Box-Muller Transform

Standard normally distributed pseudorandom numbers using the Box-Muller transform.

Installation

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

Usage

var randn = require( '@stdlib/random-base-box-muller' );

randn()

Returns a standard normally distributed pseudorandom number.

var r = randn();
// returns <number>

randn.factory( [options] )

Returns a pseudorandom number generator (PRNG) for generating standard normally distributed pseudorandom numbers.

var rand = randn.factory();

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 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 a returned 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 rand = randn.factory({
    'prng': minstd.normalized
});

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

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

var rand1 = randn.factory({
    'seed': 12345
});

var r1 = rand1();
// returns <number>

var rand2 = randn.factory({
    'seed': 12345
});

var r2 = rand2();
// returns <number>

var bool = ( r1 === r2 );
// returns true

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

var rand;
var bool;
var r;
var i;

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

// Create a new PRNG initialized to the current state of `randn`:
rand = randn.factory({
    'state': randn.state
});

// Test that the generated pseudorandom numbers are the same:
bool = ( rand() === randn() );
// returns true

randn.NAME

The generator name.

var str = randn.NAME;
// returns 'box-muller'

randn.PRNG

The underlying pseudorandom number generator for uniformly distributed numbers on the interval [0,1).

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

randn.MIN

Minimum possible value.

var min = randn.MIN;
// returns <number>

Note that this value is computed based on the minimum value of the underlying PRNG for uniformly distributed numbers. If the underlying PRNG does not have a MIN property, this value is null.

var rand = randn.factory({
    'prng': Math.random
});

var min = rand.MIN;
// returns null

randn.MAX

Maximum possible value.

var max = randn.MAX;
// returns <number>

Note that this value is computed based on the minimum value of the underlying PRNG for uniformly distributed numbers. If the underlying PRNG does not have a MIN property, this value is null.

var rand = randn.factory({
    'prng': Math.random
});

var max = rand.MAX;
// returns null

randn.seed

The value used to seed randn().

var rand;
var r;
var i;

// Generate pseudorandom values...
for ( i = 0; i < 100; i++ ) {
    r = randn();
}

// Generate the same pseudorandom values...
rand = randn.factory({
    'seed': randn.seed
});
for ( i = 0; i < 100; i++ ) {
    r = rand();
}

If provided a PRNG for uniformly distributed numbers, this value is null.

var rand = randn.factory({
    'prng': Math.random
});

var seed = rand.seed;
// returns null

randn.seedLength

Length of generator seed.

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

If provided a PRNG for uniformly distributed numbers, this value is null.

var rand = randn.factory({
    'prng': Math.random
});

var len = rand.seedLength;
// returns null

randn.state

Writable property for getting and setting the generator state.

var r = randn();
// returns <number>

r = randn();
// returns <number>

// ...

// Get a copy of the current state:
var state = randn.state;
// returns <Uint32Array>

r = randn();
// returns <number>

r = randn();
// returns <number>

// Reset the state:
randn.state = state;

// Replay the last two pseudorandom numbers:
r = randn();
// returns <number>

r = randn();
// returns <number>

// ...

If provided a PRNG for uniformly distributed numbers, this value is null.

var rand = randn.factory({
    'prng': Math.random
});

var state = rand.state;
// returns null

randn.stateLength

Length of generator state.

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

If provided a PRNG for uniformly distributed numbers, this value is null.

var rand = randn.factory({
    'prng': Math.random
});

var len = rand.stateLength;
// returns null

randn.byteLength

Size (in bytes) of generator state.

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

If provided a PRNG for uniformly distributed numbers, this value is null.

var rand = randn.factory({
    'prng': Math.random
});

var sz = rand.byteLength;
// returns null

randn.toJSON()

Serializes the pseudorandom number generator as a JSON object.

var o = randn.toJSON();
// returns { 'type': 'PRNG', 'name': '...', 'state': {...}, 'params': [] }

If provided a PRNG for uniformly distributed numbers, this method returns null.

var rand = randn.factory({
    'prng': Math.random
});

var o = rand.toJSON();
// returns null

Notes

• The minimum and maximum values are dependent on the number of bits used by the underlying PRNG. For instance, if a PRNG uses 32 bits, the smallest non-zero uniformly distributed pseudorandom number that can be generated is 2**-32. Accordingly, the algorithm would be unable to produce random variates more than 6.66 standard deviations from the mean. This corresponds to a 2.74 x 10**-11 loss due to tail truncation.
• If PRNG state is "shared" (meaning a state array was provided during PRNG creation and not copied) and one sets the generator state to a state array having a different length, the PRNG does not update the existing shared state and, instead, points to the newly provided state array. In order to synchronize PRNG output according to the new shared state array, the state array for each relevant PRNG must be explicitly set.
• If PRNG state is "shared" and one sets the generator state to a state array of the same length, the PRNG state is updated (along with the state of all other PRNGs sharing the PRNG's state array).

Examples

var randn = require( '@stdlib/random-base-box-muller' );

var seed;
var rand;
var i;

// Generate pseudorandom numbers...
for ( i = 0; i < 100; i++ ) {
    console.log( randn() );
}

// Create a new pseudorandom number generator...
seed = 1234;
rand = randn.factory({
    'seed': seed
});
for ( i = 0; i < 100; i++ ) {
    console.log( rand() );
}

// Create another pseudorandom number generator using a previous seed...
rand = randn.factory({
    'seed': randn.seed
});
for ( i = 0; i < 100; i++ ) {
    console.log( rand() );
}

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.

See Also

• @stdlib/random-iter/box-muller: create an iterator for generating pseudorandom numbers drawn from a standard normal distribution using the Box-Muller transform.
• @stdlib/random-streams/box-muller: create a readable stream for generating pseudorandom numbers drawn from a standard normal distribution using the Box-Muller transform.

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

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