TRBAK1(3F)

NAME
     TRBAK1, STRBAK1  -  EISPACK routine.  This subroutine forms the
     eigenvectors of a REAL SYMMETRIC matrix by back transforming those of the
     corresponding symmetric tridiagonal matrix determined by  TRED1.


SYNOPSYS
          subroutine  trbak1(nm, n, a, e, m, z)
          integer          nm, n, m
          double precision a(nm,n), e(n), z(nm,m)

          subroutine strbak1(nm, n, a, e, m, z)
          integer          nm, n, m
          real             a(nm,n), e(n), z(nm,m)



DESCRIPTION
     On Input

     NM must be set to the row dimension of two-dimensional array parameters
     as declared in the calling program dimension statement.

     N is the order of the matrix.

     A contains information about the orthogonal trans- formations used in the
     reduction by  TRED1 in its strict lower triangle.

     E contains the subdiagonal elements of the tridiagonal matrix in its last
     N-1 positions.  E(1) is arbitrary.

     M is the number of eigenvectors to be back transformed.

     Z contains the eigenvectors to be back transformed in its first M
     columns.  On Output

     Z contains the transformed eigenvectors in its first M columns.  Note
     that TRBAK1 preserves vector Euclidean norms.  Questions and comments
     should be directed to B. S. Garbow, APPLIED MATHEMATICS DIVISION, ARGONNE
     NATIONAL LABORATORY