NAG Library Function Document

nag_opt_lsq_check_deriv (e04yac)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{m}$ – IntegerInput

2:    $\mathbf{n}$ – IntegerInput

On entry: the number $m$ of residuals, $f_i\left(x\right)$, and the number $n$ of variables, $x_j$.

Constraint: $1\le \mathbf{n}\le \mathbf{m}$.

3:    $\mathbf{lsqfun}$ – function, supplied by the userExternal Function

lsqfun must calculate the vector of values $f_i\left(x\right)$ and their first derivatives $\frac{\partial f_i}{\partial x_j}$ at any point $x$. (The minimization function nag_opt_lsq_deriv (e04gbc) gives you the option of resetting an argument, $\mathbf{comm}\mathbf{\to }\mathbf{flag}$, to terminate the minimization process immediately. nag_opt_lsq_check_deriv (e04yac) will also terminate immediately, without finishing the checking process, if the argument in question is reset to a negative value.)

The specification of lsqfun is:

void  lsqfun (Integer m, Integer n, const double x[], double fvec[], double fjac[], Integer tdfjac, Nag_Comm *comm)

1:    $\mathbf{m}$ – IntegerInput

2:    $\mathbf{n}$ – IntegerInput

On entry: the numbers $m$ and $n$ of residuals and variables, respectively.

3:    $\mathbf{x}\left[\mathbf{n}\right]$ – const doubleInput

On entry: the point $x$ at which the values of the $f_i$ and the $\frac{\partial f_i}{\partial x_j}$ are required.

4:    $\mathbf{fvec}\left[\mathbf{m}\right]$ – doubleOutput

On exit: unless $\mathbf{comm}\mathbf{\to }\mathbf{flag}$ is reset to a negative number, then $\mathbf{fvec}\left[\mathit{i}-1\right]$ must contain the value of $f_{\mathit{i}}$ at the point $x$, for $\mathit{i}=1,2,\dots ,m$.

5:    $\mathbf{fjac}\left[\mathbf{m}\times \mathbf{tdfjac}\right]$ – doubleOutput

On exit: unless $\mathbf{comm}\mathbf{\to }\mathbf{flag}$ is reset to a negative number, then the value in $\mathbf{fjac}\left[\left(\mathit{i}-1\right)\times \mathbf{tdfjac}+\mathit{j}-1\right]$ must be the first derivative $\frac{\partial f_{\mathit{i}}}{\partial x_{\mathit{j}}}$ at the point x, for $\mathit{i}=1,2,\dots ,m$ and $\mathit{j}=1,2,\dots ,n$.

6:    $\mathbf{tdfjac}$ – IntegerInput

On entry: the stride separating matrix column elements in the array fjac.

7:    $\mathbf{comm}$ – Nag_Comm *

Pointer to structure of type Nag_Comm; the following members are relevant to lsqfun.

flag – IntegerInput/Output

On entry: $\mathbf{comm}\mathbf{\to }\mathbf{flag}$ will be set to 2.

On exit: if lsqfun resets $\mathbf{comm}\mathbf{\to }\mathbf{flag}$ to some negative number then nag_opt_lsq_check_deriv (e04yac) will terminate immediately with the error indicator NE_USER_STOP. If fail is supplied to nag_opt_lsq_check_deriv (e04yac), $\mathbf{fail}\mathbf{.}\mathbf{errnum}$ will be set to your setting of $\mathbf{comm}\mathbf{\to }\mathbf{flag}$.

first – Nag_BooleanInput

On entry: will be set to Nag_TRUE on the first call to lsqfun and Nag_FALSE for all subsequent calls.

nf – IntegerInput

On entry: the number of calls made to lsqfun including the current one.

user – double *

iuser – Integer *

p – Pointer 

The type Pointer will be void * with a C compiler that defines void * and char * otherwise. Before calling nag_opt_lsq_check_deriv (e04yac) these pointers may be allocated memory and initialized with various quantities for use by lsqfun when called from nag_opt_lsq_check_deriv (e04yac).

Note: lsqfun should not return floating-point NaN (Not a Number) or infinity values, since these are not handled by nag_opt_lsq_check_deriv (e04yac). If your code inadvertently does return any NaNs or infinities, nag_opt_lsq_check_deriv (e04yac) is likely to produce unexpected results.

The array x must not be changed within lsqfun.

4:    $\mathbf{x}\left[\mathbf{n}\right]$ – const doubleInput

On entry: $\mathbf{x}\left[\mathit{j}-1\right]$, for $\mathit{j}=1,2,\dots ,n$, must be set to the coordinates of a suitable point at which to check the derivatives calculated by lsqfun. ‘Obvious’ settings, such as 0.0 or 1.0, should not be used since, at such particular points, incorrect terms may take correct values (particularly zero), so that errors can go undetected. For a similar reason, it is preferable that no two elements of x should have the same value.

5:    $\mathbf{fvec}\left[\mathbf{m}\right]$ – doubleOutput

On exit: unless $\mathbf{comm}\mathbf{\to }\mathbf{flag}$ is set negative in the first call of lsqfun, $\mathbf{fvec}\left[\mathit{i}-1\right]$ contains the value of $f_{\mathit{i}}$ at the point given in x, for $\mathit{i}=1,2,\dots ,m$.

6:    $\mathbf{fjac}\left[\mathbf{m}\times \mathbf{tdfjac}\right]$ – doubleOutput

On exit: unless $\mathbf{comm}\mathbf{\to }\mathbf{flag}$ is set negative in the first call of lsqfun, $\mathbf{fjac}\left[\left(\mathit{i}-1\right)\times \mathbf{tdfjac}+\mathit{j}-1\right]$ contains the value of the first derivative $\frac{\partial f_{\mathit{i}}}{\partial x_{\mathit{j}}}$ at the point given in x, as calculated by lsqfun, for $\mathit{i}=1,2,\dots ,m$ and $\mathit{j}=1,2,\dots ,n$.

7:    $\mathbf{tdfjac}$ – IntegerInput

On entry: the stride separating matrix column elements in the array fjac.

Constraint: $\mathbf{tdfjac}\ge \mathbf{n}$.

8:    $\mathbf{comm}$ – Nag_Comm *Input/Output

Note: comm is a NAG defined type (see Section 3.3.1.1 in How to Use the NAG Library and its Documentation).

On entry/exit: structure containing pointers for communication to the user-defined function; see the above description of lsqfun for details. If you do not need to make use of this communication feature the null pointer NAGCOMM_NULL may be used in the call to nag_opt_lsq_check_deriv (e04yac); comm will then be declared internally for use in calls to lsqfun.

9:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_2_INT_ARG_LT

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$ while $\mathbf{n}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{m}\ge \mathbf{n}$.

On entry, $\mathbf{tdfjac}=〈\mathit{\text{value}}〉$ while $\mathbf{n}=〈\mathit{\text{value}}〉$. These arguments must satisfy $\mathbf{tdfjac}\ge \mathbf{n}$.

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_DERIV_ERRORS

Large errors were found in the derivatives of the objective function. You should check carefully the derivation and programming of expressions for the $\frac{\partial f_i}{\partial x_j}$, because it is very unlikely that lsqfun is calculating them correctly.

NE_INT_ARG_LT

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

NE_USER_STOP

User requested termination, user flag value $=〈\mathit{\text{value}}〉$.

This exit occurs if you set $\mathbf{comm}\mathbf{\to }\mathbf{flag}$ to a negative value in lsqfun. If fail is supplied the value of $\mathbf{fail}\mathbf{.}\mathbf{errnum}$ will be the same as your setting of $\mathbf{comm}\mathbf{\to }\mathbf{flag}$. The check on lsqfun will not have been completed.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (e04yace.c)

10.2

Program Data

Program Data (e04yace.d)

10.3

Program Results

Program Results (e04yace.r)