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BAKVEC(NM,N,T,E,M,Z,IERR)

       SUBROUTINE BAKVEC(NM,N,T,E,M,Z,IERR)
 C
       INTEGER I,J,M,N,NM,IERR
       REAL T(NM,3),E(N),Z(NM,M)
 C
 C     THIS SUBROUTINE FORMS THE EIGENVECTORS OF A NONSYMMETRIC
 C     TRIDIAGONAL MATRIX BY BACK TRANSFORMING THOSE OF THE
 C     CORRESPONDING SYMMETRIC MATRIX DETERMINED BY  FIGI.
 C
 C     ON INPUT
 C
 C        NM MUST BE SET TO THE ROW DIMENSION OF TWO-DIMENSIONAL
 C          ARRAY PARAMETERS AS DECLARED IN THE CALLING PROGRAM
 C          DIMENSION STATEMENT.
 C
 C        N IS THE ORDER OF THE MATRIX.
 C
 C        T CONTAINS THE NONSYMMETRIC MATRIX.  ITS SUBDIAGONAL IS
 C          STORED IN THE LAST N-1 POSITIONS OF THE FIRST COLUMN,
 C          ITS DIAGONAL IN THE N POSITIONS OF THE SECOND COLUMN,
 C          AND ITS SUPERDIAGONAL IN THE FIRST N-1 POSITIONS OF
 C          THE THIRD COLUMN.  T(1,1) AND T(N,3) ARE ARBITRARY.
 C
 C        E CONTAINS THE SUBDIAGONAL ELEMENTS OF THE SYMMETRIC
 C          MATRIX IN ITS LAST N-1 POSITIONS.  E(1) IS ARBITRARY.
 C
 C        M IS THE NUMBER OF EIGENVECTORS TO BE BACK TRANSFORMED.
 C
 C        Z CONTAINS THE EIGENVECTORS TO BE BACK TRANSFORMED
 C          IN ITS FIRST M COLUMNS.
 C
 C     ON OUTPUT
 C
 C        T IS UNALTERED.
 C
 C        E IS DESTROYED.
 C
 C        Z CONTAINS THE TRANSFORMED EIGENVECTORS
 C          IN ITS FIRST M COLUMNS.
 C
 C        IERR IS SET TO
 C          ZERO       FOR NORMAL RETURN,
 C          2*N+I      IF E(I) IS ZERO WITH T(I,1) OR T(I-1,3) NON-ZERO.
 C                     IN THIS CASE, THE SYMMETRIC MATRIX IS NOT SIMILAR
 C                     TO THE ORIGINAL MATRIX, AND THE EIGENVECTORS
 C                     CANNOT BE FOUND BY THIS PROGRAM.
 C
 C     QUESTIONS AND COMMENTS SHOULD BE DIRECTED TO BURTON S. GARBOW,
 C     MATHEMATICS AND COMPUTER SCIENCE DIV, ARGONNE NATIONAL LABORATORY
 C
 C     THIS VERSION DATED AUGUST 1983.
 C
 C     ------------------------------------------------------------------
 C