?gtcon
?gtcon
Estimates the reciprocal of the condition number of a tridiagonal matrix.
Syntax
lapack_int LAPACKE_sgtcon
(
char
norm
,
lapack_int
n
,
const float*
dl
,
const float*
d
,
const float*
du
,
const float*
du2
,
const lapack_int*
ipiv
,
float
anorm
,
float*
rcond
);
lapack_int LAPACKE_dgtcon
(
char
norm
,
lapack_int
n
,
const double*
dl
,
const double*
d
,
const double*
du
,
const double*
du2
,
const lapack_int*
ipiv
,
double
anorm
,
double*
rcond
);
lapack_int LAPACKE_cgtcon
(
char
norm
,
lapack_int
n
,
const lapack_complex_float*
dl
,
const lapack_complex_float*
d
,
const lapack_complex_float*
du
,
const lapack_complex_float*
du2
,
const lapack_int*
ipiv
,
float
anorm
,
float*
rcond
);
lapack_int LAPACKE_zgtcon
(
char
norm
,
lapack_int
n
,
const lapack_complex_double*
dl
,
const lapack_complex_double*
d
,
const lapack_complex_double*
du
,
const lapack_complex_double*
du2
,
const lapack_int*
ipiv
,
double
anorm
,
double*
rcond
);
Include Files
- mkl.h
Description
The routine estimates the reciprocal of the condition number of a real or complex tridiagonal matrix
A
in the 1-norm or infinity-norm:κ
1
(A
) = ||A
||1
||A
-1
||1
κ
∞
A
) = ||A
||∞
A
-1
||∞
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
Input Parameters
- norm
- Must be'1'or'O'or'I'.Ifnorm='1'or'O', then the routine estimates the condition number of matrixAin 1-norm.If, then the routine estimates the condition number of matrixnorm='I'Ain infinity-norm.
- n
- The order of the matrixA;n≥0.
- dl,d,du,du2
- Arrays:,dl(n-1),d(n),du(n-1).du2(n-2)The arraydlcontains the(multipliers that define the matrixn- 1)Lfrom theLUfactorization ofAas computed by?gttrf.The arraydcontains thendiagonal elements of the upper triangular matrixUfrom theLUfactorization ofA.The arrayducontains the (n- 1) elements of the first superdiagonal ofU.The arraydu2contains the (n- 2) elements of the second superdiagonal ofU.
- ipiv
- Array, size (n). The array of pivot indices, as returned by?gttrf.
- anorm
- The norm of theoriginalmatrixA(see.Description)
Output Parameters
- rcond
- An estimate of the reciprocal of the condition number. The routine setsif the estimate underflows; in this case the matrix is singular (to working precision). However, anytimercond=0rcondis 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
2
floating-point operations for real flavors and n
2
8
for complex flavors.n
2