Developer Reference

  • 2020.2
  • 07/15/2020
  • Public Content
Contents

?lahr2

Reduces the specified number of first columns of a general rectangular matrix A so that elements below the specified subdiagonal are zero, and returns auxiliary matrices which are needed to apply the transformation to the unreduced part of A.

Syntax

call slahr2
(
n
,
k
,
nb
,
a
,
lda
,
tau
,
t
,
ldt
,
y
,
ldy
)
call dlahr2
(
n
,
k
,
nb
,
a
,
lda
,
tau
,
t
,
ldt
,
y
,
ldy
)
call clahr2
(
n
,
k
,
nb
,
a
,
lda
,
tau
,
t
,
ldt
,
y
,
ldy
)
call zlahr2
(
n
,
k
,
nb
,
a
,
lda
,
tau
,
t
,
ldt
,
y
,
ldy
)
Include Files
  • mkl.fi
Description
The routine reduces the first
nb
columns of a real/complex general
n
-by-(
n
-
k
+1) matrix
A
so that elements below the
k
-th subdiagonal are zero. The reduction is performed by an orthogonal/unitary similarity transformation
Q
T
*
A
*
Q
for real flavors, or
Q
H
*
A
*
Q
for complex flavors. The routine returns the matrices
V
and
T
which determine
Q
as a block reflector
I
-
V
*
T
*
V
T
(for real flavors) or
I
-
V
*
T
*
V
H
(for real flavors), and also the matrix
Y
=
A
*
V
*
T
.
The matrix
Q
is represented as products of
nb
elementary reflectors:
Q
=
H
(1)*
H
(2)*... *
H
(
nb
)
Each
H
(i)
has the form
H
(i) =
I
-
tau
*
v
*
v
T
for real flavors, or
H
(i) =
I
-
tau
*
v
*
v
H
for complex flavors
where
tau
is a real/complex scalar, and
v
is a real/complex vector.
This is an auxiliary routine called by
?gehrd
.
Input Parameters
n
INTEGER
. The order of the matrix
A
(
n
0
).
k
INTEGER
. The offset for the reduction. Elements below the
k
-th subdiagonal in the first
nb
columns are reduced to zero (
k
<
n
).
nb
INTEGER
. The number of columns to be reduced.
a
REAL
for
slahr2
DOUBLE PRECISION
for
dlahr2
COMPLEX
for
clahr2
DOUBLE COMPLEX
for
zlahr2
.
Array,
DIMENSION
(
lda
,
n
-
k
+1) contains the
n
-by-(
n
-
k
+1) general matrix
A
to be reduced.
lda
INTEGER
. The leading dimension of the array
a
;
lda
max(1,
n
)
.
ldt
INTEGER
. The leading dimension of the output array
t
;
ldt
nb
.
ldy
INTEGER
. The leading dimension of the output array
y
;