rndLCbeta
==============================================
Purpose
----------------
Computes beta pseudo-random numbers.
.. NOTE:: This function is deprecated--use :func:`rndBeta`--but remains for backward compatibility.
Format
----------------
.. function:: { x, newstate } = rndLCbeta(r, c, a, b, state)
:param r: number of rows of resulting matrix.
:type r: scalar
:param c: number of columns of resulting matrix.
:type c: scalar
:param a: first shape argument for beta distribution, scalar or ExE conformable matrix with *r* and *c*.
:type a: matrix, vector or scalar
:param b: second shape argument for beta distribution, scalar or ExE conformable matrix with *r* and *c*.
:type b: matrix, vector or 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 x: beta distributed random numbers.
:rtype x: 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
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. Each seed is generated from the preceding seed using
the formula
.. math::
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.
Source
------
randlc.src