hide long namesshow long names
hide short namesshow short names
Integer type:  int32  int64  nag_int  show int32  show int32  show int64  show int64  show nag_int  show nag_int

PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_specfun_bessel_i0_scaled_vector (s18cs)

Purpose

nag_specfun_bessel_i0_scaled_vector (s18cs) returns an array of values of the scaled modified Bessel function e|x|I0(x)e-|x|I0(x).

Syntax

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

Description

nag_specfun_bessel_i0_scaled_vector (s18cs) evaluates an approximation to e|xi|I0(xi)e-|xi|I0(xi), where I0I0 is a modified Bessel function of the first kind for an array of arguments xixi, for i = 1,2,,ni=1,2,,n. The scaling factor e|x|e-|x| removes most of the variation in I0(x)I0(x).
The function uses the same Chebyshev expansions as nag_specfun_bessel_i0_real_vector (s18as), which returns an array of the unscaled values of I0(x)I0(x).

References

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

Parameters

Compulsory Input Parameters

1:     x(n) – double array
n, the dimension of the array, must satisfy the constraint n0n0.
The argument xixi of the function, for i = 1,2,,ni=1,2,,n.

Optional Input Parameters

1:     n – int64int32nag_int scalar
Default: The dimension of the array x.
nn, the number of points.
Constraint: n0n0.

Input Parameters Omitted from the MATLAB Interface

None.

Output Parameters

1:     f(n) – double array
e|xi|I0(xi)e-|xi|I0(xi), the function values.
2:     ifail – int64int32nag_int scalar
ifail = 0ifail=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 = 1ifail=1
Constraint: n0n0.

Accuracy

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

None.

Example

function nag_specfun_bessel_i0_scaled_vector_example
x = [0; 0.5; 1; 3; 6; 10; 1000; -1];
[f, ifail] = nag_specfun_bessel_i0_scaled_vector(x);
fprintf('\n    X           Y\n');
for i=1:numel(x)
  fprintf('%12.3e%12.3e\n', x(i), f(i));
end
 

    X           Y
   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

function s18cs_example
x = [0; 0.5; 1; 3; 6; 10; 1000; -1];
[f, ifail] = s18cs(x);
fprintf('\n    X           Y\n');
for i=1:numel(x)
  fprintf('%12.3e%12.3e\n', x(i), f(i));
end
 

    X           Y
   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


PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

© The Numerical Algorithms Group Ltd, Oxford, UK. 2009–2013