Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

?ppequ

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

Syntax

lapack_int LAPACKE_sppequ
(
int
matrix_layout
char
uplo
lapack_int
n
const float*
ap
float*
s
float*
scond
float*
amax
);
lapack_int LAPACKE_dppequ
(
int
matrix_layout
char
uplo
lapack_int
n
const double*
ap
double*
s
double*
scond
double*
amax
);
lapack_int LAPACKE_cppequ
(
int
matrix_layout
char
uplo
lapack_int
n
const lapack_complex_float*
ap
float*
s
float*
scond
float*
amax
);
lapack_int LAPACKE_zppequ
(
int
matrix_layout
char
uplo
lapack_int
n
const lapack_complex_double*
ap
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
 in packed storage 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
).
uplo
Must be
'U'
 or
'L'
.
Indicates whether the upper or lower triangular part of
A
 is packed in the array
ap
:
If
uplo
 =
'U'
, the array
ap
 stores the upper triangular part of the matrix
A
.
If
uplo
 =
'L'
, the array
ap
 stores the lower triangular part of the matrix
A
.
n
The order of matrix
A
;
n
≥
 0
.
ap
Array, size at least
max(1,
n
(
n
+1)/2)
. The array
ap
 contains the upper or the lower triangular part of the matrix
A
 (as specified by
uplo
) in packed storage (see Matrix Storage Schemes).
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.