## Developer Reference

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

# ?gelqt

?gelqt
computes a blocked LQ factorization of a real or complex
m
-by-
n
matrix
A
using the compact WY representation of
Q
.
Description
?gelqt
computes a blocked LQ factorization of a real or complex
m
-by-
n
matrix
A
using the compact WY representation of
Q
.
The matrix
V
stores the elementary reflectors
H
(
i
) in the
i
-th row above the diagonal. For example, if
m
=5 and
n
=3, the matrix
V
is
```

V = ( 1 v

1

v

1

v

1

v

1

)
(    1 v

2

v

2

v

2

)
(       1 v

3

v

3

) ```
where the
v
i
s represent the vectors which define
H
(
i
), which are returned in the array
a
. The 1 elements along the diagonal of
V
are not stored in
a
. Let
k
= min(
m
,
n
). The number of blocks is
b
= ceiling(
k
/
mb
), where each block is of order
mb
except for the last block, which is of order
ib
=
k
- (
b
-1)*
mb
. For each of the
b
blocks, a upper triangular block reflector factor is computed:
T1
,
T2
, ...,
TB
. The
mb
-by-
mb
(and
ib
-by-
ib
for the last block)
T
's are stored in the
mb
-by-
k
matrix
T
as
T
= (
T1
T2
...
TB
).
Input Parameters
m
INTEGER
.
The number of rows of the matrix
A
.
m
0.
n
INTEGER
.
The number of columns of the matrix
A
.
n
0.
mb
INTEGER
.
The block size to be used in the blocked QR. min(
m
,
n
)
mb
1.
a
REAL
for