Integer, Intent (In)	::	n
Integer, Intent (Inout)	::	state(*), ifail
Real (Kind=nag_wp), Intent (In)	::	xmin, xmed, xmax
Real (Kind=nag_wp), Intent (Out)	::	x(n)

C Header Interface

#include <nag.h>

void	g05spf_ (const Integer n, const double xmin, const double xmed, const double xmax, Integer state[], double x[], Integer *ifail)

The routine may be called by the names g05spf or nagf_rand_dist_triangular.

3 Description

The triangular distribution has a PDF (probability density function) that is triangular in profile. The base of the triangle ranges from

x = x_{\min}

x = x_{\max}

and the PDF has a maximum value of

\frac{2}{x_{\max} - x_{\min}}

x = x_{med}

. If

x_{\min} = x_{med} = x_{\max}

then

x = x_{med}

with probability 1; otherwise the triangular distribution has PDF:

\begin{array}{l} f (x) = \frac{x - x_{\min}}{x_{med} - x_{\min}} \times \frac{2}{x_{\max} - x_{\min}} & ​ if ​ x_{\min} \leq x \leq x_{med}, \\ f (x) = \frac{x_{\max} - x}{x_{\max} - x_{med}} \times \frac{2}{x_{\max} - x_{\min}} & ​ if ​ x_{med} < x \leq x_{\max}, \\ f (x) = 0 & ​ otherwise. \end{array}

One of the initialization routines g05kff (for a repeatable sequence if computed sequentially) or g05kgf (for a non-repeatable sequence) must be called prior to the first call to g05spf.

4 References

Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley

5 Arguments

1: $n$ – Integer Input: On entry: $n$ , the number of pseudorandom numbers to be generated.

Constraint: $n \geq 0$ .
2: $xmin$ – Real (Kind=nag_wp) Input: On entry: the end point $x_{\min}$ of the triangular distribution.
3: $xmed$ – Real (Kind=nag_wp) Input: On entry: the median of the distribution $x_{med}$ (also the location of the vertex of the triangular distribution at which the PDF reaches a maximum).

Constraint: $xmed \geq xmin$ .
4: $xmax$ – Real (Kind=nag_wp) Input: On entry: the end point $x_{\max}$ of the triangular distribution.

Constraint: $xmax \geq xmed$ .
5: $state (*)$ – Integer array Communication Array: Note: the actual argument supplied must be the array state supplied to the initialization routines g05kff or g05kgf.

On entry: contains information on the selected base generator and its current state.

On exit: contains updated information on the state of the generator.
6: $x (n)$ – Real (Kind=nag_wp) array Output: On exit: the $n$ pseudorandom numbers from the specified triangular distribution.
7: $ifail$ – 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 $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $n = ⟨ value ⟩$ .
Constraint: $n \geq 0$ .

$ifail = 3$: On entry, $xmed = ⟨ value ⟩$ and $xmin = ⟨ value ⟩$ .
Constraint: $xmed \geq xmin$ .

$ifail = 4$: On entry, $xmax = ⟨ value ⟩$ and $xmed = ⟨ value ⟩$ .
Constraint: $xmax \geq xmed$ .

$ifail = 5$: On entry, state vector has been corrupted or not initialized.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: 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.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

g05spf is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.

Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this routine. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9 Further Comments

None.

10 Example

This example prints five pseudorandom numbers from a triangular distribution with parameters

x_{\min} = - 1.0

x_{med} = 0.5

and

x_{\max} = 1.0

, generated by a single call to g05spf, after initialization by g05kff.

g05sp: FL CL CPP AD

NAG FL Interfaceg05spf (dist_​triangular)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
g05spf (dist_triangular)