?sycon_3
?sycon_3
Estimates the reciprocal of the condition number (in the 1-norm) of a real or complex symmetric matrix A using the factorization computed by
?sytrf_rk
.lapack_int
LAPACKE_ssycon_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const
float
*
A
,
lapack_int
lda
,
const
float
*
e
,
const
lapack_int
*
ipiv
,
float
anorm
,
float
*
rcond
);
lapack_int
LAPACKE_dsycon_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const
double
*
A
,
lapack_int
lda
,
const
double
*
e
,
const
lapack_int
*
ipiv
,
double
anorm
,
double
*
rcond
);
lapack_int
LAPACKE_csycon_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const
lapack_complex_float
*
A
,
lapack_int
lda
,
const
lapack_complex_float
*
e
,
const
lapack_int
*
ipiv
,
float
anorm
,
float
*
rcond
);
lapack_int
LAPACKE_zsycon_3
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
const
lapack_complex_double
*
A
,
lapack_int
lda
,
const
lapack_complex_double
*
e
,
const
lapack_int
*
ipiv
,
double
anorm
,
double
*
rcond
);
Description
?sycon_3
estimates the reciprocal of the condition number (in the 1-norm) of a real or complex symmetric matrix A using the factorization computed by ?sytrf_rk
. A = P*U*D*(UT
)*(PT
) or A = P*L*D*(LT
)*(PT
), where U (or L) is unit upper (or lower) triangular matrix, UT
(or LT
) is the transpose of U (or L), P is a permutation matrix, PT
is the transpose of P, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as
rcond
= 1 / (anorm
* norm(inv(A))).This routine uses BLAS3 solver
?sytrs_3
.Input Parameters
- matrix_layout
- Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
- uplo
- Specifies whether the details of the factorization are stored as an upper or lower triangular matrix:
- ='U': Upper triangular. The form is A = P*U*D*(UT)*(PT).
- ='L': Lower triangular. The form is A = P*L*D*(LT)*(PT).
- n
- The order of the matrix A.n≥ 0.
- A
- Array of size max(1,Diagonal of the block diagonal matrix D and factors U or L as computed bylda*n).?sytrf_rk:
- Onlydiagonal elements of the symmetric block diagonal matrix D on the diagonal of A; that is, D(k,k) = A(k,k). Superdiagonal (or subdiagonal) elements of D should be provided on entry in arraye).—and—
- Ifuplo='U', factor U in the superdiagonal part of A. Ifuplo='L', factor L in the subdiagonal part of A.
- lda
- The leading dimension of the arrayA.
- e
- Array of sizeOn entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks. Ifn.uplo='U', e(i) = D(i-1,i),i=2:N, and e(1) is not referenced. Ifuplo='L', e(i) = D(i+1,i),i=1:N-1, and e(n) is not referenced.For 1-by-1 diagonal block D(k), where 1 ≤k≤n, the elemente[k-1] is not referenced in both theuplo='U'anduplo='L'cases.
- ipiv
- Array of sizeDetails of the interchanges and the block structure of D as determined byn.?sytrf_rk.
- anorm
- The 1-norm of the original matrix A.
Output Parameters
- rcond
- The reciprocal of the condition number of the matrix A, computed asrcond= 1/(anorm*AINVNM), whereAINVNMis an estimate of the 1-norm of inv(A) computed in this routine.
Return Values
This function returns a value
info
.= 0: Successful exit.
< 0: If , the
info
= -i
i
th
argument had an illegal value.