# Standard Normal Random Numbers > Create an iterator for generating pseudorandom numbers drawn from a [standard normal][normal] distribution using the [Box-Muller transform][box-muller].
## Usage ```javascript var iterator = require( '@stdlib/random/iter/box-muller' ); ``` #### iterator( \[options] ) Returns an iterator for generating pseudorandom numbers drawn from a [standard normal][normal] distribution using the [Box-Muller transform][box-muller]. ```javascript var it = iterator(); // returns var r = it.next().value; // returns r = it.next().value; // returns r = it.next().value; // returns // ... ``` 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`][@stdlib/array/uint32] 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. ```javascript var minstd = require( '@stdlib/random/base/minstd' ); var it = iterator({ 'prng': minstd.normalized }); var r = it.next().value; // returns ``` To return an iterator having a specific initial state, set the iterator `state` option. ```javascript 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. ```javascript 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. ```javascript var it = iterator({ 'iter': 2 }); var r = it.next().value; // returns r = it.next().value; // returns 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 ```javascript 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][@box:1958]. - 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][@bell:1968]. - 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][@knop:1969]. - 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][@marsaglia:1964a]. - 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][@thomas:2007].
[box-muller]: https://en.wikipedia.org/wiki/Box%E2%80%93Muller_transform [normal]: https://en.wikipedia.org/wiki/Normal_distribution [@box:1958]: http://dx.doi.org/10.1214/aoms/1177706645 [@bell:1968]: http://dx.doi.org/10.1145/363397.363547 [@knop:1969]: http://dx.doi.org/10.1145/362946.362996 [@marsaglia:1964a]: http://dx.doi.org/10.1137/1006063 [@thomas:2007]: http://dx.doi.org/10.1145/1287620.128762 [@stdlib/array/uint32]: https://www.npmjs.com/package/@stdlib/array-uint32