package edu.northwestern.at.utils.math;
/* Please see the license information at the end of this file. */
/** Polynomial functions.
*/
public class Polynomial
{
/** Evaluate a polynomial expression using Horner's method.
*
* @param polycoefs Array of polynomial coefficients.
* The coefficients should be ordered
* with the constant term first and the
* coefficient for the highest powered term
* last.
*
* @param x Value for which to evaluate polynomial.
*
* @return Polynomial evaluated using Horner's method.
*
* <p>
* Horner's method is given by the following recurrence relation:
* c[i]*x^i + ... + c[1]*x + c[0] = c[0] + x*(c[i-1]*x^[i-1] + ... + c[1])
* </p>
*
* <p>
* Horner's method avoids loss of precision which can occur
* when the higher-power values of x are computed directly.
* </p>
*/
public static double hornersMethod( double polycoefs[] , double x )
{
double result = 0.0;
for ( int i = polycoefs.length - 1 ; i >= 0 ; i-- )
{
result = result * x + polycoefs[ i ] ;
}
return result;
}
/** Evaluates a Chebyschev series.
*
* @param coeffs The Chebyschev polynomial coefficients.
*
* @param x The value for which to evaluate
* the polynomial.
*
* @return The Chebyschev polynomial evaluated
* at x.
*/
public static double evaluateChebyschev
(
double coeffs[] ,
double x
)
{
double b0;
double b1;
double b2;
double twox;
int i;
b0 = 0.0D;
b1 = 0.0D;
b2 = 0.0D;
twox = x + x;
for ( i = coeffs.length - 1 ; i >= 0 ; i-- )
{
b2 = b1;
b1 = b0;
b0 = twox * b1 - b2 + coeffs[ i ];
}
return 0.5D * ( b0 - b2 );
}
/** Don't allow instantiation but do allow overrides.
*/
protected Polynomial()
{
}
}
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