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

Include Files
• mkl.h
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-1]*
a
i
,
j
*
c
[j-1]
have an absolute value of at most the radix.
r
[i-1]
and
c
[j-1]
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
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
m
The number of rows of the matrix
A
;
m
0
.
n
The number of columns of the matrix
A
;
n
0
.
a
Array: size
max(1,
lda
*
n
) for column major layout and max(1,
lda
*
m
) for row major layout
.
Contains the
m
-by-
n
matrix
A
whose equilibration factors are to be computed.
lda
The leading dimension of
a
;
lda
max(1,
m
)
.
Output Parameters
r
,
c
Arrays:
r
(
m
)
,
c
(
n
)
.
If
info
= 0
, or
info
>
m
, the array
r
contains the row scale factors for the matrix
A
.
If
info
= 0
, the array
c
contains the column scale factors for the matrix
A
.
rowcnd
If
info
= 0
or
info
>
m
,
rowcnd
contains the ratio of the smallest
r
[i]
to the largest
r
[i]
. If
rowcnd
0.1
, and
amax
is neither too large nor too small, it is not worth scaling by
r
.
colcnd
If
info
= 0
,
colcnd
contains the ratio of the smallest
c
[i]
to the largest
c
[i]
. If
colcnd
0.1
, it is not worth scaling by
c
.
amax
Absolute value of the largest element of the matrix
A
. If
amax
is very close to
SMLNUM
or very close to
BIGNUM
, the matrix should be scaled.
Return Values
This function returns a value
info
.
If
info
= 0
, the execution is successful.
If
info
=
-i
, parameter
i
had an illegal value.
If
info
=
i
,
i
> 0
, and
i
m
, the
i
-th row of
A
is exactly zero;
i
>
m
, the (
i
-
m
)-th column of
A
is exactly zero.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.