Cauchy Random Numbers

Create an array containing pseudorandom numbers drawn from a Cauchy distribution.

Usage

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

cauchy( len, x0, gamma[, options] )

Returns an array containing pseudorandom numbers drawn from a Cauchy distribution.

var out = cauchy( 10, 2.0, 5.0 );
// returns <Float64Array>

The function has the following parameters:

  • len: output array length.
  • x0: location parameter.
  • gamma: scale parameter.
  • options: function options.

The function accepts the following options:

By default, the function returns a Float64Array. To return an array having a different data type, set the dtype option.

var opts = {
    'dtype': 'generic'
};

var out = cauchy( 10, 2.0, 5.0, opts );
// returns [...]

cauchy.assign( x0, gamma, out )

Fills an array with pseudorandom numbers drawn from a Cauchy distribution.

var zeros = require( '@stdlib/array/zeros' );

var x = zeros( 10, 'float64' );
// returns <Float64Array>

var out = cauchy.assign( 2.0, 5.0, x );
// returns <Float64Array>

var bool = ( out === x );
// returns true

The function has the following parameters:

  • x0: location parameter.
  • gamma: scale parameter.
  • out: output array.

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

Returns a function for creating arrays containing pseudorandom numbers drawn from a Cauchy distribution.

var random = cauchy.factory();

var out = random( 10, 2.0, 5.0 );
// returns <Float64Array>

var len = out.length;
// returns 10

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

var random = cauchy.factory( 2.0, 5.0 );

var out = random( 10 );
// returns <Float64Array>

out = random( 10 );
// returns <Float64Array>

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

var random = cauchy.factory();

var out = random( 10, 2.0, 5.0 );
// returns <Float64Array>

out = random( 10, 2.0, 5.0 );
// returns <Float64Array>

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 underlying 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 an underlying generator has exclusive control over its internal state. Default: true.
  • dtype: default output array data type. Must be a real-valued floating-point data type or "generic". Default: 'float64'.

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 opts = {
    'prng': minstd.normalized
};
var random = cauchy.factory( 2.0, 5.0, opts );

var out = random( 10 );
// returns <Float64Array>

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

var opts = {
    'seed': 12345
};
var random = cauchy.factory( 2.0, 5.0, opts );

var out = random( 10, opts );
// returns <Float64Array>

The returned function accepts the following options:

To override the default output array data type, set the dtype option.

var random = cauchy.factory( 2.0, 5.0 );

var out = random( 10 );
// returns <Float64Array>

var opts = {
    'dtype': 'generic'
};
out = random( 10, opts );
// returns [...]

cauchy.PRNG

The underlying pseudorandom number generator.

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

cauchy.seed

The value used to seed the underlying pseudorandom number generator.

var seed = cauchy.seed;
// returns <Uint32Array>

If the factory method is provided a PRNG for uniformly distributed numbers, the associated property value on the returned function is null.

var minstd = require( '@stdlib/random/base/minstd-shuffle' ).normalized;

var random = cauchy.factory( 2.0, 5.0, {
    'prng': minstd
});

var seed = random.seed;
// returns null

cauchy.seedLength

Length of underlying pseudorandom number generator seed.

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

If the factory method is provided a PRNG for uniformly distributed numbers, the associated property value on the returned function is null.

var minstd = require( '@stdlib/random/base/minstd-shuffle' ).normalized;

var random = cauchy.factory( 2.0, 5.0, {
    'prng': minstd
});

var len = random.seedLength;
// returns null

cauchy.state

Writable property for getting and setting the underlying pseudorandom number generator state.

var state = cauchy.state;
// returns <Uint32Array>

If the factory method is provided a PRNG for uniformly distributed numbers, the associated property value on the returned function is null.

var minstd = require( '@stdlib/random/base/minstd-shuffle' ).normalized;

var random = cauchy.factory( 2.0, 5.0, {
    'prng': minstd
});

var state = random.state;
// returns null

cauchy.stateLength

Length of underlying pseudorandom number generator state.

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

If the factory method is provided a PRNG for uniformly distributed numbers, the associated property value on the returned function is null.

var minstd = require( '@stdlib/random/base/minstd-shuffle' ).normalized;

var random = cauchy.factory( 2.0, 5.0, {
    'prng': minstd
});

var len = random.stateLength;
// returns null

cauchy.byteLength

Size (in bytes) of underlying pseudorandom number generator state.

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

If the factory method is provided a PRNG for uniformly distributed numbers, the associated property value on the returned function is null.

var minstd = require( '@stdlib/random/base/minstd-shuffle' ).normalized;

var random = cauchy.factory( 2.0, 5.0, {
    'prng': minstd
});

var sz = random.byteLength;
// returns null

Notes

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

Examples

var logEach = require( '@stdlib/console/log-each' );
var cauchy = require( '@stdlib/random/array/cauchy' );

// Create a function for generating random arrays originating from the same state:
var random = cauchy.factory( 2.0, 5.0, {
    'state': cauchy.state,
    'copy': true
});

// Generate 3 arrays:
var x1 = random( 5 );
var x2 = random( 5 );
var x3 = random( 5 );

// Print the contents:
logEach( '%f, %f, %f', x1, x2, x3 );

// Create another function for generating random arrays with the original state:
random = cauchy.factory( 2.0, 5.0, {
    'state': cauchy.state,
    'copy': true
});

// Generate a single array which replicates the above pseudorandom number generation sequence:
var x4 = random( 15 );

// Print the contents:
logEach( '%f', x4 );

See Also

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