zgeqrt.f man page

zgeqrt.f —

Synopsis

Functions/Subroutines

subroutine zgeqrt (M, N, NB, A, LDA, T, LDT, WORK, INFO)
ZGEQRT

Function/Subroutine Documentation

subroutine zgeqrt (integerM, integerN, integerNB, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( ldt, * )T, integerLDT, complex*16, dimension( * )WORK, integerINFO)

ZGEQRT

Purpose:

ZGEQRT computes a blocked QR factorization of a complex M-by-N matrix A
using the compact WY representation of Q.

Parameters:

M

M is INTEGER
The number of rows of the matrix A.  M >= 0.

N

N is INTEGER
The number of columns of the matrix A.  N >= 0.

NB

NB is INTEGER
The block size to be used in the blocked QR.  MIN(M,N) >= NB >= 1.

A

A is COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A.
On exit, the elements on and above the diagonal of the array
contain the min(M,N)-by-N upper trapezoidal matrix R (R is
upper triangular if M >= N); the elements below the diagonal
are the columns of V.

LDA

LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).

T

T is COMPLEX*16 array, dimension (LDT,MIN(M,N))
The upper triangular block reflectors stored in compact form
as a sequence of upper triangular blocks.  See below
for further details.

LDT

LDT is INTEGER
The leading dimension of the array T.  LDT >= NB.

WORK

WORK is COMPLEX*16 array, dimension (NB*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

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2013

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.

Let K=MIN(M,N).  The number of blocks is B = ceiling(K/NB), where each
block is of order NB except for the last block, which is of order 
IB = K - (B-1)*NB.  For each of the B blocks, a upper triangular block
reflector factor is computed: T1, T2, ..., TB.  The NB-by-NB (and IB-by-IB 
for the last block) T's are stored in the NB-by-N matrix T as

             T = (T1 T2 ... TB).

Definition at line 142 of file zgeqrt.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

zgeqrt(3) is an alias of zgeqrt.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK