Contents

# ?trnlsp_solve

Solves a nonlinear least squares problem using the TR algorithm.

## Syntax

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
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

-3
||
F
(
x
)||
2
<
eps

-4
The Jacobian matrix is singular.
||
J
(
x
)
[
m
*(
j
-1)...
m
*
j
-1]
||
2
<
eps

,
j
= 1, ...,
n
-5
||
s
||
2
<
eps

-6
||
F
(
x
)||
2
- ||
F
(
x
) -
J
(
x
)
s
||
2
<
eps

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
See the Description section for the parameter values and their meaning.
res
res
=
TR_SUCCESS
- the routine completed the task normally.
TR_SUCCESS
is defined in the
mkl_rci.h
include file.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.