1: $x (n)$ – double array
2: $f (n)$ – double array
3: $d (n)$ – double array: n, x, f and d must be unchanged from the previous call of nag_interp_1d_monotonic (e01be).
4: $px (m)$ – double array: The $m$ values of $x$ at which the interpolant is to be evaluated.

Optional Input Parameters

1: $n$ – int64int32nag_int scalar: Default: the dimension of the arrays x, f, d. (An error is raised if these dimensions are not equal.)
n, x, f and d must be unchanged from the previous call of nag_interp_1d_monotonic (e01be).
2: $m$ – int64int32nag_int scalar: Default: the dimension of the array px.
$m$ , the number of points at which the interpolant is to be evaluated.

Constraint: $m \geq 1$ .

Output Parameters

1: $pf (m)$ – double array: $pf (i)$ contains the value of the interpolant evaluated at the point $px (i)$ , for $i = 1, 2, \dots, m$ .
2: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

$ifail = 1$

On entry,

n < 2

$ifail = 2$: The values of $x (r)$ , for $r = 1, 2, \dots, n$ , are not in strictly increasing order.

$ifail = 3$

On entry,

m < 1

W $ifail = 4$: At least one of the points $px (i)$ , for $i = 1, 2, \dots, m$ , lies outside the interval [ $x (1), x (n)$ ], and extrapolation was performed at all such points. Values computed at such points may be very unreliable.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

The computational errors in the array pf should be negligible in most practical situations.

Further Comments

The time taken by nag_interp_1d_monotonic_eval (e01bf) is approximately proportional to the number of evaluation points,

m

. The evaluation will be most efficient if the elements of px are in nondecreasing order (or, more generally, if they are grouped in increasing order of the intervals

[x (r - 1), x (r)]

). A single call of nag_interp_1d_monotonic_eval (e01bf) with

m > 1

is more efficient than several calls with

m = 1

Example

This example reads in values of n, x, f and d, and then calls nag_interp_1d_monotonic_eval (e01bf) to evaluate the interpolant at equally spaced points.

Open in the MATLAB editor: e01bf_example

function e01bf_example


fprintf('e01bf example results\n\n');

x = [7.99 8.09    8.19    8.7     9.2     10      12      15      20];
f = [0 2.7643e-05 0.04375 0.16918 0.46943 0.94374 0.99864 0.99992 0.99999];

% Theses are as returned by e01be(x,f)
d = [0;
     0.00055251;
     0.33587;
     0.34944;
     0.59696;
     0.060326;
     0.000898335;
     2.93954e-05;
     0];

m = 11;
dx = (x(end)-x(1))/(m-1);
px = [x(1):dx:x(end)];

[pf, ifail] = e01bf(x, f, d, px);

fprintf('\n                Interpolated\n     Abscissa          Value\n');
fprintf('%13.4f  %13.4f\n', [px' pf]')

e01bf example results


                Interpolated
     Abscissa          Value
       7.9900         0.0000
       9.1910         0.4640
      10.3920         0.9645
      11.5930         0.9965
      12.7940         0.9992
      13.9950         0.9998
      15.1960         0.9999
      16.3970         1.0000
      17.5980         1.0000
      18.7990         1.0000
      20.0000         1.0000

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox