Solves a nonlinear least squares problem with linear (bound) constraints using the Trust-Region algorithm.
Syntax
Fortran:
res = strnlspbc_solve(handle, fvec, fjac, RCI_Request)
res = dtrnlspbc_solve(handle, fvec, fjac, RCI_Request)
C:
res = strnlspbc_solve(&handle, fvec, fjac, &RCI_Request);
res = dtrnlspbc_solve(&handle, fvec, fjac, &RCI_Request);
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_solve routine, based on RCI, uses the Trust-Region algorithm to solve nonlinear least squares problems with linear (bound) constraints. The problem is stated as follows:
where
li ≤ xi ≤ ui
i = 1, ..., n.
The RCI_Request parameter provides additional information:
RCI_Request Value |
Description |
|---|---|
2 |
Request to calculate the Jacobian matrix and put the result into fjac |
1 |
Request to recalculate the function at vector X and put the result into fvec |
0 |
One successful iteration step on the current trust-region radius (that does not mean that the value of x has changed) |
-1 |
The algorithm has exceeded the maximum number of iterations |
-2 |
Δ < eps(1) |
-3 |
||F(x)||2 < eps(2) |
-4 |
The Jacobian matrix is singular. ||J(x)(1:m,j)||2 < eps(3), j = 1, ..., n |
-5 |
||s||2 < eps(4) |
-6 |
||F(x)||2 - ||F(x) - J(x)s||2 < eps(5) |
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
- handle
Type _TRNSPBC_HANDLE_t in C/C++ and INTEGER*8 in FORTRAN.
- fvec
REAL for strnlspbc_solve
DOUBLE PRECISION for dtrnlspbc_solve
Array of size m. Contains the function values at X, where fvec(i) = (yi – fi(x)).
- fjac
REAL for strnlspbc_solve
DOUBLE PRECISION for dtrnlspbc_solve
Array of size m by n. Contains the Jacobian matrix of the function.
Output Parameters
- fvec
REAL for strnlspbc_solve
DOUBLE PRECISION for dtrnlspbc_solve
Array of size m. Updated function evaluated at x.
- RCI_Request
INTEGER. Informs about the task stage.
See the Description section for the parameter values and their meaning.
- res
INTEGER. Informs about the task completion.
res = TR_SUCCESS means the routine completed the task normally.
TR_SUCCESS is defined in the mkl_rci.h and mkl_rci.fi include files.