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evalpoly

Evaluate a polynomial using double-precision floating-point arithmetic.

A polynomial in a variable x can be expressed as

$$c_nx^n + c_{n-1}x^{n-1} + \ldots + c_1x^1 + c_0 = \sum_{i=0}^{n} c_ix^i$$

where c_n, c_{n-1}, ..., c_0 are constants.

Installation

npm install @stdlib/math-base-tools-evalpoly

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 evalpoly = require( '@stdlib/math-base-tools-evalpoly' );

evalpoly( c, x )

Evaluates a polynomial having coefficients c and degree n at a value x, where n = c.length-1.

var v = evalpoly( [ 3.0, 2.0, 1.0 ], 10 ); // => 3*10^0 + 2*10^1 + 1*10^2
// returns 123.0

The coefficients should be ordered in ascending degree, thus matching summation notation.

evalpoly.factory( c )

Uses code generation to in-line coefficients and return a function for evaluating a polynomial using double-precision floating-point arithmetic.

var polyval = evalpoly.factory( [ 3.0, 2.0, 1.0 ] );

var v = polyval( 10.0 ); // => 3*10^0 + 2*10^1 + 1*10^2
// returns 123.0

v = polyval( 5.0 ); // => 3*5^0 + 2*5^1 + 1*5^2
// returns 38.0

Notes

• For hot code paths in which coefficients are invariant, a compiled function will be more performant than evalpoly().
• While code generation can boost performance, its use may be problematic in browser contexts enforcing a strict content security policy (CSP). If running in or targeting an environment with a CSP, avoid using code generation.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var uniform = require( '@stdlib/random-base-uniform' );
var evalpoly = require( '@stdlib/math-base-tools-evalpoly' );

// Create an array of random coefficients:
var coef = discreteUniform( 10, -100, 100 );

// Evaluate the polynomial at random values:
var v;
var i;
for ( i = 0; i < 100; i++ ) {
    v = uniform( 0.0, 100.0 );
    console.log( 'f(%d) = %d', v, evalpoly( coef, v ) );
}

// Generate an `evalpoly` function:
var polyval = evalpoly.factory( coef );
for ( i = 0; i < 100; i++ ) {
    v = uniform( -50.0, 50.0 );
    console.log( 'f(%d) = %d', v, polyval( v ) );
}

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See Also

• @stdlib/math-base/tools/evalrational: evaluate a rational function using double-precision floating-point arithmetic.

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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.