Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

  • 0.9
  • 09/09/2020
  • 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

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804