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zgeqrt3.f -

# SYNOPSIS

## Functions/Subroutines

recursive subroutine zgeqrt3 (M, N, A, LDA, T, LDT, INFO)

ZGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.

# Function/Subroutine Documentation

## recursive subroutine zgeqrt3 (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldt, * )T, integerLDT, integerINFO)

ZGEQRT3 recursively computes a QR factorization of a general real or complex matrix using the compact WY representation of Q.
Purpose:
``` ZGEQRT3 recursively computes a QR factorization of a complex M-by-N
matrix A, using the compact WY representation of Q.

Based on the algorithm of Elmroth and Gustavson,
IBM J. Res. Develop. Vol 44 No. 4 July 2000.
```
Parameters:
M
```          M is INTEGER
The number of rows of the matrix A.  M >= N.
```
N
```          N is INTEGER
The number of columns of the matrix A.  N >= 0.
```
A
```          A is COMPLEX*16 array, dimension (LDA,N)
On entry, the complex M-by-N matrix A.  On exit, the elements on
and above the diagonal contain the N-by-N upper triangular matrix R;
the elements below the diagonal are the columns of V.  See below for
further details.
```
LDA
```          LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).
```
T
```          T is COMPLEX*16 array, dimension (LDT,N)
The N-by-N upper triangular factor of the block reflector.
The elements on and above the diagonal contain the block
reflector T; the elements below the diagonal are not used.
See below for further details.
```
LDT
```          LDT is INTEGER
The leading dimension of the array T.  LDT >= max(1,N).
```
INFO
```          INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
```
Author:
Univ. of Tennessee
Univ. of California Berkeley
NAG Ltd.
Date:
September 2012
Further Details:
```  The matrix V stores the elementary reflectors H(i) in the i-th column
below the diagonal. For example, if M=5 and N=3, the matrix V is

V = (  1       )
( v1  1    )
( v1 v2  1 )
( v1 v2 v3 )
( v1 v2 v3 )

where the vi's represent the vectors which define H(i), which are returned
in the matrix A.  The 1's along the diagonal of V are not stored in A.  The
block reflector H is then given by

H = I - V * T * V**H

where V**H is the conjugate transpose of V.

For details of the algorithm, see Elmroth and Gustavson (cited above).
```
Definition at line 133 of file zgeqrt3.f.

# Author

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