SSTEDC 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 SSYTRD or SSPTRD or SSBTRD 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 dense symmetric


                  matrix also.  On entry, Z contains the orthogonal


                  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 REAL 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.

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 REAL 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 N <= 1 then LWORK must be at least 1.


          If COMPZ = 'V' and N > 1 then LWORK 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 then LWORK must be at least


                         ( 1 + 4*N + 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 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 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 then LIWORK must be at least 1.


          If COMPZ = 'V' and N > 1 then LIWORK must be at least


                         ( 6 + 6*N + 5*N*lg N ).


          If COMPZ = 'I' and N > 1 then 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 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 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.

November 2011

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