NAG Toolbox: nag_interp_5d_scat_shep_eval (e01tn)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{x}\left(5,\mathbf{m}\right)$ – double array

must be the same array supplied as argument x in the preceding call to nag_interp_5d_scat_shep (e01tm). 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_5d_scat_shep (e01tm). 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_5d_scat_shep (e01tm). It must remain unchanged between calls.

4:     $\mathrm{rq}\left(21\times \mathbf{m}+11\right)$ – double array

must be the same array returned as argument rq in the preceding call to nag_interp_5d_scat_shep (e01tm). It must remain unchanged between calls.

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

$\mathbf{xe}\left(1:5,\mathit{i}\right)$ 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 second 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_5d_scat_shep (e01tm).

Constraint: $\mathbf{m}\ge 23$.

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_5d_scat_shep_eval (e01tn) returns with $\mathbf{ifail}=\mathbf{3}$.

2:     $\mathrm{qx}\left(5,\mathbf{n}\right)$ – 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 five partial derivatives $j=1,2,3,4,5$. 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_5d_scat_shep_eval (e01tn) 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: $\mathbf{m}\ge 23$.

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_5d_scat_shep (e01tm) and nag_interp_5d_scat_shep_eval (e01tn).

On entry, values in rq appear to be invalid. Check that rq has not been corrupted between calls to nag_interp_5d_scat_shep (e01tm) and nag_interp_5d_scat_shep_eval (e01tn).

   $\mathbf{ifail}=3$

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: e01tn_example

function e01tn_example


fprintf('e01tn 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(5*30), state);
x = reshape(x, 5, 30);

% Evaluate function
f = ((1.25+cos(5.4*x(5,:))).*cos(6*x(1,:)).*cos(6*x(2,:)).*cos(6*x(3,:)))./...
    (6+6*(3*x(4,:)-1).^2);

% Generate the interpolant
nq = int64(0);
nw = int64(0);
[iq, rq, ifail] = e01tm(x, f, nw, nq);

% Generate repeatable evaluation points
[state, ifail] = g05kf(genid, subid, seed2);
[state, xe, ifail] = g05sa(int64(5*8), state);
xe = reshape(xe, 5, 8);

% Evaluate function at xe
fun = ((1.25+cos(5.4*xe(5,:))).*cos(6*xe(1,:)).*cos(6*xe(2,:)).*...
      cos(6*xe(3,:)))./(6+6*(3*xe(4,:)-1).^2);

% Evaluate the interpolant
[q, qx, ifail] = e01tn(x, f, iq, rq, xe);

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

e01tn example results


 i |  f(i)       q(i)   |f(i)-q(i)|
---|--------------------+---------+
 1 |  0.0058    0.0464    0.0407 
 2 |  0.0034    0.4855    0.4821 
 3 | -0.1096    0.0724    0.1820 
 4 |  0.0875    0.0320    0.0555 
 5 |  0.0015    0.0373    0.0358 
 6 | -0.0158   -0.1170    0.1012 
 7 |  0.0046   -0.0484    0.0530 
 8 | -0.0090   -0.0134    0.0043