LAPACK 3.11.0
LAPACK: Linear Algebra PACKage

subroutine checon_3  (  character  UPLO, 
integer  N,  
complex, dimension( lda, * )  A,  
integer  LDA,  
complex, dimension( * )  E,  
integer, dimension( * )  IPIV,  
real  ANORM,  
real  RCOND,  
complex, dimension( * )  WORK,  
integer  INFO  
) 
CHECON_3
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CHECON_3 estimates the reciprocal of the condition number (in the 1norm) of a complex Hermitian matrix A using the factorization computed by CHETRF_RK or CHETRF_BK: A = P*U*D*(U**H)*(P**T) or A = P*L*D*(L**H)*(P**T), where U (or L) is unit upper (or lower) triangular matrix, U**H (or L**H) is the conjugate of U (or L), P is a permutation matrix, P**T is the transpose of P, and D is Hermitian and block diagonal with 1by1 and 2by2 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 CHETRS_3.
[in]  UPLO  UPLO is 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*(U**H)*(P**T); = 'L': Lower triangular, form is A = P*L*D*(L**H)*(P**T). 
[in]  N  N is INTEGER The order of the matrix A. N >= 0. 
[in]  A  A is COMPLEX array, dimension (LDA,N) Diagonal of the block diagonal matrix D and factors U or L as computed by CHETRF_RK and CHETRF_BK: a) ONLY diagonal elements of the Hermitian block diagonal matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); (superdiagonal (or subdiagonal) elements of D should be provided on entry in array E), and b) If UPLO = 'U': factor U in the superdiagonal part of A. If UPLO = 'L': factor L in the subdiagonal part of A. 
[in]  LDA  LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N). 
[in]  E  E is COMPLEX array, dimension (N) On entry, contains the superdiagonal (or subdiagonal) elements of the Hermitian block diagonal matrix D with 1by1 or 2by2 diagonal blocks, where If UPLO = 'U': E(i) = D(i1,i),i=2:N, E(1) not referenced; If UPLO = 'L': E(i) = D(i+1,i),i=1:N1, E(N) not referenced. NOTE: For 1by1 diagonal block D(k), where 1 <= k <= N, the element E(k) is not referenced in both UPLO = 'U' or UPLO = 'L' cases. 
[in]  IPIV  IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by CHETRF_RK or CHETRF_BK. 
[in]  ANORM  ANORM is REAL The 1norm of the original matrix A. 
[out]  RCOND  RCOND is REAL The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM * AINVNM), where AINVNM is an estimate of the 1norm of inv(A) computed in this routine. 
[out]  WORK  WORK is COMPLEX array, dimension (2*N) 
[out]  INFO  INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value 
June 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, School of Mathematics, University of Manchester
Definition at line 164 of file checon_3.f.