Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 2021.1
  • 12/04/2020
  • Public Content
Contents

?unglq

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

Syntax

lapack_int
LAPACKE_cunglq
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
lapack_complex_float
*
a
,
lapack_int
lda
,
const
lapack_complex_float
*
tau
);
lapack_int
LAPACKE_zunglq
(
int
matrix_layout
,
lapack_int
m
,
lapack_int
n
,
lapack_int
k
,
lapack_complex_double
*
a
,
lapack_int
lda
,
const
lapack_complex_double
*
tau
);
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)
To compute the leading
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
 factorization of the leading
k
 rows of
A
, use: 
info = LAPACKE_?unglq(matrix_layout, n, n, k, a, lda, tau)
To compute the leading
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
The leading dimension of
a
; at least max(1,
m
)
for column major layout and max(1,
n
) for row major layout
.
Output Parameters
a
Overwritten by
m
 leading rows of the
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.