Developer Reference

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

?geqrt2

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

Syntax

call sgeqrt2
(
m
,
n
,
a
,
lda
,
t
,
ldt
,
info
)
call dgeqrt2
(
m
,
n
,
a
,
lda
,
t
,
ldt
,
info
)
call cgeqrt2
(
m
,
n
,
a
,
lda
,
t
,
ldt
,
info
)
call zgeqrt2
(
m
,
n
,
a
,
lda
,
t
,
ldt
,
info
)
call geqrt2
(
a
,
t
,
[
info
]
)
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
Equation
where
v
i
represents the vector that defines
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
.
The block reflector
H
is then given by
H
=
I
-
V
*
T
*
V
T
for real flavors, and
H
=
I
-
V
*
T
*
V
H
for complex flavors,
where
V
T
is the transpose and
V
H
is the conjugate transpose of
V
.
Input Parameters
m
INTEGER
.
The number of rows in the matrix
A
(
m
n
).
n
INTEGER
.
The number of columns in
A
(
n
≥ 0).
a
REAL
for
sgeqrt2
DOUBLE PRECISION
for
dgeqrt2
COMPLEX
for
cgeqrt2
COMPLEX*16
for
zgeqrt2
.
Array, size
lda
by
n
. Array
a
contains the
m
-by-
n
matrix
A
.
lda
INTEGER
.
The leading dimension of
a
; at least max(1,
m
).
ldt
INTEGER
.
The leading dimension of
t
; at least max(1,
n
).
Output Parameters
a
Overwritten by the factorization data as follows:
The elements on and above the diagonal of the array contain the
n
-by-
n
upper triangular matrix
R