polynomial

Evaluates a polynomial.

Installation

$ npm install compute-polynomial

For use in the browser, use browserify.

Usage

var polyval = require( 'compute-polynomial' );

polyval( coef, x[, options] )

Evaluates a polynomial whose coefficients are defined by coef. x may be either a single numeric value or an array of values at which to evaluate to the polynomial.

The coefficients should be ordered in descending degree. For example, for a polynomial

a_nx^n + a_(n-1)x^(n-1) + ... + a_1x^1 + a_0x^0

the coefficients would be

[a_n, a_(n-1),..., a_1, a_0]

Consider the polynomial 4x^3 + 2x^2 + 6x - 17. To evaluate the polynomial at a single value,

var val = polyval( [ 4, 2, 6, -17 ], 10 );
// returns 4243

To evaluate the polynomial at multiple values,

var vals = polyval( [ 4, 2, 6, -17 ], [ 10, -3 ] );
// returns [ 4243, -125 ]

When provided an input array, the function accepts the following options:

• copy: boolean indicating whether to return a new array. Default: true.
• accessor: accessor function for accessing numeric values in object arrays.

To mutate the input array (e.g., when input values can be discarded or when optimizing memory usage), set the copy option to false.

var coefs = [ 4, 2, 6, -17 ],
	x = [ 10, -3 ];

var vals = polyval( coefs, x, {
	'copy': false
});
// returns [ 4243, -125 ]

console.log( x === vals );
// returns true

For object arrays, provide an accessor function for accessing array values.

var coefs = [ 4, 2, 6, -17 ];

var data = [
	['beep', 10],
	['boop', -3]
];

function getValue( d, i ) {
	return d[ 1 ];
}

var vals = polyval( coefs, data, {
	'accessor': getValue
});
// returns [ 4243, -125 ]

Examples

var polyval = require( 'compute-polynomial' );

var coef = new Array( 25 ),
	sign;

for ( var i = 0; i < coef.length; i++ ) {
	sign = 1;
	if ( Math.random()-0.5 < 0 ) {
		sign = -1;
	}
	coef[ i ] = sign * Math.round( Math.random()*i );
}

// Evaluate the polynomial at a single value:
console.log( polyval( coef, 10 ) );

// Evaluate the polynomial at multiple values:
console.log( polyval( coef, [ 10, -10 ] ) );

To run the example code from the top-level application directory,

$ node ./examples/index.js

Notes

This method implements Horner's rule to achieve efficient computation.

Tests

Unit

Unit tests use the Mocha test framework with Chai assertions. To run the tests, execute the following command in the top-level application directory:

$ make test

All new feature development should have corresponding unit tests to validate correct functionality.

Test Coverage

This repository uses Istanbul as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory:

$ make test-cov

Istanbul creates a ./reports/coverage directory. To access an HTML version of the report,

$ make view-cov

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License

MIT license.

Copyright

Copyright © 2014-2015. Athan Reines.