Developer Reference

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

?heequb

Computes row and column scaling factors intended to equilibrate a Hermitian indefinite matrix and reduce its condition number.

Syntax

call cheequb
(
uplo
,
n
,
a
,
lda
,
s
,
scond
,
amax
,
work
,
info
)
call zheequb
(
uplo
,
n
,
a
,
lda
,
s
,
scond
,
amax
,
work
,
info
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine computes row and column scalings intended to equilibrate a Hermitian indefinite matrix
A
and reduce its condition number (with respect to the two-norm).
The array
s
contains the scale factors,
s
(
i
) = 1/sqrt(A(i,i))
. These factors are chosen so that the scaled matrix
B
with elements
b
(
i
,
j
)=
s
(i)*
a
(
i
,
j
)*
s
(j)
has ones on the diagonal.
This choice of
s
puts the condition number of
B
within a factor
n
of the smallest possible condition number over all possible diagonal scalings.
Input Parameters
uplo
CHARACTER*1
.
Must be
'U'
or
'L'
.
Indicates whether the upper or lower triangular part of
A
is stored:
If
uplo
=
'U'
, the array
a
stores the upper triangular part of the matrix
A
.
If
uplo
=
'L'
, the array
a
stores the lower triangular part of the matrix
A
.
n
INTEGER
.
The order of the matrix
A
;
n
0
.
a
,
work
COMPLEX
for
cheequb
DOUBLE COMPLEX
for
zheequb
.
Array
a
: size
lda
by *
.
Contains the
n
-by-
n
symmetric indefinite matrix
A
whose scaling factors are to be computed. Only the diagonal elements of
A
are referenced.
The second dimension of
a
must be at least
max(1,
n
)
.
work(*)
is a workspace array. The dimension of
work
is at least
max(1,3*
n
)
.
lda
INTEGER
.
The leading dimension of
a
;
lda
max(1,
m
)
.
Output Parameters
s
REAL
for
cheequb
DOUBLE PRECISION
for
zheequb
.
Array, size (
n
).
If
info
= 0
, the array
s
contains the scale factors for
A
.
scond
REAL
for
cheequb
DOUBLE PRECISION
for
zheequb
.
If
info
= 0
,
scond
contains the ratio of the smallest
s
(i)
to the largest
s
(i)
. If
scond