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NAG Toolbox: nag_rand_int_log (g05tf)

Purpose

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

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 nn integers xixi from a discrete logarithmic distribution, where the probability of xi = Ixi=I is
P (xi = I) = (aI)/( I × log(1a) ) ,   I = 1,2, ,
P (xi=I) = - aI I × log(1-a) ,   I=1,2, ,
where 0 < a < 1.0<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 = 0mode=0
Set up reference vector only.
mode = 1mode=1
Generate variates using reference vector set up in a prior call to nag_rand_int_log (g05tf).
mode = 2mode=2
Set up reference vector and generate variates.
mode = 3mode=3
Generate variates without using the reference vector.
Constraint: mode = 0mode=0, 11, 22 or 33.
2:     n – int64int32nag_int scalar
nn, the number of pseudorandom numbers to be generated.
Constraint: n0n0.
3:     a – double scalar
aa, the parameter of the logarithmic distribution.
Constraint: 0.0 < a < 1.00.0<a<1.0.
4:     r(lr) – double array
lr, the dimension of the array, must satisfy the constraint
  • if mode = 0mode=0 or 22, lr must not be too small, but the lower limit is too complicated to specify;
  • if mode = 1mode=1, lr must remain unchanged from the previous call to nag_rand_int_log (g05tf).
If mode = 1mode=1, the reference vector from the previous call to nag_rand_int_log (g05tf).
If mode = 3mode=3, r is not referenced by nag_rand_int_log (g05tf).
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.

Input Parameters Omitted from the MATLAB Interface

lr

Output Parameters

1:     r(lr) – double array
The reference vector.
2:     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.
3:     x(n) – int64int32nag_int array
The nn pseudorandom numbers from the specified logarithmic distribution.
4:     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, mode0mode0, 11, 22 or 33.
  ifail = 2ifail=2
On entry, n < 0n<0.
  ifail = 3ifail=3
On entry,a0.0a0.0,
ora1.0a1.0.
  ifail = 4ifail=4
On entry, a is not the same as when r was set up in a previous call to nag_rand_int_log (g05tf) with mode = 0mode=0 or 22.
On entry, the r vector was not initialized correctly, or has been corrupted.
  ifail = 5ifail=5
On entry, lr is too small when mode = 0mode=0 or 22.
  ifail = 6ifail=6
On entry,state vector was not initialized or has been corrupted.

Accuracy

Not applicable.

Further Comments

None.

Example

function nag_rand_int_log_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
mode = int64(3);
n = int64(10);
a = 0.9999;
r = zeros(1, 1);
% Initialize the generator to a repeatable sequence
[state, ifail] = nag_rand_init_repeat(genid, subid, seed);
[r, state, x, ifail] = nag_rand_int_log(mode, n, a, r, state)
 

r =

     0


state =

                   17
                 1234
                    1
                    0
                 6694
                27818
                10435
                15383
                17917
                13895
                19930
                    8
                    0
                 1234
                    1
                    1
                 1234


x =

                    6
                   23
                 2765
                   30
                    3
                    1
                  299
                  968
                  166
                    4


ifail =

                    0


function g05tf_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
mode = int64(3);
n = int64(10);
a = 0.9999;
r = zeros(1, 1);
% Initialize the generator to a repeatable sequence
[state, ifail] = g05kf(genid, subid, seed);
[r, state, x, ifail] = g05tf(mode, n, a, r, state)
 

r =

     0


state =

                   17
                 1234
                    1
                    0
                 6694
                27818
                10435
                15383
                17917
                13895
                19930
                    8
                    0
                 1234
                    1
                    1
                 1234


x =

                    6
                   23
                 2765
                   30
                    3
                    1
                  299
                  968
                  166
                    4


ifail =

                    0



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Chapter Introduction
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