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

Include Files
• mkl.h
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
:
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':
where
A
is
k
-by-
n
,
B
is
m
-by-
n
and
V
is
m
-by-
k
.
If
side
= 'R':
where
A
is
m
-by-
k
,
B
is
m
-by-
n
and
V
is
n
-by-
k
.
The real/complex orthogonal matrix
Q
is formed from
V
and
T
.
If
trans
='N' and
side
='L',
c
contains
Q
*
C
on exit.
If
trans
='T' and
side
='L',
C
contains
Q
T
*
C
on exit.
If
trans
='C' and
side
='L',
C
contains
Q
H
*
C
on exit.
If
trans
='N' and
side
='R',
C
contains
C
*
Q
on exit.
If
trans
='T' and
side
='R',
C
contains
C
*
Q
T
on exit.
If
trans
='C' and
side
='R',
C
contains
C
*
Q
H
on exit.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
side
=
'L'
: apply
Q
,
Q
T
, or
Q
H
from the left.
=
'R'
: apply
Q
,
Q
T
, or
Q
H
from the right.
trans
=
'N'
, no transpose, apply
Q
.
=
'T'
, transpose, apply
Q
T
.
=
'C'
, transpose, apply
Q
H
.
m
The number of rows in the matrix
B
,
(
m
≥ 0)
.
n
The number of columns in the matrix
B
,
(
n
≥ 0)
.
k
The number of elementary reflectors whose product defines the matrix
Q
,
(
k
≥ 0)
.
l
The order of the trapezoidal part of
V
(
k
l
≥ 0).
nb
The block size used for the storage of
t
,
k
nb
≥ 1. This must be the same value of
nb
used to generate
t
in
tpqrt
.
v
Size
ldv
*
k
for column major layout;
ldv
*
m
for row major layout and
side
= 'L',
ldv
*
n
for row major layout and
side
= 'R'.
The
i
th column must contain the vector which defines the elementary reflector
H
(
i
), for
i
= 1,2,...,
k
, as returned by
tpqrt
in array argument
b
.
ldv
The leading dimension of the array
v
.
If
side
= 'L',
ldv
must be at least max(1,
m
)
for column major layout and max(1,
k
for row major layout
;
If
side
= 'R',
ldv
must be at least max(1,
n
)
for column major layout and max(1,
k
for row major layout
.
t
Array, size
ldt
*
k
for column major layout and
ldt
*
nb
for row major layout
.
The upper triangular factors of the block reflectors as returned by
tpqrt
ldt
The leading dimension of the array
t
.
ldt
must be at least
nb
for column major layout and max(1,
k
for row major layout
.
a
If
side
= 'L', size
lda
*
n
for column major layout and
lda
*
k
for row major layout .
.
If
side
= 'R', size
lda
*
k
for column major layout and
lda
*
m
for row major layout .
.
The
k
-by-
n
or
m
-by-
k
matrix
A
.
lda
The leading dimension of the array
a
.
If
side
= 'L',
lda
must be at least max(1,
k
)
for column major layout and max(1,
n
for row major layout
.
If
side
= 'R',
lda
must be at least max(1,
m
)
for column major layout and max(1,
k
for row major layout
.
b
Size
ldb
*
n
for column major layout and
ldb
*
m
for row major layout
.
The
m
-by-
n
matrix
B
.
ldb
The leading dimension of the array
b
.
ldb
must be at least max(1,
m
)
for column major layout and max(1,
n
for row major layout
.
Output Parameters
a
Overwritten by the corresponding block of the product
Q
*
C
,
C
*
Q
,
Q
T
*
C
,
C
*
Q
T
,
Q
H
*
C
, or
C
*
Q
H
.
b
Overwritten by the corresponding block of the product
Q
*
C
,
C
*
Q
,
Q
T
*
C
,
C
*
Q
T
,
Q
H
*
C
, or
C
*
Q
H
.
Return Values
This function returns a value
info
.
If
info
=0
, the execution is successful.
If
info
=
-i
, the
i
-th parameter had an illegal value.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.