NAG Toolbox: nag_interp_4d_scat_shep_eval (e01tl)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{x}\left(4,\mathbf{m}\right)$ – double array

Note: the coordinates of $x_r$ are stored in $\mathbf{x}\left(1,r\right)\dots \mathbf{x}\left(4,r\right)$.

must be the same array supplied as argument x in the preceding call to nag_interp_4d_scat_shep (e01tk). It must remain unchanged between calls.

2:     $\mathrm{f}\left(\mathbf{m}\right)$ – double array

must be the same array supplied as argument f in the preceding call to nag_interp_4d_scat_shep (e01tk). It must remain unchanged between calls.

3:     $\mathrm{iq}\left(2\times \mathbf{m}+1\right)$ – int64int32nag_int array

must be the same array returned as argument iq in the preceding call to nag_interp_4d_scat_shep (e01tk). It must remain unchanged between calls.

4:     $\mathrm{rq}\left(15\times \mathbf{m}+9\right)$ – double array

must be the same array returned as argument rq in the preceding call to nag_interp_4d_scat_shep (e01tk). It must remain unchanged between calls.

5:     $\mathrm{xe}\left(4,\mathbf{n}\right)$ – double array

$\mathbf{xe}\left(1:4,\mathit{i}\right)$ must be set to the evaluation point ${\mathbf{x}}_{\mathit{i}}$ , for $\mathit{i}=1,2,\dots ,n$.

Optional Input Parameters

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

Default: the dimension of the array f and the first dimension of the array x. (An error is raised if these dimensions are not equal.)

must be the same value supplied for argument m in the preceding call to nag_interp_4d_scat_shep (e01tk).

Constraint: $\mathbf{m}\ge 16$.

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

Default: the second dimension of the array xe.

$n$, the number of evaluation points.

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

Output Parameters

1:     $\mathrm{q}\left(\mathbf{n}\right)$ – double array

$\mathbf{q}\left(\mathit{i}\right)$ contains the value of the interpolant, at ${\mathbf{x}}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$. If any of these evaluation points lie outside the region of definition of the interpolant the corresponding entries in q are set to the largest machine representable number (see nag_machine_real_largest (x02al)), and nag_interp_4d_scat_shep_eval (e01tl) returns with $\mathbf{ifail}=\mathbf{3}$.

2:     $\mathrm{qx}\left(4,\mathbf{n}\right)$ – double array

$\mathbf{qx}\left(j,i\right)$ contains the value of the partial derivatives with respect to ${\mathbf{x}}_j$ of the interpolant $Q\left(\mathbf{x}\right)$ at ${\mathbf{x}}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$, and for each of the four partial derivatives $j=1,2,3,4$. If any of these evaluation points lie outside the region of definition of the interpolant, the corresponding entries in qx are set to the largest machine representable number (see nag_machine_real_largest (x02al)), and nag_interp_4d_scat_shep_eval (e01tl) returns with $\mathbf{ifail}=\mathbf{3}$.

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

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

Error Indicators and Warnings

   $\mathbf{ifail}=1$

Constraint: $\mathbf{m}\ge 16$.

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

   $\mathbf{ifail}=2$

On entry, values in iq appear to be invalid. Check that iq has not been corrupted between calls to nag_interp_4d_scat_shep (e01tk) and nag_interp_4d_scat_shep_eval (e01tl).

On entry, values in rq appear to be invalid. Check that rq has not been corrupted between calls to nag_interp_4d_scat_shep (e01tk) and nag_interp_4d_scat_shep_eval (e01tl).

   $\mathbf{ifail}=3$

On entry, at least one evaluation point lies outside the region of definition of the interpolant.

   $\mathbf{ifail}=-99$

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: e01tl_example

function e01tl_example


fprintf('e01tl example results\n\n');

genid = int64(1);
subid = int64(1);
seed  = [int64(1762543)];
seed2 = [int64(43331)];


% Initialize the generator to a repeatable sequence
[state, ifail] = g05kf(genid, subid, seed);

% Generate the data points x
[state, x, ifail] = g05sa(int64(120), state);

% Put x into the right shape for the e01 routines
x = reshape(x, 4, 30);

% Create function values
c1 = cos(6*x(1,:));
c2 = cos(6*x(2,:));
c3 = 6 + 6*(3*x(3,:)-1).^2;
c4 = 1.25 + cos(5.4*x(4,:));
f  = c4.*c1.*c2./c3;


% Generate the interpolant
nq = int64(0);
nw = int64(0);
[iq, rq, ifail] = e01tk(x, f, nw, nq);

% Generate repeatable evaluation points
[state, ifail] = g05kf(genid, subid, seed2);
[state, xe, ifail] = g05sa(int64(32), state);
xe = reshape(xe, 4, 8);

% Evaluate the interpolant
[q, qx, ifail] = e01tl(x, f, iq, rq, xe);

% Evaluate function at xe
c1  = cos(6*xe(1,:));
c2  = cos(6*xe(2,:));
c3  = 6 + 6*(3*xe(3,:)-1).^2;
c4  = 1.25 + cos(5.4*xe(4,:));
fun = c4.*c1.*c2./c3;

fprintf('\n i |  f(i)       q(i)   |f(i)-q(i)|\n');
fprintf('---|--------------------+---------+\n');
for i=1:8
  fprintf(' %d |%8.4f  %8.4f  %8.4f \n', i, fun(i), q(i), abs(fun(i)-q(i)));
end

e01tl example results


 i |  f(i)       q(i)   |f(i)-q(i)|
---|--------------------+---------+
 1 | -0.0189   -0.0394    0.0205 
 2 | -0.0186    0.0967    0.1153 
 3 |  0.1147    0.0606    0.0541 
 4 |  0.0096   -0.1313    0.1409 
 5 | -0.1354   -0.1878    0.0524 
 6 |  0.0022   -0.1595    0.1617 
 7 | -0.0095   -0.1179    0.1084 
 8 |  0.0113   -0.3950    0.4063