?trnlspbc

Initializes the solver of nonlinear least squares problem with linear (boundary) constraints.

Syntax

Fortran:

res = strnlspbc_init(handle, n, m, x, LW, UP, eps, iter1, iter2, rs)

res = dtrnlspbc_init(handle, n, m, x, LW, UP, eps, iter1, iter2, rs)

res = strnlspbc_init(&handle, &n, &m, x, LW, UP, eps, &iter1, &iter2, &rs);

res = dtrnlspbc_init(&handle, &n, &m, x, LW, UP, eps, &iter1, &iter2, &rs);

Include Files

The Fortran interfaces are specified in the mkl_rci.fi include file and the C interfaces are specified in the mkl_rci.h include file.

Description

The ?trnlspbc_init routine initializes the solver.

After initialization all subsequent invocations of the ?trnlspbc_solve routine should use the values of the handle returned by ?trnlspbc_init.

The eps array contains the stopping criteria:

eps Value	Description
1	`Δ < eps(1)`
2	`\|\|F(x)\|\|₂ < eps(2)`
3	The Jacobian matrix is singular. `\|\|J(x)_(1:m,j)\|\|₂ < eps(3), j = 1, ..., n`
4	`\|\|s\|\|₂ < eps(4)`
5	`\|\|F(x)\|\|₂ - \|\|F(x) - J(x)s\|\|₂ < eps(5)`
6	The trial step precision. If `eps(6)` = 0, then the trial step meets the required precision (≤ 1.0D-10).

Note:

J(x) is the Jacobian matrix.
Δ is the trust-region area.
F(x) is the value of the functional.
s is the trial step.

Input Parameters

n

INTEGER. Length of x.

m

INTEGER. Length of F(x).

x

REAL for strnlspbc_init

DOUBLE PRECISION for dtrnlspbc_init

Array of size n. Initial guess.

LW

REAL for strnlspbc_init

DOUBLE PRECISION for dtrnlspbc_init

Array of size n.

Contains low bounds for x (lw_i < x_i ).

UP

REAL for strnlspbc_init

DOUBLE PRECISION for dtrnlspbc_init

Array of size n.

Contains upper bounds for x (up_i > x_i ).

eps

REAL for strnlspbc_init

DOUBLE PRECISION for dtrnlspbc_init

Array of size 6; contains stopping criteria. See the values in the Description section.

iter1

INTEGER. Specifies the maximum number of iterations.

iter2

INTEGER. Specifies the maximum number of iterations of trial step calculation.

rs

REAL for strnlspbc_init

DOUBLE PRECISION for dtrnlspbc_init

Definition of initial size of the trust region (boundary of the trial step). The minimum value is 0.1, and the maximum value is 100.0. Based on your knowledge of the objective function and initial guess you can increase or decrease the initial trust region. It can influence the iteration process, for example, the direction of the iteration process and the number of iterations. The default value is 100.0.

Output Parameters

handle

Type _TRNSPBC_HANDLE_t in C/C++ and INTEGER*8 in FORTRAN.

res

INTEGER. Informs about the task completion.

res = TR_SUCCESS - the routine completed the task normally.
res = TR_INVALID_OPTION - there was an error in the input parameters.
res = TR_OUT_OF_MEMORY - there was a memory error.

TR_SUCCESS, TR_INVALID_OPTION, and TR_OUT_OF_MEMORY are defined in mkl_rci.fi (Fortran) and mkl_rci.h (C) include files.