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Standard Normal Random Numbers

Create an iterator for generating pseudorandom numbers drawn from a standard normal distribution using the Box-Muller transform.

Installation

npm install @stdlib/random-iter-box-muller

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

var iterator = require( '@stdlib/random-iter-box-muller' );

iterator( [options] )

Returns an iterator for generating pseudorandom numbers drawn from a standard normal distribution using the Box-Muller transform.

var it = iterator();
// returns <Object>

var r = it.next().value;
// returns <number>

r = it.next().value;
// returns <number>

r = it.next().value;
// 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 iterator, 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 iterator has exclusive control over its internal pseudorandom number generator state. Default: true.
• iter: number of iterations.

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 it = iterator({
    'prng': minstd.normalized
});

var r = it.next().value;
// returns <number>

To return an iterator having a specific initial state, set the iterator state option.

var bool;
var it1;
var it2;
var r;
var i;

it1 = iterator();

// Generate pseudorandom numbers, thus progressing the generator state:
for ( i = 0; i < 1000; i++ ) {
    r = it1.next().value;
}

// Create a new iterator initialized to the current state of `it1`:
it2 = iterator({
    'state': it1.state
});

// Test that the generated pseudorandom numbers are the same:
bool = ( it1.next().value === it2.next().value );
// returns true

To seed the iterator, set the seed option.

var it = iterator({
    'seed': 12345
});

var r = it.next().value;
// returns ~0.349

it = iterator({
    'seed': 12345
});

r = it.next().value;
// returns ~0.349

To limit the number of iterations, set the iter option.

var it = iterator({
    'iter': 2
});

var r = it.next().value;
// returns <number>

r = it.next().value;
// returns <number>

r = it.next().done;
// returns true

The returned iterator protocol-compliant object has the following properties:

• next: function which returns an iterator protocol-compliant object containing the next iterated value (if one exists) assigned to a value property and a done property having a boolean value indicating whether the iterator is finished.
• return: function which closes an iterator and returns a single (optional) argument in an iterator protocol-compliant object.
• seed: pseudorandom number generator seed. If provided a prng option, the property value is null.
• seedLength: length of generator seed. If provided a prng option, the property value is null.
• state: writable property for getting and setting the generator state. If provided a prng option, the property value is null.
• stateLength: length of generator state. If provided a prng option, the property value is null.
• byteLength: size (in bytes) of generator state. If provided a prng option, the property value is null.
• PRNG: underlying pseudorandom number generator.

Notes

• If an environment supports Symbol.iterator, the returned iterator is iterable.
• If PRNG state is "shared" (meaning a state array was provided during iterator creation and not copied) and one sets the underlying generator state to a state array having a different length, the iterator 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 iterator 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 iterator and/or PRNGs sharing the PRNG's state array).

Examples

var iterator = require( '@stdlib/random-iter-box-muller' );

var it;
var r;

// Create a seeded iterator for generating pseudorandom numbers:
it = iterator({
    'seed': 1234,
    'iter': 10
});

// Perform manual iteration...
while ( true ) {
    r = it.next();
    if ( r.done ) {
        break;
    }
    console.log( r.value );
}

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References

• Box, G. E. P., and Mervin E. Muller. 1958. "A Note on the Generation of Random Normal Deviates." The Annals of Mathematical Statistics 29 (2). The Institute of Mathematical Statistics: 610–11. doi:10.1214/aoms/1177706645.
• Bell, James R. 1968. "Algorithm 334: Normal Random Deviates." Communications of the ACM 11 (7). New York, NY, USA: ACM: 498. doi:10.1145/363397.363547.
• Knop, R. 1969. "Remark on Algorithm 334 [G5]: Normal Random Deviates." Communications of the ACM 12 (5). New York, NY, USA: ACM: 281. doi:10.1145/362946.362996.
• Marsaglia, G., and T. A. Bray. 1964. "A Convenient Method for Generating Normal Variables." SIAM Review 6 (3). Society for Industrial; Applied Mathematics: 260–64. doi:10.1137/1006063.
• Thomas, David B., Wayne Luk, Philip H.W. Leong, and John D. Villasenor. 2007. "Gaussian Random Number Generators." ACM Computing Surveys 39 (4). New York, NY, USA: ACM. doi:10.1145/1287620.1287622.

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See Also

• @stdlib/random-base/box-muller: normally distributed pseudorandom numbers using the Box-Muller transform.

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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

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.