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.

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

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

  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