Developer Reference

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

?tpqrt

Computes a blocked QR factorization of a real or complex "triangular-pentagonal" matrix, which is composed of a triangular block and a pentagonal block, using the compact WY representation for Q.

Syntax

call stpqrt
(
m
,
n
,
l
,
nb
,
a
,
lda
,
b
,
ldb
,
t
,
ldt
,
work
,
info
)
call dtpqrt
(
m
,
n
,
l
,
nb
,
a
,
lda
,
b
,
ldb
,
t
,
ldt
,
work
,
info
)
call ctpqrt
(
m
,
n
,
l
,
nb
,
a
,
lda
,
b
,
ldb
,
t
,
ldt
,
work
,
info
)
call ztpqrt
(
m
,
n
,
l
,
nb
,
a
,
lda
,
b
,
ldb
,
t
,
ldt
,
work
,
info
)
call tpqrt
(
a
,
b
,
t
,
nb
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The input matrix
C
is an (
n
+
m
)-by-
n
matrix
Equation
where
A
is an
n
-by-
n
upper triangular matrix, and
B
is an
m
-by-
n
pentagonal matrix consisting of an (
m
-
l
)-by-
n
rectangular matrix
B1
on top of an
l
-by-
n
upper trapezoidal matrix
B2
:
Equation
The upper trapezoidal matrix
B2
consists of the first
l
rows of an
n
-by-
n
upper triangular matrix, where 0 ≤
l
≤ min(
m
,
n
). If
l
=0,
B
is an
m
-by-
n
rectangular matrix. If
m
=
l
=
n
,
B
is upper triangular. The elementary reflectors
H(i)
are stored in the
i
th column below the diagonal in the (
n
+
m
)-by-
n
input matrix
C
. The structure of vectors defining the elementary reflectors is illustrated by:
Equation
The elements of the unit matrix
I
are not stored. Thus,
V
contains all of the necessary information, and is returned in array
b
.
Note that