?ptcon
?ptcon
Estimates the reciprocal of the condition number of a symmetric (Hermitian) positive-definite tridiagonal matrix.
Syntax
lapack_int LAPACKE_sptcon
(
lapack_int
n
,
const float*
d
,
const float*
e
,
float
anorm
,
float*
rcond
);
lapack_int LAPACKE_dptcon
(
lapack_int
n
,
const double*
d
,
const double*
e
,
double
anorm
,
double*
rcond
);
lapack_int LAPACKE_cptcon
(
lapack_int
n
,
const float*
d
,
const lapack_complex_float*
e
,
float
anorm
,
float*
rcond
);
lapack_int LAPACKE_zptcon
(
lapack_int
n
,
const double*
d
,
const lapack_complex_double*
e
,
double
anorm
,
double*
rcond
);
Include Files
- mkl.h
Description
The routine computes the reciprocal of the condition number (in the 1-norm) of a real symmetric or complex Hermitian positive-definite tridiagonal matrix using the factorization for real flavors and for complex flavors or for real flavors and for complex flavors computed by
A
= L*D*L
T
A
= L*D*L
H
A
= U
T
*D*U
A
= U
H
*D*U
?pttrf
:κ
1
(A
) = ||A
||1
||A
-1
||1
A
is symmetric or Hermitian, κ
∞
A
) = κ
1
(A
)The norm .
||
is computed by a direct method, and the reciprocal of the condition number is computed as A
-1
||rcond
= 1 / (||A
|| ||A
-1
||)Before calling this routine:
- computeanormas||A||1= maxjΣ|ia|ij
- call?pttrfto compute the factorization ofA.
Input Parameters
- n
- The order of the matrixA;n≥0.
- d
- Arrays, dimension (n).The arraydcontains thendiagonal elements of the diagonal matrixDfrom the factorization ofA, as computed by?pttrf;
- e
- Array, size(.n-1)Contains off-diagonal elements of the unit bidiagonal factorUorLfrom the factorization computed by?pttrf.
- anorm
- The 1- norm of theoriginalmatrixA(see.Description)
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 , parameter
info
= -i
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
4*
floating-point operations for real flavors and n
(kd
+ 1)16*
for complex flavors.n
(kd
+ 1)