Developer Reference

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

?ggqrf

Computes the generalized QR factorization of two matrices.

Syntax

call sggqrf
(
n
,
m
,
p
,
a
,
lda
,
taua
,
b
,
ldb
,
taub
,
work
,
lwork
,
info
)
call dggqrf
(
n
,
m
,
p
,
a
,
lda
,
taua
,
b
,
ldb
,
taub
,
work
,
lwork
,
info
)
call cggqrf
(
n
,
m
,
p
,
a
,
lda
,
taua
,
b
,
ldb
,
taub
,
work
,
lwork
,
info
)
call zggqrf
(
n
,
m
,
p
,
a
,
lda
,
taua
,
b
,
ldb
,
taub
,
work
,
lwork
,
info
)
call ggqrf
(
a
,
b
[
,
taua
]
[
,
taub
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine forms the generalized
QR
factorization of an
n
-by-
m
matrix
A
and an
n
-by-
p
matrix
B
as
A
=
Q
*
R
,
B
=
Q
*
T
*
Z
, where
Q
is an
n
-by-
n
orthogonal/unitary matrix,
Z
is a
p
-by-
p
orthogonal/unitary matrix, and
R
and
T
assume one of the forms:
Equation
or
Equation
where
R
11
is upper triangular, and
Equation
Equation
where
T
12
or
T
21
is a
p
-by-
p
upper triangular matrix.
In particular, if
B
is square and nonsingular, the
GQR
factorization of
A
and
B
implicitly gives the
QR
factorization of
B
-1
A
as:
B
-1
*
A
=
Z
T
*(
T
-1
*
R
)
(for real flavors) or
B
-1
*
A
=
Z
H
*(
T
-1
*
R
)
(for complex flavors).
Input Parameters
n
INTEGER
.
The number of rows of the matrices
A
and
B
(
n
0
).
m
INTEGER
.
The number of colu