NAG Library Function Document

nag_check_derivs (c05zdc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{mode}$ – IntegerInput

On entry: the value $1$ on the first call and the value $2$ on the second call of nag_check_derivs (c05zdc).

Constraint: $\mathbf{mode}=1$ or $2$.

2:    $\mathbf{m}$ – IntegerInput

On entry: $m$, the number of functions.

Constraint: $\mathbf{m}\ge 1$.

3:    $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of variables. For use with nag_zero_nonlin_eqns_deriv_easy (c05rbc), nag_zero_nonlin_eqns_deriv_expert (c05rcc) and nag_zero_nonlin_eqns_deriv_rcomm (c05rdc), $\mathbf{m}=\mathbf{n}$.

Constraint: $\mathbf{n}\ge 1$.

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

On entry: the components of a point $x$, at which the consistency check is to be made. (See Section 7.)

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

On entry: if $\mathbf{mode}=2$, fvec must contain the value of the functions evaluated at $x$. If $\mathbf{mode}=1$, fvec is not referenced.

6:    $\mathbf{fjac}\left[\mathbf{m}\times \mathbf{n}\right]$ – const doubleInput

Note: the $\left(i,j\right)$th element of the matrix is stored in $\mathbf{fjac}\left[\left(j-1\right)\times \mathbf{m}+i-1\right]$.

On entry: if $\mathbf{mode}=2$, fjac must contain the value of $\frac{\partial f_i}{\partial x_j}$ at the point $x$, for $\mathit{i}=1,2,\dots ,m$ and $\mathit{j}=1,2,\dots ,n$. If $\mathbf{mode}=1$, fjac is not referenced.

7:    $\mathbf{xp}\left[\mathbf{n}\right]$ – doubleOutput

On exit: if $\mathbf{mode}=1$, xp is set to a point neighbouring x. If $\mathbf{mode}=2$, xp is undefined.

8:    $\mathbf{fvecp}\left[\mathbf{m}\right]$ – const doubleInput

On entry: if $\mathbf{mode}=2$, fvecp must contain the value of the functions evaluated at xp (as output by a preceding call to nag_check_derivs (c05zdc) with $\mathbf{mode}=1$). If $\mathbf{mode}=1$, fvecp is not referenced.

9:    $\mathbf{err}\left[\mathbf{m}\right]$ – doubleOutput

On exit: if $\mathbf{mode}=2$, err contains measures of correctness of the respective gradients. If $\mathbf{mode}=1$, err is undefined. If there is no loss of significance (see Section 7), if $\mathbf{err}\left[i-1\right]$ is $1.0$ the $i$th user-supplied gradient $\frac{\partial f_i}{\partial x_j}$, for $\mathit{j}=1,2,\dots ,n$ is correct, whilst if $\mathbf{err}\left[i-1\right]$ is $0.0$ the $i$th gradient is incorrect. For values of $\mathbf{err}\left[i-1\right]$ between $0.0$ and $1.0$ the categorisation is less certain. In general, a value of $\mathbf{err}\left[i-1\right]>0.5$ indicates that the $i$th gradient is probably correct.

10:  $\mathbf{fail}$ – 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_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT

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

On entry, $\mathbf{mode}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{mode}=1$ or $2$.

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

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (c05zdce.c)

10.2

Program Data

10.3

Program Results

Program Results (c05zdce.r)