Developer Reference

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

?poequ

Computes row and column scaling factors intended to equilibrate a symmetric (Hermitian) positive definite matrix and reduce its condition number.

Syntax

call spoequ
(
n
,
a
,
lda
,
s
,
scond
,
amax
,
info
)
call dpoequ
(
n
,
a
,
lda
,
s
,
scond
,
amax
,
info
)
call cpoequ
(
n
,
a
,
lda
,
s
,
scond
,
amax
,
info
)
call zpoequ
(
n
,
a
,
lda
,
s
,
scond
,
amax
,
info
)
call poequ
(
a
,
s
[
,
scond
]
[
,
amax
]
[
,
info
]
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine computes row and column scalings intended to equilibrate a symmetric (Hermitian) positive-definite matrix
A
and reduce its condition number (with respect to the two-norm).
The output array
s
returns scale factors such that
s
(
i
)
s
[
i
+ 1]
contains
Equation
These factors are chosen so that the scaled matrix
B
with elements
B
i
,
j
=
s
(i)*
A
i
,
j
*
s
(j)
has diagonal elements equal to 1.
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.
See
?laqsy
auxiliary function that uses scaling factors computed by
?poequ
.
Input Parameters
n
INTEGER
.
The order of the matrix
A
;
n
0
.
a
REAL
for
spoequ
DOUBLE PRECISION
for
dpoequ
COMPLEX
for
cpoequ
DOUBLE COMPLEX
for
zpoequ
.
Array: size
lda
by *
.
Contains the
n
-by-
n
symmetric or Hermitian positive definite 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
)
.
lda
INTEGER
.
The leading dimension of
a
;
lda
max(1,
n
)
.
Output Parameters
s
REAL
for single precision flavors
DOUBLE PRECISION
for double precision flavors.
Array, size
n
.
If
info
= 0
, the array
s
contains the scale factors for
A
.
scond
REAL
for single precision flavors
DOUBLE PRECISION
for double precision flavors.
If
info
= 0
,
scond
contains the ratio of the smallest
s
(i)
to the largest
s
(i)
.
amax
REAL
for single precision flavors
DOUBLE PRECISION
for double precision flavors.
Absolute value of the largest element of the matrix
A
.