# zgeqrt.f(3) [centos man page]

```zgeqrt.f(3)							      LAPACK							       zgeqrt.f(3)

NAME
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

NAG Ltd.

Date:
November 2011

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.

Version 3.4.2							  Tue Sep 25 2012						       zgeqrt.f(3)```

## Check Out this Related Man Page

```zgeqrt.f(3)							      LAPACK							       zgeqrt.f(3)

NAME
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

NAG Ltd.

Date:
November 2011

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.

Version 3.4.1							  Sun May 26 2013						       zgeqrt.f(3)```
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