NAG Toolbox: nag_pde_2d_gen_order2_checkgrid (d03ry)

Purpose

Syntax

Description

 XX XX XX XX XX XX XX XX XX XX XX XX XX XX
 XX 23  3  3  3  3  3  3  3  3  3  3 34 XX
 XX  2 .. .. .. .. .. .. .. .. .. ..  4 XX
 XX  2 .. .. .. .. .. .. .. .. .. ..  4 XX
 XX  2 .. .. 14  1  1  1  1 21 .. ..  4 XX
 XX  2 .. ..  4 XX XX XX XX  2 .. ..  4 XX
 XX  2 .. ..  4 XX XX XX XX  2 .. ..  4 XX
 XX  2 .. ..  4 XX XX XX XX  2 .. ..  4 XX
 XX  2 .. ..  4 XX XX XX XX  2 .. ..  4 XX
 XX  2 .. ..  4 XX XX XX XX  2 .. ..  4 XX
 XX  2 .. .. 43  3  3  3  3 32 .. ..  4 XX
 XX  2 .. .. .. .. .. .. .. .. .. ..  4 XX
 XX  2 .. .. .. .. .. .. .. .. .. ..  4 XX
 XX 12  1  1  1  1  1  1  1  1  1  1 41 XX
 XX XX XX XX XX XX XX XX XX XX XX XX XX XX

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{nx}$ – int64int32nag_int scalar

2:     $\mathrm{ny}$ – int64int32nag_int scalar

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:     $\mathrm{lrow}\left(\mathbf{nrows}\right)$ – int64int32nag_int array

$\mathbf{lrow}\left(\mathit{i}\right)$, 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 $\mathit{i}=2,3,\dots ,\mathbf{nrows}$.

4:     $\mathrm{irow}\left(\mathbf{nrows}\right)$ – int64int32nag_int array

$\mathbf{irow}\left(\mathit{i}\right)$, 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 $\mathit{i}=2,3,\dots ,\mathbf{nrows}$.

5:     $\mathrm{icol}\left(\mathbf{npts}\right)$ – int64int32nag_int array

$\mathbf{icol}\left(\mathit{i}\right)$, 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 $\mathit{i}=1,2,\dots ,\mathbf{npts}$.

6:     $\mathrm{llbnd}\left(\mathbf{nbnds}\right)$ – int64int32nag_int array

$\mathbf{llbnd}\left(\mathit{i}\right)$, 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 $\mathit{i}=2,3,\dots ,\mathbf{nbnds}$.

7:     $\mathrm{ilbnd}\left(\mathbf{nbnds}\right)$ – int64int32nag_int array

$\mathbf{ilbnd}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{nbnds}$, contains the type of the $\mathit{i}$th boundary (or corner), as defined in nag_pde_2d_gen_order2_rectilinear (d03rb).

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 $\mathit{i}=1,2,\dots ,\mathbf{nbnds}$.

8:     $\mathrm{lbnd}\left(\mathbf{nbpts}\right)$ – int64int32nag_int array

$\mathbf{lbnd}\left(\mathit{i}\right)$, 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 $\mathit{i}=1,2,\dots ,\mathbf{nbpts}$.

Optional Input Parameters

1:     $\mathrm{npts}$ – int64int32nag_int scalar

Default: the dimension of the array icol.

The total number of points in the base grid.

Constraint: $\mathbf{npts}\le \mathbf{nx}\times \mathbf{ny}$.

2:     $\mathrm{nrows}$ – int64int32nag_int scalar

Default: the dimension of the arrays lrow, irow. (An error is raised if these dimensions are not equal.)

The total number of rows of the virtual grid that contain base grid points.

Constraint: $4\le \mathbf{nrows}\le \mathbf{ny}$.

3:     $\mathrm{nbnds}$ – int64int32nag_int scalar

Default: the dimension of the arrays llbnd, ilbnd. (An error is raised if these dimensions are not equal.)

The total number of physical boundaries and corners in the base grid.

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

4:     $\mathrm{nbpts}$ – int64int32nag_int scalar

Default: the dimension of the array lbnd.

The total number of boundary points in the base grid.

Constraint: $12\le \mathbf{nbpts}<\mathbf{npts}$.

Output Parameters

1:     $\mathrm{pgrid}\left(\mathbf{ny}\right)$ – cell array of strings

$\mathbf{pgrid}\left(\mathit{i}\right)$, for $\mathit{i}=1,2,\dots ,\mathbf{ny}$, contains a graphical representation of row $\mathbf{ny}-\mathit{i}+1$ of the virtual grid (see Description).

2:     $\mathrm{ifail}$ – int64int32nag_int scalar

$\mathbf{ifail}=\mathbf{0}$ unless the function detects an error (see Error Indicators and Warnings).

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	$\mathit{leniwk}<\mathbf{nx}\times \mathbf{ny}+1$,
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.

   $\mathbf{ifail}=-399$

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

   $\mathbf{ifail}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: d03ry_example

function d03ry_example


fprintf('d03ry example results\n\n');

nx = int64(11);
ny = int64(11);
lrow = int64([1, 4, 15:11:37, 46:11:79, 88, 97]);
irow = int64([0:10]);
icol = int64([0:2, 0:10, 0:10, 0:10, 0:5, 8:10, ...
                0:10, 0:10, 0:10, 0:8, 0:9, 0:8]);
llbnd = int64([1, 2,11,18,19,24,31,37,42,48,53,55,56,58,59,60,61,62, ...
                 63,64,65,66,67,68,69,70,71,72]);
ilbnd = int64([1, 2, 3, 4, 1, 4, 1, 2, 3, 4, 3, 4, 1, 2,12,23,34,41, ...
                 14,41,12,23,34,41,43,14,21,32]);
lbnd  = int64([2, 4, 15:11:37, 46:11:79, 88, 98:104, ...
                96, 86:-1:82, 70:-11:48, 39:-11:6, 8:13, ...
                18:11:40, 49, 60, 72:77, 67:-11:45, 36, 25, ...
                33, 32, 42, 52, 53, 43, 1, 97, 105, 87, 81, ...
                3, 7, 71, 78, 14, 31, 51, 54, 34]);

[pgrid, ifail] = d03ry(nx, ny, lrow, irow, icol, llbnd, ilbnd, lbnd);

disp('Textual representation of grid:');
disp(pgrid);

d03ry example results

Textual representation of grid:
    '  3  3  3  3  3  3  3 34 .. 23 XX'
    '  2 .. .. .. .. .. .. ..  4 XX XX'
    '  2 .. 14  1  1  1  1  1 41 XX XX'
    '  2 ..  4 23  3  3  3  3  3  3 34'
    '  2 ..  4  2 .. .. .. .. .. ..  4'
    '  2 ..  4  2 .. 14  1  1 21 ..  4'
    '  2 ..  4  2 ..  4 XX XX  2 ..  4'
    '  2 ..  4  2 .. 43  3  3 32 ..  4'
    '  2 ..  4  2 .. .. .. .. .. ..  4'
    '  2 ..  4 12  1  1  1  1  1  1 41'
    ' 12  1 41 XX XX XX XX XX XX XX XX'