?gecon
?gecon
Estimates the reciprocal of the condition number of a general matrix in the 1-norm or the infinity-norm.
Syntax
lapack_int LAPACKE_sgecon
(
int
matrix_layout
,
char
norm
,
lapack_int
n
,
const float*
a
,
lapack_int
lda
,
float
anorm
,
float*
rcond
);
lapack_int LAPACKE_dgecon
(
int
matrix_layout
,
char
norm
,
lapack_int
n
,
const double*
a
,
lapack_int
lda
,
double
anorm
,
double*
rcond
);
lapack_int LAPACKE_cgecon
(
int
matrix_layout
,
char
norm
,
lapack_int
n
,
const lapack_complex_float*
a
,
lapack_int
lda
,
float
anorm
,
float*
rcond
);
lapack_int LAPACKE_zgecon
(
int
matrix_layout
,
char
norm
,
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 general 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||orA||1= maxjΣ|ia|ij||A||= 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.
- a
- anorm
- lda
- The leading dimension of.a;lda≥max(1,n)
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 10r
. A call to this routine involves solving a number of systems of linear equations A
*x
= b
A
H
x
= b
2
floating-point operations for real flavors and *n
2
8
for complex flavors.*n
2