SRC/zhecon_3.f(3)          Library Functions Manual          SRC/zhecon_3.f(3)

NAME
       SRC/zhecon_3.f

SYNOPSIS
   Functions/Subroutines
       subroutine zhecon_3 (uplo, n, a, lda, e, ipiv, anorm, rcond, work,
           info)
           ZHECON_3

Function/Subroutine Documentation
   subroutine zhecon_3 (character uplo, integer n, complex*16, dimension( lda,
       * ) a, integer lda, complex*16, dimension( * ) e, integer, dimension( *
       ) ipiv, double precision anorm, double precision rcond, complex*16,
       dimension( * ) work, integer info)
       ZHECON_3

       Purpose:


            ZHECON_3 estimates the reciprocal of the condition number (in the
            1-norm) of a complex Hermitian matrix A using the factorization
            computed by ZHETRF_RK or ZHETRF_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 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 ZHETRS_3.

       Parameters
           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).

           N

                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           A

                     A is COMPLEX*16 array, dimension (LDA,N)
                     Diagonal of the block diagonal matrix D and factors U or L
                     as computed by ZHETRF_RK and ZHETRF_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.

           LDA

                     LDA is INTEGER
                     The leading dimension of the array A.  LDA >= max(1,N).

           E

                     E is COMPLEX*16 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, where
                     If UPLO = 'U': E(i) = D(i-1,i),i=2:N, E(1) not referenced;
                     If UPLO = 'L': E(i) = D(i+1,i),i=1:N-1, E(N) not referenced.

                     NOTE: For 1-by-1 diagonal block D(k), where
                     1 <= k <= N, the element E(k) is not referenced in both
                     UPLO = 'U' or UPLO = 'L' cases.

           IPIV

                     IPIV is INTEGER array, dimension (N)
                     Details of the interchanges and the block structure of D
                     as determined by ZHETRF_RK or ZHETRF_BK.

           ANORM

                     ANORM is DOUBLE PRECISION
                     The 1-norm of the original matrix A.

           RCOND

                     RCOND is DOUBLE PRECISION
                     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

                     WORK is COMPLEX*16 array, dimension (2*N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit
                     < 0:  if INFO = -i, the i-th argument had an illegal value

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:


             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 zhecon_3.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0               SRC/zhecon_3.f(3)