overview of functions provided

// typedefs

typedef float spc_;
typedef double rpc_;
typedef int ipc_;

// structs

struct nls_subproblem_control_type;
struct nls_control_type;
struct nls_subproblem_inform_type;
struct nls_inform_type;
struct nls_time_type;

// function calls

void nls_initialize(
    void **data,
    struct nls_control_type* control,
    struct nls_inform_type* inform
);

void nls_read_specfile(struct nls_control_type* control, const char specfile[]);

void nls_import(
    struct nls_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ m,
    const char J_type[],
    ipc_ J_ne,
    const ipc_ J_row[],
    const ipc_ J_col[],
    const ipc_ J_ptr[],
    const char H_type[],
    ipc_ H_ne,
    const ipc_ H_row[],
    const ipc_ H_col[],
    const ipc_ H_ptr[],
    const char P_type[],
    ipc_ P_ne,
    const ipc_ P_row[],
    const ipc_ P_col[],
    const ipc_ P_ptr[],
    const rpc_ w[]
);

void nls_reset_control(
    struct nls_control_type* control,
    void **data,
    ipc_ *status
);

void nls_solve_with_mat(
    void **data,
    void *userdata,
    ipc_ *status,
    ipc_ n,
    ipc_ m,
    rpc_ x[],
    rpc_ c[],
    rpc_ g[],
    ipc_(*)(ipc_, ipc_, const rpc_[], rpc_[], const void*) eval_c,
    ipc_ j_ne,
    ipc_(*)(ipc_, ipc_, ipc_, const rpc_[], rpc_[], const void*) eval_j,
    ipc_ h_ne,
    ipc_(*)(ipc_, ipc_, ipc_, const rpc_[], const rpc_[], rpc_[], const void*) eval_h,
    ipc_ p_ne,
    ipc_(*)(ipc_, ipc_, ipc_, const rpc_[], const rpc_[], rpc_[], bool, const void*) eval_hprods
);

void nls_solve_without_mat(
    void **data,
    void *userdata,
    ipc_ *status,
    ipc_ n,
    ipc_ m,
    rpc_ x[],
    rpc_ c[],
    rpc_ g[],
    ipc_(*)(ipc_, ipc_, const rpc_[], rpc_[], const void*) eval_c,
    ipc_(*)(ipc_, ipc_, const rpc_[], const bool, rpc_[], const rpc_[], bool, const void*) eval_jprod,
    ipc_(*)(ipc_, ipc_, const rpc_[], const rpc_[], rpc_[], const rpc_[], bool, const void*) eval_hprod,
    ipc_ p_ne,
    ipc_(*)(ipc_, ipc_, ipc_, const rpc_[], const rpc_[], rpc_[], bool, const void*) eval_hprods
);

void nls_solve_reverse_with_mat(
    void **data,
    ipc_ *status,
    ipc_ *eval_status,
    ipc_ n,
    ipc_ m,
    rpc_ x[],
    rpc_ c[],
    rpc_ g[],
    ipc_ j_ne,
    rpc_ J_val[],
    const rpc_ y[],
    ipc_ h_ne,
    rpc_ H_val[],
    rpc_ v[],
    ipc_ p_ne,
    rpc_ P_val[]
);

void nls_solve_reverse_without_mat(
    void **data,
    ipc_ *status,
    ipc_ *eval_status,
    ipc_ n,
    ipc_ m,
    rpc_ x[],
    rpc_ c[],
    rpc_ g[],
    bool* transpose,
    rpc_ u[],
    rpc_ v[],
    rpc_ y[],
    ipc_ p_ne,
    rpc_ P_val[]
);

void nls_information(void **data, struct nls_inform_type* inform, ipc_ *status);

void nls_terminate(
    void **data,
    struct nls_control_type* control,
    struct nls_inform_type* inform
);

typedefs

typedef float spc_

spc_ is real single precision

typedef double rpc_

rpc_ is the real working precision used, but may be changed to float by defining the preprocessor variable SINGLE.

typedef int ipc_

ipc_ is the default integer word length used, but may be changed to int64_t by defining the preprocessor variable INTEGER_64.

function calls

void nls_initialize(
    void **data,
    struct nls_control_type* control,
    struct nls_inform_type* inform
)

Set default control values and initialize private data

Parameters:

data	holds private internal data
control	is a struct containing control information (see nls_control_type)
inform	is a struct containing output information (see nls_inform_type)

void nls_read_specfile(struct nls_control_type* control, const char specfile[])

Read the content of a specification file, and assign values associated with given keywords to the corresponding control parameters. An in-depth discussion of specification files is available, and a detailed list of keywords with associated default values is provided in $GALAHAD/src/nls/NLS.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/nls.pdf for a list of how these keywords relate to the components of the control structure.

Parameters:

control	is a struct containing control information (see nls_control_type)
specfile	is a character string containing the name of the specification file

void nls_import(
    struct nls_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    ipc_ m,
    const char J_type[],
    ipc_ J_ne,
    const ipc_ J_row[],
    const ipc_ J_col[],
    const ipc_ J_ptr[],
    const char H_type[],
    ipc_ H_ne,
    const ipc_ H_row[],
    const ipc_ H_col[],
    const ipc_ H_ptr[],
    const char P_type[],
    ipc_ P_ne,
    const ipc_ P_row[],
    const ipc_ P_col[],
    const ipc_ P_ptr[],
    const rpc_ w[]
)

Import problem data into internal storage prior to solution.

Parameters:

control	is a struct whose members provide control paramters for the remaining prcedures (see nls_control_type)
data	holds private internal data
status	is a scalar variable of type ipc_, that gives the exit status from the package. Possible values are: 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 restrictions n > 0, m > 0 or requirement that J/H/P_type contains its relevant string ‘dense’, ‘dense_by_columns’, ‘coordinate’, ‘sparse_by_rows’, ‘sparse_by_columns’, ‘diagonal’ or ‘absent’ has been violated.
n	is a scalar variable of type ipc_, that holds the number of variables.
m	is a scalar variable of type ipc_, that holds the number of residuals.
J_type	is a one-dimensional array of type char that specifies the unsymmetric storage scheme used for the Jacobian, \(J\). It should be one of ‘coordinate’, ‘sparse_by_rows’, ‘dense’ or ‘absent’, the latter if access to the Jacobian is via matrix-vector products; lower or upper case variants are allowed.
J_ne	is a scalar variable of type ipc_, that holds the number of entries in \(J\) in the sparse co-ordinate storage scheme. It need not be set for any of the other schemes.
J_row	is a one-dimensional array of size J_ne and type ipc_, that holds the row indices of \(J\) in the sparse co-ordinate storage scheme. It need not be set for any of the other schemes, and in this case can be NULL.
J_col	is a one-dimensional array of size J_ne and type ipc_, that holds the column indices of \(J\) in either the sparse co-ordinate, or the sparse row-wise storage scheme. It need not be set when the dense or diagonal storage schemes are used, and in this case can be NULL.
J_ptr	is a one-dimensional array of size m+1 and type ipc_, that holds the starting position of each row of \(J\), as well as the total number of entries, in the sparse row-wise storage scheme. It need not be set when the other schemes are used, and in this case can be NULL.
H_type	is a one-dimensional array of type char that specifies the symmetric storage scheme used for the Hessian, \(H\). It should be one of ‘coordinate’, ‘sparse_by_rows’, ‘dense’, ‘diagonal’ or ‘absent’, the latter if access to \(H\) is via matrix-vector products; lower or upper case variants are allowed.
H_ne	is a scalar variable of type ipc_, that holds the number of entries in the lower triangular part of \(H\) in the sparse co-ordinate storage scheme. It need not be set for any of the other three schemes.
H_row	is a one-dimensional array of size H_ne and type ipc_, that holds the row indices of the lower triangular part of \(H\) in the sparse co-ordinate storage scheme. It need not be set for any of the other three schemes, and in this case can be NULL.
H_col	is a one-dimensional array of size H_ne and type ipc_, that holds the column indices of the lower triangular part of \(H\) in either the sparse co-ordinate, or the sparse row-wise storage scheme. It need not be set when the dense or diagonal storage schemes are used, and in this case can be NULL.
H_ptr	is a one-dimensional array of size n+1 and type ipc_, that holds the starting position of each row of the lower triangular part of \(H\), as well as the total number of entries, in the sparse row-wise storage scheme. It need not be set when the other schemes are used, and in this case can be NULL.
P_type	is a one-dimensional array of type char that specifies the unsymmetric storage scheme used for the residual-Hessians-vector product matrix, \(P\). It should be one of ‘coordinate’, ‘sparse_by_columns’, ‘dense_by_columns’ or ‘absent’, the latter if access to \(P\) is via matrix-vector products; lower or upper case variants are allowed.
P_ne	is a scalar variable of type ipc_, that holds the number of entries in \(P\) in the sparse co-ordinate storage scheme. It need not be set for any of the other schemes.
P_row	is a one-dimensional array of size P_ne and type ipc_, that holds the row indices of \(P\) in either the sparse co-ordinate, or the sparse column-wise storage scheme. It need not be set when the dense storage scheme is used, and in this case can be NULL.
P_col	is a one-dimensional array of size P_ne and type ipc_, that holds the row indices of \(P\) in the sparse co-ordinate storage scheme. It need not be set for any of the other schemes, and in this case can be NULL.
P_ptr	is a one-dimensional array of size n+1 and type ipc_, that holds the starting position of each row of \(P\), as well as the total number of entries, in the sparse row-wise storage scheme. It need not be set when the other schemes are used, and in this case can be NULL.
w	is a one-dimensional array of size m and type rpc_, that holds the values \(w\) of the weights on the residuals in the least-squares objective function. It need not be set if the weights are all ones, and in this case can be NULL.

void nls_reset_control(
    struct nls_control_type* control,
    void **data,
    ipc_ *status
)

Reset control parameters after import if required.

Parameters:

control	is a struct whose members provide control paramters for the remaining prcedures (see nls_control_type)
data	holds private internal data
status	is a scalar variable of type ipc_, that gives the exit status from the package. Possible values are: The import was successful, and the package is ready for the solve phase

void nls_solve_with_mat(
    void **data,
    void *userdata,
    ipc_ *status,
    ipc_ n,
    ipc_ m,
    rpc_ x[],
    rpc_ c[],
    rpc_ g[],
    ipc_(*)(ipc_, ipc_, const rpc_[], rpc_[], const void*) eval_c,
    ipc_ j_ne,
    ipc_(*)(ipc_, ipc_, ipc_, const rpc_[], rpc_[], const void*) eval_j,
    ipc_ h_ne,
    ipc_(*)(ipc_, ipc_, ipc_, const rpc_[], const rpc_[], rpc_[], const void*) eval_h,
    ipc_ p_ne,
    ipc_(*)(ipc_, ipc_, ipc_, const rpc_[], const rpc_[], rpc_[], bool, const void*) eval_hprods
)

Find a local minimizer of a given function using a trust-region method.

This call is for the case where \(H = \nabla_{xx}f(x)\) 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 ipc_, 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. -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. -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 ipc_, that holds the number of variables.
m	is a scalar variable of type ipc_, that holds the number of residuals.
x	is a one-dimensional array of size n and type rpc_, that holds the values \(x\) of the optimization variables. The j-th component of x, j = 0, … , n-1, contains \(x_j\).
c	is a one-dimensional array of size m and type rpc_, that holds the residual \(c(x)\). The i-th component of c, j = 0, … , n-1, contains \(c_j(x)\).
g	is a one-dimensional array of size n and type rpc_, that holds the gradient \(g = \nabla_xf(x)\) of the objective function. The j-th component of g, j = 0, … , n-1, contains \(g_j\).
eval_c	is a user-supplied function that must have the following signature: ipc_ eval_c( ipc_ n, const rpc_ x[], rpc_ c[], const void *userdata ) The componnts of the residual function \(c(x)\) evaluated at x= \(x\) must be assigned to c, 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_c via the structure userdata.
j_ne	is a scalar variable of type ipc_, that holds the number of entries in the Jacobian matrix \(J\).
eval_j	is a user-supplied function that must have the following signature: ipc_ eval_j( ipc_ n, ipc_ m, ipc_ jne, const rpc_ x[], rpc_ j[], const void *userdata ) The components of the Jacobian \(J = \nabla_x c(x\)) of the residuals must be assigned to j in the same order as presented to nls_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_j via the structure userdata.
h_ne	is a scalar variable of type ipc_, that holds the number of entries in the lower triangular part of the Hessian matrix \(H\) if it is used.
eval_h	is a user-supplied function that must have the following signature: ipc_ eval_h( ipc_ n, ipc_ m, ipc_ hne, const rpc_ x[], const rpc_ y[], rpc_ h[], const void *userdata ) The nonzeros of the matrix \(H = \sum_{i=1}^m y_i \nabla_{xx}c_i(x)\) of the weighted residual Hessian evaluated at x= \(x\) and y= \(y\) must be assigned to h in the same order as presented to nls_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.
p_ne	is a scalar variable of type ipc_, that holds the number of entries in the residual-Hessians-vector product matrix \(P\) if it is used.
eval_hprods	is an optional user-supplied function that may be NULL. If non-NULL, it must have the following signature: ipc_ eval_hprods( ipc_ n, ipc_ m, ipc_ pne, const rpc_ x[], const rpc_ v[], rpc_ p[], bool got_h, const void *userdata ) ); The entries of the matrix \(P\), whose i-th column is the product \(\nabla_{xx}c_i(x) v\) between \(\nabla_{xx}c_i(x)\), the Hessian of the i-th component of the residual \(c(x)\) at x= \(x\), and v= \(v\) must be returned in p 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_hprods via the structure userdata.

void nls_solve_without_mat(
    void **data,
    void *userdata,
    ipc_ *status,
    ipc_ n,
    ipc_ m,
    rpc_ x[],
    rpc_ c[],
    rpc_ g[],
    ipc_(*)(ipc_, ipc_, const rpc_[], rpc_[], const void*) eval_c,
    ipc_(*)(ipc_, ipc_, const rpc_[], const bool, rpc_[], const rpc_[], bool, const void*) eval_jprod,
    ipc_(*)(ipc_, ipc_, const rpc_[], const rpc_[], rpc_[], const rpc_[], bool, const void*) eval_hprod,
    ipc_ p_ne,
    ipc_(*)(ipc_, ipc_, ipc_, const rpc_[], const rpc_[], rpc_[], bool, const void*) eval_hprods
)

Find a local minimizer of a given function using a trust-region method.

This call is for the case where access to \(H = \nabla_{xx}f(x)\) 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 ipc_, 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. -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. -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 ipc_, that holds the number of variables
m	is a scalar variable of type ipc_, that holds the number of residuals.
x	is a one-dimensional array of size n and type rpc_, that holds the values \(x\) of the optimization variables. The j-th component of x, j = 0, … , n-1, contains \(x_j\).
c	is a one-dimensional array of size m and type rpc_, that holds the residual \(c(x)\). The i-th component of c, j = 0, … , n-1, contains \(c_j(x)\).
g	is a one-dimensional array of size n and type rpc_, that holds the gradient \(g = \nabla_xf(x)\) of the objective function. The j-th component of g, j = 0, … , n-1, contains \(g_j\).
eval_c	is a user-supplied function that must have the following signature: ipc_ eval_c( ipc_ n, const rpc_ x[], rpc_ c[], const void *userdata ) The componnts of the residual function \(c(x)\) evaluated at x= \(x\) must be assigned to c, 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_c via the structure userdata.
eval_jprod	is a user-supplied function that must have the following signature: ipc_ eval_jprod( ipc_ n, ipc_ m, const rpc_ x[], bool transpose, rpc_ u[], const rpc_ v[], bool got_j, const void *userdata ) The sum \(u + \nabla_{x}c_(x) v\) (if tranpose is false) or The sum \(u + (\nabla_{x}c_(x))^T v\) (if tranpose is true) bewteen the product of the Jacobian \(\nabla_{x}c_(x)\) or its tranpose 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. Data may be passed into eval_jprod via the structure userdata.
eval_hprod	is a user-supplied function that must have the following signature: ipc_ eval_hprod( ipc_ n, ipc_ m, const rpc_ x[], const rpc_ y[], rpc_ u[], const rpc_ v[], bool got_h, const void *userdata ) The sum \(u + \sum_{i=1}^m y_i \nabla_{xx}c_i(x) v\) of the product of the weighted residual Hessian \(H = \sum_{i=1}^m y_i \nabla_{xx}c_i(x)\) evaluated at x= \(x\) and y= \(y\) 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 Hessians have already been evaluated or used at x if got_h is true. Data may be passed into eval_hprod via the structure userdata.
p_ne	is a scalar variable of type ipc_, that holds the number of entries in the residual-Hessians-vector product matrix \(P\) if it is used.
eval_hprods	is an optional user-supplied function that may be NULL. If non-NULL, it must have the following signature: ipc_ eval_hprods( ipc_ n, ipc_ m, ipc_ p_ne, const rpc_ x[], const rpc_ v[], rpc_ pval[], bool got_h, const void *userdata ) The entries of the matrix \(P\), whose i-th column is the product \(\nabla_{xx}c_i(x) v\) between \(\nabla_{xx}c_i(x)\), the Hessian of the i-th component of the residual \(c(x)\) at x= \(x\), and v= \(v\) must be returned in pval 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_hprods via the structure userdata.

void nls_solve_reverse_with_mat(
    void **data,
    ipc_ *status,
    ipc_ *eval_status,
    ipc_ n,
    ipc_ m,
    rpc_ x[],
    rpc_ c[],
    rpc_ g[],
    ipc_ j_ne,
    rpc_ J_val[],
    const rpc_ y[],
    ipc_ h_ne,
    rpc_ H_val[],
    rpc_ v[],
    ipc_ p_ne,
    rpc_ P_val[]
)

Find a local minimizer of a given function using a trust-region method.

This call is for the case where \(H = \nabla_{xx}f(x)\) 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 ipc_, 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. -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. -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 vector of residuals \(c(x)\) at the point \(x\) indicated in x and then re-enter the function. The required value should be set in c, and eval_status should be set to 0. If the user is unable to evaluate \(c(x)\) for instance, if the function is undefined at \(x\) the user need not set c, but should then set eval_status to a non-zero value. 3 The user should compute the Jacobian of the vector of residual functions, \(\nabla_x c(x)\), at the point \(x\) indicated in x and then re-enter the function. The l-th component of the Jacobian stored according to the scheme specified for the remainder of \(J\) in the earlier call to nls_import should be set in J_val[l], for l = 0, …, J_ne-1 and eval_status should be set to 0. If the user is unable to evaluate a component of \(J\) for instance, if a component of the matrix is undefined at \(x\) the user need not set J_val, but should then set eval_status to a non-zero value. 4 The user should compute the matrix \(H = \sum_{i=1}^m v_i \nabla_{xx}c_i(x)\) of weighted residual Hessian evaluated at x= \(x\) and v= \(v\) and then re-enter the function. The l-th component of the matrix stored according to the scheme specified for the remainder of \(H\) in the earlier call to nls_import should be set in H_val[l], for l = 0, …, H_ne-1 and eval_status should be set to 0. If the user is unable to evaluate a component of \(H\) for instance, if a component of the matrix is undefined at \(x\) the user need not set H_val, but should then set eval_status to a non-zero value. Note that this return will not happen if the Gauss-Newton model is selected. 7 The user should compute the entries of the matrix \(P\), whose i-th column is the product \(\nabla_{xx}c_i(x) v\) between \(\nabla_{xx}c_i(x)\), the Hessian of the i-th component of the residual \(c(x)\) at x= \(x\), and v= \(v\) and then re-enter the function. The l-th component of the matrix stored according to the scheme specified for the remainder of \(P\) in the earlier call to nls_import should be set in P_val[l], for l = 0, …, P_ne-1 and eval_status should be set to 0. If the user is unable to evaluate a component of \(P\) for instance, if a component of the matrix is undefined at \(x\) the user need not set P_val, but should then set eval_status to a non-zero value. Note that this return will not happen if either the Gauss-Newton or Newton models is selected.
eval_status	is a scalar variable of type ipc_, that is used to indicate if objective function/gradient/Hessian values can be provided (see above)
n	is a scalar variable of type ipc_, that holds the number of variables
m	is a scalar variable of type ipc_, that holds the number of residuals.
x	is a one-dimensional array of size n and type rpc_, that holds the values \(x\) of the optimization variables. The j-th component of x, j = 0, … , n-1, contains \(x_j\).
c	is a one-dimensional array of size m and type rpc_, that holds the residual \(c(x)\). The i-th component of c, j = 0, … , n-1, contains \(c_j(x)\). See status = 2, above, for more details.
g	is a one-dimensional array of size n and type rpc_, that holds the gradient \(g = \nabla_xf(x)\) of the objective function. The j-th component of g, j = 0, … , n-1, contains \(g_j\).
j_ne	is a scalar variable of type ipc_, that holds the number of entries in the Jacobian matrix \(J\).
J_val	is a one-dimensional array of size j_ne and type rpc_, that holds the values of the entries of the Jacobian matrix \(J\) in any of the available storage schemes. See status = 3, above, for more details.
y	is a one-dimensional array of size m and type rpc_, that is used for reverse communication. See status = 4 above for more details.
h_ne	is a scalar variable of type ipc_, that holds the number of entries in the lower triangular part of the Hessian matrix \(H\).
H_val	is a one-dimensional array of size h_ne and type rpc_, that holds the values of the entries of the lower triangular part of the Hessian matrix \(H\) in any of the available storage schemes. See status = 4, above, for more details.
v	is a one-dimensional array of size n and type rpc_, that is used for reverse communication. See status = 7, above, for more details.
p_ne	is a scalar variable of type ipc_, that holds the number of entries in the residual-Hessians-vector product matrix, \(P\).
P_val	is a one-dimensional array of size p_ne and type rpc_, that holds the values of the entries of the residual-Hessians-vector product matrix, \(P\). See status = 7, above, for more details.

void nls_solve_reverse_without_mat(
    void **data,
    ipc_ *status,
    ipc_ *eval_status,
    ipc_ n,
    ipc_ m,
    rpc_ x[],
    rpc_ c[],
    rpc_ g[],
    bool* transpose,
    rpc_ u[],
    rpc_ v[],
    rpc_ y[],
    ipc_ p_ne,
    rpc_ P_val[]
)

Find a local minimizer of a given function using a trust-region method.

This call is for the case where access to \(H = \nabla_{xx}f(x)\) 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 ipc_, 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. -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. -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 vector of residuals \(c(x)\) at the point \(x\) indicated in x and then re-enter the function. The required value should be set in c, and eval_status should be set to 0. If the user is unable to evaluate \(c(x)\) for instance, if the function is undefined at \(x\) the user need not set c, but should then set eval_status to a non-zero value. 5 The user should compute the sum \(u + \nabla_{x}c_(x) v\) (if tranpose is false) or \(u + (\nabla_{x}c_(x))^T v\) (if tranpose is true) between the product of the Jacobian \(\nabla_{x}c_(x)\) or its tranpose with the vector v= \(v\) and the vector u = $ \(u\), and then re-enter the function. The result should be set in u, and eval_status should be set to 0. If the user is unable to evaluate the sum for instance, if the Jacobian is undefined at \(x\) the user need not set u, but should then set eval_status to a non-zero value. 6 The user should compute the sum \(u + \sum_{i=1}^m y_i \nabla_{xx}c_i(x) v\) between the product of the weighted residual Hessian \(H = \sum_{i=1}^m y_i \nabla_{xx}c_i(x)\) evaluated at x= \(x\) and y= \(y\) with the vector v= \(v\) and the the vector u = $ \(u\), and then re-enter the function. The result should be set in u, and eval_status should be set to 0. If the user is unable to evaluate the sum for instance, if the weifghted residual Hessian 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 entries of the matrix \(P\), whose i-th column is the product \(\nabla_{xx}c_i(x) v\) between \(\nabla_{xx}c_i(x)\), the Hessian of the i-th component of the residual \(c(x)\) at x= \(x\), and v= \(v\) and then re-enter the function. The l-th component of the matrix stored according to the scheme specified for the remainder of \(P\) in the earlier call to nls_import should be set in P_val[l], for l = 0, …, P_ne-1 and eval_status should be set to 0. If the user is unable to evaluate a component of \(P\) for instance, if a component of the matrix is undefined at \(x\) the user need not set P_val, but should then set eval_status to a non-zero value. Note that this return will not happen if either the Gauss-Newton or Newton models is selected.
eval_status	is a scalar variable of type ipc_, that is used to indicate if objective function/gradient/Hessian values can be provided (see above)
n	is a scalar variable of type ipc_, that holds the number of variables
m	is a scalar variable of type ipc_, that holds the number of residuals.
x	is a one-dimensional array of size n and type rpc_, that holds the values \(x\) of the optimization variables. The j-th component of x, j = 0, … , n-1, contains \(x_j\).
c	is a one-dimensional array of size m and type rpc_, that holds the residual \(c(x)\). The i-th component of c, j = 0, … , n-1, contains \(c_j(x)\). See status = 2, above, for more details.
g	is a one-dimensional array of size n and type rpc_, that holds the gradient \(g = \nabla_xf(x)\) of the objective function. The j-th component of g, j = 0, … , n-1, contains \(g_j\).
transpose	is a scalar variable of type bool, that indicates whether the product with Jacobian or its transpose should be obtained when status=5.
u	is a one-dimensional array of size max(n,m) and type rpc_, that is used for reverse communication. See status = 5,6 above for more details.
v	is a one-dimensional array of size max(n,m) and type rpc_, that is used for reverse communication. See status = 5,6,7 above for more details.
y	is a one-dimensional array of size m and type rpc_, that is used for reverse communication. See status = 6 above for more details.
p_ne	is a scalar variable of type ipc_, that holds the number of entries in the residual-Hessians-vector product matrix, \(P\).
P_val	is a one-dimensional array of size P_ne and type rpc_, that holds the values of the entries of the residual-Hessians-vector product matrix, \(P\). See status = 7, above, for more details.

void nls_information(void **data, struct nls_inform_type* inform, ipc_ *status)

Provides output information

Parameters:

data	holds private internal data
inform	is a struct containing output information (see nls_inform_type)
status	is a scalar variable of type ipc_, that gives the exit status from the package. Possible values are (currently): 0 The values were recorded successfully

void nls_terminate(
    void **data,
    struct nls_control_type* control,
    struct nls_inform_type* inform
)

Deallocate all internal private storage

Parameters:

data	holds private internal data
control	is a struct containing control information (see nls_control_type)
inform	is a struct containing output information (see nls_inform_type)