?poequ
?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
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).
- n
- The order of the matrixA;.n≥0
- a
- Array: sizemax(1,.lda*n)Contains then-by-nsymmetric or Hermitian positive definite matrixAwhose scaling factors are to be computed. Only the diagonal elements ofAare referenced.
- lda
- The leading dimension ofa;.lda≥max(1,n)
Output Parameters
- s
- Array, sizen.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.