Developer Reference

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

?geequb

Computes row and column scaling factors restricted to a power of radix to equilibrate a general matrix and reduce its condition number.

Syntax

call sgeequb
(
m
,
n
,
a
,
lda
,
r
,
c
,
rowcnd
,
colcnd
,
amax
,
info
)
call dgeequb
(
m
,
n
,
a
,
lda
,
r
,
c
,
rowcnd
,
colcnd
,
amax
,
info
)
call cgeequb
(
m
,
n
,
a
,
lda
,
r
,
c
,
rowcnd
,
colcnd
,
amax
,
info
)
call zgeequb
(
m
,
n
,
a
,
lda
,
r
,
c
,
rowcnd
,
colcnd
,
amax
,
info
)
Include Files
  • mkl.fi
    ,
    lapack.f90
Description
The routine computes row and column scalings intended to equilibrate an
m
-by-
n
general matrix
A
and reduce its condition number. The output array
r
returns the row scale factors and the array
c
- the column scale factors. These factors are chosen to try to make the largest element in each row and column of the matrix
B
with elements
b
i
,
j
=
r
(i)*
a
i
,
j
*
c
(j)
have an absolute value of at most the radix.
r
(i)
and
c
(j)
are restricted to be a power of the radix between
SMLNUM
= smallest safe number and
BIGNUM
= largest safe number. Use of these scaling factors is not guaranteed to reduce the condition number of
a
but works well in practice.
SMLNUM
and
BIGNUM
are parameters representing machine precision. You can use the
?lamch
routines to compute them. For example, compute single precision values of
SMLNUM
and
BIGNUM
as follows:
SMLNUM = slamch ('s') BIGNUM = 1 / SMLNUM
This routine differs from
?geequ
by restricting the scaling factors to a power of the radix. Except for over- and underflow, scaling by these factors introduces no additional rounding errors. However, the scaled entries' magnitudes are no longer equal to approximately 1 but lie between
sqrt(radix)
and
1/sqrt(radix)
.
Input Parameters
m
INTEGER
.
The number of rows of the matrix
A
;
m
0
.
n
INTEGER
.
The number of columns of the matrix
A
;
n
0
.
a
REAL
for
sgeequb
DOUBLE PRECISION
for
dgeequb
COMPLEX
for
cgeequb
DOUBLE COMPLEX
for
zgeequb
.
Array: size
(
lda
,*)
.
Contains the
m
-by-
n
matrix
A
whose equilibration factors are to be computed.
The second dimension of
a
must be at least
max(1,
n
)
.
lda
INTEGER
.
The leading dimension of
a
;
lda
max(1,
m
)
.
Output Parameters
r
,
c
REAL
for single precision flavors
DOUBLE PRECISION
for double precision flavors.
Arrays:
r
(
m
)
,
c
(
n
)
.