Exponential Random Numbers

Generate pseudorandom numbers drawn from an exponential distribution.

Installation

npm install @stdlib/random-exponential

Usage

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

exponential( shape, lambda[, options] )

Returns an ndarray containing pseudorandom numbers drawn from an exponential distribution.

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

The function has the following parameters:

• shape: output array shape.
• lambda: rate parameter.
• options: function options.

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

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

var shape = arr.shape;
// returns []

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

Distribution parameters may be either scalars or ndarrays. When providing an ndarray, the ndarray must be broadcast compatible with the specified output array shape.

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

var lambda = array( [ [ [ 2.0 ] ], [ [ 5.0 ] ] ] );
// returns <ndarray>

var shape = lambda.shape;
// returns [ 2, 1, 1 ]

var arr = exponential( [ 2, 3, 3 ], lambda );
// returns <ndarray>

The function accepts the following options:

• dtype: output array data type. Must be a real-valued floating-point data type or "generic". Default: 'float64'.
• order: array 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 array 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 array dimensions. If provided fewer modes than dimensions, an ndarray instance recycles modes using modulo arithmetic. Default: [ options.mode ].
• readonly: boolean indicating whether an array should be read-only. Default: false.

By default, the function returns an ndarray having a float64 data type. To return an ndarray having a different data type, set the dtype option.

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

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

var dt = arr.dtype;
// returns 'generic'

exponential.assign( out, lambda )

Fills an ndarray with pseudorandom numbers drawn from an exponential distribution.

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

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

var out = exponential.assign( arr, 2.0 );
// returns <ndarray>

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

Distribution parameters may be either scalars or ndarrays. When providing an ndarray, the ndarray must be broadcast compatible with the output ndarray.

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

var lambda = array( [ [ [ 2.0 ] ], [ [ 5.0 ] ] ] );
// returns <ndarray>

var shape = lambda.shape;
// returns [ 2, 1, 1 ]

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

var out = exponential.assign( arr, lambda );
// returns <ndarray>

exponential.factory( [options] )

Returns a function for generating pseudorandom numbers drawn from an exponential distribution.

var random = exponential.factory();

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

var sh = out.shape;
// returns [ 3, 3 ]

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'.
• order: default array order (i.e., memory layout), which is either row-major (C-style) or column-major (Fortran-style). Default: 'row-major'.
• mode: default specifying how to handle indices which exceed array dimensions. For a list of supported modes, see ndarray. Default: 'throw'.
• submode: default specifying for each dimension how to handle subscripts which exceed array dimensions. If the number of modes is less than the number of dimensions, an ndarray instance recycles modes using modulo arithmetic. Default: [ options.mode ].
• readonly: default indicating whether an array should be read-only. Default: false.

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 = exponential.factory( opts );

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

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

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

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

The returned function accepts the following options, each of which overrides the respective default:

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

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

var random = exponential.factory();

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

var dt = out.dtype;
// returns 'float64'

var opts = {
    'dtype': 'generic'
};
out = random( [ 3, 3 ], 2.0, opts );
// returns <ndarray>

dt = out.dtype;
// returns 'generic'

exponential.PRNG

The underlying pseudorandom number generator.

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

exponential.seed

The value used to seed the underlying pseudorandom number generator.

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

var seed = random.seed;
// returns null

exponential.seedLength

Length of underlying pseudorandom number generator seed.

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

var len = random.seedLength;
// returns null

exponential.state

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

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

var state = random.state;
// returns null

exponential.stateLength

Length of underlying pseudorandom number generator state.

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

var len = random.stateLength;
// returns null

exponential.byteLength

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

var sz = exponential.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 = exponential.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).

Examples

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

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

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

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

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

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

// Convert to a list of nested arrays:
var arr = toArray( 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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.