Developer Reference

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

?laqhb

Scales a Hermetian band matrix, using scaling factors computed by
?pbequ
.

Syntax

call claqhb
(
uplo
,
n
,
kd
,
ab
,
ldab
,
s
,
scond
,
amax
,
equed
)
call zlaqhb
(
uplo
,
n
,
kd
,
ab
,
ldab
,
s
,
scond
,
amax
,
equed
)
Include Files
  • mkl.fi
Description
The routine equilibrates a Hermetian band matrix
A
using the scaling factors in the vector
s
.
Input Parameters
uplo
CHARACTER*1
.
Specifies whether the upper or lower triangular part of the band matrix
A
is stored.
If
uplo
=
'U'
: upper triangular.
If
uplo
=
'L'
: lower triangular.
n
INTEGER
. The order of the matrix
A
.
n
0
.
kd
INTEGER
. The number of super-diagonals of the matrix
A
if
uplo
=
'U'
, or the number of sub-diagonals if
uplo
=
'L'
.
kd
0
.
ab
COMPLEX
for
claqhb
DOUBLE COMPLEX
for
zlaqhb
Array,
DIMENSION
(
ldab
,
n
). On entry, the upper or lower triangle of the band matrix
A
, stored in the first
kd
+1 rows of the array. The
j
-th column of
A
is stored in the
j
-th column of the array
ab
as follows:
if
uplo
=
'U'
,
ab
(
kd
+1+
i
-
j
,
j
) = A(
i
,
j
)
for
max(1,
j
-
kd
) ≤
i
j
;
if
uplo
=
'L'
,
ab
(1+
i
-
j
,
j
) = A(
i
,
j
)
for
j
i
≤ min(
n
,
j
+
kd
)
.
ldab
INTEGER
. The leading dimension of the array
ab
.
ldab
kd
+1
.
scond
REAL
for
claqsb
DOUBLE PRECISION
for
zlaqsb
Ratio of the smallest
s
(
i
) to the largest
s
(
i
).
amax
REAL
for
claqsb
DOUBLE PRECISION
for
zlaqsb
Absolute value of largest matrix entry.
Output Parameters
ab
On exit, if
info
= 0
, the triangular factor
U
or
L
from the Cholesky factorization
A
=
U
H
*
U
or
A
=
L
*
L
H
of the band matrix
A
, in the same storage format as
A
.
s
REAL
for
claqsb
DOUBLE PRECISION
for
zlaqsb
Array,
DIMENSION
(
n
). The scale factors for
A
.
equed
CHARACTER*1
.
Specifies whether or not equilibration was done.
If
equed
=
'N'
: No equilibration.
If
equed
=
'Y'
: Equilibration was done, that is,
A
has been replaced by
diag(
s
)*
A
*diag(
s
)
.
Application Notes
The routine uses internal parameters
thresh
,
large
, and