NAG Library Routine Document

D03NEF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{T0}$ – REAL (KIND=nag_wp)Input

On entry: the current time $t_0$.

Constraint: $\mathbf{TD}\left(1\right)\le \mathbf{T0}\le \mathbf{TD}\left(\mathbf{NTD}\right)$.

2:     $\mathrm{TMAT}$ – REAL (KIND=nag_wp)Input

On entry: the maturity time $T$.

Constraint: $\mathbf{TD}\left(1\right)\le \mathbf{TMAT}\le \mathbf{TD}\left(\mathbf{NTD}\right)$.

3:     $\mathrm{NTD}$ – INTEGERInput

On entry: the number of discrete times at which $\varphi$ is given.

Constraint: $\mathbf{NTD}\ge 2$.

4:     $\mathrm{TD}\left(\mathbf{NTD}\right)$ – REAL (KIND=nag_wp) arrayInput

On entry: the discrete times at which $\varphi$ is specified.

Constraint: $\mathbf{TD}\left(1\right)<\mathbf{TD}\left(2\right)<\cdots <\mathbf{TD}\left(\mathbf{NTD}\right)$.

5:     $\mathrm{PHID}\left(\mathbf{NTD}\right)$ – REAL (KIND=nag_wp) arrayInput

On entry: $\mathbf{PHID}\left(\mathit{i}\right)$ must contain the value of $\varphi$ at time $\mathbf{TD}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{NTD}$.

6:     $\mathrm{PHIAV}\left(3\right)$ – REAL (KIND=nag_wp) arrayOutput

On exit: $\mathbf{PHIAV}\left(1\right)$ contains the value of $\varphi$ interpolated to $t_0$, $\mathbf{PHIAV}\left(2\right)$ contains the first-order average $\hat{\varphi }$ and $\mathbf{PHIAV}\left(3\right)$ contains the second-order average $\stackrel{-}{\varphi }$, where:

$$\begin{array}{cc}\hat{\varphi }=\frac{1}{T-t_0}\underset{t_0}{\overset{T}{\int }}\varphi \left(\zeta \right)d\zeta \text{, \hspace{1em}}& \stackrel{-}{\varphi }={\left(\frac{1}{T-t_0}\underset{t_0}{\overset{T}{\int }}{\varphi }^2\left(\zeta \right)d\zeta \right)}^{1/2}\text{.}\end{array}$$

7:     $\mathrm{WORK}\left(\mathbf{LWORK}\right)$ – REAL (KIND=nag_wp) arrayWorkspace

8:     $\mathrm{LWORK}$ – INTEGERInput

On entry: the dimension of the array WORK as declared in the (sub)program from which D03NEF is called.

Constraint: $\mathbf{LWORK}\ge 9\times \mathbf{NTD}+24$.

9:     $\mathrm{IFAIL}$ – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry,	T0 lies outside the range [$\mathbf{TD}\left(1\right),\mathbf{TD}\left(\mathbf{NTD}\right)$],
or	TMAT lies outside the range [$\mathbf{TD}\left(1\right),\mathbf{TD}\left(\mathbf{NTD}\right)$],
or	$\mathbf{NTD}<2$,
or	TD badly ordered,
or	$\mathbf{LWORK}<9\times \mathbf{NTD}+24$.

$\mathbf{IFAIL}=2$

Unexpected failure in internal call to E01BAF or E02BBF.

$\mathbf{IFAIL}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.8 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.7 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-999$

Dynamic memory allocation failed.

See Section 3.6 in the Essential Introduction for further information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

9.1  Timing

9.2  Use with D03NDF

9.3  Algorithmic Details

10  Example

10.1  Program Text

Program Text (d03nefe.f90)

10.2  Program Data

Program Data (d03nefe.d)

10.3  Program Results

Program Results (d03nefe.r)