?trcon
?trcon
Estimates the reciprocal of the condition number of a triangular matrix.
Syntax
lapack_int LAPACKE_strcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
const float*
a
,
lapack_int
lda
,
float*
rcond
);
lapack_int LAPACKE_dtrcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
const double*
a
,
lapack_int
lda
,
double*
rcond
);
lapack_int LAPACKE_ctrcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
const lapack_complex_float*
a
,
lapack_int
lda
,
float*
rcond
);
lapack_int LAPACKE_ztrcon
(
int
matrix_layout
,
char
norm
,
char
uplo
,
char
diag
,
lapack_int
n
,
const lapack_complex_double*
a
,
lapack_int
lda
,
double*
rcond
);
Include Files
- mkl.h
Description
The routine estimates the reciprocal of the condition number of a triangular 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
||∞
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'astores the upper triangle ofA, other array elements are not referenced.If, the arrayuplo='L'astores the lower triangle ofA, other array elements are not referenced.
- 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 arraya.
- n
- The order of the matrixA;n≥0.
- a
- The arrayaof size max(1,contains the matrixlda*n)A.
- lda
- The leading dimension ofa;.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
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 floating-point operations for real flavors and
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
n
2
4
operations for complex flavors.n
2