?trnlsp_solve

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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?trnlsp_solve

Solves a nonlinear least squares problem using the TR algorithm.

Syntax

MKL_INT strnlsp_solve (_TRNSP_HANDLE_t* handle, float* fvec, float* fjac, MKL_INT* RCI_Request);

MKL_INT dtrnlsp_solve (_TRNSP_HANDLE_t* handle, double* fvec, double* fjac, MKL_INT* RCI_Request);

Include Files

mkl.h

Description

The ?trnlsp_solve routine uses the TR algorithm to solve nonlinear least squares problems.

The problem is stated as follows:

where

F(x):Rⁿ → R^m
m ≥ n

From a current point x_current, the algorithm uses the trust-region approach:

to get x_new = x_current + s that satisfies

where

J(x) is the Jacobian matrix
s is the trial step
||s||₂ ≤ Δ_current
Δ is the trust-region area.

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[0]`
-3	`\|\|F(x)\|\|₂ < eps[1]`
-4	The Jacobian matrix is singular. `\|\|J(x)_{[m(j-1)...mj-1]}\|\|₂ < eps[2], j = 1, ..., n`
-5	`\|\|s\|\|₂ < eps[3]`
-6	`\|\|F(x)\|\|₂ - \|\|F(x) - J(x)s\|\|₂ < eps[4]`

NOTE:

If it is possible to combine computations of the function and the jacobian (RCI_Request = 1 and 2), you can do that and provide both updated values for fvec and fjac as fulfillment of RCI_Request =1 (and do nothing for RCI_Request = 2).

Input Parameters

handle: Type _TRNSP_HANDLE_t.
fvec: Array of size m. Contains the function values at X, where fvec[i] = (y_i – f_i(x)).
fjac: Array of size m by n. Contains the Jacobian matrix of the function.

Output Parameters

fvec

Array of size m. Updated function evaluated at x.

RCI_Request

Informs about the task stage.

See the Description section for the parameter values and their meaning.

res

Indicates the task completion.

res = TR_SUCCESS - the routine completed the task normally.

TR_SUCCESS is defined in the mkl_rci.h include file.

Parent topic: Nonlinear Least Squares Problem without Constraints

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?trnlsp_solve