Gumbel Random Numbers

Generate pseudorandom numbers drawn from a Gumbel distribution.

Installation

npm install @stdlib/random-gumbel

Usage

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

gumbel( shape, mu, beta[, options] )

Returns an ndarray containing pseudorandom numbers drawn from a Gumbel distribution.

var arr = gumbel( [ 3, 3 ], 2.0, 5.0 );
// returns <ndarray>

The function has the following parameters:

• shape: output shape.
• mu: mean. May be either a scalar or an ndarray. When providing an ndarray, the ndarray must be broadcast compatible with the specified output shape.
• beta: scale parameter. May be either a scalar or an ndarray. When providing an ndarray, the ndarray must be broadcast compatible with the specified output shape.
• options: function options.

When provided scalar distribution parameters, every element in the output ndarray is drawn from the same distribution. To generate pseudorandom numbers drawn from different distributions, provide distribution parameter arguments as ndarrays. The following example demonstrates broadcasting an ndarray containing distribution parameters to generate sub-matrices drawn from different distributions.

var getShape = require( '@stdlib/ndarray-shape' );
var array = require( '@stdlib/ndarray-array' );

var mu = array( [ [ [ 2.0 ] ], [ [ 10.0 ] ] ] );
// returns <ndarray>

var beta = array( [ [ [ 5.0 ] ], [ [ 20.0 ] ] ] );
// returns <ndarray>

var shape = getShape( mu );
// returns [ 2, 1, 1 ]

var arr = gumbel( [ 2, 3, 3 ], mu, beta );
// returns <ndarray>

If provided an empty shape, the function returns a zero-dimensional ndarray.

var getShape = require( '@stdlib/ndarray-shape' );

var arr = gumbel( [], 2.0, 5.0 );
// returns <ndarray>

var shape = getShape( arr );
// returns []

var v = arr.get();
// returns <number>

The function accepts the following options:

• dtype: output ndarray data type. Must be a real-valued floating-point or "generic" data type.
• order: ndarray order (i.e., memory layout), which is either row-major (C-style) or column-major (Fortran-style). Default: 'row-major'.
• mode: specifies how to handle indices which exceed ndarray dimensions. For a list of supported modes, see ndarray. Default: 'throw'.
• submode: a mode array which specifies for each dimension how to handle subscripts which exceed ndarray dimensions. If provided fewer modes than dimensions, an ndarray instance recycles modes using modulo arithmetic. Default: [ options.mode ].
• readonly: boolean indicating whether an ndarray should be read-only. Default: false.

By default, the function returns an ndarray having a data type determined by the function's output data type policy. To override the default behavior, set the dtype option.

var getDType = require( '@stdlib/ndarray-dtype' );

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

var arr = gumbel( [ 3, 3 ], 2.0, 5.0, opts );
// returns <ndarray>

var dt = String( getDType( arr ) );
// returns 'generic'

gumbel.assign( mu, beta, out )

Fills an ndarray with pseudorandom numbers drawn from a Gumbel distribution.

var zeros = require( '@stdlib/ndarray-zeros' );

var out = zeros( [ 3, 3 ] );
// returns <ndarray>

var v = gumbel.assign( 2.0, 5.0, out );
// returns <ndarray>

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

The method has the following parameters:

• mu: mean. May be either a scalar or an ndarray. When providing an ndarray, the ndarray must be broadcast compatible with the output ndarray.
• beta: scale parameter. May be either a scalar or an ndarray. When providing an ndarray, the ndarray must be broadcast compatible with the output ndarray.
• out: output ndarray.

gumbel.factory( [options] )

Returns a function for generating pseudorandom numbers drawn from a Gumbel distribution.

var getShape = require( '@stdlib/ndarray-shape' );

var random = gumbel.factory();

var out = random( [ 3, 3 ], 2.0, 5.0 );
// returns <ndarray>

var sh = getShape( out );
// returns [ 3, 3 ]

The method 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.

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 = gumbel.factory( opts );

var out = random( [ 3, 3 ], 2.0, 5.0 );
// returns <ndarray>

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

var opts = {
    'seed': 12345
};
var random = gumbel.factory( opts );

var out = random( [ 3, 3 ], 2.0, 5.0 );
// returns <ndarray>

The function returned by the factory method has the same interface and accepts the same options as the gumbel function above.

gumbel.PRNG

The underlying pseudorandom number generator.

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

gumbel.seed

The value used to seed the underlying pseudorandom number generator.

var seed = gumbel.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 = gumbel.factory({
    'prng': minstd
});

var seed = random.seed;
// returns null

gumbel.seedLength

Length of underlying pseudorandom number generator seed.

var len = gumbel.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 = gumbel.factory({
    'prng': minstd
});

var len = random.seedLength;
// returns null

gumbel.state

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

var state = gumbel.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 = gumbel.factory({
    'prng': minstd
});

var state = random.state;
// returns null

gumbel.stateLength

Length of underlying pseudorandom number generator state.

var len = gumbel.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 = gumbel.factory({
    'prng': minstd
});

var len = random.stateLength;
// returns null

gumbel.byteLength

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

var sz = gumbel.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 = gumbel.factory({
    '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).
• The output data type policy only applies to the main function and specifies that, by default, the function must return an ndarray having a real-valued floating-point or "generic" data type. For the assign method, the output ndarray is allowed to have any supported output data type.

Examples

var logEach = require( '@stdlib/console-log-each' );
var ndarray2array = require( '@stdlib/ndarray-to-array' );
var gumbel = require( '@stdlib/random-gumbel' );

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

// Generate 3 one-dimensional arrays:
var x1 = random( [ 5 ], 2.0, 5.0 );
var x2 = random( [ 5 ], 2.0, 5.0 );
var x3 = random( [ 5 ], 2.0, 5.0 );

// Print the contents:
logEach( '%f, %f, %f', ndarray2array( x1 ), ndarray2array( x2 ), ndarray2array( x3 ) );

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

// Generate a two-dimensional array which replicates the above pseudorandom number generation sequence:
var x4 = random( [ 3, 5 ], 2.0, 5.0 );

// Convert to a list of nested arrays:
var arr = ndarray2array( x4 );

// Print the contents:
console.log( '' );
logEach( '%f, %f, %f', arr[ 0 ], arr[ 1 ], arr[ 2 ] );

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.

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License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.