SYEV_2STAGE - 5.2 English - 68552

SYEV_2STAGE computes the eigenvalues and, optionally, the left

and/or right eigenvectors for SY matrices.

Purpose:

    SYEV_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
    real symmetric matrix A using the 2stage technique for
    the reduction to tridiagonal.

Parameters:

• JOBZ – [in]

  JOBZ is CHARACTER*1

  = ‘N’: Compute eigenvalues only;

  = ‘V’: Compute eigenvalues and eigenvectors. Not available in this release.

• UPLO – [in]

  UPLO is CHARACTER*1

  = ‘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, the symmetric matrix A. If UPLO = ‘U’, the leading N-by-N upper triangular part of A contains the upper triangular part of the matrix A. If UPLO = ‘L’, the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A.

  On exit, if JOBZ = ‘V’, then if INFO = 0, A contains the orthonormal eigenvectors of the matrix A. If JOBZ = ‘N’, then on exit the lower triangle (if UPLO=’L’) or the upper triangle (if UPLO=’U’) of A, including the diagonal, is destroyed.

• LDA – [in]

  LDA is INTEGER

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

• W – [out]

  W is REAL array, dimension (N)

  If INFO = 0, the eigenvalues in ascending order.

• WORK – [out]

  WORK is REAL array, dimension LWORK

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

• LWORK – [in]

  LWORK is INTEGER

  The length of the array WORK. LWORK >= 1, when N <= 1;

  otherwise

  If JOBZ = ‘N’ and N > 1, LWORK must be queried. LWORK = MAX(1, dimension) where

  dimension = fla_max(stage1,stage2) + (KD+1)*N + 2*N

  = N*KD + N*max(KD+1,FACTOPTNB)

  • fla_max(2*KD*KD, KD*NTHREADS)

  • (KD+1)*N + 2*N

    where KD is the blocking size of the reduction, FACTOPTNB is the blocking used by the QR or LQ algorithm, usually FACTOPTNB=128 is a good choice NTHREADS is the number of threads used when openMP compilation is enabled, otherwise =1.

    If JOBZ = ‘V’ and N > 1, LWORK must be queried. Not yet available

    If LWORK = -1, then a workspace query is assumed; the routine only calculates 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, the algorithm failed to converge; i off-diagonal elements of an intermediate tridiagonal form did not converge to zero.