naginterfaces.library.roots.sys_​deriv_​check

naginterfaces.library.roots.sys_deriv_check(mode, x, fvec, fjac, fvecp)

sys_deriv_check checks the user-supplied gradients of a set of nonlinear functions in several variables, for consistency with the functions themselves. The function must be called twice.

For full information please refer to the NAG Library document for c05zd

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/c05/c05zdf.html

Parameters

modeint

The value $1$ on the first call and the value $2$ on the second call of sys_deriv_check.

xfloat, array-like, shape $\left(n\right)$

The components of a point $x$, at which the consistency check is to be made. (See Accuracy.)

fvecfloat, array-like, shape $\left(m\right)$

If $mode=2$, $fvec$ must contain the value of the functions evaluated at $x$. If $mode=1$, $fvec$ is not referenced.

fjacfloat, array-like, shape $(m,n)$

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

fvecpfloat, array-like, shape $\left(m\right)$

If $mode=2$, $fvecp$ must contain the value of the functions evaluated at $xp$ (as output by a preceding call to sys_deriv_check with $mode=1$). If $mode=1$, $fvecp$ is not referenced.

Returns

xpfloat, ndarray, shape $\left(n\right)$

If $mode=1$, $xp$ is set to a point neighbouring $x$. If $mode=2$, $xp$ is undefined.

errfloat, ndarray, shape $\left(m\right)$

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

Raises

NagValueError

(errno $1$)

On entry, $mode=⟨value⟩$.

Constraint: $mode=1$ or $2$.

(errno $2$)

On entry, $m=⟨value⟩$.

Constraint: $m\ge 1$.

(errno $3$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 1$.

Notes

sys_deriv_check is based on the MINPACK routine CHKDER (see Moré et al. (1980)). It checks the $i$th gradient for consistency with the $i$th function by computing a forward-difference approximation along a suitably chosen direction and comparing this approximation with the user-supplied gradient along the same direction. The principal characteristic of sys_deriv_check is its invariance under changes in scale of the variables or functions.

References

Moré, J J, Garbow, B S and Hillstrom, K E, 1980, User guide for MINPACK-1, Technical Report ANL-80-74, Argonne National Laboratory