Visible to Intel only — GUID: GUID-F4D7AE03-6715-4F96-8ED7-1AB51F932DFC
Visible to Intel only — GUID: GUID-F4D7AE03-6715-4F96-8ED7-1AB51F932DFC
?hecon_3
Estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian matrix A.
call checon_3 (uplo, n, A, lda, e, ipiv, anorm, rcond, work, info)
call zhecon_3(uplo, n, A, lda, e, ipiv, anorm, rcond, work, info)
Description
?hecon_3 estimates the reciprocal of the condition number (in the 1-norm) of a complex Hermitian matrix A using the factorization computed by ?hetrf_rk: A = P*U*D*(UH)*(PT) or A = P*L*D*(LH)*(PT), where U (or L) is unit upper (or lower) triangular matrix, UH (or LH) is the conjugate of U (or L), P is a permutation matrix, PT is the transpose of P, and D is Hermitian 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 ?hetrs_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, form is A = P*U*D*(UH)*(PT); = 'L': Lower triangular, form is A = P*L*D*(LH)*(PT).
- n
-
INTEGER. The order of the matrix A. n ≥ 0.
- A
-
COMPLEX for checon_3
COMPLEX*16 for zhecon_3
Array, dimension (lda,n). Diagonal of the block diagonal matrix D and factor U or L as computed by ?hetrf_rk:
Only diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A—that is, D(k,k) = A(k,k). Superdiagonal (or subdiagonal) elements of D must 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
-
COMPLEX for checon_3
COMPLEX*16 for zhecon_3
Array, dimension (n). On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian 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 ?hetrf_rk.
- anorm
-
COMPLEX for checon_3
COMPLEX*16 for zhecon_3
The 1-norm of the original matrix A.
Output Parameters
- rcond
-
COMPLEX for checon_3
COMPLEX*16 for zhecon_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
-
COMPLEX for checon_3
COMPLEX*16 for zhecon_3
Array, dimension (2*n).
- info
-
INTEGER.
- = 0: Successful exit.
- < 0: If info = -i, the ith argument had an illegal value.