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NAG Toolbox

NAG Toolbox: nag_stat_pdf_landau_deriv (g01rt)

▸▿ Contents

    1  Purpose
    2  Syntax
    3  Description
    4  References
▸▿ 5  Parameters
    6  Error Indicators and Warnings
    7  Accuracy
    8  Further Comments
    9  Example

Purpose

nag_stat_pdf_landau_deriv (g01rt) returns the value of the derivative ϕ′λ of the Landau density function.

Syntax

[result] = g01rt(x)
[result] = nag_stat_pdf_landau_deriv(x)

Description

nag_stat_pdf_landau_deriv (g01rt) evaluates an approximation to the derivative ϕ′λ of the Landau density function given by
ϕ′λ=dϕλ dλ ,  
where ϕλ is described in nag_stat_pdf_landau (g01mt), using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).
To obtain the value of ϕλ, nag_stat_pdf_landau (g01mt) can be used.

References

Kölbig K S and Schorr B (1984) A program package for the Landau distribution Comp. Phys. Comm. 31 97–111

Parameters

Compulsory Input Parameters

1:     x – double scalar
The argument λ of the function.

Optional Input Parameters

None.

Output Parameters

1:     result – double scalar
The result of the function.

Error Indicators and Warnings

None.

Accuracy

At least 7 significant digits are usually correct, but occasionally only 6. Such accuracy is normally considered to be adequate for applications in experimental physics.
Because of the asymptotic behaviour of ϕ′λ, which is of the order of exp-exp-λ, underflow may occur on some machines when λ is moderately large and negative.

Further Comments

None.

Example

This example evaluates ϕ′λ at λ=0.5, and prints the results.

Open in the MATLAB editor: g01rt_example

function g01rt_example


fprintf('g01rt example results\n\n');

x = 0.5;
[phid] = g01rt(x);

fprintf('phi''(%5.2f) = %8.4f\n', x, phid);



g01rt example results

phi'( 0.50) =  -0.0360
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