NAG Library Function Document

nag_normal_pdf_vector (g01kqc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     ilog – Nag_BooleanInput

On entry: the value of ilog determines whether the logarithmic value is returned in PDF.

$\mathbf{ilog}=\mathrm{Nag\_FALSE}$

$f\left(x_i,{\mu }_i,{\sigma }_i\right)$, the probability density function is returned.

$\mathbf{ilog}=\mathrm{Nag\_TRUE}$

$\log \left(f\left(x_i,{\mu }_i,{\sigma }_i\right)\right)$, the logarithm of the probability density function is returned.

2:     lx – IntegerInput

On entry: the length of the array x.

Constraint: $\mathbf{lx}>0$.

3:     x[lx] – const doubleInput

On entry: $x_i$, the values at which the PDF is to be evaluated with $x_i=\mathbf{x}\left[j\right]$, $j=\left(i-1\right)\mathrm{ mod }\mathbf{lx}$, for $i=1,2,\dots ,\max \left(\mathbf{lx},\mathbf{lxstd},\mathbf{lxmu}\right)$.

4:     lxmu – IntegerInput

On entry: the length of the array xmu.

Constraint: $\mathbf{lxmu}>0$.

5:     xmu[lxmu] – const doubleInput

On entry: ${\mu }_i$, the means with ${\mu }_i=\mathbf{xmu}\left[j\right]$, $j=\left(i-1\right)\mathrm{ mod }\mathbf{lxmu}$.

6:     lxstd – IntegerInput

On entry: the length of the array xstd.

Constraint: $\mathbf{lxstd}>0$.

7:     xstd[lxstd] – const doubleInput

On entry: ${\sigma }_i$, the standard deviations with ${\sigma }_i=\mathbf{xstd}\left[j\right]$, $j=\left(i-1\right)\mathrm{ mod }\mathbf{lxstd}$.

Constraint: $\mathbf{xstd}\left[\mathit{j}-1\right]\ge 0.0$, for $\mathit{j}=1,2,\dots ,\mathbf{lxstd}$.

8:     pdf[$\mathit{dim}$] – doubleOutput

Note: the dimension, dim, of the array pdf must be at least $\max \left(\mathbf{lx},\mathbf{lxstd},\mathbf{lxmu}\right)$.

On exit: $f\left(x_i,{\mu }_i,{\sigma }_i\right)$ or $\log \left(f\left(x_i,{\mu }_i,{\sigma }_i\right)\right)$.

9:     ivalid[$\mathit{dim}$] – IntegerOutput

Note: the dimension, dim, of the array ivalid must be at least $\max \left(\mathbf{lx},\mathbf{lxstd},\mathbf{lxmu}\right)$.

On exit: $\mathbf{ivalid}\left[i-1\right]$ indicates any errors with the input arguments, with

$\mathbf{ivalid}\left[i-1\right]=0$

No error.

$\mathbf{ivalid}\left[i-1\right]=1$

${\sigma }_i<0$.

10:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ARRAY_SIZE

On entry, $\text{array size}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{lx}>0$.

On entry, $\text{array size}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{lxmu}>0$.

On entry, $\text{array size}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{lxstd}>0$.

NE_BAD_PARAM

On entry, argument $⟨\mathit{\text{value}}⟩$ had an illegal value.

NE_INTERNAL_ERROR

An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

NW_IVALID

On entry, at least one value of xstd was invalid.
Check ivalid for more information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (g01kqce.c)

10.2  Program Data

Program Data (g01kqce.d)

10.3  Program Results

Program Results (g01kqce.r)