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), then if
${\mathbf{ERR}}\left(i\right)$ 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
${\mathbf{ERR}}\left(i\right)$ is
$0.0$ the
$i$th gradient is incorrect. For values of
${\mathbf{ERR}}\left(i\right)$ between
$0.0$ and
$1.0$ the categorisation is less certain. In general, a value of
${\mathbf{ERR}}\left(i\right)>0.5$ indicates that the
$i$th gradient is probably correct.