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NAG Toolbox

NAG Toolbox: nag_specfun_bessel_i0_scaled_vector (s18cs)


    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example


nag_specfun_bessel_i0_scaled_vector (s18cs) returns an array of values of the scaled modified Bessel function e-xI0x.


[f, ifail] = s18cs(x, 'n', n)
[f, ifail] = nag_specfun_bessel_i0_scaled_vector(x, 'n', n)


nag_specfun_bessel_i0_scaled_vector (s18cs) evaluates an approximation to e-xiI0xi, where I0 is a modified Bessel function of the first kind for an array of arguments xi, for i=1,2,,n. The scaling factor e-x removes most of the variation in I0x.
The function uses the same Chebyshev expansions as nag_specfun_bessel_i0_real_vector (s18as), which returns an array of the unscaled values of I0x.


Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications


Compulsory Input Parameters

1:     xn – double array
The argument xi of the function, for i=1,2,,n.

Optional Input Parameters

1:     n int64int32nag_int scalar
Default: the dimension of the array x.
n, the number of points.
Constraint: n0.

Output Parameters

1:     fn – double array
e-xiI0xi, the function values.
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.

W  ifail=1
Constraint: n0.
An unexpected error has been triggered by this routine. Please contact NAG.
Your licence key may have expired or may not have been installed correctly.
Dynamic memory allocation failed.


Relative errors in the argument are attenuated when propagated into the function value. When the accuracy of the argument is essentially limited by the machine precision, the accuracy of the function value will be similarly limited by at most a small multiple of the machine precision.

Further Comments



This example reads values of x from a file, evaluates the function at each value of xi and prints the results.
function s18cs_example

fprintf('s18cs example results\n\n');

x = [0; 0.5; 1; 3; 6; 10; 1000; -1];

[f, ifail] = s18cs(x);

fprintf('     x        e^-|x| I_0(x)\n');
for i=1:numel(x)
  fprintf('%12.3e%12.3e\n', x(i), f(i));

s18cs example results

     x        e^-|x| I_0(x)
   0.000e+00   1.000e+00
   5.000e-01   6.450e-01
   1.000e+00   4.658e-01
   3.000e+00   2.430e-01
   6.000e+00   1.667e-01
   1.000e+01   1.278e-01
   1.000e+03   1.262e-02
  -1.000e+00   4.658e-01

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Chapter Introduction
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