## Developer Reference

• 2020.2
• 07/15/2020
• Public Content
Contents

# ?geqrt

Computes a blocked QR factorization of a general real or complex matrix using the compact WY representation of Q.

## Syntax

Include Files
• mkl.fi
,
lapack.f90
Description
The strictly lower triangular matrix
V
contains 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 where
v
i
represents one of the vectors that define
H
(
i
). The vectors are returned in the lower triangular part of array
a
.
The 1s 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
array
t
as
t
= (
t1
t2
...
tb
)
.
Input Parameters
m
INTEGER
.
The number of rows in the matrix
A
(
m
≥ 0).
n
INTEGER
.
The number of columns in
A
(
n
≥ 0).
nb
INTEGER
.
The block size to be used in the blocked QR (min(
m
,
n
) ≥
nb
≥ 1).
a
,
work
REAL
for
sgeqrt
DOUBLE PRECISION
for
dgeqrt
COMPLEX
for
cgeqrt
COMPLEX*16
for
zgeqrt
.
Arrays:
a
DIMENSION
(
lda
,
n
) contains the
m
-by-
n
matrix
A
.
work
DIMENSION
(
nb
,
n
) is a workspace array.
lda