?pocon
?pocon
Estimates the reciprocal of the condition number of a symmetric (Hermitian) positive-definite matrix.
Syntax
lapack_int LAPACKE_spocon
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const float*
a
,
lapack_int
lda
,
float
anorm
,
float*
rcond
);
lapack_int LAPACKE_dpocon
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const double*
a
,
lapack_int
lda
,
double
anorm
,
double*
rcond
);
lapack_int LAPACKE_cpocon
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const lapack_complex_float*
a
,
lapack_int
lda
,
float
anorm
,
float*
rcond
);
lapack_int LAPACKE_zpocon
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const lapack_complex_double*
a
,
lapack_int
lda
,
double
anorm
,
double*
rcond
);
Include Files
- mkl.h
Description
The routine estimates the reciprocal of the condition number of a symmetric (Hermitian) positive-definite matrix
A
:κ
1
(A
) = ||A
||1
||A
-1
||1
A
is symmetric or Hermitian, κ
∞
A
) = κ
1
(A
)An estimate is obtained for .
||
, and the reciprocal of the condition number is computed as A
-1
||rcond
= 1 / (||A
|| ||A
-1
||)Before calling this routine:
- computeanorm(either||orA||1= maxjΣ|ia|ij||A||= max∞iΣ|ja|)ij
- call?potrfto compute the Cholesky factorization ofA.
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 how the input matrixAhas been factored:If,uplo='U'Ais factored asfor real flavors orA=UT*Ufor complex flavors, andA=UH*UUis stored.If,uplo='L'Ais factored asfor real flavors orA=L*LTfor complex flavors, andA=L*LHLis stored.
- n
- The order of the matrixA;n≥0.
- a
- lda
- The leading dimension ofa;.lda≥max(1,n)
- anorm
- The norm of theoriginalmatrixA.(seeDescription)
Output Parameters
- rcond
- An estimate of the reciprocal of the condition number. The routine setsrcond=0 if the estimate underflows; in this case the matrix is singular (to working precision). However, anytimercondis small compared to 1.0, for the working precision, the matrix may be poorly conditioned or even singular.
Return Values
This function returns a value
info
.If , the execution is successful.
info
= 0If
info
= -i
, parameter i
had an illegal value.Application Notes
The computed ; the number is usually 4 or 5 and never more than 11. Each solution requires approximately
rcond
is never less than r
(the reciprocal of the true condition number) and in practice is nearly always less than 10r
. A call to this routine involves solving a number of systems of linear equations A
*x
= b
2
floating-point operations for real flavors and n
2
8
for complex flavors.n
2