## Developer Reference

• 0.10
• 10/21/2020
• Public Content
Contents

# p?larzt

Forms the triangular factor T of a block reflector H=I-V*T*V
H
as returned by
p?tzrzf
.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?larzt
function
forms the triangular factor
T
of a real/complex block reflector
H
of order greater than
n
, which is defined as a product of
k
elementary reflectors as returned by
p?tzrzf
.
If
direct
=
'F'
,
H
=
H
(1)*
H
(2)*...*
H
(
k
)
, and
T
is upper triangular;
If
direct
=
'B'
,
H
=
H
(
k
)*...*
H
(2)*
H
(1)
, and
T
is lower triangular.
If
storev
=
'C'
, the vector which defines the elementary reflector
H
(
i
),
is stored in the
i
-th column of the array
v
, and
H
=
i
-
v
*
t
*
v'.
If
storev
=
'R'
, the vector, which defines the elementary reflector
H
(
i
),
is stored in the
i
-th row of the array
v
, and
H
=
i
-
v
'*
t
*
v
Currently, only
storev
=
'R'
and
direct
=
'B'
are supported.
Input Parameters
direct
(global)
Specifies the order in which the elementary reflectors are multiplied to form the block reflector:
if
direct
=
'F'
:
H
=
H
(1)*
H
(2)*...*
H
(
k
)
(Forward, not supported)
if
direct
=
'B'
:
H
=
H
(
k
)*...*
H
(2)*
H
(1)
(Backward).
storev
(global)
Specifies how the vectors which defines the elementary reflectors are stored:
if
storev
=
'C'
: columnwise (not supported);
if
storev
=
'R'
: rowwise.
n
(global)
The order of the block reflector
H
.
n
0
.
k
(global)
The order of the triangular factor
T
(= the number of elementary reflectors).
1≤
k
mb_v
(=
nb_v
)
.
v
Pointer into the local memory to an array of local size
LOCr
(
iv
+
k
-1)
*
LOCc
(
jv
+
n
-1)
.
The distributed matrix
V
contains the Householder vectors.
See
Application Notes
below.
iv
,
jv
(global) The row and column indices in the global matrix
V
indicating the first row and the first column of the matrix sub(
V
), respectively.
descv
(local) array of size
dlen_
. The array descriptor for the distributed matrix
V
.
tau
(local)
Array of size
LOCr
(
iv
+
k
-1)
if
incv
=
m_v
, and
LOCc
(
jv
+
k
-1) otherwise. This array contains the Householder scalars related to the Householder vectors.
tau
is tied to the distributed matrix
V
.
work
(local).
Workspace array of size
(
k*
(
k
-1)/2)
.
Output Parameters
v
t
(local)
Array of size
mb_v
*
mb_v
. It contains the
k
-by-
k
triangular factor of the block reflector associated with
v
.
t
is lower triangular.
Application Notes
The shape of the matrix
V
and the storage of the vectors which define the
H
(
i
)
is best illustrated by the following example with
n
= 5
and
k
= 3
. The elements equal to 1 are not stored; the corresponding array elements are modified but restored on exit. The rest of the array is not used.    #### 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