|
|||||||||
PREV CLASS NEXT CLASS | FRAMES NO FRAMES | ||||||||
SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |
java.lang.Objectorg.apache.commons.math.analysis.polynomials.PolynomialsUtils
public class PolynomialsUtils
A collection of static methods that operate on or return polynomials.
Nested Class Summary | |
---|---|
private static interface |
PolynomialsUtils.RecurrenceCoefficientsGenerator
Interface for recurrence coefficients generation. |
Field Summary | |
---|---|
private static java.util.ArrayList<BigFraction> |
CHEBYSHEV_COEFFICIENTS
Coefficients for Chebyshev polynomials. |
private static java.util.ArrayList<BigFraction> |
HERMITE_COEFFICIENTS
Coefficients for Hermite polynomials. |
private static java.util.ArrayList<BigFraction> |
LAGUERRE_COEFFICIENTS
Coefficients for Laguerre polynomials. |
private static java.util.ArrayList<BigFraction> |
LEGENDRE_COEFFICIENTS
Coefficients for Legendre polynomials. |
Constructor Summary | |
---|---|
private |
PolynomialsUtils()
Private constructor, to prevent instantiation. |
Method Summary | |
---|---|
private static PolynomialFunction |
buildPolynomial(int degree,
java.util.ArrayList<BigFraction> coefficients,
PolynomialsUtils.RecurrenceCoefficientsGenerator generator)
Get the coefficients array for a given degree. |
private static void |
computeUpToDegree(int degree,
int maxDegree,
PolynomialsUtils.RecurrenceCoefficientsGenerator generator,
java.util.ArrayList<BigFraction> coefficients)
Compute polynomial coefficients up to a given degree. |
static PolynomialFunction |
createChebyshevPolynomial(int degree)
Create a Chebyshev polynomial of the first kind. |
static PolynomialFunction |
createHermitePolynomial(int degree)
Create a Hermite polynomial. |
static PolynomialFunction |
createLaguerrePolynomial(int degree)
Create a Laguerre polynomial. |
static PolynomialFunction |
createLegendrePolynomial(int degree)
Create a Legendre polynomial. |
Methods inherited from class java.lang.Object |
---|
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Field Detail |
---|
private static final java.util.ArrayList<BigFraction> CHEBYSHEV_COEFFICIENTS
private static final java.util.ArrayList<BigFraction> HERMITE_COEFFICIENTS
private static final java.util.ArrayList<BigFraction> LAGUERRE_COEFFICIENTS
private static final java.util.ArrayList<BigFraction> LEGENDRE_COEFFICIENTS
Constructor Detail |
---|
private PolynomialsUtils()
Method Detail |
---|
public static PolynomialFunction createChebyshevPolynomial(int degree)
Chebyshev polynomials of the first kind are orthogonal polynomials. They can be defined by the following recurrence relations:
T0(X) = 1 T1(X) = X Tk+1(X) = 2X Tk(X) - Tk-1(X)
degree
- degree of the polynomial
public static PolynomialFunction createHermitePolynomial(int degree)
Hermite polynomials are orthogonal polynomials. They can be defined by the following recurrence relations:
H0(X) = 1 H1(X) = 2X Hk+1(X) = 2X Hk(X) - 2k Hk-1(X)
degree
- degree of the polynomial
public static PolynomialFunction createLaguerrePolynomial(int degree)
Laguerre polynomials are orthogonal polynomials. They can be defined by the following recurrence relations:
L0(X) = 1 L1(X) = 1 - X (k+1) Lk+1(X) = (2k + 1 - X) Lk(X) - k Lk-1(X)
degree
- degree of the polynomial
public static PolynomialFunction createLegendrePolynomial(int degree)
Legendre polynomials are orthogonal polynomials. They can be defined by the following recurrence relations:
P0(X) = 1 P1(X) = X (k+1) Pk+1(X) = (2k+1) X Pk(X) - k Pk-1(X)
degree
- degree of the polynomial
private static PolynomialFunction buildPolynomial(int degree, java.util.ArrayList<BigFraction> coefficients, PolynomialsUtils.RecurrenceCoefficientsGenerator generator)
degree
- degree of the polynomialcoefficients
- list where the computed coefficients are storedgenerator
- recurrence coefficients generator
private static void computeUpToDegree(int degree, int maxDegree, PolynomialsUtils.RecurrenceCoefficientsGenerator generator, java.util.ArrayList<BigFraction> coefficients)
degree
- maximal degreemaxDegree
- current maximal degreegenerator
- recurrence coefficients generatorcoefficients
- list where the computed coefficients should be appended
|
|||||||||
PREV CLASS NEXT CLASS | FRAMES NO FRAMES | ||||||||
SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |