de.jtem.ellipticFunctions

## Class Elliptic

• Direct Known Subclasses:
Jacobi

```public class Elliptic
extends Object```
Class provides Jacobi's elliptic theta functions.
Author:
Markus Schmies, Boris Springborn
• ### Method Summary

All Methods
Modifier and Type Method and Description
`static de.jtem.mfc.field.Complex` ```theta(de.jtem.mfc.field.Complex z, de.jtem.mfc.field.Complex tau)```
Computes θ(z,τ).
`static void` ```theta(de.jtem.mfc.field.Complex w, de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex z, de.jtem.mfc.field.Complex logOfC, de.jtem.mfc.field.Complex thetaOfZ)```
Helps to compute θ(w,τ) = c θ(z,τ).
`static de.jtem.mfc.field.Complex` ```theta0(de.jtem.mfc.field.Complex z, de.jtem.mfc.field.Complex tau)```
Computes θ0(z,τ).
`static void` ```theta0(de.jtem.mfc.field.Complex w, de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex z, de.jtem.mfc.field.Complex logOfC, de.jtem.mfc.field.Complex thetaOfZ)```
Helps to compute θ0(w,τ) = c θ(z,τ).
`static de.jtem.mfc.field.Complex` ```theta1(de.jtem.mfc.field.Complex z, de.jtem.mfc.field.Complex tau)```
Computes θ1(z,τ).
`static void` ```theta1(de.jtem.mfc.field.Complex w, de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex z, de.jtem.mfc.field.Complex logOfC, de.jtem.mfc.field.Complex thetaOfZ)```
Helps to compute θ1(w,τ) = c θ(z,τ).
`static de.jtem.mfc.field.Complex` ```theta2(de.jtem.mfc.field.Complex z, de.jtem.mfc.field.Complex tau)```
Computes θ2(z,τ).
`static void` ```theta2(de.jtem.mfc.field.Complex w, de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex z, de.jtem.mfc.field.Complex logOfC, de.jtem.mfc.field.Complex thetaOfZ)```
Helps to compute θ2(w,τ) = c θ(z,τ).
`static de.jtem.mfc.field.Complex` ```theta3(de.jtem.mfc.field.Complex z, de.jtem.mfc.field.Complex tau)```
Computes θ3(z,τ).
`static void` ```theta3(de.jtem.mfc.field.Complex w, de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex z, de.jtem.mfc.field.Complex logOfC, de.jtem.mfc.field.Complex thetaOfZ)```
Helps to compute θ3(w,τ) = c θ(z,τ).
`static de.jtem.mfc.field.Complex` ```theta4(de.jtem.mfc.field.Complex z, de.jtem.mfc.field.Complex tau)```
Computes θ4(w,τ).
`static void` ```theta4(de.jtem.mfc.field.Complex w, de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.Complex z, de.jtem.mfc.field.Complex logOfC, de.jtem.mfc.field.Complex thetaOfZ)```
Helps to compute θ4(w,τ) = c θ(z,τ).
`static de.jtem.mfc.field.Complex[]` `thetaConstants(de.jtem.mfc.field.Complex tau)`
Returns theta constants θ0(0,τ), θ1(0,τ) = 0, θ2(0,τ) = 0, and θ3(0,τ).
`static void` ```thetaConstants(de.jtem.mfc.field.Complex tau, de.jtem.mfc.field.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

• #### theta1

```public static de.jtem.mfc.field.Complex theta1(de.jtem.mfc.field.Complex z,
de.jtem.mfc.field.Complex tau)```
Computes θ1(z,τ).
Parameters:
`z` - argument
`tau` - lattice parameter
Returns:
θ1(z,τ)
`theta1(Complex,Complex,Complex,Complex,Complex)`
• #### theta1

```public static void theta1(de.jtem.mfc.field.Complex w,
de.jtem.mfc.field.Complex tau,
de.jtem.mfc.field.Complex z,
de.jtem.mfc.field.Complex logOfC,
de.jtem.mfc.field.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)
`theta1(Complex,Complex)`
• #### theta2

```public static de.jtem.mfc.field.Complex theta2(de.jtem.mfc.field.Complex z,
de.jtem.mfc.field.Complex tau)```
Computes θ2(z,τ).
Parameters:
`z` - argument
`tau` - lattice parameter
Returns:
θ2(z,τ)
`theta2(Complex,Complex,Complex,Complex,Complex)`
• #### theta2

```public static void theta2(de.jtem.mfc.field.Complex w,
de.jtem.mfc.field.Complex tau,
de.jtem.mfc.field.Complex z,
de.jtem.mfc.field.Complex logOfC,
de.jtem.mfc.field.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)
`theta2(Complex,Complex)`
• #### theta3

```public static de.jtem.mfc.field.Complex theta3(de.jtem.mfc.field.Complex z,
de.jtem.mfc.field.Complex tau)```
Computes θ3(z,τ).
Parameters:
`z` - argument
`tau` - lattice parameter
Returns:
θ3(z,τ)
`theta3(Complex,Complex,Complex,Complex,Complex)`
• #### theta3

```public static void theta3(de.jtem.mfc.field.Complex w,
de.jtem.mfc.field.Complex tau,
de.jtem.mfc.field.Complex z,
de.jtem.mfc.field.Complex logOfC,
de.jtem.mfc.field.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)
`theta3(Complex,Complex)`
• #### thetaConstants

`public static de.jtem.mfc.field.Complex[] thetaConstants(de.jtem.mfc.field.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)
• #### thetaConstants

```public static void thetaConstants(de.jtem.mfc.field.Complex tau,
de.jtem.mfc.field.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
`c` - array with the four theta constants (on output)

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