rndLCn
==============================================
Purpose
----------------
Returns a matrix of standard normal (pseudo) random variables and the state of the random number generator.
.. NOTE:: This function is deprecated--use :func:`rndn`--but remains for backward compatibility.
Format
----------------
.. function:: { y, newstate } = rndLCn(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. 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**
.. csv-table::
:widths: auto
"[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.
:type state: scalar or vector
:return y: of standard normal random numbers.
:rtype y: RxC matrix
:return newstate:
.. csv-table::
:widths: auto
"[1]", "the updated seed"
"[2]", "the multiplicative constant"
"[3]", "the additive constant"
"[4]", "the original initialization seed"
:rtype newstate: 4x1 vector
Examples
----------------
::
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;
endo;
mean = meanc(submean);
print mean;
Remarks
-------
*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 :func:`rndLCu` for a description of the uniform random number generator algorithm.
.. seealso:: Functions :func:`rndLCu`, :func:`rndLCi`, :func:`rndcon`, :func:`rndmult`