?tbcon
?tbcon
Estimates the reciprocal of the condition number of a triangular band matrix.
Syntax
lapack_int LAPACKE_stbcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
lapack_int
kd
,
const float*
ab
,
lapack_int
ldab
,
float*
rcond
);
lapack_int LAPACKE_dtbcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
lapack_int
kd
,
const double*
ab
,
lapack_int
ldab
,
double*
rcond
);
lapack_int LAPACKE_ctbcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
lapack_int
kd
,
const lapack_complex_float*
ab
,
lapack_int
ldab
,
float*
rcond
);
lapack_int LAPACKE_ztbcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
lapack_int
kd
,
const lapack_complex_double*
ab
,
lapack_int
ldab
,
double*
rcond
);
Include Files
- mkl.h
Description
The routine estimates the reciprocal of the condition number of a triangular band matrix
A
in either 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
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.
- uplo
- Must be'U'or'L'. Indicates whetherAis upper or lower triangular:If, the arrayuplo='U'apstores the upper triangle ofAin packed form.If, the arrayuplo='L'apstores the lower triangle ofAin packed form.
- diag
- Must be'N'or'U'.If, thendiag='N'Ais not a unit triangular matrix.If, thendiag='U'Ais unit triangular: diagonal elements are assumed to be 1 and not referenced in the arrayab.
- n
- The order of the matrixA;n≥0.
- kd
- The number of superdiagonals or subdiagonals in the matrixA;kd≥0.
- ab
- The arrayabof size max(1,contains the band matrixldab*n)A.
- ldab
- The leading dimension of the arrayab. (ldab≥kd+1).
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
(kd
+ 1)8*
operations for complex flavors.n
(kd
+ 1)