?trnlsp_solve

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

Version

Public

?trnlsp_solve

Solves a nonlinear least squares problem using the TR algorithm.

Syntax

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

MKL_INTdtrnlsp_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):R^{n} → 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(1)[0]`
-3	`\|\|F(x)\|\|_{2} < eps(2)[1]`
-4	The Jacobian matrix is singular. `\|\|J(x)`_(1:m,j)_{[m(j-1)…mj-1]}`\|\|`₂ :code:` < ` `eps(3)[2], j = 1, ..., n`
-5	`\|\|s\|\|_{2} < eps(4)[3]`
-6	`\|\|F(x)\|\|_{2} - \|\|F(x) - J(x)s\|\|_{2} < eps(5)[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)[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.hmkl_rci.fi include file.

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?trnlsp_solve

Syntax

Include Files

Description

Input Parameters

Output Parameters