naginterfaces.library.ode.ivp_​adams_​rootdiag

naginterfaces.library.ode.ivp_adams_rootdiag(neqg, comm)

ivp_adams_rootdiag is a diagnostic function which may be called after a call to the integrator functions ivp_adams_roots() or ivp_adams_roots_revcom().

For full information please refer to the NAG Library document for d02qy

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/d02/d02qyf.html

Parameters

neqgint

The number of event functions defined for the integration function. It must be the same argument $neqg$ supplied to the setup function ivp_adams_setup() and to the integration function (ivp_adams_roots() or ivp_adams_roots_revcom()).

commdict, communication object

Communication structure.

This argument must have been initialized by prior calls to ivp_adams_setup() and one of ivp_adams_roots() or ivp_adams_roots_revcom().

Returns

indexint

The index $k$ of the event equation $g_k(x,y,y^{\prime })=0$ for which the root has been detected.

itypeint

Information about the root detected for the event equation defined by $index$. The possible values of $itype$ with their interpretations are as follows:

$itype=1$

A simple root, or lack of distinguishing information available.

$itype=2$

A root of even multiplicity is believed to have been detected, that is no change in sign of the event function was found.

$itype=3$

A high-order root of odd multiplicity.

$itype=4$

A possible root, but due to high multiplicity or a clustering of roots accurate evaluation of the event function was prohibited by round-off error and/or cancellation.

In general, the accuracy of the root is less reliable for values of $itype>1$.

eventsint, ndarray, shape $\left(neqg\right)$

Information about the $k$th event function on a very small interval containing the root, $\text{t}$ (see ivp_adams_roots() and ivp_adams_roots_revcom()), as output from the integration function. All roots lying in this interval are considered indistinguishable numerically and, therefore, should be regarded as defining a root at $\text{t}$. The possible values of $events[k-1]$ with their interpretations are as follows:

$events[k-1]=0$

The $k$th event function did not have a root.

$events[k-1]=-1$

The $k$th event function changed sign from positive to negative about a root, in the direction of integration.

$events[k-1]=1$

The $k$th event function changed sign from negative to positive about a root, in the direction of integration.

$events[k-1]=2$

A root was identified, but no change in sign was observed.

residsfloat, ndarray, shape $\left(neqg\right)$

The value of the $k$th event function computed at the root, $\text{t}$ (see ivp_adams_roots() and ivp_adams_roots_revcom()).

Raises

NagValueError

(errno $1$)

On entry, $neqg=⟨value⟩$ and $\text{neqg}=⟨value⟩$ in ivp_adams_setup().

Constraint: $neqg=\text{neqg}$ in ivp_adams_setup().

(errno $1$)

The integrator did not end at an event.

(errno $1$)

Neither of the appropriate two integrator functions has been called.

Notes

In the NAG Library the traditional C interface for this routine uses a different algorithmic base. Please contact NAG if you have any questions about compatibility.

ivp_adams_rootdiag should be called only after a call to ivp_adams_roots() or ivp_adams_roots_revcom() results in the output value $\text{root}=True$, indicating that a root has been detected. ivp_adams_rootdiag permits you to examine information about the root detected, such as the indices of the event equations for which there is a root, the type of root (odd or even) and the residuals of the event equations.