RANDOMU

Syntax | Return Value | Arguments | Keywords | Examples | Version History | See Also

The RANDOMU function returns one or more uniformly-distributed, floating-point, pseudo-random numbers in the range 0 < Y <1.0.

The random number generator is taken from: "Random Number Generators: Good Ones are Hard to Find", Park and Miller, Communications of the ACM, Oct 1988, Vol 31, No. 10, p. 1192. To remove low-order serial correlations, a Bays-Durham shuffle is added, resulting in a random number generator similar to ran1() in Section 7.1 of Numerical Recipes in C: The Art of Scientific Computing (Second Edition), published by Cambridge University Press.

Syntax

Result = RANDOMU( Seed [, D₁ [, ..., D₈]] [ [, BINOMIAL=[trials, probability]] [, /DOUBLE] [, GAMMA=integer{>0}] [, /NORMAL] [, POISSON=value] [, /UNIFORM] | [, /LONG] ] )

Return Value

Returns an array of uniformly distributed random numbers of the specified dimensions.

Arguments

Seed

A variable or constant used to initialize the random sequence on input, and in which the state of the random number generator is saved on output.

The state of the random number generator is contained in a long integer vector. This state is saved in the Seed argument when the argument is a named variable. To continue the pseudo-random number sequence, input the variable containing the saved state as the Seed argument in the next call to RANDOMN or RANDOMU. Each independent random number sequence should maintain its own state variable. To maintain a state over repeated calls to a procedure, the seed variable may be stored in a COMMON block.

In addition to states maintained by the user in variables, the RANDOMU and RANDOMN functions contain a single shared generic state that is used if a named variable is not supplied as the Seed argument or the named variable supplied is undefined. The generic state is initialized once using the time-of-day, and may be re-initialized by providing a Seed argument that is a constant or expression.

If the Seed argument is:

D_i

Either an array or a series of scalar expressions specifying the dimensions of the result. If a single argument is specified, it can be either a scalar expression or an array of up to eight elements. If multiple arguments are specified, they must all be scalar expressions. Up to eight dimensions can be specified. If no dimensions are specified, RANDOMU returns a scalar result

Keywords

The formulas for the binomial, gamma, and Poisson distributions are from Section 7.3 of Numerical Recipes in C: The Art of Scientific Computing (Second Edition), published by Cambridge University Press.

BINOMIAL

Set this keyword to a 2-element array, [n, p], to generate random deviates from a binomial distribution. If an event occurs with probability p, with n trials, then the number of times it occurs has a binomial distribution.

Note
For n > 1.0 × 10⁷, you should set the DOUBLE keyword.

DOUBLE

Set this keyword to force the computation to be done using double-precision arithmetic.

RANDOMU constructs double-precision uniform random deviates using the formula:

where i1 and i2 are integer random deviates in the range [1...imax], and
imax = 2³¹– 2 is the largest possible integer random deviate. The Y values will be in the range 0 < Y < 1.

GAMMA

Set this keyword to an integer order i > 0 to generate random deviates from a gamma distribution. The gamma distribution is the waiting time to the ith event in a Poisson random process of unit mean. A gamma distribution of order equal to 1 is the same as the exponential distribution.

Note
For GAMMA > 1.0 x 10⁷, you should set the DOUBLE keyword.

LONG

Set this keyword to return integer uniform random deviates in the range
[1...2³¹ – 2]. If LONG is set, all other keywords are ignored.

NORMAL

Set this keyword to generate random deviates from a normal distribution.

POISSON

Set this keyword to the mean number of events occurring during a unit of time. The POISSON keyword returns a random deviate drawn from a Poisson distribution with that mean.

Note
For POISSON > 1.0 × 10⁷, you should set the DOUBLE keyword.

UNIFORM

Set this keyword to generate random deviates from a uniform distribution.

Examples

This example simulates rolling two dice 10,000 times and plots the distribution of the total using RANDOMU. Enter:

PLOT, HISTOGRAM(FIX(6 * RANDOMU(S, 10000)) + $
   FIX(6 * RANDOMU(S, 10000)) + 2)

In the above statement, the expression RANDOMU(S, 10000) is a 10,000-element, floating-point array of random numbers greater than or equal to 0 and less than 1. Multiplying this array by 6 converts the range to 0 ≤ Y < 6.

Applying the FIX function yields a 10,000-point integer vector with values from 0 to 5, one less than the numbers on one die. This computation is done twice, once for each die, then 2 is added to obtain a vector from 2 to 12, the total of two dice.

The HISTOGRAM function makes a vector in which each element contains the number of occurrences of dice rolls whose total is equal to the subscript of the element. Finally, this vector is plotted by the PLOT procedure.

An example of reusing a state vector to generate a repeatable sequence:

; Init seed for a repeatable sequence:
seed = 1001L

; Print 1st 5 numbers of sequence:
print,randomu(seed,5)

IDL prints:

     0.705884     0.285924     0.231151     0.715447     0.532836 

Reuse a state vector:

; Re-init seed to same sequence:
seed = 1001L

; Get 5 number of sequence with 5 calls:
for i=0,4 do print, randomu(seed)

IDL prints:

     0.705884 
     0.285924 
     0.231151 
     0.715447 
     0.532836 

Version History

See Also

RANDOMN