evalpoly

Evaluate a polynomial.

A polynomial in a variable x can be expressed as

c Subscript n Baseline x Superscript n Baseline plus c Subscript n minus 1 Baseline x Superscript n minus 1 Baseline plus ellipsis plus c 1 x Superscript 1 Baseline plus c 0 equals sigma-summation Underscript i equals 0 Overscript n Endscripts c Subscript i Baseline x Superscript i

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

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.

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 randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var Float64Array = require( '@stdlib/array/float64' );
var evalpoly = require( '@stdlib/math/base/tools/evalpoly' );

var polyval;
var coef;
var sign;
var v;
var i;

// Create an array of random coefficients...
coef = new Float64Array( 10 );
for ( i = 0; i < coef.length; i++ ) {
    if ( randu() < 0.5 ) {
        sign = -1.0;
    } else {
        sign = 1.0;
    }
    coef[ i ] = sign * round( randu()*100.0 );
}

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

// Generate an `evalpoly` function...
polyval = evalpoly.factory( coef );
for ( i = 0; i < 100; i++ ) {
    v = (randu()*100.0) - 50.0;
    console.log( 'f(%d) = %d', v, polyval( v ) );
}