?ppequ
?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
These factors are chosen so that the scaled matrix =* has diagonal elements equal to 1.
B
with elements b
i
j
s
[i-1]*a
i
j
s
[j-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 ofAis packed in the arrayap:If, the arrayuplo='U'apstores the upper triangular part of the matrixA.If, the arrayuplo='L'apstores the lower triangular part of the matrixA.
- n
- The order of matrixA;.n≥0
- ap
- Array, size at leastmax(1,. The arrayn(n+1)/2)apcontains the upper or the lower triangular part of the matrixA(as specified byuplo) in packed storage (see Matrix Storage Schemes).
Output Parameters
- s
- Array, size (n).If, the arrayinfo= 0scontains the scale factors forA.
- scond
- If,info= 0scondcontains the ratio of the smallestto the largests[i].s[i]
- amax
- Absolute value of the largest element of the matrixA.
Return Values
This function returns a value
info
.If , the execution is successful.
info
= 0If , parameter
info
= -i
i
had an illegal value.If , the
info
= i
i
-th diagonal element of A
is nonpositive.Application Notes
If and
scond
≥
0.1amax
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.