SYTRI_3X - 5.2 English - 68552

SYTRI_3X computes the inverse of a real symmetric indefinite matrix A.

Purpose:

   SYTRI_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.

Parameters:

• UPLO – [in]

  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 – [in]

  N is INTEGER

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

• A – [inout]

  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 – [in]

  LDA is INTEGER

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

• E – [in]

  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 – [in]

  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 – [out] WORK is REAL array, dimension (N+NB+1,NB+3).

• NB – [in]

  NB is INTEGER

  Block size.

• INFO – [out]

  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.