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java.lang.Object  +numericalMethods.algebra.linear.decompose.QR
Computes for a square matrix A the matrices Q and R complying A=Q·R. The algorithm used is equivalent to Gram Schmidt orthonormalising.
This algorithm is implemented for both real and complex valued equation systems. And each method is again available in two version.
One version is an optimized version that consumes as few resources as possible.
The other version is an easy to use version that takes care of for example not changing any arguments where not expected. But this version can sometimes be very resource consuming!
Method versions for A=Q·R:
This class does not check any arguments for validity!
optimized easy to use real valued decompose(Q,R)
decompose(A,Q,R)
complex valued decompose(Q,R)
decompose(A,Q,R)
Constructor Summary  
QR()

Method Summary  
static double 
decompose(double[][] Q,
double[][] R)
Decomposes a real matrix. 
static double 
decompose(double[][] A,
double[][] Q,
double[][] R)
Decomposes a real matrix. 
static double[] 
decompose(double[][] Q_re,
double[][] Q_im,
double[][] R_re,
double[][] R_im)
Decomposes a complex matrix. 
static double[] 
decompose(double[][] A_re,
double[][] A_im,
double[][] Q_re,
double[][] Q_im,
double[][] R_re,
double[][] R_im)
Decomposes a complex matrix. 
Methods inherited from class java.lang.Object 

Constructor Detail 
public QR()
Method Detail 
public static double decompose(double[][] Q, double[][] R)
Q
 The matrix to decompose and afterwards the orthogonal
matrix.R
 A matrix taking the right triangular matrix.public static double decompose(double[][] A, double[][] Q, double[][] R)
A
 The matrix to decompose.Q
 A matrix taking the orthogonal matrix.R
 A matrix taking the right triangular matrix.public static double[] decompose(double[][] Q_re, double[][] Q_im, double[][] R_re, double[][] R_im)
Q_re
 The real part of the matrix to decompose and afterwards
the real part of the unitary matrix.Q_im
 The imaginary part of the matrix to decompose and
afterwards the imaginary part of the unitary matrix.R_re
 A matrix taking the real part of the right triangular
matrix.R_im
 A matrix taking the imaginary part of the right
triangular matrix.public static double[] decompose(double[][] A_re, double[][] A_im, double[][] Q_re, double[][] Q_im, double[][] R_re, double[][] R_im)
A_re
 The real part of the matrix to decompose.A_im
 The imaginary part of the matrix to decompose.Q_re
 A matrix taking the real part of the unitary matrix.Q_im
 A matrix taking the imaginary part of the unitary
matrix.R_re
 A matrix taking the real part of the right triangular
matrix.R_im
 A matrix taking the imaginary part of the right
triangular matrix.


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