biz.source_code.dsp.math

Class PolynomialUtils

java.lang.Object

biz.source_code.dsp.math.PolynomialUtils

public class PolynomialUtils
extends Object

Plynomial utility routines.

In this module, polynomial coefficients are stored in arrays ordered in descending powers. When an awway a[] contains the coefficients, the polynomial has the following form:
a[0] * x^n + a[1] * x^(n-1) + ... a[n-1] * x + a[n]

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	PolynomialUtils.RationalFraction Structure for the coefficients of a rational fraction (a fraction of two polynomials) with real coefficients.

Method Summary

Modifier and Type	Method and Description
static Complex[]	deflate(Complex[] a, Complex z, double eps) Forward deflation of a polynomial with a known zero.
static Complex	evaluate(double[] a, Complex x) Computes the value of a polynomial with real coefficients.
static Complex	evaluate(PolynomialUtils.RationalFraction f, Complex x) Computes the value of a rational fraction.
static Complex[]	expand(Complex[] zeros) Computes the coefficients of a polynomial from it's complex zeros.
static Complex[]	multiply(Complex[] a1, Complex[] a2) Multiplies two polynomials with complex coefficients.
static double[]	multiply(double[] a1, double[] a2) Multiplies two polynomials with real coefficients.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

evaluate

public static Complex evaluate(double[] a,
                               Complex x)

Computes the value of a polynomial with real coefficients.

Parameters:

a - The coefficients of the polynomial, ordered in descending powers.

x - The x value for which the polynomial is to be evaluated.

Returns:

The result.

evaluate

public static Complex evaluate(PolynomialUtils.RationalFraction f,
                               Complex x)

Computes the value of a rational fraction. Returns evaluate(f.top, x) / evaluate(f.bottom, x).

multiply

public static double[] multiply(double[] a1,
                                double[] a2)

Multiplies two polynomials with real coefficients.

multiply

public static Complex[] multiply(Complex[] a1,
                                 Complex[] a2)

Multiplies two polynomials with complex coefficients.

deflate

public static Complex[] deflate(Complex[] a,
                                Complex z,
                                double eps)

Forward deflation of a polynomial with a known zero. Divides the polynomial with coefficients a[] by (x - z), where z is a zero of the polynomial.

Parameters:

a - Coefficients of the polynomial.

z - A known zero of the polynomial

eps - The maximum value allowed for the absolute real and imaginary parts of the remainder, or 0 to ignore the reminder.

Returns:

The coefficients of the resulting polynomial.

expand

public static Complex[] expand(Complex[] zeros)

Computes the coefficients of a polynomial from it's complex zeros.

Parameters:

zeros - The zeros of the polynomial. The polynomial formula is: (x - zero[0]) * (x - zero[1]) * ... (x - zero[n - 1])

Returns:

The coefficients of the expanded polynomial, ordered in descending powers.