rndKMn ============================================== Purpose ---------------- Returns a matrix of standard normal (pseudo) random variables and the state of the random number generator. Format ---------------- .. function:: { y, newstate } = rndKMn(r, c, state) :param r: row dimension. :type r: scalar :param c: column dimension. :type c: scalar :param state: **scalar case** *state* = starting seed value only. If -1, GAUSS computes the starting seed based on the system clock. **500x1 vector case** *state* = the state vector returned from a previous call to one of the ``rndKM`` random number functions. :type state: scalar or 500x1 vector :return y: Standard normal random numbers. :rtype y: RxC matrix :return newstate: the updated state. :rtype newstate: 500x1 vector Examples ---------------- This example generates two thousand vectors of standard normal random numbers, each with one million elements. The state of the random number generator after each iteration is used as an input to the next generation of random numbers. :: state = 13; n = 2000; k = 1000000; c = 0; submean = {}; do while c < n; { y,state } = rndKMn(k,1,state); submean = submean | meanc(y); c = c + k; endo; mean = meanc(submean); print mean; Remarks ------- *r* and *c* will be truncated to integers if necessary. Technical Notes --------------- :func:`rndKMn` calls the uniform random number generator that is the basis for :func:`rndKMu` multiple times for each normal random number generated. This is the recur-with-carry KISS+Monster algorithm described in the :func:`rndKMi` Technical Notes. Potential normal random numbers are filtered 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. It employs the error correction from Tirler et al. (2004), "An error in the Kinderman-Ramage method and how to fix it," *Computational and Data Analysis*, Vol. 47, 433-40. .. seealso:: Functions :func:`rndKMu`, :func:`rndKMi`