﻿ g01rt Method
g01rt returns the value of the derivative ${\varphi }^{\prime }\left(\lambda \right)$ of the Landau density function.

Syntax

C#
```public static double g01rt(
double x
)```
Visual Basic
```Public Shared Function g01rt ( _
x As Double _
) As Double```
Visual C++
```public:
static double g01rt(
double x
)```
F#
```static member g01rt :
x : float -> float
```

Parameters

x
Type: System..::..Double
On entry: the argument $\lambda$ of the function.

Return Value

g01rt returns the value of the derivative ${\varphi }^{\prime }\left(\lambda \right)$ of the Landau density function.

Description

g01rt evaluates an approximation to the derivative ${\varphi }^{\prime }\left(\lambda \right)$ of the Landau density function given by
 $ϕ′λ=dϕλdλ,$
where $\varphi \left(\lambda \right)$ is described in g01mt, using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).
To obtain the value of $\varphi \left(\lambda \right)$, 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

Error Indicators and Warnings

There are no failure exits from this routine.

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 ${\varphi }^{\prime }\left(\lambda \right)$, which is of the order of $\mathrm{exp}\left[-\mathrm{exp}\left(-\lambda \right)\right]$, underflow may occur on some machines when $\lambda$ is moderately large and negative.

None.

None.

Example

This example evaluates ${\varphi }^{\prime }\left(\lambda \right)$ at $\lambda =0.5$, and prints the results.

Example program (C#): g01rte.cs

Example program data: g01rte.d

Example program results: g01rte.r