numericalMethods.algebra.loopGroup
Class IwasawaFactorization

java.lang.Object
  |
  +--numericalMethods.algebra.loopGroup.IwasawaFactorization

public class IwasawaFactorization
extends java.lang.Object

Computes the Iwasawa factorization of a GL_n(C)-valued loop.


Constructor Summary
IwasawaFactorization()
           
 
Method Summary
static void factor(double[][][] xRe, double[][][] xIm, double[][][] fRe, double[][][] fIm, double[][] uRe, double[][] uIm, double[] dRe, double[] dIm, double[] pRe, double[] pIm, double[][] zRe, double[][] zIm, double[][] gRe, double[][] gIm, int blockSize)
          Compute Iwasawa factorization.
static void factor(double[][][] xRe, double[][][] xIm, double[][][] fRe, double[][][] fIm, int blockSize)
          Compute Iwasawa factorization Input: (xRe, xIm), R Output: (fRe, fIm)
static void positivePart(double[][][] xRe, double[][][] xIm, double[][][] fRe, double[][][] fIm, double[][][] bRe, double[][][] bIm)
          Matrix Laurent series multiplication b = star(f) * x Assumes degrees f: (-N, N), x: (-N, N), b: (0, N) Used to compute the positive part of the factorization.
static void positivePart(double[][][] xRe, double[][][] xIm, double[][][] fRe, double[][][] fIm, double[][][] bRe, double[][][] bIm, double[] tmpRe, double[] tmpIm)
           
 
Methods inherited from class java.lang.Object
, clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

IwasawaFactorization

public IwasawaFactorization()
Method Detail

factor

public static void factor(double[][][] xRe,
                          double[][][] xIm,
                          double[][][] fRe,
                          double[][][] fIm,
                          int blockSize)
Compute Iwasawa factorization Input: (xRe, xIm), R Output: (fRe, fIm)

factor

public static void factor(double[][][] xRe,
                          double[][][] xIm,
                          double[][][] fRe,
                          double[][][] fIm,
                          double[][] uRe,
                          double[][] uIm,
                          double[] dRe,
                          double[] dIm,
                          double[] pRe,
                          double[] pIm,
                          double[][] zRe,
                          double[][] zIm,
                          double[][] gRe,
                          double[][] gIm,
                          int blockSize)
Compute Iwasawa factorization. Input: (xRe, xIm) Output: (fRe, fIm) The rest are temporaries.

positivePart

public static void positivePart(double[][][] xRe,
                                double[][][] xIm,
                                double[][][] fRe,
                                double[][][] fIm,
                                double[][][] bRe,
                                double[][][] bIm)
Matrix Laurent series multiplication b = star(f) * x Assumes degrees f: (-N, N), x: (-N, N), b: (0, N) Used to compute the positive part of the factorization.

positivePart

public static void positivePart(double[][][] xRe,
                                double[][][] xIm,
                                double[][][] fRe,
                                double[][][] fIm,
                                double[][][] bRe,
                                double[][][] bIm,
                                double[] tmpRe,
                                double[] tmpIm)