nagcpp::opt::handle_set_nlnls (e04rm) : NAG Library, Mark 28

1 Purpose

handle_set_nlnls is a part of the NAG optimization modelling suite and defines the residual functions for nonlinear regression problems (such as nonlinear least squares and general nonlinear data fitting) with the given number of residuals and, optionally, the sparsity structure of their first derivatives.

2 Specification

#include "e04/nagcpp_e04rm.hpp" #include "e04/nagcpp_class_CommE04RA.hpp"

template <typename COMM, typename IROWRD, typename ICOLRD> void function handle_set_nlnls(COMM &comm, const types::f77_integer nres, const IROWRD &irowrd, const ICOLRD &icolrd, OptionalE04RM opt)

template <typename COMM, typename IROWRD, typename ICOLRD> void function handle_set_nlnls(COMM &comm, const types::f77_integer nres, const IROWRD &irowrd, const ICOLRD &icolrd)

3 Description

After the handle has been initialized (e.g., handle_init has been called), handle_set_nlnls may be used to define the residual functions in the objective function of nonlinear least squares or general nonlinear data fitting problems. If the objective function has already been defined, it will be overwritten. It will typically be used in data fitting or calibration problems of the form

\begin{array}{l} \underset{x \in ℝ^{n}}{minimize} & f (x) = \sum_{j = 1}^{m_{r}} χ (r_{j} (x)) \\ subject to & l_{x} \leq x \leq u_{x}, \end{array}

where

x

is an

n

-dimensional variable vector,

r_{j} (x)

are nonlinear residuals (see Section 2.2.3 in the E04 Chapter Introduction), and

χ

is a type of loss function. For example, the model of a least squares problem can be written as

\begin{array}{l} \underset{x \in ℝ^{n}}{minimize} & f (x) = \sum_{j = 1}^{m_{r}} {r_{j} (x)}^{2} \\ subject to & l_{x} \leq x \leq u_{x}, \end{array}

The values of the residuals, and possibly their derivatives, will be communicated to the solver by a user-supplied function. handle_set_nlnls also allows the structured first derivative matrix

{[\frac{\partial r_{j} (x)}{\partial x_{i}}]}_{i = 1, \dots, n, ​ j = 1, \dots, m_{r}}

to be declared as being dense or sparse. If declared as sparse, its sparsity structure must be specified by handle_set_nlnls. If handle_set_nlnls is called with

m_{r} = 0

, any existing objective function is removed, no new one is added and the problem will be solved as a feasible point problem. Note that it is possible to temporarily disable and enable individual residuals in the model by e04tcf (no CPP interface) and e04tbf (no CPP interface), respectively.

See Section 3.1 in the E04 Chapter Introduction for more details about the NAG optimization modelling suite.

5 Arguments

comm

– CommE04RA Input/Output

Communication structure. An object of either the derived class CommE04RA or its base class NoneCopyableComm can be supplied. It is recommended that the derived class is used. If the base class is supplied it must first be initialized via a call to opt::handle_init (e04ra).

nres

– types::f77_integer Input

On entry:

m_{r}

, the number of residuals in the objective function.

nres = 0

, no objective function will be defined and irowrd and icolrd will not be referenced.

Constraint:

nres \geq 0

irowrd (nnzrd)

– types::f77_integer array Input

On entry: arrays irowrd and icolrd store the sparsity structure (pattern) of the first derivative matrix as nnzrd nonzeros in coordinate storage (CS) format (see Section 2.1.1 in the F11 Chapter Introduction). The matrix has dimensions

n \times m_{r}

. irowrd specifies one-based row indices and icolrd specifies one-based column indices. No particular order of elements is expected, but elements should not repeat and the same order should be used when the first derivative matrix is evaluated for the solver.

If irowrd and icolrd are both nullptr then the first derivative matrix is considered dense and irowrd and icolrd will not be referenced. The ordering is assumed to be column-wise, namely the function will behave as if

nnzrd = n \times m_{r}

and the vectors irowrd and icolrd filled as:

$irowrd = (1, 2, \dots, n, 1, 2, \dots, n, \dots, 1, 2, \dots, n)$ ;
$icolrd = (1, 1, \dots, 1, 2, 2, \dots, 2, \dots, m_{r}, m_{r}, \dots, m_{r})$ .

Constraints:

$1 \leq irowrd (l - 1) \leq n$ , for $l = 1, 2, \dots, nnzrd$ ;
$1 \leq icolrd (l - 1) \leq nres$ , for $l = 1, 2, \dots, nnzrd$ .

icolrd (nnzrd)

– types::f77_integer array Input

n \times m_{r}

nnzrd = n \times m_{r}

and the vectors irowrd and icolrd filled as:

$irowrd = (1, 2, \dots, n, 1, 2, \dots, n, \dots, 1, 2, \dots, n)$ ;
$icolrd = (1, 1, \dots, 1, 2, 2, \dots, 2, \dots, m_{r}, m_{r}, \dots, m_{r})$ .

Constraints:

$1 \leq irowrd (l - 1) \leq n$ , for $l = 1, 2, \dots, nnzrd$ ;
$1 \leq icolrd (l - 1) \leq nres$ , for $l = 1, 2, \dots, nnzrd$ .

opt

– OptionalE04RM Input/Output

Optional parameter container, derived from Optional.

5.1Additional Quantities

1: $nnzrd$: The number of nonzeros in the first derivative matrix.

6 Exceptions and Warnings

Errors or warnings detected by the function:

All errors and warnings have an associated numeric error code field, errorid, stored either as a member of the thrown exception object (see errorid), or as a member of opt.ifail, depending on how errors and warnings are being handled (see Error Handling for more details).

Raises: ErrorException

$errorid = 9$: All of the following must be provided if one is provided:
irowrd, icolrd.

$errorid = 1$: comm::handle has not been initialized.

$errorid = 1$: comm::handle does not belong to the NAG optimization modelling suite,
has not been initialized properly or is corrupted.

$errorid = 1$: comm::handle has not been initialized properly or is corrupted.

$errorid = 2$: The problem cannot be modified right now, the solver is running.

$errorid = 6$: On entry, $nres = ⟨ value ⟩$ .
Constraint: $nres \geq 0$ .

$errorid = 6$: On entry, $nnzrd = ⟨ value ⟩$ .
Constraint: $nnzrd > 0$ .

$errorid = 8$: On entry, $i = ⟨ value ⟩$ , $irowrd [i - 1] = ⟨ value ⟩$ and
$n = ⟨ value ⟩$ .
Constraint: $1 \leq irowrd [i - 1] \leq n$ .

$errorid = 8$: On entry, $i = ⟨ value ⟩$ , $icolrd [i - 1] = ⟨ value ⟩$ and
$nres = ⟨ value ⟩$ .
Constraint: $1 \leq icolrd [i - 1] \leq nres$ .

$errorid = 8$: On entry, more than one element of first derivative matrix has row index
$⟨ value ⟩$ and column index $⟨ value ⟩$ .
Constraint: each element of first derivative matrix must have a unique
row and column index.

$errorid = 10601$: On entry, argument $⟨ value ⟩$ must be a vector of size $⟨ value ⟩$ array.
Supplied argument has $⟨ value ⟩$ dimensions.

$errorid = 10601$: On entry, argument $⟨ value ⟩$ must be a vector of size $⟨ value ⟩$ array.
Supplied argument was a vector of size $⟨ value ⟩$ .

$errorid = 10601$: On entry, argument $⟨ value ⟩$ must be a vector of size $⟨ value ⟩$ array.
The size for the supplied array could not be ascertained.

$errorid = 10602$: On entry, the raw data component of $⟨ value ⟩$ is null.

$errorid = 10603$: On entry, unable to ascertain a value for $⟨ value ⟩$ .

$errorid = 10605$: On entry, the communication class $⟨ value ⟩$ has not been initialized correctly.

$errorid = −99$: An unexpected error has been triggered by this routine.

$errorid = −399$: Your licence key may have expired or may not have been installed correctly.

$errorid = −999$: Dynamic memory allocation failed.

NAG CPP Interface
nagcpp::opt::handle_set_nlnls (e04rm)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

5.1Additional Quantities

6 Exceptions and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

NAG CPP Interfacenagcpp::opt::handle_set_nlnls (e04rm)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

5.1Additional Quantities

6 Exceptions and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

NAG CPP Interface
nagcpp::opt::handle_set_nlnls (e04rm)