## Developer Reference

• 2021.1
• 12/04/2020
• Public Content
Contents

# ?gbequ

Computes row and column scaling factors intended to equilibrate a banded 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
band 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 absolute value 1.
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
.
kl
The number of subdiagonals within the band of
A
;
kl
0
.
ku
The number of superdiagonals within the band of
A
;
ku
0
.
ab
Array, size
max(1,
ldab
*
n
) for column major layout and max(1,
ldab
*
m
) for row major layout
. Contains the original band matrix
A
.
ldab
ab
;
ldab
kl
+
ku
+1.
Output Parameters
r
,
c
Arrays:
r
(size
m
),
c
(size
n
).
If
info
= 0
, or
info
>
m
, the array
r
contains the row scale factors of the matrix
A
.
If
info
= 0
, the array
c
contains the column scale factors of the matrix
A
.
rowcnd
If
info
= 0
or
info
>
m
,
rowcnd
contains the ratio of the smallest
r
[i]
to the largest
r
[i]
.
colcnd
If
info
= 0
,
colcnd
contains the ratio of the smallest
c
[i]
to the largest
c
[i]
.
amax
Absolute value of the largest element of the matrix
A
.
Return Values
This function returns a value
info
.
If
info
= 0
, the execution is successful.
If
info
=
-i
, parameter
i
If
info
=
i
and
i
m
, the
i
-th row of
A
is exactly zero;
i
>
m
, the (
i
-
m
)th column of
A
is exactly zero.
Application Notes
All the components of
r
and
c
are restricted to be 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```
If
rowcnd
0.1
and
amax
is neither too large nor too small, it is not worth scaling by
r
.
If
colcnd
0.1
, it is not worth scaling by
c
.
If
amax
is very close to
SMLNUM
or very close to
BIGNUM
, the matrix
A
should be scaled.

#### Product and Performance Information

1

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