CSTEDC computes all eigenvalues and, optionally, eigenvectors of a


 symmetric tridiagonal matrix using the divide and conquer method.


 The eigenvectors of a full or band complex Hermitian matrix can also


 be found if CHETRD or CHPTRD or CHBTRD 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 SLAED3 for details.

COMPZ

          COMPZ is CHARACTER*1


          = 'N':  Compute eigenvalues only.


          = 'I':  Compute eigenvectors of tridiagonal matrix also.


          = 'V':  Compute eigenvectors of original Hermitian matrix


                  also.  On entry, Z contains the unitary matrix used


                  to reduce the original matrix to tridiagonal form.

N

          N is INTEGER


          The dimension of the symmetric tridiagonal matrix.  N >= 0.

D

          D is REAL array, dimension (N)


          On entry, the diagonal elements of the tridiagonal matrix.


          On exit, if INFO = 0, the eigenvalues in ascending order.

E

          E is REAL array, dimension (N-1)


          On entry, the subdiagonal elements of the tridiagonal matrix.


          On exit, E has been destroyed.

Z

          Z is COMPLEX array, dimension (LDZ,N)


          On entry, if COMPZ = 'V', then Z contains the unitary


          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 Hermitian matrix,


          and if COMPZ = 'I', Z contains the orthonormal eigenvectors


          of the symmetric tridiagonal matrix.


          If  COMPZ = 'N', then Z is not referenced.

LDZ

          LDZ is INTEGER


          The leading dimension of the array Z.  LDZ >= 1.


          If eigenvectors are desired, then LDZ >= max(1,N).

WORK

          WORK is COMPLEX array, dimension (MAX(1,LWORK))


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

LWORK

          LWORK is INTEGER


          The dimension of the array WORK.


          If COMPZ = 'N' or 'I', or N <= 1, LWORK must be at least 1.


          If COMPZ = 'V' and N > 1, LWORK must be at least N*N.


          Note that for COMPZ = 'V', then if N is less than or


          equal to the minimum divide size, usually 25, then LWORK need


          only be 1.


          If LWORK = -1, then a workspace query is assumed; the routine


          only calculates the optimal sizes of the WORK, RWORK and


          IWORK arrays, returns these values as the first entries of


          the WORK, RWORK and IWORK arrays, and no error message


          related to LWORK or LRWORK or LIWORK is issued by XERBLA.

RWORK

          RWORK is REAL array, dimension (MAX(1,LRWORK))


          On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.

LRWORK

          LRWORK is INTEGER


          The dimension of the array RWORK.


          If COMPZ = 'N' or N <= 1, LRWORK must be at least 1.


          If COMPZ = 'V' and N > 1, LRWORK must be at least


                         1 + 3*N + 2*N*lg N + 4*N**2 ,


                         where lg( N ) = smallest integer k such


                         that 2**k >= N.


          If COMPZ = 'I' and N > 1, LRWORK must be at least


                         1 + 4*N + 2*N**2 .


          Note that for COMPZ = 'I' or 'V', then if N is less than or


          equal to the minimum divide size, usually 25, then LRWORK


          need only be max(1,2*(N-1)).


          If LRWORK = -1, then a workspace query is assumed; the


          routine only calculates the optimal sizes of the WORK, RWORK


          and IWORK arrays, returns these values as the first entries


          of the WORK, RWORK and IWORK arrays, and no error message


          related to LWORK or LRWORK or LIWORK is issued by XERBLA.

IWORK

          IWORK is INTEGER array, dimension (MAX(1,LIWORK))


          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.

LIWORK

          LIWORK is INTEGER


          The dimension of the array IWORK.


          If COMPZ = 'N' or N <= 1, LIWORK must be at least 1.


          If COMPZ = 'V' or N > 1,  LIWORK must be at least


                                    6 + 6*N + 5*N*lg N.


          If COMPZ = 'I' or N > 1,  LIWORK must be at least


                                    3 + 5*N .


          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 sizes of the WORK, RWORK


          and IWORK arrays, returns these values as the first entries


          of the WORK, RWORK and IWORK arrays, and no error message


          related to LWORK or LRWORK or LIWORK is issued by XERBLA.

INFO

          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).

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

December 2016

Jeff Rutter, Computer Science Division, University of California at Berkeley, USA