SYTRI_3 - 5.2 English - 68552

SYTRI_3 computes the inverse of a real symmetric indefinite

matrix A using the factorization computed by SYTRF_RK or SYTRF_BK.

Purpose:

    SYTRI_3 computes the inverse of a real symmetric indefinite
    matrix A using the factorization computed by SYTRF_RK or SYTRF_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.

    SYTRI_3 sets the leading dimension of the workspace  before calling
    SYTRI_3X that actually computes the inverse.  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 SSYTRF_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).

  On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

• LWORK – [in]

  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 – [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.