Cauchy Random Numbers

Cauchy distributed pseudorandom numbers.

Installation

npm install @stdlib/random-base-cauchy

Usage

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

cauchy( x0, gamma )

Returns a pseudorandom number drawn from a Cauchy distribution with parameters x0 (location parameter) and gamma > 0 (scale parameter).

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

If x0 or gamma is NaN or gamma <= 0, the function returns NaN.

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

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

r = cauchy( 2.0, NaN );
// returns NaN

cauchy.factory( [x0, gamma, ][options] )

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

var rand = cauchy.factory();

var r = rand( 0.0, 1.5 );
// returns <number>

If provided x0 and gamma, the returned generator returns random variates from the specified distribution.

// Draw from Cauchy( 0.0, 1.5 ) distribution:
var rand = cauchy.factory( 0.0, 1.5 );

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

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

If not provided x0 and gamma, the returned generator requires that both parameters be provided at each invocation.

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

var r = rand( 2.0, 3.0 );
// returns <number>

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

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

var r1 = rand1( 2.0, 3.0 );
// returns <number>

var rand2 = cauchy.factory( 2.0, 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 = cauchy( 2.0, 3.0 );
}

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

// Test that the generated pseudorandom numbers are the same:
bool = ( rand( 2.0, 3.0 ) === cauchy( 2.0, 3.0 ) );
// returns true

cauchy.NAME

The generator name.

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

cauchy.PRNG

The underlying pseudorandom number generator.

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

cauchy.seed

The value used to seed cauchy().

var rand;
var r;
var i;

// Generate pseudorandom values...
for ( i = 0; i < 100; i++ ) {
    r = cauchy( 0.0, 2.0 );
}

// Generate the same pseudorandom values...
rand = cauchy.factory( 0.0, 2.0, {
    'seed': cauchy.seed
});
for ( i = 0; i < 100; i++ ) {
    r = rand();
}

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

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

var seed = rand.seed;
// returns null

cauchy.seedLength

Length of generator seed.

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

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

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

var len = rand.seedLength;
// returns null

cauchy.state

Writable property for getting and setting the generator state.

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

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

// ...

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

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

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

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

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

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

// ...

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

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

var state = rand.state;
// returns null

cauchy.stateLength

Length of generator state.

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

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

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

var len = rand.stateLength;
// returns null

cauchy.byteLength

Size (in bytes) of generator state.

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

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

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

var sz = rand.byteLength;
// returns null

cauchy.toJSON()

Serializes the pseudorandom number generator as a JSON object.

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

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

var rand = cauchy.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 cauchy = require( '@stdlib/random-base-cauchy' );

var seed;
var rand;
var i;

// Generate pseudorandom numbers...
for ( i = 0; i < 100; i++ ) {
    console.log( cauchy( 2.0, 2.0 ) );
}

// Create a new pseudorandom number generator...
seed = 1234;
rand = cauchy.factory( -6.0, 2.0, {
    'seed': seed
});
for ( i = 0; i < 100; i++ ) {
    console.log( rand() );
}

// Create another pseudorandom number generator using a previous seed...
rand = cauchy.factory( 2.0, 2.0, {
    'seed': cauchy.seed
});
for ( i = 0; i < 100; i++ ) {
    console.log( rand() );
}

See Also

• @stdlib/random-array/cauchy: create an array containing pseudorandom numbers drawn from a Cauchy distribution.
• @stdlib/random-iter/cauchy: create an iterator for generating pseudorandom numbers drawn from a Cauchy distribution.
• @stdlib/random-streams/cauchy: create a readable stream for generating pseudorandom numbers drawn from a Cauchy distribution.

Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.