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incrprod

Compute a product incrementally.

The product is defined as

$$p = \prod_{i=0}^{n-1} x_i$$

Installation

npm install @stdlib/stats-incr-prod

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 incrprod = require( '@stdlib/stats-incr-prod' );

incrprod()

Returns an accumulator function which incrementally computes a product.

var accumulator = incrprod();

accumulator( [x] )

If provided an input value x, the accumulator function returns an updated product. If not provided an input value x, the accumulator function returns the current product.

var accumulator = incrprod();

var prod = accumulator( 2.0 );
// returns 2.0

prod = accumulator( 1.0 );
// returns 2.0

prod = accumulator( 3.0 );
// returns 6.0

prod = accumulator();
// returns 6.0

Under certain conditions, overflow may be transient.

// Large values:
var x = 5.0e+300;
var y = 1.0e+300;

// Tiny value:
var z = 2.0e-302;

// Initialize an accumulator:
var accumulator = incrprod();

var prod = accumulator( x );
// returns 5.0e+300

// Transient overflow:
prod = accumulator( y );
// returns Infinity

// Recover a finite result:
prod = accumulator( z );
// returns 1.0e+299

Similarly, under certain conditions, underflow may be transient.

// Tiny values:
var x = 4.0e-302;
var y = 9.0e-303;

// Large value:
var z = 2.0e+300;

// Initialize an accumulator:
var accumulator = incrprod();

var prod = accumulator( x );
// returns 4.0e-302

// Transient underflow:
prod = accumulator( y );
// returns 0.0

// Recover a non-zero result:
prod = accumulator( z );
// returns 7.2e-304

Notes

• Input values are not type checked. If provided NaN or a value which, when used in computations, results in NaN, the accumulated value is NaN for all future invocations. If non-numeric inputs are possible, you are advised to type check and handle accordingly before passing the value to the accumulator function.
• For long running accumulations or accumulations of either large or small numbers, care should be taken to prevent overflow and underflow. Note, however, that overflow/underflow may be transient, as the accumulator does not use a double-precision floating-point number to store an accumulated product. Instead, the accumulator splits an accumulated product into a normalized fraction and exponent and updates each component separately. Doing so guards against a loss in precision.

Examples

var randu = require( '@stdlib/random-base-randu' );
var incrprod = require( '@stdlib/stats-incr-prod' );

var accumulator;
var v;
var i;

// Initialize an accumulator:
accumulator = incrprod();

// For each simulated value, update the product...
for ( i = 0; i < 100; i++ ) {
    v = randu() * 100.0;
    accumulator( v );
}
console.log( accumulator() );

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See Also

• @stdlib/stats-incr/mprod: compute a moving product incrementally.
• @stdlib/stats-incr/sum: compute a sum incrementally.
• @stdlib/stats-incr/summary: compute a statistical summary incrementally.

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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.