# Cauchy Random Numbers

Cauchy distributed pseudorandom numbers.

## 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`:

• seed: pseudorandom number generator seed.

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

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

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

rand = cauchy.factory( 2.0, 3.0, {
'seed': 12345
});

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

#### 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();
}
``````

## Examples

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

var seed;
var rand;
var i;

// Generate pseudorandom numbers...
console.log( '\nseed: %d', cauchy.SEED );
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
});
console.log( '\nseed: %d', 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
});
console.log( '\nseed: %d', cauchy.SEED );
for ( i = 0; i < 100; i++ ) {
console.log( rand() );
}
``````