NAG Library Routine Document

D03RYF

1  Purpose

2  Specification

3  Description

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4  References

5  Parameters

1:     $\mathrm{NX}$ – INTEGERInput

2:     $\mathrm{NY}$ – INTEGERInput

On entry: the number of virtual grid points in the $x$- and $y$-direction respectively (including the boundary points).

Constraint: NX and $\mathbf{NY}\ge 4$.

3:     $\mathrm{NPTS}$ – INTEGERInput

On entry: the total number of points in the base grid.

Constraint: $\mathbf{NPTS}\le \mathbf{NX}\times \mathbf{NY}$.

4:     $\mathrm{NROWS}$ – INTEGERInput

On entry: the total number of rows of the virtual grid that contain base grid points.

Constraint: $4\le \mathbf{NROWS}\le \mathbf{NY}$.

5:     $\mathrm{NBNDS}$ – INTEGERInput

On entry: the total number of physical boundaries and corners in the base grid.

Constraint: $\mathbf{NBNDS}\ge 8$.

6:     $\mathrm{NBPTS}$ – INTEGERInput

On entry: the total number of boundary points in the base grid.

Constraint: $12\le \mathbf{NBPTS}<\mathbf{NPTS}$.

7:     $\mathrm{LROW}\left(\mathbf{NROWS}\right)$ – INTEGER arrayInput

On entry: $\mathbf{LROW}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{NROWS}$, contains the base grid index of the first grid point in base grid row $\mathit{i}$.

Constraints:

• $1\le \mathbf{LROW}\left(\mathit{i}\right)\le \mathbf{NPTS}$, for $\mathit{i}=1,2,\dots ,\mathbf{NROWS}$;
• $\mathbf{LROW}\left(\mathit{i}-1\right)<\mathbf{LROW}\left(\mathit{i}\right)$, for $\mathit{i}=2,3,\dots ,\mathbf{NROWS}$.

8:     $\mathrm{IROW}\left(\mathbf{NROWS}\right)$ – INTEGER arrayInput

On entry: $\mathbf{IROW}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{NROWS}$, contains the virtual grid row number that corresponds to base grid row $\mathit{i}$.

Constraints:

• $0\le \mathbf{IROW}\left(\mathit{i}\right)\le \mathbf{NY}$, for $\mathit{i}=1,2,\dots ,\mathbf{NROWS}$;
• $\mathbf{IROW}\left(\mathit{i}-1\right)<\mathbf{IROW}\left(\mathit{i}\right)$, for $\mathit{i}=2,3,\dots ,\mathbf{NROWS}$.

9:     $\mathrm{ICOL}\left(\mathbf{NPTS}\right)$ – INTEGER arrayInput

On entry: $\mathbf{ICOL}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{NPTS}$, contains the virtual grid column number that contains base grid point $\mathit{i}$.

Constraint: $0\le \mathbf{ICOL}\left(\mathit{i}\right)\le \mathbf{NX}$, for $\mathit{i}=1,2,\dots ,\mathbf{NPTS}$.

10:   $\mathrm{LLBND}\left(\mathbf{NBNDS}\right)$ – INTEGER arrayInput

On entry: $\mathbf{LLBND}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{NBNDS}$, contains the element of LBND corresponding to the start of the $\mathit{i}$th boundary (or corner).

Constraints:

• $1\le \mathbf{LLBND}\left(\mathit{i}\right)\le \mathbf{NBPTS}$, for $\mathit{i}=1,2,\dots ,\mathbf{NBNDS}$;
• $\mathbf{LLBND}\left(\mathit{i}-1\right)<\mathbf{LLBND}\left(\mathit{i}\right)$, for $\mathit{i}=2,3,\dots ,\mathbf{NBNDS}$.

11:   $\mathrm{ILBND}\left(\mathbf{NBNDS}\right)$ – INTEGER arrayInput

On entry: $\mathbf{ILBND}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{NBNDS}$, contains the type of the $\mathit{i}$th boundary (or corner), as defined in D03RBF.

Constraint: $\mathbf{ILBND}\left(\mathit{i}\right)$ must be equal to one of the following: $1$, $2$, $3$, $4$, $12$, $23$, $34$, $41$, $21$, $32$, $43$ or $14$, for $\mathit{i}=1,2,\dots ,\mathbf{NBNDS}$.

12:   $\mathrm{LBND}\left(\mathbf{NBPTS}\right)$ – INTEGER arrayInput

On entry: $\mathbf{LBND}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{NBPTS}$, contains the grid index of the $\mathit{i}$th boundary point.

Constraint: $1\le \mathbf{LBND}\left(\mathit{i}\right)\le \mathbf{NPTS}$, for $\mathit{i}=1,2,\dots ,\mathbf{NBPTS}$.

13:   $\mathrm{IWK}\left(\mathbf{LENIWK}\right)$ – INTEGER arrayWorkspace

14:   $\mathrm{LENIWK}$ – INTEGERInput

On entry: the dimension of the array IWK as declared in the (sub)program from which D03RYF is called.

Constraint: $\mathbf{LENIWK}\ge \mathbf{NX}\times \mathbf{NY}+1$.

15:   $\mathrm{PGRID}\left(\mathbf{NY}\right)$ – CHARACTER(*) arrayOutput

On exit: $\mathbf{PGRID}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{NY}$, contains a graphical representation of row $\mathbf{NY}-\mathit{i}+1$ of the virtual grid (see Section 3).

Constraint: $\mathrm{LEN}\left(\mathbf{PGRID}\left(1\right)\right)\ge 3\times \mathbf{NX}$.

16:   $\mathrm{IFAIL}$ – 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,	NX or $\mathbf{NY}<4$,
or	$\mathbf{NPTS}>\mathbf{NX}\times \mathbf{NY}$,
or	$\mathbf{NROWS}<4$,
or	$\mathbf{NROWS}>\mathbf{NY}$,
or	$\mathbf{NBNDS}<8$,
or	$\mathbf{NBPTS}<12$,
or	$\mathbf{NBPTS}\ge \mathbf{NPTS}$,
or	$\mathbf{LROW}\left(i\right)<1$, for some $i=1,2,\dots ,\mathbf{NROWS}$,
or	$\mathbf{LROW}\left(i\right)>\mathbf{NPTS}$, for some $i=1,2,\dots ,\mathbf{NROWS}$,
or	$\mathbf{LROW}\left(i\right)\le \mathbf{LROW}\left(i-1\right)$, for some $i=2,3,\dots ,\mathbf{NROWS}$,
or	$\mathbf{IROW}\left(i\right)<0$, for some $i=1,2,\dots ,\mathbf{NROWS}$,
or	$\mathbf{IROW}\left(i\right)>\mathbf{NY}$, for some $i=1,2,\dots ,\mathbf{NROWS}$,
or	$\mathbf{IROW}\left(i\right)\le \mathbf{IROW}\left(i-1\right)$, for some $i=2,3,\dots ,\mathbf{NROWS}$,
or	$\mathbf{ICOL}\left(i\right)<0$, for some $i=1,2,\dots ,\mathbf{NPTS}$,
or	$\mathbf{ICOL}\left(i\right)>\mathbf{NX}$, for some $i=1,2,\dots ,\mathbf{NPTS}$,
or	$\mathbf{LLBND}\left(i\right)<1$, for some $i=1,2,\dots ,\mathbf{NBNDS}$,
or	$\mathbf{LLBND}\left(i\right)>\mathbf{NBPTS}$, for some $i=1,2,\dots ,\mathbf{NBNDS}$,
or	$\mathbf{LLBND}\left(i\right)\le \mathbf{LLBND}\left(i-1\right)$, for some $i=2,3,\dots ,\mathbf{NBPTS}$,
or	$\mathbf{ILBND}\left(i\right)\ne 1$, $2$, $3$, $4$, $12$, $23$, $34$, $41$, $21$, $32$, $43$ or $14$, for some $i=1,2,\dots ,\mathbf{NBNDS}$,
or	$\mathbf{LBND}\left(i\right)<1$, for some $i=1,2,\dots ,\mathbf{NBPTS}$,
or	$\mathbf{LBND}\left(i\right)>\mathbf{NPTS}$, for some $i=1,2,\dots ,\mathbf{NBPTS}$,
or	$\mathbf{LENIWK}<\mathbf{NX}\times \mathbf{NY}+1$,
or	$\mathrm{LEN}\left(\mathbf{PGRID}\left(1\right)\right)<3\times \mathbf{NX}$.

$\mathbf{IFAIL}=-99$

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

10  Example