Developer Reference

  • 098
  • 03/30/2020
  • Public Content
Contents

?tpmqrt

Applies a real or complex orthogonal matrix obtained from a "triangular-pentagonal" complex block reflector to a general real or complex matrix, which consists of two blocks.

Syntax

call stpmqrt
(
side
,
trans
,
m
,
n
,
k
,
l
,
nb
,
v
,
ldv
,
t
,
ldt
,
a
,
lda
,
b
,
ldb
,
work
,
info
)
call dtpmqrt
(
side
,
trans
,
m
,
n
,
k
,
l
,
nb
,
v
,
ldv
,
t
,
ldt
,
a
,
lda
,
b
,
ldb
,
work
,
info
)
call ctpmqrt
(
side
,
trans
,
m
,
n
,
k
,
l
,
nb
,
v
,
ldv
,
t
,
ldt
,
a
,
lda
,
b
,
ldb
,
work
,
info
)
call ztpmqrt
(
side
,
trans
,
m
,
n
,
k
,
l
,
nb
,
v
,
ldv
,
t
,
ldt
,
a
,
lda
,
b
,
ldb
,
work
,
info
)
call tpmqrt
(
v
,
t
,
a
,
b
,
k
,
nb
[
,
trans
]
[
,
side
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The columns of the pentagonal matrix
V
contain the elementary reflectors
H
(1),
H
(2), ...,
H
(
k
);
V
is composed of a rectangular block
V1
and a trapezoidal block
V2
:
Equation
The size of the trapezoidal block
V2
is determined by the parameter
l
, where 0 ≤
l
k
.
V2
is upper trapezoidal, consisting of the first
l
rows of a
k
-by-
k
upper triangular matrix.
If
l
=
k
,
V2
is upper triangular;
If
l
=0, there is no trapezoidal block, so
V
=
V1
is rectangular.
If
side
= 'L':
Equation
where
A
is
k
-by-
n
,
B
is
m
-by-
n
and
V
is
m
-by-
k
.
If
side
= 'R':
Equation
where
A
is
m
-by-
k
,
B
is