SSYTRI_3X computes the inverse of a real symmetric indefinite


 matrix A using the factorization computed by SSYTRF_RK or SSYTRF_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

          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

          N is INTEGER


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

A

          A is REAL array, dimension (LDA,N)


          On entry, diagonal of the block diagonal matrix D and


          factors U or L as computed by SYTRF_RK and SSYTRF_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


          matrix.


             If UPLO = 'U': the upper triangular part of the inverse


             is formed and the part of A below the diagonal is not


             referenced;


             If UPLO = 'L': the lower triangular part of the inverse


             is formed and the part of A above the diagonal is not


             referenced.

LDA

          LDA is INTEGER


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

E

          E is REAL 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

          IPIV is INTEGER array, dimension (N)


          Details of the interchanges and the block structure of D


          as determined by SSYTRF_RK or SSYTRF_BK.

WORK

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

NB

          NB is INTEGER


          Block size.

INFO

          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,  Igor Kozachenko,


                  Computer Science Division,


                  University of California, Berkeley