marytts.util.math

Class Polynomial

java.lang.Object

marytts.util.math.Polynomial

public class Polynomial
extends Object

Author:

marc

Field Summary

Fields

Modifier and Type	Field and Description
double[]	coeffs

Constructor Summary

Constructors

Constructor and Description
Polynomial(double[] coeffs) Create a new polynomial with the given coefficients.
Polynomial(int order) Create a new polynomial of the requested order with all coefficients set to 0.

Method Summary

Methods

Modifier and Type	Method and Description
void	copyCoeffs(Polynomial other)
static double[]	fitPolynomial(double[] data, int order) Fit a polynomial of the given order to the given data.
static double[]	generatePolynomialValues(double[] coeffs, int numSamples, double a, double b) For a polynomial with the given coefficients, compute numSamples values, equally spaced in the interval [a, b[.
double[]	generatePolynomialValues(int numSamples, double a, double b) For a polynomial with the given coefficients, compute numSamples values, equally spaced in the interval [a, b[.
int	getOrder()
double	getValueAt(double x) For a polynomial with the given coefficients, compute the value at the given position.
static double	getValueAt(double[] coeffs, double x) For a polynomial with the given coefficients, compute the value at the given position.
static double[]	mean(double[][] p) Compute the mean polynomial from the given polynomials, by building a polynomial of the averaged coefficients.
static float[]	mean(float[][] p) Compute the mean polynomial from the given polynomials, by building a polynomial of the averaged coefficients.
static Polynomial	mean(Polynomial[] p) Compute the mean polynomial from the given polynomials, by building a polynomial of the averaged coefficients.
static double	polynomialDistance(double[] coeffs1, double[] coeffs2) Compute the integrated distance between two polynomials of same order.
static double	polynomialDistance(float[] coeffs1, float[] coeffs2) Compute the integrated distance between two polynomials of same order.
double	polynomialDistance(Polynomial other) Compute the integrated distance between two polynomials of same order.
static double	polynomialPearsonProductMomentCorr(double[] coeffs1, double[] coeffs2) Compute one minus the Pearson product moment correlation between two polynomials of same order.
static double	polynomialSquaredDistance(double[] coeffs1, double[] coeffs2) Compute the integral of the squared difference between two polynomials of same order.
static double	polynomialSquaredDistance(float[] coeffs1, float[] coeffs2) Compute the integral of the squared difference between two polynomials of same order.
double	polynomialSquaredDistance(Polynomial other) Compute the integral of the squared difference between two polynomials of same order.
static double	variance(double[][] p, double[] mean) For the given collection of polynomials, for which a mean polynomial has already been computed using mean(double[][]), compute a variance as follows.
static double	variance(float[][] p, float[] mean) For the given collection of polynomials, for which a mean polynomial has already been computed using mean(float[][]), compute a variance as follows.
static double	variance(Polynomial[] p, Polynomial mean) For the given collection of polynomials, for which a mean polynomial has already been computed using mean(Polynomial[]), compute a variance as follows.

Methods inherited from class java.lang.Object

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

Field Detail

coeffs

public final double[] coeffs

Constructor Detail

Polynomial

public Polynomial(int order)

Create a new polynomial of the requested order with all coefficients set to 0.

Parameters:

order - the polynomial order.

Polynomial

public Polynomial(double[] coeffs)

Create a new polynomial with the given coefficients.

Parameters:

coeffs - the polynomial coefficients. The code assumes that the polynomial is a_order t^order + a_(order-1) t^(order-1) + ... + a_1 t + a_0, and will interpret coeffs as a_order, a_(order-1), ..., a_1, a_0, where order is coeffs.length-1.

Method Detail

getOrder

public int getOrder()

copyCoeffs

public void copyCoeffs(Polynomial other)

generatePolynomialValues

public double[] generatePolynomialValues(int numSamples,
                                double a,
                                double b)

For a polynomial with the given coefficients, compute numSamples values, equally spaced in the interval [a, b[.

Parameters:

numSamples - num samples

a - lower bound (inclusive)

b - upper bound (exclusive)

Returns:

the predicted samples.

Throws:

NullPointerException - if coeffs is null

IllegalArgumentException - if coeffs has length 0

IllegalArgumentException - if numSamples is ≤ 0

IllegalArgumentException - if a is not less than b.

getValueAt

public double getValueAt(double x)

For a polynomial with the given coefficients, compute the value at the given position.

Parameters:

x - the position where to compute the value

Returns:

the predicted value

Throws:

NullPointerException - if coeffs is null

IllegalArgumentException - if coeffs has length 0

polynomialDistance

public double polynomialDistance(Polynomial other)

Compute the integrated distance between two polynomials of same order. More precisely, this will return the absolute value of the integral from 0 to 1 of the difference between the two functions.

Parameters:

other - polynomial with the same order as this polynomial.

Returns:

polynomialDistance(self.coeffs, other.coeffs)

polynomialSquaredDistance

public double polynomialSquaredDistance(Polynomial other)

Compute the integral of the squared difference between two polynomials of same order. More precisely, this will return the the integral from 0 to 1 of the square of the difference between the two functions.

This implements the algebraic solution proposed by Maxima from the following command: expand(integrate((sum(a[i]*x**i, i, 0, order))**2, x, 0, 1));, with order varied from 0 to 4. Increasing order by 1 adds (order+1) summands.

Parameters:

other - polynomial with the same order as this polynomial.

Returns:

polynomialSquaredDistance(this.coeffs, other.coeffs)

fitPolynomial

public static double[] fitPolynomial(double[] data,
                     int order)

Fit a polynomial of the given order to the given data.

Parameters:

data - the data points, assumed to be in the interval [0, 1[

order - the order of the polynomial. Must be non-negative.

Returns:

the polynomial coefficients, highest power first. In other words, if the polynomial is a_order t^order + a_(order-1) t^(order-1) + ... + a_1 t + a_0, then the array returned contains a_order, a_(order-1), ..., a_1, a_0. throws NullPointerException if data is null throws IllegalArgumentException if data.length < order or if order < 0.

generatePolynomialValues

public static double[] generatePolynomialValues(double[] coeffs,
                                int numSamples,
                                double a,
                                double b)

For a polynomial with the given coefficients, compute numSamples values, equally spaced in the interval [a, b[.

Parameters:

coeffs - the polynomial coefficients. The code assumes that the polynomial is a_order t^order + a_(order-1) t^(order-1) + ... + a_1 t + a_0, and will interpret coeffs as a_order, a_(order-1), ..., a_1, a_0, where order is coeffs.length-1.

numSamples - num samples

a - lower bound (inclusive)

b - upper bound (exclusive)

Returns:

the predicted samples.

Throws:

NullPointerException - if coeffs is null

IllegalArgumentException - if coeffs has length 0

IllegalArgumentException - if numSamples is ≤ 0

IllegalArgumentException - if a is not less than b.

getValueAt

public static double getValueAt(double[] coeffs,
                double x)

For a polynomial with the given coefficients, compute the value at the given position.

Parameters:

coeffs - the polynomial coefficients. The code assumes that the polynomial is a_order t^order + a_(order-1) t^(order-1) + ... + a_1 t + a_0, and will interpret coeffs as a_order, a_(order-1), ..., a_1, a_0, where order is coeffs.length-1.

x - the position where to compute the value

Returns:

the predicted value

Throws:

NullPointerException - if coeffs is null

IllegalArgumentException - if coeffs has length 0

mean

public static Polynomial mean(Polynomial[] p)

Compute the mean polynomial from the given polynomials, by building a polynomial of the averaged coefficients.

Parameters:

p - the polynomials from which to compute the mean. they must all have the same order

Returns:

the mean polynomial, of the same order.

mean

public static double[] mean(double[][] p)

Compute the mean polynomial from the given polynomials, by building a polynomial of the averaged coefficients.

Parameters:

p - the polynomials from which to compute the mean. they must all have the same order

Returns:

the mean polynomial, of the same order.

mean

public static float[] mean(float[][] p)

Compute the mean polynomial from the given polynomials, by building a polynomial of the averaged coefficients.

Parameters:

p - the polynomials from which to compute the mean. they must all have the same order

Returns:

the mean polynomial, of the same order.

variance

public static double variance(Polynomial[] p,
              Polynomial mean)

For the given collection of polynomials, for which a mean polynomial has already been computed using mean(Polynomial[]), compute a variance as follows.

V = 1/(p-1) * sum i from 0 to p-1 of integral from 0 to 1 of (p[i]-mean)^2; in other words, the sum of the squared distances (@see{#polynomialSquaredDistance()}) between each polynomial in p and the mean, divided by (p-1).

Parameters:

p - p

mean - mean

Returns:

the variance, a single non-negative double value.

variance

public static double variance(double[][] p,
              double[] mean)

For the given collection of polynomials, for which a mean polynomial has already been computed using mean(double[][]), compute a variance as follows.

V = 1/(p-1) * sum i from 0 to p-1 of integral from 0 to 1 of (p[i]-mean)^2; in other words, the sum of the squared distances (@see{#polynomialSquaredDistance()}) between each polynomial in p and the mean, divided by (p-1).

Parameters:

p - p

mean - mean

Returns:

the variance, a single non-negative double value.

variance

public static double variance(float[][] p,
              float[] mean)

For the given collection of polynomials, for which a mean polynomial has already been computed using mean(float[][]), compute a variance as follows.

V = 1/(p-1) * sum i from 0 to p-1 of integral from 0 to 1 of (p[i]-mean)^2; in other words, the sum of the squared distances (@see{#polynomialSquaredDistance()}) between each polynomial in p and the mean, divided by (p-1).

Parameters:

p - p

mean - mean

Returns:

the variance, a single non-negative double value.

polynomialDistance

public static double polynomialDistance(double[] coeffs1,
                        double[] coeffs2)

Compute the integrated distance between two polynomials of same order. More precisely, this will return the absolute value of the integral from 0 to 1 of the difference between the two functions.

Parameters:

coeffs1 - polynomial coefficients, [a_order, a_(order-1), ..., a_1, a_0]

coeffs2 - polynomial coefficients, [a_order, a_(order-1), ..., a_1, a_0]

Returns:

abs(dist)

polynomialDistance

public static double polynomialDistance(float[] coeffs1,
                        float[] coeffs2)

Compute the integrated distance between two polynomials of same order. More precisely, this will return the absolute value of the integral from 0 to 1 of the difference between the two functions.

Parameters:

coeffs1 - polynomial coefficients, [a_order, a_(order-1), ..., a_1, a_0]

coeffs2 - polynomial coefficients, [a_order, a_(order-1), ..., a_1, a_0]

Returns:

abs(dist)

polynomialSquaredDistance

public static double polynomialSquaredDistance(double[] coeffs1,
                               double[] coeffs2)

Compute the integral of the squared difference between two polynomials of same order. More precisely, this will return the the integral from 0 to 1 of the square of the difference between the two functions.

This implements the algebraic solution proposed by Maxima from the following command: expand(integrate((sum(a[i]*x**i, i, 0, order))**2, x, 0, 1));, with order varied from 0 to 4. Increasing order by 1 adds (order+1) summands.

Parameters:

coeffs1 - polynomial coefficients, [a_order, a_(order-1), ..., a_1, a_0]

coeffs2 - polynomial coefficients, [a_order, a_(order-1), ..., a_1, a_0]

Returns:

integrateSquared(order, a)

polynomialSquaredDistance

public static double polynomialSquaredDistance(float[] coeffs1,
                               float[] coeffs2)

Compute the integral of the squared difference between two polynomials of same order. More precisely, this will return the the integral from 0 to 1 of the square of the difference between the two functions.

This implements the algebraic solution proposed by Maxima from the following command: expand(integrate((sum(a[i]*x**i, i, 0, order))**2, x, 0, 1));, with order varied from 0 to 4. Increasing order by 1 adds (order+1) summands.

Parameters:

coeffs1 - polynomial coefficients, [a_order, a_(order-1), ..., a_1, a_0]

coeffs2 - polynomial coefficients, [a_order, a_(order-1), ..., a_1, a_0]

Returns:

integrateSquared(order, a)

polynomialPearsonProductMomentCorr

public static double polynomialPearsonProductMomentCorr(double[] coeffs1,
                                        double[] coeffs2)

Compute one minus the Pearson product moment correlation between two polynomials of same order.

Equation: D = 1 - corr(F1 * F2)

Purpose: the distance should be less for contours that have a similar shape, so differences in pitch height or pitch range should not be included in the distance measure.

Parameters:

coeffs1 - polynomial coefficients that are not null

coeffs2 - polynomial coefficients that are not null coeffs1, coeffs2 are expected to be coefficients of same order polynomials

Returns:

double distance between two polynomial coefficients

Throws:

NullPointerException - if received polynomial coeffs null

IllegalArgumentException - if the length of coeffs are not equal