csytri_3x.f man page




subroutine csytri_3x (UPLO, N, A, LDA, E, IPIV, WORK, NB, INFO)

Function/Subroutine Documentation

subroutine csytri_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)



 CSYTRI_3X computes the inverse of a complex symmetric indefinite
 matrix A using the factorization computed by CSYTRF_RK or CSYTRF_BK:

     A = P*U*D*(U**T)*(P**T) or A = P*L*D*(L**T)*(P**T),

 where U (or L) is unit upper (or lower) triangular matrix,
 U**T (or L**T) is the transpose of U (or L), P is a permutation
 matrix, P**T is the transpose of P, and D is symmetric 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 CSYTRF_RK and CSYTRF_BK:
            a) ONLY diagonal elements of the symmetric 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 symmetric 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 symmetric 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 CSYTRF_RK or CSYTRF_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 csytri_3x.f.


Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page csytri_3x(3) is an alias of csytri_3x.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK