Lévy Random Numbers

Lévy distributed pseudorandom numbers.

Usage

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

levy( mu, c )

Returns a pseudorandom number drawn from a Lévy distribution with parameters `mu` (location parameter) and `c` (scale parameter).

``````var r = levy( 2.0, 5.0 );
// returns <number>
``````

If `mu` or `c` is `NaN` or `c <= 0`, the function returns `NaN`.

``````var r = levy( 2.0, -2.0 );
// returns NaN

r = levy( NaN, 5.0 );
// returns NaN

r = levy( 2.0, NaN );
// returns NaN
``````

levy.factory( [mu, c, ][options] )

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

``````var rand = levy.factory();

var r = rand( 0.1, 1.5 );
// returns <number>
``````

If provided `mu` and `c`, the returned generator returns random variates from the specified distribution.

``````var rand = levy.factory( 10.0, 2.0 );

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

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

If not provided `mu` and `c`, the returned generator requires that both parameters be provided at each invocation.

``````var rand = levy.factory();

var r = rand( 0.0, 1.0 );
// returns <number>

r = rand( -2.0, 2.0 );
// 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 = levy.factory({
'prng': minstd.normalized
});

var r = rand( 1.0, 2.0 );
// returns <number>
``````

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

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

var r1 = rand1( 1.0, 2.0 );
// returns <number>

var rand2 = levy.factory( 1.0, 2.0, {
'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 = levy( 1.0, 2.0 );
}

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

// Test that the generated pseudorandom numbers are the same:
bool = ( rand( 1.0, 2.0 ) === levy( 1.0, 2.0 ) );
// returns true
``````

levy.NAME

The generator name.

``````var str = levy.NAME;
// returns 'levy'
``````

levy.PRNG

The underlying pseudorandom number generator.

``````var prng = levy.PRNG;
// returns <Function>
``````

levy.seed

The value used to seed `levy()`.

``````var rand;
var r;
var i;

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

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

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

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

var seed = rand.seed;
// returns null
``````

levy.seedLength

Length of generator seed.

``````var len = levy.seedLength;
// returns <number>
``````

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

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

var len = rand.seedLength;
// returns null
``````

levy.state

Writable property for getting and setting the generator state.

``````var r = levy( 2.0, 5.0 );
// returns <number>

r = levy( 2.0, 5.0 );
// returns <number>

// ...

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

r = levy( 2.0, 5.0 );
// returns <number>

r = levy( 2.0, 5.0 );
// returns <number>

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

// Replay the last two pseudorandom numbers:
r = levy( 2.0, 5.0 );
// returns <number>

r = levy( 2.0, 5.0 );
// returns <number>

// ...
``````

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

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

var state = rand.state;
// returns null
``````

levy.stateLength

Length of generator state.

``````var len = levy.stateLength;
// returns <number>
``````

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

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

var len = rand.stateLength;
// returns null
``````

levy.byteLength

Size (in bytes) of generator state.

``````var sz = levy.byteLength;
// returns <number>
``````

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

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

var sz = rand.byteLength;
// returns null
``````

levy.toJSON()

Serializes the pseudorandom number generator as a JSON object.

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

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

``````var rand = levy.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 levy = require( '@stdlib/random/base/levy' );

var seed;
var rand;
var i;

// Generate pseudorandom numbers...
for ( i = 0; i < 100; i++ ) {
console.log( levy( 0.0, 1.0 ) );
}

// Create a new pseudorandom number generator...
seed = 1234;
rand = levy.factory( 5.0, 2.0, {
'seed': seed
});
for ( i = 0; i < 100; i++ ) {
console.log( rand() );
}

// Create another pseudorandom number generator using a previous seed...
rand = levy.factory( 0.0, 1.0, {
'seed': levy.seed
});
for ( i = 0; i < 100; i++ ) {
console.log( rand() );
}
``````