# NAG FL Interfaceg01mtf (pdf_​landau)

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## 1Purpose

g01mtf returns the value of the Landau density function $\varphi \left(\lambda \right)$.

## 2Specification

Fortran Interface
 Function g01mtf ( x)
 Real (Kind=nag_wp) :: g01mtf Real (Kind=nag_wp), Intent (In) :: x
C Header Interface
#include <nag.h>
 double g01mtf_ (const double *x)
The routine may be called by the names g01mtf or nagf_stat_pdf_landau.

## 3Description

g01mtf evaluates an approximation to the Landau density function $\varphi \left(\lambda \right)$ given by
 $ϕ(λ)=12πi ∫c-i∞ c+i∞exp(λs+sln⁡s)ds,$
where $c$ is an arbitrary real constant, using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).
To obtain the value of ${\varphi }^{\prime }\left(\lambda \right)$, g01rtf can be used.

## 4References

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

## 5Arguments

1: $\mathbf{x}$Real (Kind=nag_wp) Input
On entry: the argument $\lambda$ of the function.

None.

## 7Accuracy

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 $\varphi \left(\lambda \right)$, 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.

## 8Parallelism and Performance

g01mtf is not threaded in any implementation.

None.

## 10Example

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

### 10.1Program Text

Program Text (g01mtfe.f90)

### 10.2Program Data

Program Data (g01mtfe.d)

### 10.3Program Results

Program Results (g01mtfe.r)