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Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_rand_int_log (g05tf)

 Contents

    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example

Purpose

nag_rand_int_log (g05tf) generates a vector of pseudorandom integers from the discrete logarithmic distribution with parameter a.

Syntax

[r, state, x, ifail] = g05tf(mode, n, a, r, state)
[r, state, x, ifail] = nag_rand_int_log(mode, n, a, r, state)

Description

nag_rand_int_log (g05tf) generates n integers xi from a discrete logarithmic distribution, where the probability of xi=I is
P xi=I = - aI I × log1-a ,   I=1,2, ,  
where 0<a<1.
The variates can be generated with or without using a search table and index. If a search table is used then it is stored with the index in a reference vector and subsequent calls to nag_rand_int_log (g05tf) with the same parameter value can then use this reference vector to generate further variates.
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_int_log (g05tf).

References

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

Parameters

Compulsory Input Parameters

1:     mode int64int32nag_int scalar
A code for selecting the operation to be performed by the function.
mode=0
Set up reference vector only.
mode=1
Generate variates using reference vector set up in a prior call to nag_rand_int_log (g05tf).
mode=2
Set up reference vector and generate variates.
mode=3
Generate variates without using the reference vector.
Constraint: mode=0, 1, 2 or 3.
2:     n int64int32nag_int scalar
n, the number of pseudorandom numbers to be generated.
Constraint: n0.
3:     a – double scalar
a, the parameter of the logarithmic distribution.
Constraint: 0.0<a<1.0.
4:     rlr – double array
lr, the dimension of the array, must satisfy the constraint
  • if mode=0 or 2, lr must not be too small, but the lower limit is too complicated to specify;
  • if mode=1, lr must remain unchanged from the previous call to nag_rand_int_log (g05tf).
If mode=1, the reference vector from the previous call to nag_rand_int_log (g05tf).
If mode=3, r is not referenced.
5:     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:     rlr – double array
mode3, the reference vector.
2:     state: int64int32nag_int array
Contains updated information on the state of the generator.
3:     xn int64int32nag_int array
The n pseudorandom numbers from the specified logarithmic distribution.
4:     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: mode=0, 1, 2 or 3.
   ifail=2
Constraint: n0.
   ifail=3
Constraint: 0.0<a<1.0.
   ifail=4
On entry, some of the elements of the array r have been corrupted or have not been initialized.
The value of a is not the same as when r was set up in a previous call.
   ifail=5
On entry, lr is too small when mode=0 or 2.
   ifail=6
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

None.

Example

This example prints 10 pseudorandom integers from a logarithmic distribution with parameter a=0.9999, generated by a single call to nag_rand_int_log (g05tf), after initialization by nag_rand_init_repeat (g05kf).
function g05tf_example


fprintf('g05tf 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(10);

% Parameters
a = 0.9999;

% Generate variates from logarithmic distribution without reference vector
mode = int64(3);
r = [0];
[r, state, x, ifail] = g05tf( ...
                              mode, n, a, r, state);

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


g05tf example results

Variates
           6
          23
        2765
          30
           3
           1
         299
         968
         166
           4


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