Contents

# ?syequb

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

## Syntax

Include Files
• mkl.h
Description
The routine computes row and column scalings intended to equilibrate a symmetric indefinite matrix
A
and reduce its condition number (with respect to the two-norm).
The array
s
contains the scale factors,
s
[
i
-1]
= 1/sqrt(A(i,i))
. These factors are chosen so that the scaled matrix
B
with elements
b
i
,
j
=
s
[i-1]*
a
i
,
j
*
s
[j-1]
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
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
uplo
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
The order of the matrix
A
;
n
0
.
a
Array
a
:
max(1,
lda
*
n
)
.
Contains the
n
-by-
n
symmetric indefinite matrix
A
whose scaling factors are to be computed. Only the diagonal elements of
A
are referenced.
lda
a
;
lda
max(1,
m
)
.
Output Parameters
s
Array, size (
n
).
If
info
= 0
, the array
s
contains the scale factors for
A
.
scond
If
info
= 0
,
scond
contains the ratio of the smallest
s
[i]
to the largest
s
[i]
. If
scond
0.1
, and
amax
is neither too large nor too small, it is not worth scaling by
s
.
amax
Absolute value of the largest element of the matrix
A
. If
amax
is very close to
SMLNUM
or
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
If
info
=
i
, the
i
-th diagonal element of
A
is nonpositive.

#### Product and Performance Information

1

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