Visible to Intel only — GUID: GUID-6E1A6C2C-87E0-43FB-A688-065FF67873B4
Visible to Intel only — GUID: GUID-6E1A6C2C-87E0-43FB-A688-065FF67873B4
?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.
call ssycon_3(uplo, n, A, lda, e, ipiv, anorm, rcond, work, iwork, info)
call dsycon_3(uplo, n, A, lda, e, ipiv, anorm, rcond, work, iwork, info)
call csycon_3(uplo, n, A, lda, e, ipiv, anorm, rcond, work, info)
call zsycon_3(uplo, n, A, lda, e, ipiv, anorm, rcond, work, info)
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
- uplo
-
CHARACTER*1
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
-
INTEGER
The order of the matrix A. n ≥ 0.
- A
-
REAL for ssycon_3
DOUBLE PRECISION for dsycon_3
COMPLEX for csycon_3
COMPLEX*16 for zsycon_3
Array, dimension (lda,n). Diagonal of the block diagonal matrix D and factors U or L as computed by ?sytrf_rk:
Only diagonal 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 array e).
—and—
If uplo = 'U', factor U in the superdiagonal part of A. If uplo = 'L', factor L in the subdiagonal part of A.
- lda
-
INTEGER
The leading dimension of the array A.lda ≥ max(1, n).
- e
-
REAL for ssycon_3
DOUBLE PRECISION for dsycon_3
COMPLEX for csycon_3
COMPLEX*16 for zsycon_3
Array, dimension (n). On entry, contains the superdiagonal (or subdiagonal) elements of the symmetric block diagonal matrix D with 1-by-1 or 2-by-2 diagonal blocks. If uplo = 'U', e(i) = D(i-1,i), i=2:N, and e(1) is not referenced. If uplo = 'L', e(i) = D(i+1,i), i=1:N-1, and e(n) is not referenced.
NOTE:For 1-by-1 diagonal block D(k), where 1 ≤ k ≤ n, the element e(k) is not referenced in both the uplo = 'U' and uplo = 'L' cases. - ipiv
-
INTEGER
Array, dimension (n). Details of the interchanges and the block structure of D as determined by ?sytrf_rk.
- anorm
-
REAL for ssycon_3
DOUBLE PRECISION for dsycon_3
REAL for csycon_3
DOUBLE PRECISION for zsycon_3
The 1-norm of the original matrix A.
Output Parameters
- rcond
-
REAL for ssycon_3
DOUBLE PRECISION for dsycon_3
REAL for csycon_3
DOUBLE PRECISION for zsycon_3
The reciprocal of the condition number of the matrix A, computed as rcond = 1/(anorm * AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.
- work
-
REAL for ssycon_3
DOUBLE PRECISION for dsycon_3
COMPLEX for csycon_3
COMPLEX*16 for zsycon_3
Array, dimension (2*n)
- iwork
-
INTEGER
Array, dimension (n).
- info
-
INTEGER
- = 0: Successful exit.
- < 0: If info = -i, the ith argument had an illegal value.