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NAG Toolbox: nag_rand_dist_uniform (g05sq)

 Contents

    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example

Purpose

nag_rand_dist_uniform (g05sq) generates a vector of pseudorandom numbers uniformly distributed over the interval a,b.

Syntax

[state, x, ifail] = g05sq(n, a, b, state)
[state, x, ifail] = nag_rand_dist_uniform(n, a, b, state)

Description

If a=0 and b=1, nag_rand_dist_uniform (g05sq) returns the next n values yi from a uniform 0,1 generator (see nag_rand_dist_uniform01 (g05sa) for details).
For other values of a and b, nag_rand_dist_uniform (g05sq) applies the transformation
xi=a+b-ayi.  
The function ensures that the values xi lie in the closed interval a,b.
One of the initialization functions nag_rand_init_repeat (g05kf) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeat (g05kg) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_dist_uniform (g05sq).

References

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

Parameters

Compulsory Input Parameters

1:     n int64int32nag_int scalar
n, the number of pseudorandom numbers to be generated.
Constraint: n0.
2:     a – double scalar
3:     b – double scalar
The end points a and b of the uniform distribution.
Constraint: ab.
4:     state: int64int32nag_int array
Note: the actual argument supplied must be the array state supplied to the initialization routines nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg).
Contains information on the selected base generator and its current state.

Optional Input Parameters

None.

Output Parameters

1:     state: int64int32nag_int array
Contains updated information on the state of the generator.
2:     xn – double array
The n pseudorandom numbers from the specified uniform distribution.
3:     ifail int64int32nag_int scalar
ifail=0 unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:
   ifail=1
Constraint: n0.
   ifail=3
Constraint: ba.
   ifail=4
On entry, state vector has been corrupted or not initialized.
   ifail=-99
An unexpected error has been triggered by this routine. Please contact NAG.
   ifail=-399
Your licence key may have expired or may not have been installed correctly.
   ifail=-999
Dynamic memory allocation failed.

Accuracy

Not applicable.

Further Comments

Although yi takes a value from the half closed interval 0,1 and xi=a+b-ayi, xi is documented as taking values from the closed interval a,b. This is because for some values of a and b, nag_rand_dist_uniform (g05sq) may return a value of a due to numerical rounding.

Example

This example prints five pseudorandom numbers from a uniform distribution between -1.0 and 1.0, generated by a single call to nag_rand_dist_uniform (g05sq), after initialization by nag_rand_init_repeat (g05kf).
function g05sq_example


fprintf('g05sq example results\n\n');

% Initialize the base generator to a repeatable sequence
seed  = [int64(1762543)];
genid = int64(1);
subid = int64(1);
[state, ifail] = g05kf( ...
                        genid, subid, seed);

% Number of variates
n = int64(5);

% Parameters
a = -1;
b = 1;

% Generate variates from a Uniform (a,b) distribution
[state, x, ifail] = g05sq( ...
                           n, a, b, state);

disp('Variates');
disp(x);


g05sq example results

Variates
    0.2727
   -0.7870
    0.4921
    0.5965
   -0.7908


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Chapter Introduction
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