|
||||||||||
| PREV CLASS NEXT CLASS | FRAMES NO FRAMES | |||||||||
| SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD | |||||||||
java.lang.Objectorg.apache.commons.math3.analysis.polynomials.PolynomialsUtils
public class PolynomialsUtils
A collection of static methods that operate on or return polynomials.
| Method Summary | |
|---|---|
static PolynomialFunction |
createChebyshevPolynomial(int degree)
Create a Chebyshev polynomial of the first kind. |
static PolynomialFunction |
createHermitePolynomial(int degree)
Create a Hermite polynomial. |
static PolynomialFunction |
createJacobiPolynomial(int degree,
int v,
int w)
Create a Jacobi polynomial. |
static PolynomialFunction |
createLaguerrePolynomial(int degree)
Create a Laguerre polynomial. |
static PolynomialFunction |
createLegendrePolynomial(int degree)
Create a Legendre polynomial. |
static double[] |
shift(double[] coefficients,
double shift)
Compute the coefficients of the polynomial Ps(x)
whose values at point x will be the same as the those from the
original polynomial P(x) when computed at x + shift. |
| Methods inherited from class java.lang.Object |
|---|
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
| 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
public static PolynomialFunction createJacobiPolynomial(int degree,
int v,
int w)
Jacobi polynomials are orthogonal polynomials. They can be defined by the following recurrence relations:
P0vw(X) = 1
P-1vw(X) = 0
2k(k + v + w)(2k + v + w - 2) Pkvw(X) =
(2k + v + w - 1)[(2k + v + w)(2k + v + w - 2) X + v2 - w2] Pk-1vw(X)
- 2(k + v - 1)(k + w - 1)(2k + v + w) Pk-2vw(X)
degree - degree of the polynomialv - first exponentw - second exponent
public static double[] shift(double[] coefficients,
double shift)
Ps(x)
whose values at point x will be the same as the those from the
original polynomial P(x) when computed at x + shift.
Thus, if P(x) = Σi ai xi,
then
Ps(x) |
= Σi bi xi |
| = Σi ai (x + shift)i |
coefficients - Coefficients of the original polynomial.shift - Shift value.
bi of the shifted
polynomial.
|
||||||||||
| PREV CLASS NEXT CLASS | FRAMES NO FRAMES | |||||||||
| SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD | |||||||||