SLAED0 computes all eigenvalues and corresponding eigenvectors of a


 symmetric tridiagonal matrix using the divide and conquer method.

ICOMPQ

          ICOMPQ is INTEGER


          = 0:  Compute eigenvalues only.


          = 1:  Compute eigenvectors of original dense symmetric matrix


                also.  On entry, Q contains the orthogonal matrix used


                to reduce the original matrix to tridiagonal form.


          = 2:  Compute eigenvalues and eigenvectors of tridiagonal


                matrix.

QSIZ

          QSIZ is INTEGER


         The dimension of the orthogonal matrix used to reduce


         the full matrix to tridiagonal form.  QSIZ >= N if ICOMPQ = 1.

N

          N is INTEGER


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

D

          D is REAL array, dimension (N)


         On entry, the main diagonal of the tridiagonal matrix.


         On exit, its eigenvalues.

E

          E is REAL array, dimension (N-1)


         The off-diagonal elements of the tridiagonal matrix.


         On exit, E has been destroyed.

Q

          Q is REAL array, dimension (LDQ, N)


         On entry, Q must contain an N-by-N orthogonal matrix.


         If ICOMPQ = 0    Q is not referenced.


         If ICOMPQ = 1    On entry, Q is a subset of the columns of the


                          orthogonal matrix used to reduce the full


                          matrix to tridiagonal form corresponding to


                          the subset of the full matrix which is being


                          decomposed at this time.


         If ICOMPQ = 2    On entry, Q will be the identity matrix.


                          On exit, Q contains the eigenvectors of the


                          tridiagonal matrix.

LDQ

          LDQ is INTEGER


         The leading dimension of the array Q.  If eigenvectors are


         desired, then  LDQ >= max(1,N).  In any case,  LDQ >= 1.

QSTORE

          QSTORE is REAL array, dimension (LDQS, N)


         Referenced only when ICOMPQ = 1.  Used to store parts of


         the eigenvector matrix when the updating matrix multiplies


         take place.

LDQS

          LDQS is INTEGER


         The leading dimension of the array QSTORE.  If ICOMPQ = 1,


         then  LDQS >= max(1,N).  In any case,  LDQS >= 1.

WORK

          WORK is REAL array,


         If ICOMPQ = 0 or 1, the dimension of WORK must be at least


                     1 + 3*N + 2*N*lg N + 3*N**2


                     ( lg( N ) = smallest integer k


                                 such that 2^k >= N )


         If ICOMPQ = 2, the dimension of WORK must be at least


                     4*N + N**2.

IWORK

          IWORK is INTEGER array,


         If ICOMPQ = 0 or 1, the dimension of IWORK must be at least


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


                        ( lg( N ) = smallest integer k


                                    such that 2^k >= N )


         If ICOMPQ = 2, the dimension of IWORK must be at least


                        3 + 5*N.

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