zhetri_3.f - Man Page



subroutine zhetri_3 (UPLO, N, A, LDA, E, IPIV, WORK, LWORK, INFO)

Function/Subroutine Documentation

subroutine zhetri_3 (character UPLO, integer N, complex*16, dimension( lda, * ) A, integer LDA, complex*16, dimension( * ) E, integer, dimension( * ) IPIV, complex*16, dimension( * ) WORK, integer LWORK, integer INFO)



 ZHETRI_3 computes the inverse of a complex Hermitian indefinite
 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.

 ZHETRI_3 sets the leading dimension of the workspace  before calling
 ZHETRI_3X that actually computes the inverse.  This is the blocked
 version of the algorithm, calling Level 3 BLAS.


          UPLO is CHARACTER*1
          Specifies whether the details of the factorization are
          stored as an upper or lower triangular matrix.
          = 'U':  Upper triangle of A is stored;
          = 'L':  Lower triangle of A is stored.


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


          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, 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.

          On exit, if INFO = 0, the Hermitian inverse of the original
             If UPLO = 'U': the upper triangular part of the inverse
             is formed and the part of A below the diagonal is not
             If UPLO = 'L': the lower triangular part of the inverse
             is formed and the part of A above the diagonal is not


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


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


          WORK is COMPLEX*16 array, dimension (N+NB+1)*(NB+3).
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.


          LWORK is INTEGER
          The length of WORK. LWORK >= (N+NB+1)*(NB+3).

          If LDWORK = -1, then a workspace query is assumed;
          the routine only calculates the optimal size of the optimal
          size of the WORK array, returns this value as the first
          entry of the WORK array, and no error message related to
          LWORK is issued by XERBLA.


          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument had an illegal value
          > 0: if INFO = i, D(i,i) = 0; the matrix is singular and its
               inverse could not be computed.

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.


November 2017


November 2017, Igor Kozachenko, Computer Science Division, University of California, Berkeley

Definition at line 172 of file zhetri_3.f.


Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page zhetri_3(3) is an alias of zhetri_3.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK