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

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804