# Rayleigh Random Numbers

Rayleigh distributed pseudorandom 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

## Notes

• If PRNG state is "shared" (meaning a state array was provided during PRNG creation and not copied) and one sets the generator state to a state array having a different length, the PRNG does not update the existing shared state and, instead, points to the newly provided state array. In order to synchronize PRNG output according to the new shared state array, the state array for each relevant PRNG must be explicitly set.
• If PRNG state is "shared" and one sets the generator state to a state array of the same length, the PRNG state is updated (along with the state of all other PRNGs sharing the PRNG's state array).

## Examples

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

var seed;
var rand;
var i;

// Generate pseudorandom numbers...
for ( i = 0; i < 100; i++ ) {
console.log( rayleigh( 0.5 ) );
}

// Create a new pseudorandom number generator...
seed = 1234;
rand = rayleigh.factory( 0.8, {
'seed': seed
});
for ( i = 0; i < 100; i++ ) {
console.log( rand() );
}

// Create another pseudorandom number generator using a previous seed...
rand = rayleigh.factory( 0.5, {
'seed': rayleigh.seed
});
for ( i = 0; i < 100; i++ ) {
console.log( rand() );
}