# NAG FL Interfaceg01kqf (pdf_​normal_​vector)

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## 1Purpose

g01kqf returns a number of values of the probability density function (PDF), or its logarithm, for the Normal (Gaussian) distributions.

## 2Specification

Fortran Interface
 Subroutine g01kqf ( ilog, lx, x, lxmu, xmu, xstd, pdf,
 Integer, Intent (In) :: ilog, lx, lxmu, lxstd Integer, Intent (Inout) :: ifail Integer, Intent (Out) :: ivalid(*) Real (Kind=nag_wp), Intent (In) :: x(lx), xmu(lxmu), xstd(lxstd) Real (Kind=nag_wp), Intent (Out) :: pdf(*)
#include <nag.h>
 void g01kqf_ (const Integer *ilog, const Integer *lx, const double x[], const Integer *lxmu, const double xmu[], const Integer *lxstd, const double xstd[], double pdf[], Integer ivalid[], Integer *ifail)
The routine may be called by the names g01kqf or nagf_stat_pdf_normal_vector.

## 3Description

The Normal distribution with mean ${\mu }_{i}$, variance ${{\sigma }_{i}}^{2}$; has probability density function (PDF)
 $f (xi,μi,σi) = 1 σi⁢2π e -(xi-μi)2/2σi2 , σi>0 .$
The input arrays to this routine are designed to allow maximum flexibility in the supply of vector arguments by re-using elements of any arrays that are shorter than the total number of evaluations required. See Section 2.6 in the G01 Chapter Introduction for further information.
None.

## 5Arguments

1: $\mathbf{ilog}$Integer Input
On entry: the value of ilog determines whether the logarithmic value is returned in PDF.
${\mathbf{ilog}}=0$
$f\left({x}_{i},{\mu }_{i},{\sigma }_{i}\right)$, the probability density function is returned.
${\mathbf{ilog}}=1$
$\mathrm{log}\left(f\left({x}_{i},{\mu }_{i},{\sigma }_{i}\right)\right)$, the logarithm of the probability density function is returned.
Constraint: ${\mathbf{ilog}}=0$ or $1$.
2: $\mathbf{lx}$Integer Input
On entry: the length of the array x.
Constraint: ${\mathbf{lx}}>0$.
3: $\mathbf{x}\left({\mathbf{lx}}\right)$Real (Kind=nag_wp) array Input
On entry: ${x}_{i}$, the values at which the PDF is to be evaluated with ${x}_{i}={\mathbf{x}}\left(j\right)$, , for $i=1,2,\dots ,\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left({\mathbf{lx}},{\mathbf{lxstd}},{\mathbf{lxmu}}\right)$.
4: $\mathbf{lxmu}$Integer Input
On entry: the length of the array xmu.
Constraint: ${\mathbf{lxmu}}>0$.
5: $\mathbf{xmu}\left({\mathbf{lxmu}}\right)$Real (Kind=nag_wp) array Input
On entry: ${\mu }_{i}$, the means with ${\mu }_{i}={\mathbf{xmu}}\left(j\right)$, .
6: $\mathbf{lxstd}$Integer Input
On entry: the length of the array xstd.
Constraint: ${\mathbf{lxstd}}>0$.
7: $\mathbf{xstd}\left({\mathbf{lxstd}}\right)$Real (Kind=nag_wp) array Input
On entry: ${\sigma }_{i}$, the standard deviations with ${\sigma }_{i}={\mathbf{xstd}}\left(j\right)$, .
Constraint: ${\mathbf{xstd}}\left(\mathit{j}\right)\ge 0.0$, for $\mathit{j}=1,2,\dots ,{\mathbf{lxstd}}$.
8: $\mathbf{pdf}\left(*\right)$Real (Kind=nag_wp) array Output
Note: the dimension of the array pdf must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left({\mathbf{lx}},{\mathbf{lxstd}},{\mathbf{lxmu}}\right)$.
On exit: $f\left({x}_{i},{\mu }_{i},{\sigma }_{i}\right)$ or $\mathrm{log}\left(f\left({x}_{i},{\mu }_{i},{\sigma }_{i}\right)\right)$.
9: $\mathbf{ivalid}\left(*\right)$Integer array Output
Note: the dimension of the array ivalid must be at least $\mathrm{max}\phantom{\rule{0.125em}{0ex}}\left({\mathbf{lx}},{\mathbf{lxstd}},{\mathbf{lxmu}}\right)$.
On exit: ${\mathbf{ivalid}}\left(i\right)$ indicates any errors with the input arguments, with
${\mathbf{ivalid}}\left(i\right)=0$
No error.
${\mathbf{ivalid}}\left(i\right)=1$
${\sigma }_{i}<0$.
10: $\mathbf{ifail}$Integer Input/Output
On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.
If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.
On exit: ${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

## 6Error Indicators and Warnings

If on entry ${\mathbf{ifail}}=0$ or $-1$, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
${\mathbf{ifail}}=1$
On entry, at least one value of xstd was invalid.
${\mathbf{ifail}}=2$
On entry, ${\mathbf{ilog}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{ilog}}=0$ or $1$.
${\mathbf{ifail}}=3$
On entry, $\text{array size}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{lx}}>0$.
${\mathbf{ifail}}=4$
On entry, $\text{array size}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{lxmu}}>0$.
${\mathbf{ifail}}=5$
On entry, $\text{array size}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{lxstd}}>0$.
${\mathbf{ifail}}=-99$
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-399$
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
${\mathbf{ifail}}=-999$
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

Not applicable.

## 8Parallelism and Performance

g01kqf is not threaded in any implementation.

None.

## 10Example

This example prints the value of the Normal distribution PDF at four different points ${x}_{i}$ with differing ${\mu }_{i}$ and ${\sigma }_{i}$.

### 10.1Program Text

Program Text (g01kqfe.f90)

### 10.2Program Data

Program Data (g01kqfe.d)

### 10.3Program Results

Program Results (g01kqfe.r)