# zgeqrt.f - Man Page

SRC/zgeqrt.f

## Synopsis

### Functions/Subroutines

subroutine zgeqrt (m, n, nb, a, lda, t, ldt, work, info)
ZGEQRT

## Function/Subroutine Documentation

### subroutine zgeqrt (integer m, integer n, integer nb, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( * ) work, integer info)

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.

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-K matrix T as

T = (T1 T2 ... TB).```

Definition at line 140 of file zgeqrt.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zgeqrt(3) is an alias of zgeqrt.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK