Contents

# p?larft

Forms the triangular vector
T
of a block reflector
H=I-V*T*V
H
.

## Syntax

Include Files
• mkl_scalapack.h
Description
The
p?larft
function
forms the triangular factor
T
of a real/complex block reflector
H
of order
n
, which is defined as a product of
k
elementary reflectors.
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 distributed matrix
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 distributed matrix
V
, and
H
=
I
-
V'
*
T
*
V
.
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)
if
direct
=
'B'
:
H
=
H
(
k
)*...*
H
(2)*
H
(1)
(backward).
storev
(global)
Specifies how the vectors that define the elementary reflectors are stored
(See
Application Notes
below)
:
if
storev
=
'C'
: columnwise;
if
storev
=
'R'
: rowwise.
n
(global)
The order of the block reflector
H
.
n
0
.
k
(global)
The order of the triangular factor
T
, is equal to 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
+
n
-1)
*
LOCc
(
jv
+
k
-1)
if
storev
=
'C'
, and
LOCr
(
iv
+
k
-1)
*
LOCc
(
jv
+
n
-1)
if
storev
=
'R'
.
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
nb_v
*
nb_v
if
storev
= 'C'
, and
mb_v
*
mb_v
otherwise. It contains the
k
-by-
k
triangular factor of the block reflector associated with
v
. If
direct
=
'F'
,
t
is upper triangular;
if
direct
=
'B'
,
t
is lower triangular.
Application Notes
The shape of the matrix
V
and the storage of the vectors that 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

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Notice revision #20110804