chetri_3x.f man page




subroutine chetri_3x (UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO)

Function/Subroutine Documentation

subroutine chetri_3x (character UPLO, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) E, integer, dimension( * ) IPIV, complex, dimension( n+nb+1, * ) WORK, integer NB, integer INFO)



 CHETRI_3X computes the inverse of a complex Hermitian indefinite
 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 1-by-1 and 2-by-2 diagonal blocks.

 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 array, dimension (LDA,N)
          On entry, 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.

          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 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 CHETRF_RK or CHETRF_BK.


          WORK is COMPLEX array, dimension (N+NB+1,NB+3).


          NB is INTEGER
          Block size.


          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.


June 2017


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

Definition at line 161 of file chetri_3x.f.


Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page chetri_3x(3) is an alias of chetri_3x.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK