de.jtem.riemann.theta

Class ExampleSlice

java.lang.Object

de.jtem.riemann.theta.ExampleSlice

public class ExampleSlice
extends Object

Example from the paper Computing Riemann Theta Functions.

The example computes the following slice on a 101x101 sample:

(x,y) |-> thetaSum( (x+iy,0) |B) .

Attention! This example has no visual output.

Below the source code of this example:

  package de.jtem.riemann.theta;
 
  import de.jtem.mfc.field.Field;
  import de.jtem.blas.ComplexVector;
  import de.jtem.blas.ComplexMatrix;
  
  public class ExampleSlice {
 
     public static void main( String [] argv ) { 
 
        Field.Complex factor = new Field.Complex();
        Field.Complex sum    = new Field.Complex();

        // create the period matrix
        ComplexMatrix B = new ComplexMatrix( 2 ); 
 
        // set the period matrix
 
        B.set( 0,0, 1.690983006, 0.9510565162 ); 
        B.set( 0,1, 1.500000000, 0.3632712640 );
 
        B.set( 1,0, 1.500000000, 0.3632712640 ); 
        B.set( 1,1, 1.309016994, 0.9510565162 );
 
        // use the different normalization
        B.assignTimes( new Field.Complex( 0, 2 * Math.PI ) );
 
        // create a complex argument vector
        ComplexVector V = new ComplexVector( 2 );
 
        // create a theta function instance with period matrix 
        Theta theta = new Theta( B, 0.0001 ); 
 
        // create storage for the slice
        Field.Complex[][] slice = new Field.Complex[101][101]; 
 
        // create dummy variable for the factor
        Field.Complex factor = new Field.Complex();

        // loop over grid
        for( int i=0; i<101; i++ )
 
        for( int j=0; j<101; j++ ) {
 
             // set grid vector
             V.set( 0, 2 * i * Math.PI / 100, 2 * j *  Math.PI / 100 ); 
 
             // evaluate theta function at grid vector
             theta.theta( V, factor, slice[i][j] ); 
        }
     }
  }
 

Author:

Markus Schmies

See Also:

Theta

Constructor Summary

Constructors

Constructor and Description
ExampleSlice()

Method Summary

Modifier and Type	Method and Description
static void	main(String[] argv)

Methods inherited from class java.lang.Object

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

Constructor Detail

ExampleSlice

public ExampleSlice()

Method Detail

main

public static void main(String[] argv)