rndLCu

Purpose

Returns a matrix of uniform (pseudo) random variables and the state of the random number generator. NOTE: This function is deprecated but remains for backward compatibility.

Format

{ y, newstate } = rndLCu(r, c, state)

Parameters:

• r (scalar) – row dimension.

• c (scalar) – column dimension.

• state (scalar or vector) –

  scalar case

  state = starting seed value only. System default values are used for the additive and multiplicative constants.

  The defaults are 1013904223, and 1664525, respectively. These may be changed with Format and Format.

  If state = -1, GAUSS computes the starting seed based on the system clock.

  3x1 vector case

  [1]	the starting seed, uses the system clock if -1
  [2]	the multiplicative constant
  [3]	the additive constant

  4x1 vector case

  state = the state vector returned from a previous call to one of the rndLC random number generators.

Returns:

• y (RxC matrix) – uniform (\(0 < x < 1\)) random numbers.

• newstate (4x1 vector) –

  [1]	the updated seed
  [2]	the multiplicative constant
  [3]	the additive constant
  [4]	the original initialization seed

Examples

state = 13;
n = 2000000000;
k = 1000000;
c = 0;
submean = {};

do while c < n;
   { y,state } = rndLCu(k,1,state);
   submean = submean | meanc(y);
   c = c + k;
endo;

mean = meanc(submean);
print 0.5-mean;

Remarks

r and c will be truncated to integers if necessary.

Each seed is generated from the preceding seed using the formula

\[new\_seed = (((a * seed) \% 2^{32})+ c) \% 2^{32}\]

where % is the mod operator and where a is the multiplicative constant and c is the additive constant. A number between 0 and 1 is created by dividing new_seed by \(2\ :sup:`32`\).

Technical Notes

This function uses a linear congruential method, discussed in Kennedy, W.J. Jr., and J.E. Gentle, Statistical Computing, Marcel Dekker, Inc. 1980, pp. 136-147.

See also

Functions rndLCn(), rndLCi(), rndcon(), rndmult()