callable functions

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

    function trb_import(T, INT, control, data, status, n, x_l, x_u,
                        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 trb_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’, ‘diagonal’ or ‘absent’ has been violated.
n	is a scalar variable of type INT that holds the number of variables.
x_l	is a one-dimensional array of size n and type T that holds the values $x^l$ of the lower bounds on the optimization variables $x$. The j-th component of x_l, $j=1,\dots ,n$, contains $x_j^l$.
x_u	is a one-dimensional array of size n and type T that holds the values $x^u$ of the upper bounds on the optimization variables $x$. The j-th component of x_u, $j=1,\dots ,n$, contains $x_j^u$.
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 trb_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 trb_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 trb_solve_with_mat(T, INT, data, userdata, status, n, x, g, ne,
                                eval_f, eval_g, eval_h, eval_prec)

Find a local minimizer of a given function subject to simple bounds on the variables using a trust-region method.

This call is for the case where $H={\mathrm{\nabla }}_{xx}f(x)$ is provided specifically, and all function/derivative information is available by function calls.

Parameters:

data	holds private internal data
userdata	is a structure that allows data to be passed into the function and derivative evaluation programs.
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 type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’, ‘diagonal’ or ‘absent’ has been violated. -7 The objective function appears to be unbounded from below -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. -82 The user has forced termination of solver by removing the file named control.alive_file from unit unit control.alive_unit.
n	is a scalar variable of type INT that holds the number of variables
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 $x_j$.
g	is a one-dimensional array of size n and type T that holds the gradient $g={\mathrm{\nabla }}_{x}f(x)$ of the objective function. The j-th component of g, j = 1, … , n, contains $g_j$. On successful termination, g will equivalently hold the optimal dual variables, $z$.
ne	is a scalar variable of type INT that holds the number of entries in the lower triangular part of the Hessian matrix $H$.
eval_f	is a user-supplied function that must have the following signature: function eval_f(n, x, f, userdata) The value of the objective function $f(x)$ evaluated at x=$x$ must be assigned to f, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into eval_f via the structure userdata.
eval_g	is a user-supplied function that must have the following signature: function eval_g(n, x, g, userdata) The components of the gradient $g={\mathrm{\nabla }}_{x}f(x$) of the objective function evaluated at x=$x$ must be assigned to g, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into eval_g via the structure userdata.
eval_h	is a user-supplied function that must have the following signature: function eval_h(n, ne, x, h, userdata) The nonzeros of the Hessian $H={\mathrm{\nabla }}_{xx}f(x)$ of the objective function evaluated at x=$x$ must be assigned to h in the same order as presented to trb_import, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into eval_h via the structure userdata.
eval_prec	is an optional user-supplied function that may be C_NULL. If non-NULL, it must have the following signature: function eval_prec(n, x, u, v, userdata) The product $u=P(x)v$ of the user’s preconditioner $P(x)$ evaluated at $x$ with the vector v=$v$, the result $u$ must be retured in u, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into eval_prec via the structure userdata.

    function trb_solve_without_mat(T, INT, data, userdata, status, n, x, g,
                                   eval_f, eval_g, eval_hprod,
                                   eval_shprod, eval_prec)

Find a local minimizer of a given function subject to simple bounds on the variables using a trust-region method.

This call is for the case where access to $H={\mathrm{\nabla }}_{xx}f(x)$ is provided by Hessian-vector products, and all function/derivative information is available by function calls.

Parameters:

data	holds private internal data
userdata	is a structure that allows data to be passed into the function and derivative evaluation programs.
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 type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’, ‘diagonal’ or ‘absent’ has been violated. -7 The objective function appears to be unbounded from below -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. -82 The user has forced termination of solver by removing the file named control.alive_file from unit unit control.alive_unit.
n	is a scalar variable of type INT that holds the number of variables
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 $x_j$.
g	is a one-dimensional array of size n and type T that holds the gradient $g={\mathrm{\nabla }}_{x}f(x)$ of the objective function. The j-th component of g, j = 1, … , n, contains $g_j$. On successful termination, g will equivalently hold the optimal dual variables, $z$.
eval_f	is a user-supplied function that must have the following signature: function eval_f(n, x, f, userdata) The value of the objective function $f(x)$ evaluated at x=$x$ must be assigned to f, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into eval_f via the structure userdata.
eval_g	is a user-supplied function that must have the following signature: function eval_g(n, x, g, userdata) The components of the gradient $g={\mathrm{\nabla }}_{x}f(x$) of the objective function evaluated at x=$x$ must be assigned to g, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into eval_g via the structure userdata.
eval_hprod	is a user-supplied function that must have the following signature: function eval_hprod(n, x, u, v, got_h, userdata) The sum $u+{\mathrm{\nabla }}_{xx}f(x)v$ of the product of the Hessian ${\mathrm{\nabla }}_{xx}f(x)$ of the objective function evaluated at x=$x$ with the vector v=$v$ and the vector $ $u$ must be returned in u, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. The Hessian has already been evaluated or used at x if got_h is true. Data may be passed into eval_hprod via the structure userdata.
eval_shprod	is a user-supplied function that must have the following signature: function eval_shprod(n, x, nnz_v, index_nz_v, v, nnz_u, index_nz_u, u, got_h, userdata) The product $u={\mathrm{\nabla }}_{xx}f(x)v$ of the Hessian ${\mathrm{\nabla }}_{xx}f(x)$ of the objective function evaluated at $x$ with the sparse vector v=$v$ must be returned in u, and the function return value set to 0. Only the components index_nz_v[0:nnz_v-1] of v are nonzero, and the remaining components may not have been be set. On exit, the user must indicate the nnz_u indices of u that are nonzero in index_nz_u[0:nnz_u-1], and only these components of u need be set. If the evaluation is impossible at x, return should be set to a nonzero value. The Hessian has already been evaluated or used at x if got_h is true. Data may be passed into eval_prec via the structure userdata.
eval_prec	is an optional user-supplied function that may be C_NULL. If non-NULL, it must have the following signature: function eval_prec(n, x, u, v, userdata) The product $u=P(x)v$ of the user’s preconditioner $P(x)$ evaluated at $x$ with the vector v=$v$, the result $u$ must be retured in u, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into eval_prec via the structure userdata.

    function trb_solve_reverse_with_mat(T, INT, data, status, eval_status, n, x,
                                        f, g, ne, H_val, u, v)

Find a local minimizer of a given function subject to simple bounds on the variables using a trust-region method.

This call is for the case where $H={\mathrm{\nabla }}_{xx}f(x)$ is provided specifically, but function/derivative information is only available by returning to the calling procedure

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 type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’, ‘diagonal’ or ‘absent’ has been violated. -7 The objective function appears to be unbounded from below -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. -82 The user has forced termination of solver by removing the file named control.alive_file from unit unit control.alive_unit. 2 The user should compute the objective function value $f(x)$ at the point $x$ indicated in x and then re-enter the function. The required value should be set in f, and eval_status should be set to 0. If the user is unable to evaluate $f(x)$ for instance, if the function is undefined at $x$ the user need not set f, but should then set eval_status to a non-zero value. 3 The user should compute the gradient of the objective function ${\mathrm{\nabla }}_{x}f(x)$ at the point $x$ indicated in x and then re-enter the function. The value of the i-th component of the gradient should be set in g[i], for i = 1, …, n and eval_status should be set to 0. If the user is unable to evaluate a component of ${\mathrm{\nabla }}_{x}f(x)$ for instance if a component of the gradient is undefined at $x$ -the user need not set g, but should then set eval_status to a non-zero value. 4 The user should compute the Hessian of the objective function ${\mathrm{\nabla }}_{xx}f(x)$ at the point x indicated in $x$ and then re-enter the function. The value l-th component of the Hessian stored according to the scheme input in the remainder of $H$ should be set in H_val[l], for l = 0, …, ne-1 and eval_status should be set to 0. If the user is unable to evaluate a component of ${\mathrm{\nabla }}_{xx}f(x)$ for instance, if a component of the Hessian is undefined at $x$ the user need not set H_val, but should then set eval_status to a non-zero value. 6 The user should compute the product $u=P(x)v$ of their preconditioner $P(x)$ at the point x indicated in $x$ with the vector $v$ and then re-enter the function. The vector $v$ is given in v, the resulting vector $u=P(x)v$ should be set in u and eval_status should be set to 0. If the user is unable to evaluate the product for instance, if a component of the preconditioner is undefined at $x$ the user need not set u, but should then set eval_status to a non-zero value.
eval_status	is a scalar variable of type INT that is used to indicate if objective function/gradient/Hessian values can be provided (see above)
n	is a scalar variable of type INT that holds the number of variables
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 $x_j$.
f	is a scalar variable pointer of type T that holds the value of the objective function.
g	is a one-dimensional array of size n and type T that holds the gradient $g={\mathrm{\nabla }}_{x}f(x)$ of the objective function. The j-th component of g, j = 1, … , n, contains $g_j$. On successful termination, g will equivalently hold the optimal dual variables, $z$.
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 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.
u	is a one-dimensional array of size n and type T that is used for reverse communication (see above for details)
v	is a one-dimensional array of size n and type T that is used for reverse communication (see above for details)

    function trb_solve_reverse_without_mat(T, INT, data, status, eval_status,
                                           n, x, f, g, u, v, index_nz_v,
                                           nnz_v, index_nz_u, nnz_u)

Find a local minimizer of a given function subject to simple bounds on the variables using a trust-region method.

This call is for the case where access to $H={\mathrm{\nabla }}_{xx}f(x)$ is provided by Hessian-vector products, but function/derivative information is only available by returning to the calling procedure.

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 type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’, ‘diagonal’ or ‘absent’ has been violated. -7 The objective function appears to be unbounded from below -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. -82 The user has forced termination of solver by removing the file named control.alive_file from unit unit control.alive_unit. 2 The user should compute the objective function value $f(x)$ at the point $x$ indicated in x and then re-enter the function. The required value should be set in f, and eval_status should be set to 0. If the user is unable to evaluate $f(x)$ for instance, if the function is undefined at $x$ the user need not set f, but should then set eval_status to a non-zero value. 3 The user should compute the gradient of the objective function ${\mathrm{\nabla }}_{x}f(x)$ at the point $x$ indicated in x and then re-enter the function. The value of the i-th component of the gradient should be set in g[i], for i = 1, …, n and eval_status should be set to 0. If the user is unable to evaluate a component of ${\mathrm{\nabla }}_{x}f(x)$ for instance if a component of the gradient is undefined at $x$ -the user need not set g, but should then set eval_status to a non-zero value. 5 The user should compute the product ${\mathrm{\nabla }}_{xx}f(x)v$ of the Hessian of the objective function ${\mathrm{\nabla }}_{xx}f(x)$ at the point $x$ indicated in x with the vector $v$, add the result to the vector $u$ and then re-enter the function. The vectors $u$ and $v$ are given in u and v respectively, the resulting vector $u+{\mathrm{\nabla }}_{xx}f(x)v$ should be set in u and eval_status should be set to 0. If the user is unable to evaluate the product for instance, if a component of the Hessian is undefined at $x$ the user need not alter u, but should then set eval_status to a non-zero value. 6 The user should compute the product $u=P(x)v$ of their preconditioner $P(x)$ at the point x indicated in $x$ with the vector $v$ and then re-enter the function. The vector $v$ is given in v, the resulting vector $u=P(x)v$ should be set in u and eval_status should be set to 0. If the user is unable to evaluate the product for instance, if a component of the preconditioner is undefined at $x$ the user need not set u, but should then set eval_status to a non-zero value. 7 The user should compute the product $u={\mathrm{\nabla }}_{xx}f(x)v$ of the Hessian of the objective function ${\mathrm{\nabla }}_{xx}f(x)$ at the point $x$ indicated in x with the sparse vector v=$v$ and then re-enter the function. The nonzeros of $v$ are stored in v[index_nz_v[0:nnz_v-1]] while the nonzeros of $u$ should be returned in u[index_nz_u[0:nnz_u-1]]; the user must set nnz_u and index_nz_u accordingly, and set eval_status to 0. If the user is unable to evaluate the product for instance, if a component of the Hessian is undefined at $x$ the user need not alter u, but should then set eval_status to a non-zero value.
eval_status	is a scalar variable of type INT that is used to indicate if objective function/gradient/Hessian values can be provided (see above)
n	is a scalar variable of type INT that holds the number of variables
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 $x_j$.
f	is a scalar variable pointer of type T that holds the value of the objective function.
g	is a one-dimensional array of size n and type T that holds the gradient $g={\mathrm{\nabla }}_{x}f(x)$ of the objective function. The j-th component of g, j = 1, … , n, contains $g_j$.
u	is a one-dimensional array of size n and type T that is used for reverse communication (see status=5,6,7 above for details)
v	is a one-dimensional array of size n and type T that is used for reverse communication (see status=5,6,7 above for details)
index_nz_v	is a one-dimensional array of size n and type INT that is used for reverse communication (see status=7 above for details)
nnz_v	is a scalar variable of type INT that is used for reverse communication (see status=7 above for details)
index_nz_u	is a one-dimensional array of size n and type INT that is used for reverse communication (see status=7 above for details)
nnz_u	is a scalar variable of type INT that is used for reverse communication (see status=7 above for details). On initial (status=1) entry, nnz_u should be set to an (arbitrary) nonzero value, and nnz_u=0 is recommended

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

Provides output information

Parameters:

data	holds private internal data
inform	is a structure containing output information (see trb_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 trb_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 trb_control_type)
inform	is a structure containing output information (see trb_inform_type)