rndLCi

Purpose

Returns a matrix of random integers, \(0 ≤ y < 232\), and the state of the random number generator.

Note

This function is deprecated but remains for backward compatibility.

Format

{ y, newstate } = rndLCi(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 (r x c matrix) – of random integers between 0 and 232 - 1, inclusive.

• 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;
min = 2^32+1;
max = -1;

do while c < n;
   { y, state } = rndLCi(k, 1, state);
   min = minc(min | minc(y));
   max = maxc(max | maxc(y));
   c = c + k;
endo;

print "min " min;
print "max " max;

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. The new seeds are the values returned.

See also

Functions rndLCn(), rndLCu(), rndcon(), rndmult()