org.jscience.mathematics.analysis.elliptic
Class Elliptic

java.lang.Object
  extended by org.jscience.mathematics.analysis.elliptic.Elliptic
Direct Known Subclasses:
Jacobi

public class Elliptic
extends java.lang.Object

Class provides Jacobi's elliptic theta functions.


Method Summary
static Complex theta(Complex z, Complex tau)
          Computes θ(z,τ).
static void theta(Complex w, Complex tau, Complex z, Complex logOfC, Complex thetaOfZ)
          Helps to compute θ(w,τ) = c θ(z,τ).
static Complex theta0(Complex z, Complex tau)
          Computes θ0(z,τ).
static void theta0(Complex w, Complex tau, Complex z, Complex logOfC, Complex thetaOfZ)
          Helps to compute θ0(w,τ) = c θ(z,τ).
static Complex theta1(Complex z, Complex tau)
          Computes θ1(z,τ).
static void theta1(Complex w, Complex tau, Complex z, Complex logOfC, Complex thetaOfZ)
          Helps to compute θ1(w,τ) = c θ(z,τ).
static Complex theta2(Complex z, Complex tau)
          Computes θ2(z,τ).
static void theta2(Complex w, Complex tau, Complex z, Complex logOfC, Complex thetaOfZ)
          Helps to compute θ2(w,τ) = c θ(z,τ).
static Complex theta3(Complex z, Complex tau)
          Computes θ3(z,τ).
static void theta3(Complex w, Complex tau, Complex z, Complex logOfC, Complex thetaOfZ)
          Helps to compute θ3(w,τ) = c θ(z,τ).
static Complex theta4(Complex z, Complex tau)
          Computes θ4(w,τ).
static void theta4(Complex w, Complex tau, Complex z, Complex logOfC, Complex thetaOfZ)
          Helps to compute θ4(w,τ) = c θ(z,τ).
static Complex[] thetaConstants(Complex tau)
          Returns theta constants θ0(0,τ), θ1(0,τ) = 0, θ2(0,τ) = 0, and θ3(0,τ).
static void thetaConstants(Complex tau, Complex[] c)
          Computes theta constants θ0(0,τ), θ1(0,τ) = 0, θ2(0,τ) = 0, and θ3(0,τ).
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Method Detail

thetaConstants

public static void thetaConstants(Complex tau,
                                  Complex[] c)
Computes theta constants θ0(0,τ), θ1(0,τ) = 0, θ2(0,τ) = 0, and θ3(0,τ). The result is stored in the array c. The array may have null entries, which causes the routine to create instances.

Parameters:
tau - lattice paramter τ
eps - absoute error for theta functions
c - array with the four theta constants (on output)

thetaConstants

public static Complex[] thetaConstants(Complex tau)
Returns theta constants θ0(0,τ), θ1(0,τ) = 0, θ2(0,τ) = 0, and θ3(0,τ). The result is stored in the array c. The array may have null entries, which causes the routine to create instances.

Parameters:
tau - lattice paramter τ
Returns:
array with the four theta constants (on output)

theta

public static Complex theta(Complex z,
                            Complex tau)
Computes θ(z,τ). θ, θ0, θ4 refer to the same function, thus theta(Complex,Complex) , theta0(Complex,Complex), and theta4(Complex,Complex) are identical.

Parameters:
z - argument
tau - lattice parameter
Returns:
θ(z,τ)
See Also:
theta(Complex,Complex,Complex,Complex,Complex)

theta

public static void theta(Complex w,
                         Complex tau,
                         Complex z,
                         Complex logOfC,
                         Complex thetaOfZ)
Helps to compute θ(w,τ) = c θ(z,τ). θ, θ0, θ4 refer to the same function, thus theta(Complex,Complex,Complex,Complex,Complex), theta0(Complex,Complex,Complex,Complex,Complex), and theta4(Complex,Complex,Complex,Complex,Complex) are idenical.

Parameters:
w - argument
tau - lattice parameter
z - = x π + y π τ with -0.5 <= x,y <= 0.5 (on output)
logOfC - equals log(c) (on output)
thetaOfZ - equals θ(z,τ) (on output)
See Also:
theta(Complex,Complex)

theta0

public static Complex theta0(Complex z,
                             Complex tau)
Computes θ0(z,τ). θ, θ0, θ4 refer to the same function, thus theta(Complex,Complex), theta0(Complex,Complex), and theta4(Complex,Complex) are identical.

Parameters:
z - argument
tau - lattice parameter
Returns:
θ0(z,τ)
See Also:
theta0(Complex,Complex,Complex,Complex,Complex)

theta0

public static void theta0(Complex w,
                          Complex tau,
                          Complex z,
                          Complex logOfC,
                          Complex thetaOfZ)
Helps to compute θ0(w,τ) = c θ(z,τ). θ, θ0, θ4 refer to the same function, thus theta(Complex,Complex,Complex,Complex,Complex), theta0(Complex,Complex,Complex,Complex,Complex), and theta4(Complex,Complex,Complex,Complex,Complex) are identical.

Parameters:
w - argument
tau - lattice parameter
z - = x π + y π τ with -0.5 <= x,y <= 0.5 (on output)
logOfC - equals log(c) (on output)
thetaOfZ - equals θ(z,τ) (on output)
See Also:
theta0(Complex,Complex)

theta1

public static Complex theta1(Complex z,
                             Complex tau)
Computes θ1(z,τ).

Parameters:
z - argument
tau - lattice parameter
Returns:
θ1(z,τ)
See Also:
theta1(Complex,Complex,Complex,Complex,Complex)

theta1

public static void theta1(Complex w,
                          Complex tau,
                          Complex z,
                          Complex logOfC,
                          Complex thetaOfZ)
Helps to compute θ1(w,τ) = c θ(z,τ).

Parameters:
w - argument
tau - lattice parameter
z - equals x π + y π τ with -0.5 <= x,y <= 0.5 (on output)
logOfC - equals log(c) (on output)
thetaOfZ - equals θ(z,τ) (on output)
See Also:
theta1(Complex,Complex)

theta2

public static Complex theta2(Complex z,
                             Complex tau)
Computes θ2(z,τ).

Parameters:
z - argument
tau - lattice parameter
Returns:
θ2(z,τ)
See Also:
theta2(Complex,Complex,Complex,Complex,Complex)

theta2

public static void theta2(Complex w,
                          Complex tau,
                          Complex z,
                          Complex logOfC,
                          Complex thetaOfZ)
Helps to compute θ2(w,τ) = c θ(z,τ).

Parameters:
w - argument
tau - lattice parameter
z - equals x π + y π τ with -0.5 <= x,y <= 0.5 (on output)
logOfC - equals log(c) (on output)
thetaOfZ - equals θ(z,τ) (on output)
See Also:
theta2(Complex,Complex)

theta3

public static Complex theta3(Complex z,
                             Complex tau)
Computes θ3(z,τ).

Parameters:
z - argument
tau - lattice parameter
Returns:
θ3(z,τ)
See Also:
theta3(Complex,Complex,Complex,Complex,Complex)

theta3

public static void theta3(Complex w,
                          Complex tau,
                          Complex z,
                          Complex logOfC,
                          Complex thetaOfZ)
Helps to compute θ3(w,τ) = c θ(z,τ).

Parameters:
w - argument
tau - lattice parameter
z - equals x π + y π τ with -0.5 <= x,y <= 0.5 (on output)
logOfC - equals log(c) (on output)
thetaOfZ - equals θ(z,τ) (on output)
See Also:
theta3(Complex,Complex)

theta4

public static Complex theta4(Complex z,
                             Complex tau)
Computes θ4(w,τ). θ, θ0, θ4 refer to the same function, thus theta(Complex,Complex), theta0(Complex,Complex), and theta4(Complex,Complex) are identical.

Parameters:
z - argument
tau - lattice parameter
See Also:
theta4(Complex,Complex,Complex,Complex,Complex)

theta4

public static void theta4(Complex w,
                          Complex tau,
                          Complex z,
                          Complex logOfC,
                          Complex thetaOfZ)
Helps to compute θ4(w,τ) = c θ(z,τ). θ, θ0, θ4 refer to the same function, thus theta(Complex,Complex,Complex,Complex,Complex), theta0(Complex,Complex,Complex,Complex,Complex), and theta4(Complex,Complex,Complex,Complex,Complex) are identical.

Parameters:
w - argument
tau - lattice parameter
z - = x π + y π τ with -0.5 <= x,y <= 0.5 (on output)
logOfC - =log(c) (on output)
theta3OfZ - = θ4(z,τ) (on output)
See Also:
theta4(Complex,Complex)