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NAG Toolbox: nag_rand_dist_uniform (g05sq)

Purpose

nag_rand_dist_uniform (g05sq) generates a vector of pseudorandom numbers uniformly distributed over the interval [a,b][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 = 0a=0 and b = 1b=1, nag_rand_dist_uniform (g05sq) returns the next nn values yiyi from a uniform (0,1](0,1] generator (see nag_rand_dist_uniform01 (g05sa) for details).
For other values of aa and bb, nag_rand_dist_uniform (g05sq) applies the transformation
xi = a + (ba)yi.
xi=a+(b-a)yi.
The function ensures that the values xixi lie in the closed interval [a,b][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
nn, the number of pseudorandom numbers to be generated.
Constraint: n0n0.
2:     a – double scalar
3:     b – double scalar
The end points aa and bb of the uniform distribution.
Constraint: abab.
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.

Input Parameters Omitted from the MATLAB Interface

None.

Output Parameters

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

Error Indicators and Warnings

Errors or warnings detected by the function:
  ifail = 1ifail=1
On entry, n < 0n<0.
  ifail = 3ifail=3
On entry, b < ab<a.
  ifail = 4ifail=4
On entry,state vector was not initialized or has been corrupted.

Accuracy

Not applicable.

Further Comments

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

Example

function nag_rand_dist_uniform_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
a = -1;
b = 1;
% Initialize the generator to a repeatable sequence
[state, ifail] = nag_rand_init_repeat(genid, subid, seed);
[state, x, ifail] = nag_rand_dist_uniform(n, a, b, state)
 

state =

                   17
                 1234
                    1
                    0
                 4110
                11820
                23399
                29340
                17917
                13895
                19930
                    8
                    0
                 1234
                    1
                    1
                 1234


x =

    0.2727
   -0.7870
    0.4921
    0.5965
   -0.7908


ifail =

                    0


function g05sq_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
n = int64(5);
a = -1;
b = 1;
% Initialize the generator to a repeatable sequence
[state, ifail] = g05kf(genid, subid, seed);
[state, x, ifail] = g05sq(n, a, b, state)
 

state =

                   17
                 1234
                    1
                    0
                 4110
                11820
                23399
                29340
                17917
                13895
                19930
                    8
                    0
                 1234
                    1
                    1
                 1234


x =

    0.2727
   -0.7870
    0.4921
    0.5965
   -0.7908


ifail =

                    0



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