ESMF_DSTEDC Subroutine

subroutine ESMF_DSTEDC(COMPZ, N, D, E, Z, LDZ, WORK, LWORK, IWORK, LIWORK, INFO)

\brief \b ESMF_DSTEDC \htmlonly Download ESMF_DSTEDC + dependencies [TGZ] [ZIP] [TXT] \endhtmlonly \par Purpose:

\verbatim

ESMF_DSTEDC computes all eigenvalues and, optionally, eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method. The eigenvectors of a full or band real symmetric matrix can also be found if ESMF_DSYTRD or DSPTRD or DSBTRD has been used to reduce this matrix to tridiagonal form.

This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. See ESMF_DLAED3 for details. \endverbatim \param[in] COMPZ \verbatim COMPZ is CHARACTER*1 = ‘N’: Compute eigenvalues only. = ‘I’: Compute eigenvectors of tridiagonal matrix also. = ‘V’: Compute eigenvectors of original dense symmetric matrix also. On entry, Z contains the orthogonal matrix used to reduce the original matrix to tridiagonal form. \endverbatim

\param[in] N \verbatim N is INTEGER The dimension of the symmetric tridiagonal matrix. N >= 0. \endverbatim

\param[in,out] D \verbatim D is DOUBLE PRECISION array, dimension (N) On entry, the diagonal elements of the tridiagonal matrix. On exit, if INFO = 0, the eigenvalues in ascending order. \endverbatim

\param[in,out] E \verbatim E is DOUBLE PRECISION array, dimension (N-1) On entry, the subdiagonal elements of the tridiagonal matrix. On exit, E has been destroyed. \endverbatim

\param[in,out] Z \verbatim Z is DOUBLE PRECISION array, dimension (LDZ,N) On entry, if COMPZ = ‘V’, then Z contains the orthogonal matrix used in the reduction to tridiagonal form. On exit, if INFO = 0, then if COMPZ = ‘V’, Z contains the orthonormal eigenvectors of the original symmetric matrix, and if COMPZ = ‘I’, Z contains the orthonormal eigenvectors of the symmetric tridiagonal matrix. If COMPZ = ‘N’, then Z is not referenced. \endverbatim

\param[in] LDZ \verbatim LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1. If eigenvectors are desired, then LDZ >= max(1,N). \endverbatim

\param[out] WORK \verbatim WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. \endverbatim

\param[in] LWORK \verbatim LWORK is INTEGER The dimension of the array WORK. If COMPZ = ‘N’ or N <= 1 then LWORK must be at least 1. If COMPZ = ‘V’ and N > 1 then LWORK must be at least ( 1 + 3N + 2Nlg N + 4N2 ), where lg( N ) = smallest integer k such that 2k >= N. If COMPZ = ‘I’ and N > 1 then LWORK must be at least ( 1 + 4N + N2 ). Note that for COMPZ = ‘I’ or ‘V’, then if N is less than or equal to the minimum divide size, usually 25, then LWORK need only be max(1,2(N-1)).

     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 ESMF_XERBLA.

\endverbatim

\param[out] IWORK \verbatim IWORK is INTEGER array, dimension (MAX(1,LIWORK)) On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK. \endverbatim

\param[in] LIWORK \verbatim LIWORK is INTEGER The dimension of the array IWORK. If COMPZ = ‘N’ or N <= 1 then LIWORK must be at least 1. If COMPZ = ‘V’ and N > 1 then LIWORK must be at least ( 6 + 6N + 5Nlg N ). If COMPZ = ‘I’ and N > 1 then LIWORK must be at least ( 3 + 5N ). Note that for COMPZ = ‘I’ or ‘V’, then if N is less than or equal to the minimum divide size, usually 25, then LIWORK need only be 1.

     If LIWORK = -1, then a workspace query is assumed; the
     routine only calculates the optimal size of the IWORK array,
     returns this value as the first entry of the IWORK array, and
     no error message related to LIWORK is issued by ESMF_XERBLA.

\endverbatim

\param[out] INFO \verbatim INFO is INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. > 0: The algorithm failed to compute an eigenvalue while working on the submatrix lying in rows and columns INFO/(N+1) through mod(INFO,N+1). \endverbatim \author Univ. of Tennessee \author Univ. of California Berkeley \author Univ. of Colorado Denver \author NAG Ltd. \date June 2017 \ingroup auxOTHERcomputational \par Contributors:

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA \n Modified by Francoise Tisseur, University of Tennessee

Arguments