Contents

# ?poequ

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

## Syntax

Include Files
• mkl.h
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 contains
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 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.
Input Parameters
matrix_layout
Specifies whether matrix storage layout is row major (
LAPACK_ROW_MAJOR
) or column major (
LAPACK_COL_MAJOR
).
n
The order of the matrix
A
;
n
0
.
a
Array: size
max(1,
lda
*
n
)
.
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.
lda
The leading dimension of
a
;
lda
max(1,
n
)
.
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]
.
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
had an illegal value.
If
info
=
i
, the
i
-th diagonal element of
A
is nonpositive.
Application Notes
If
scond
0.1
and
amax
is neither too large nor too small, it is not worth scaling by
s
.
If
amax
is very close to
SMLNUM
or very close to
BIGNUM
, the matrix
A
should be scaled.

#### Product and Performance Information

1

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Notice revision #20110804