Contents

# ?unglq

Generates the complex unitary matrix Q of the LQ factorization formed by
?gelqf
.

## Syntax

Include Files
• mkl.h
Description
The routine generates the whole or part of
n
-by-
n
unitary matrix
Q
of the
LQ
factorization formed by the routines gelqf. Use this routine after a call to
cgelqf
/
zgelqf
.
Usually
Q
is determined from the
LQ
factorization of an
p
-by-
n
matrix
A
with
n
<
p
. To compute the whole matrix
Q
, use:
`info = LAPACKE_?unglq(matrix_layout, n, n, p, a, lda, tau)`
p
rows of
Q
, which form an orthonormal basis in the space spanned by the rows of
A
, use:
`info = LAPACKE_?unglq(matrix_layout, p, n, p, a, lda, tau)`
To compute the matrix
Q
k
of the
LQ
k
rows of
A
, use:
`info = LAPACKE_?unglq(matrix_layout, n, n, k, a, lda, tau)`
k
rows of
Q
k
, which form an orthonormal basis in the space spanned by the leading
k
rows of
A
, use:
`info = LAPACKE_?ungqr(matrix_layout, k, n, k, a, lda, tau)`
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
m
The number of rows of
Q
to be computed (
0
m
n
).
n
The order of the unitary matrix
Q
(
n
m
).
k
The number of elementary reflectors whose product defines the matrix
Q
(
0
k
m
).
a
,
tau
Arrays:
a
(size max(1,
lda
*
n
) for column major layout and max(1,
lda
*
m
) for row major layout)
and
tau
are the arrays returned by
cgelqf
/
zgelqf
.
The dimension of
tau
must be at least max(1,
k
).
lda
a
; at least max(1,
m
)
for column major layout and max(1,
n
) for row major layout
.
Output Parameters
a
Overwritten by
m
n
-by-
n
unitary matrix
Q
.
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
=
-i
, the
i
-th parameter had an illegal value.
Application Notes
The computed
Q
differs from an exactly unitary matrix by a matrix
E
such that
||
E
||
2
=
O
(
ε
)*||
A
||
2
, where
ε
is the machine precision.
The total number of floating-point operations is approximately
16*
m
*
n
*
k
- 8*(
m
+
n
)*
k
2
+ (16/3)*
k
3
.
If
m
=
k
, the number is approximately
(8/3)*
m
2
*(3
n
-
m
)
.
The real counterpart of this routine is orglq.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.