Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

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

?poequ

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

Syntax

lapack_int LAPACKE_spoequ
(
int
matrix_layout
,
lapack_int
n
,
const float*
a
,
lapack_int
lda
,
float*
s
,
float*
scond
,
float*
amax
);
lapack_int LAPACKE_dpoequ
(
int
matrix_layout
,
lapack_int
n
,
const double*
a
,
lapack_int
lda
,
double*
s
,
double*
scond
,
double*
amax
);
lapack_int LAPACKE_cpoequ
(
int
matrix_layout
,
lapack_int
n
,
const lapack_complex_float*
a
,
lapack_int
lda
,
float*
s
,
float*
scond
,
float*
amax
);
lapack_int LAPACKE_zpoequ
(
int
matrix_layout
,
lapack_int
n
,
const lapack_complex_double*
a
,
lapack_int
lda
,
double*
s
,
double*
scond
,
double*
amax
);
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
Equation
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

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