Rayleigh Random Numbers

Usage

var rayleigh = require( '@stdlib/random/base/rayleigh' );

rayleigh( sigma )

Returns a pseudorandom number drawn from a Rayleigh distribution with scale parameter sigma.

var r = rayleigh( 2.5 );
// returns <number>

If sigma <= 0 or sigma is NaN, the function returns NaN.

var r = rayleigh( -2.0 );
// returns NaN

r = rayleigh( NaN );
// returns NaN

rayleigh.factory( [sigma, ][options] )

Returns a pseudorandom number generator (PRNG) for generating pseudorandom numbers drawn from a Rayleigh distribution.

var rand = rayleigh.factory();

var r = rand( 5.0 );
// returns <number>

If provided sigma, the returned generator returns random variates from the specified distribution.

var rand = rayleigh.factory( 10.0 );

var r = rand();
// returns <number>

r = rand();
// returns <number>

If not provided sigma, the returned generator requires that sigma be provided at each invocation.

var rand = rayleigh.factory();

var r = rand( 4.0 );
// returns <number>

r = rand( 3.14 );
// returns <number>

The function accepts the following options:

• prng: pseudorandom number generator for generating uniformly distributed pseudorandom numbers on the interval [0,1). If provided, the function ignores both the state and seed options. In order to seed the returned pseudorandom number generator, one must seed the provided prng (assuming the provided prng is seedable).
• seed: pseudorandom number generator seed.
• state: a Uint32Array containing pseudorandom number generator state. If provided, the function ignores the seed option.
• copy: boolean indicating whether to copy a provided pseudorandom number generator state. Setting this option to false allows sharing state between two or more pseudorandom number generators. Setting this option to true ensures that a returned generator has exclusive control over its internal state. Default: true.

To use a custom PRNG as the underlying source of uniformly distributed pseudorandom numbers, set the prng option.

var minstd = require( '@stdlib/random/base/minstd' );

var rand = rayleigh.factory({
    'prng': minstd.normalized
});

var r = rand( 3.0 );
// returns <number>

To seed a pseudorandom number generator, set the seed option.

var rand1 = rayleigh.factory({
    'seed': 12345
});

var r1 = rand1( 3.0 );
// returns <number>

var rand2 = rayleigh.factory( 3.0, {
    'seed': 12345
});

var r2 = rand2();
// returns <number>

var bool = ( r1 === r2 );
// returns true

To return a generator having a specific initial state, set the generator state option.

var rand;
var bool;
var r;
var i;

// Generate pseudorandom numbers, thus progressing the generator state:
for ( i = 0; i < 1000; i++ ) {
    r = rayleigh( 5.0 );
}

// Create a new PRNG initialized to the current state of `rayleigh`:
rand = rayleigh.factory({
    'state': rayleigh.state
});

// Test that the generated pseudorandom numbers are the same:
bool = ( rand( 5.0 ) === rayleigh( 5.0 ) );
// returns true

rayleigh.NAME

The generator name.

var str = rayleigh.NAME;
// returns 'rayleigh'

rayleigh.PRNG

The underlying pseudorandom number generator.

var prng = rayleigh.PRNG;
// returns <Function>

rayleigh.seed

The value used to seed rayleigh().

var rand;
var r;
var i;

// Generate pseudorandom values...
for ( i = 0; i < 100; i++ ) {
    r = rayleigh( 2.0 );
}

// Generate the same pseudorandom values...
rand = rayleigh.factory( 2.0, {
    'seed': rayleigh.seed
});
for ( i = 0; i < 100; i++ ) {
    r = rand();
}

If provided a PRNG for uniformly distributed numbers, this value is null.

var rand = rayleigh.factory({
    'prng': Math.random
});

var seed = rand.seed;
// returns null

rayleigh.seedLength

Length of generator seed.

var len = rayleigh.seedLength;
// returns <number>

If provided a PRNG for uniformly distributed numbers, this value is null.

var rand = rayleigh.factory({
    'prng': Math.random
});

var len = rand.seedLength;
// returns null

rayleigh.state

Writable property for getting and setting the generator state.

var r = rayleigh( 5.0 );
// returns <number>

r = rayleigh( 5.0 );
// returns <number>

// ...

// Get a copy of the current state:
var state = rayleigh.state;
// returns <Uint32Array>

r = rayleigh( 5.0 );
// returns <number>

r = rayleigh( 5.0 );
// returns <number>

// Reset the state:
rayleigh.state = state;

// Replay the last two pseudorandom numbers:
r = rayleigh( 5.0 );
// returns <number>

r = rayleigh( 5.0 );
// returns <number>

// ...

If provided a PRNG for uniformly distributed numbers, this value is null.

var rand = rayleigh.factory({
    'prng': Math.random
});

var state = rand.state;
// returns null

rayleigh.stateLength

Length of generator state.

var len = rayleigh.stateLength;
// returns <number>

If provided a PRNG for uniformly distributed numbers, this value is null.

var rand = rayleigh.factory({
    'prng': Math.random
});

var len = rand.stateLength;
// returns null

rayleigh.byteLength

Size (in bytes) of generator state.

var sz = rayleigh.byteLength;
// returns <number>

If provided a PRNG for uniformly distributed numbers, this value is null.

var rand = rayleigh.factory({
    'prng': Math.random
});

var sz = rand.byteLength;
// returns null

rayleigh.toJSON()

Serializes the pseudorandom number generator as a JSON object.

var o = rayleigh.toJSON();
// returns { 'type': 'PRNG', 'name': '...', 'state': {...}, 'params': [] }

If provided a PRNG for uniformly distributed numbers, this method returns null.

var rand = rayleigh.factory({
    'prng': Math.random
});

var o = rand.toJSON();
// returns null