?gbcon
?gbcon
Estimates the reciprocal of the condition number of a band matrix in the 1-norm or the infinity-norm.
Syntax
lapack_int LAPACKE_sgbcon
(
int
matrix_layout
,
char
norm
,
lapack_int
n
,
lapack_int
kl
,
lapack_int
ku
,
const float*
ab
,
lapack_int
ldab
,
const lapack_int*
ipiv
,
float
anorm
,
float*
rcond
);
lapack_int LAPACKE_dgbcon
(
int
matrix_layout
,
char
norm
,
lapack_int
n
,
lapack_int
kl
,
lapack_int
ku
,
const double*
ab
,
lapack_int
ldab
,
const lapack_int*
ipiv
,
double
anorm
,
double*
rcond
);
lapack_int LAPACKE_cgbcon
(
int
matrix_layout
,
char
norm
,
lapack_int
n
,
lapack_int
kl
,
lapack_int
ku
,
const lapack_complex_float*
ab
,
lapack_int
ldab
,
const lapack_int*
ipiv
,
float
anorm
,
float*
rcond
);
lapack_int LAPACKE_zgbcon
(
int
matrix_layout
,
char
norm
,
lapack_int
n
,
lapack_int
kl
,
lapack_int
ku
,
const lapack_complex_double*
ab
,
lapack_int
ldab
,
const lapack_int*
ipiv
,
double
anorm
,
double*
rcond
);
Include Files
- mkl.h
Description
The routine estimates the reciprocal of the condition number of a general band matrix
A
in the 1-norm or infinity-norm:κ
1
(A
) = ||A
||1
||A
-1
||1
= κ
∞
A
T
κ
∞
A
H
κ
∞
A
) = ||A
||∞
A
-1
||∞
κ
1
(A
T
κ
1
(A
H
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 ||A||1= maxjΣ|ia| or ||ijA||= max∞iΣ|ja|)ij
Input Parameters
- matrix_layout
- Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
- 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.
- kl
- The number of subdiagonals within the band ofA;kl≥0.
- ku
- The number of superdiagonals within the band ofA;ku≥0.
- ldab
- The leading dimension of the arrayab. (ldab≥2*kl+ku+1).
- ipiv
- ab
- anorm
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 or *; 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 10
. A call to this routine involves solving a number of systems of linear equations r
A
*x
= b
A
H
x
= b
2
floating-point operations for real flavors and n
(ku
+ 2kl
)8
for complex flavors.n
(ku
+ 2kl
)