Developer Reference

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

?ungqr

Generates the complex unitary matrix Q of the QR factorization formed by
?geqrf
.

Syntax

lapack_int
LAPACKE_cungqr
(
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_zungqr
(
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
m
-by-
m
unitary matrix
Q
of the
QR
factorization formed by the routines
?geqrf
or geqpf. Use this routine after a call to
cgeqrf
/
zgeqrf
or
cgeqpf
/
zgeqpf
.
Usually
Q
is determined from the
QR
factorization of an
m
by
p
matrix
A
with
m
p
. To compute the whole matrix
Q
, use:
LAPACKE_?ungqr(matrix_layout, m, m, p, a, lda, tau)
To compute the leading
p
columns of
Q
(which form an orthonormal basis in the space spanned by the columns of
A
):
LAPACKE_?ungqr(matrix_layout, m, p, p, a, lda, tau)
To compute the matrix
Q
k
of the
QR
factorization of the leading
k
columns of the matrix
A
:
LAPACKE_?ungqr(matrix_layout, m, m, k, a, lda, tau)
To compute the leading
k
columns of
Q
k
(which form an orthonormal basis in the space spanned by the leading
k
columns of the matrix
A
):
LAPACKE_?ungqr(matrix_layout, m, k, 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 order of the unitary matrix
Q
(
m
0
).
n
The number of columns of
Q
to be computed
(0
n
m
).
k
The number of elementary reflectors whose product defines the matrix
Q
(0
k
n
).
a
,
tau
Arrays:
a
and
tau
are the arrays returned by
cgeqrf
/
zgeqrf
or
cgeqpf
/
zgeqpf
.
The size of
a
is max(1,
lda
*
n
) for column major layout and max(1,
lda
*
m
) for row major layout .
The size 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
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
n
=
k
, the number is approximately
(8/3)*
n
2
*(3
m
-
n
)
.
The real counterpart of this routine is orgqr.

Product and Performance Information

1

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