 dual variables. The j-th component of `z`, j = 1, … , n, contains $z_j$.
x_stat	is a one-dimensional array of size n and type Int32 that gives the current 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. On entry, if control.cold_start = 0, x_stat should be set as above to provide a guide to the initial working set.
c_stat	is a one-dimensional array of size m and type Int32 that gives the current 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. On entry, if control.cold_start = 0, c_stat should be set as above to provide a guide to the initial working set.

    function qpa_solve_l1qp(data, status, n, m, h_ne, H_val, g, f,
                             rho_g, rho_b, a_ne, A_val, c_l, c_u,
                             x_l, x_u, x, c, y, z, x_stat, c_stat)

Solve the l_1 quadratic program (1).

Parameters:

data	holds private internal data
status	is a scalar variable of type Int32 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. -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 Int32 that holds the number of variables
m	is a scalar variable of type Int32 that holds the number of general linear constraints.
h_ne	is a scalar variable of type Int32 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 $g_j$.
f	is a scalar of type T that holds the constant term $f$ of the objective function.
rho_g	is a scalar of type T that holds the parameter $\rho_g$ associated with the linear constraints.
rho_b	is a scalar of type T that holds the parameter $\rho_b$ associated with the simple bound constraints.
a_ne	is a scalar variable of type Int32 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 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 $x^l_j$.
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 $x_j$.
c	is a one-dimensional array of size m and type T that holds the 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 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 dual variables. The j-th component of `z`, j = 1, … , n, contains $z_j$.
x_stat	is a one-dimensional array of size n and type Int32 that gives the current 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. On entry, if control.cold_start = 0, x_stat should be set as above to provide a guide to the initial working set.
c_stat	is a one-dimensional array of size m and type Int32 that gives the current 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. On entry, if control.cold_start = 0, c_stat should be set as above to provide a guide to the initial working set.

    function qpa_solve_bcl1qp(data, status, n, m, h_ne, H_val, g, f,
                              rho_g, a_ne, A_val, c_l, c_u, x_l, x_u,
                              x, c, y, z, x_stat, c_stat)

Solve the bound-constrained l_1 quadratic program (4)-(5)

Parameters:

data	holds private internal data
status	is a scalar variable of type Int32 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. -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 Int32 that holds the number of variables
m	is a scalar variable of type Int32 that holds the number of general linear constraints.
h_ne	is a scalar variable of type Int32 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 $g_j$.
f	is a scalar of type T that holds the constant term $f$ of the objective function.
rho_g	is a scalar of type T that holds the parameter $\rho_g$ associated with the linear constraints.
a_ne	is a scalar variable of type Int32 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 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 $x^l_j$.
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 $x_j$.
c	is a one-dimensional array of size m and type T that holds the 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 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 dual variables. The j-th component of `z`, j = 1, … , n, contains $z_j$.
x_stat	is a one-dimensional array of size n and type Int32 that gives the current 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. On entry, if control.cold_start = 0, x_stat should be set as above to provide a guide to the initial working set.
c_stat	is a one-dimensional array of size m and type Int32 that gives the current 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. On entry, if control.cold_start = 0, c_stat should be set as above to provide a guide to the initial working set.

    function qpa_information(data, inform, status)

Provides output information

Parameters:

data

holds private internal data

inform

is a structure containing output information (see qpa_inform_type)

status

is a scalar variable of type Int32 that gives the exit status from the package. Possible values are (currently):

0
The values were recorded successfully

    function qpa_terminate(data, control, inform)

Deallocate all internal private storage

Parameters:

data	holds private internal data
control	is a structure containing control information (see qpa_control_type)
inform	is a structure containing output information (see qpa_inform_type)

data	holds private internal data
status	is a scalar variable of type Int32 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. -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 Int32 that holds the number of variables
m	is a scalar variable of type Int32 that holds the number of general linear constraints.
h_ne	is a scalar variable of type Int32 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 \(g_j\).
f	is a scalar of type T that holds the constant term \(f\) of the objective function.
a_ne	is a scalar variable of type Int32 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 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 \(x^l_j\).
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 \(x_j\).
c	is a one-dimensional array of size m and type T that holds the 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 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 dual variables. The j-th component of `z`, j = 1, … , n, contains \(z_j\).
x_stat	is a one-dimensional array of size n and type Int32 that gives the current 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. On entry, if control.cold_start = 0, x_stat should be set as above to provide a guide to the initial working set.
c_stat	is a one-dimensional array of size m and type Int32 that gives the current 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. On entry, if control.cold_start = 0, c_stat should be set as above to provide a guide to the initial working set.

data	holds private internal data
status	is a scalar variable of type Int32 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. -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 Int32 that holds the number of variables
m	is a scalar variable of type Int32 that holds the number of general linear constraints.
h_ne	is a scalar variable of type Int32 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 \(g_j\).
f	is a scalar of type T that holds the constant term \(f\) of the objective function.
rho_g	is a scalar of type T that holds the parameter \(\rho_g\) associated with the linear constraints.
rho_b	is a scalar of type T that holds the parameter \(\rho_b\) associated with the simple bound constraints.
a_ne	is a scalar variable of type Int32 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 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 \(x^l_j\).
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 \(x_j\).
c	is a one-dimensional array of size m and type T that holds the 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 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 dual variables. The j-th component of `z`, j = 1, … , n, contains \(z_j\).
x_stat	is a one-dimensional array of size n and type Int32 that gives the current 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. On entry, if control.cold_start = 0, x_stat should be set as above to provide a guide to the initial working set.
c_stat	is a one-dimensional array of size m and type Int32 that gives the current 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. On entry, if control.cold_start = 0, c_stat should be set as above to provide a guide to the initial working set.

data	holds private internal data
status	is a scalar variable of type Int32 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. -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 Int32 that holds the number of variables
m	is a scalar variable of type Int32 that holds the number of general linear constraints.
h_ne	is a scalar variable of type Int32 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 \(g_j\).
f	is a scalar of type T that holds the constant term \(f\) of the objective function.
rho_g	is a scalar of type T that holds the parameter \(\rho_g\) associated with the linear constraints.
a_ne	is a scalar variable of type Int32 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 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 \(x^l_j\).
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 \(x_j\).
c	is a one-dimensional array of size m and type T that holds the 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 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 dual variables. The j-th component of `z`, j = 1, … , n, contains \(z_j\).
x_stat	is a one-dimensional array of size n and type Int32 that gives the current 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. On entry, if control.cold_start = 0, x_stat should be set as above to provide a guide to the initial working set.
c_stat	is a one-dimensional array of size m and type Int32 that gives the current 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. On entry, if control.cold_start = 0, c_stat should be set as above to provide a guide to the initial working set.