Developer Reference

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

p?ggqrf

Computes the generalized QR factorization.

Syntax

call psggqrf
(
n
,
m
,
p
,
a
,
ia
,
ja
,
desca
,
taua
,
b
,
ib
,
jb
,
descb
,
taub
,
work
,
lwork
,
info
)
call pdggqrf
(
n
,
m
,
p
,
a
,
ia
,
ja
,
desca
,
taua
,
b
,
ib
,
jb
,
descb
,
taub
,
work
,
lwork
,
info
)
call pcggqrf
(
n
,
m
,
p
,
a
,
ia
,
ja
,
desca
,
taua
,
b
,
ib
,
jb
,
descb
,
taub
,
work
,
lwork
,
info
)
call pzggqrf
(
n
,
m
,
p
,
a
,
ia
,
ja
,
desca
,
taua
,
b
,
ib
,
jb
,
descb
,
taub
,
work
,
lwork
,
info
)
Include Files
Description
The
p?ggqrf
routine
forms the generalized
Q
R
factorization of an
n
-by-
m
matrix
sub(
A
) =
A
(
ia
:
ia
+
n
-1,
ja
:
ja
+
m
-1)
and an
n
-by-
p
matrix
sub(
B
) =
B
(
ib
:
ib
+
n
-1,
jb
:
jb
+
p
-1):
as
sub(
A) =
Q
*
R
, sub(
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:
If
n
m
Equation
or if
n
<
m
Equation
where
R
11
is upper triangular, and
Equation
Equation
where
T
12
or
T
21
is an upper triangular matrix.
In particular, if sub(
B
) is square and nonsingular, the
GQR
factorization of sub(
A
) and sub(
B
) implicitly gives the
Q
R
factorization of inv (sub(
B
))* sub (
A
):
inv(sub(
B
))*sub(
A
) =
Z
H
*(inv(
T)
*
R
)
Input Parameters
n
(global)