Returns a matrix of standard normal (pseudo) random variables and the state of the random number generator.


This function is deprecated–use rndn()–but remains for backward compatibility.


{ y, newstate } = rndLCn(r, c, state)
  • 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 rndcon and rndmult.

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

    3x1 vector case


    the starting seed, uses the system clock if -1


    the multiplicative constant


    the additive constant

    4x1 vector case

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

  • y (RxC matrix) – of standard normal random numbers.

  • newstate (4x1 vector) –


    the updated seed


    the multiplicative constant


    the additive constant


    the original initialization seed


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

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

mean = meanc(submean);
print mean;


r and c will be truncated to integers if necessary.

Technical Notes

The normal random number generator is based on the uniform random number generator, using the fast acceptance-rejection algorithm proposed by Kinderman, A.J. and J.G. Ramage, “Computer Generation of Normal Random Numbers,” Journal of the American Statistical Association, December 1976, Volume 71, Number 356, pp. 893-896. This algorithm calls the linear congruential uniform random number generator multiple times for each normal random number generated.

See rndLCu() for a description of the uniform random number generator algorithm.

See also

Functions rndLCu(), rndLCi(), rndcon(), rndmult()