NAG FL Interface
d03pyf (dim1_​parab_​coll_​interp)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{npde}$ – Integer Input

On entry: the number of PDEs.

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

2: $\mathbf{u}\left(\mathbf{npde},\mathbf{npts}\right)$ – Real (Kind=nag_wp) array Input

On entry: the PDE part of the original solution returned in the argument u by the routine d03pdf/​d03pda or d03pjf/​d03pja.

3: $\mathbf{nbkpts}$ – Integer Input

On entry: the number of break-points.

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

4: $\mathbf{xbkpts}\left(\mathbf{nbkpts}\right)$ – Real (Kind=nag_wp) array Input

On entry: $\mathbf{xbkpts}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{nbkpts}$, must contain the break-points as used by d03pdf/​d03pda or d03pjf/​d03pja.

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

5: $\mathbf{npoly}$ – Integer Input

On entry: the degree of the Chebyshev polynomial used for approximation as used by d03pdf/​d03pda or d03pjf/​d03pja.

Constraint: $1\le \mathbf{npoly}\le 49$.

6: $\mathbf{npts}$ – Integer Input

On entry: the number of mesh points as used by d03pdf/​d03pda or d03pjf/​d03pja.

Constraint: $\mathbf{npts}=\left(\mathbf{nbkpts}-1\right)\times \mathbf{npoly}+1$.

7: $\mathbf{xp}\left(\mathbf{intpts}\right)$ – Real (Kind=nag_wp) array Input

On entry: $\mathbf{xp}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{intpts}$, must contain the spatial interpolation points.

Constraints:

• $\mathbf{xbkpts}\left(1\right)\le \mathbf{xp}\left(1\right)<\mathbf{xp}\left(2\right)<\cdots <\mathbf{xp}\left(\mathbf{intpts}\right)\le \mathbf{xbkpts}\left(\mathbf{nbkpts}\right)$;
• if $\mathbf{itype}=2$, $\mathbf{xp}\left(\mathit{i}\right)\ne \mathbf{xbkpts}\left(\mathit{j}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{intpts}$ and $\mathit{j}=2,3,\dots ,\mathbf{nbkpts}-1$.

8: $\mathbf{intpts}$ – Integer Input

On entry: the number of interpolation points.

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

9: $\mathbf{itype}$ – Integer Input

On entry: specifies the interpolation to be performed.

$\mathbf{itype}=1$

The solution at the interpolation points are computed.

$\mathbf{itype}=2$

Both the solution and the first derivative at the interpolation points are computed.

Constraint: $\mathbf{itype}=1$ or $2$.

10: $\mathbf{up}\left(\mathbf{npde},\mathbf{intpts},\mathbf{itype}\right)$ – Real (Kind=nag_wp) array Output

On exit: if $\mathbf{itype}=1$, $\mathbf{up}\left(\mathit{i},\mathit{j},1\right)$, contains the value of the solution $U_{\mathit{i}}\left(x_{\mathit{j}},t_{\mathrm{out}}\right)$, at the interpolation points $x_{\mathit{j}}=\mathbf{xp}\left(\mathit{j}\right)$, for $\mathit{j}=1,2,\dots ,\mathbf{intpts}$ and $\mathit{i}=1,2,\dots ,\mathbf{npde}$.

If $\mathbf{itype}=2$, $\mathbf{up}\left(\mathit{i},\mathit{j},1\right)$ contains $U_{\mathit{i}}\left(x_{\mathit{j}},t_{\mathrm{out}}\right)$ and $\mathbf{up}\left(\mathit{i},\mathit{j},2\right)$ contains $\frac{\partial U_{\mathit{i}}}{\partial x}$ at these points.

11: $\mathbf{rsave}\left(\mathbf{lrsave}\right)$ – Real (Kind=nag_wp) array Communication Array

The array rsave contains information required by d03pyf as returned by d03pdf/​d03pda or d03pjf/​d03pja. The contents of rsave must not be changed from the call to d03pdf/​d03pda or d03pjf/​d03pja. Some elements of this array are overwritten on exit.

12: $\mathbf{lrsave}$ – Integer Input

On entry: the size of the workspace rsave, as in d03pdf/​d03pda or d03pjf/​d03pja.

13: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 4 in the Introduction to the NAG Library FL Interface 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 argument, 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, $\mathit{i}=〈\mathit{\text{value}}〉$, $\mathbf{xbkpts}\left(\mathit{i}\right)=〈\mathit{\text{value}}〉$, $\mathit{j}=〈\mathit{\text{value}}〉$ and $\mathbf{xbkpts}\left(\mathit{j}\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{xbkpts}\left(1\right)<\mathbf{xbkpts}\left(2\right)<\cdots <\mathbf{xbkpts}\left(\mathbf{nbkpts}\right)$.

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

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

On entry, $\mathbf{nbkpts}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nbkpts}\ge 2$.

On entry, $\mathbf{npde}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{npde}>0$.

On entry, $\mathbf{npoly}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{npoly}>0$.

On entry, $\mathbf{npts}=〈\mathit{\text{value}}〉$, $\mathbf{nbkpts}=〈\mathit{\text{value}}〉$ and $\mathbf{npoly}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{npts}=\left(\mathbf{nbkpts}-1\right)\times \mathbf{npoly}+1$.

$\mathbf{ifail}=2$

On entry, $\mathit{i}=〈\mathit{\text{value}}〉$, $\mathbf{xp}\left(\mathit{i}\right)=〈\mathit{\text{value}}〉$, $\mathit{j}=〈\mathit{\text{value}}〉$ and $\mathbf{xp}\left(\mathit{j}\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{xbkpts}\left(1\right)\le \mathbf{xp}\left(1\right)<\mathbf{xp}\left(2\right)<\cdots <\mathbf{xp}\left(\mathbf{intpts}\right)\le \mathbf{xbkpts}\left(\mathbf{nbkpts}\right)$.

On entry, $\mathbf{itype}=2$ and at least one interpolation point coincides with a break-point, i.e., interpolation point no $〈\mathit{\text{value}}〉$ with value $〈\mathit{\text{value}}〉$ is close to break-point $〈\mathit{\text{value}}〉$ with value $〈\mathit{\text{value}}〉$.

$\mathbf{ifail}=3$

Extrapolation is not allowed.

$\mathbf{ifail}=-99$

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

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

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

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example