*DECK BAKVEC
SUBROUTINE BAKVEC (NM, N, T, E, M, Z, IERR)
C***BEGIN PROLOGUE BAKVEC
C***PURPOSE Form the eigenvectors of a certain real non-symmetric
C tridiagonal matrix from a symmetric tridiagonal matrix
C output from FIGI.
C***LIBRARY SLATEC (EISPACK)
C***CATEGORY D4C4
C***TYPE SINGLE PRECISION (BAKVEC-S)
C***KEYWORDS EIGENVECTORS, EISPACK
C***AUTHOR Smith, B. T., et al.
C***DESCRIPTION
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 the two-dimensional
C array parameters, T and Z, as declared in the calling
C program dimension statement. NM is an INTEGER variable.
C
C N is the order of the matrix T. N is an INTEGER variable.
C N must be less than or equal to NM.
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 T is a two-dimensional REAL array, dimensioned T(NM,3).
C
C E contains the subdiagonal elements of the symmetric
C matrix in its last N-1 positions. E(1) is arbitrary.
C E is a one-dimensional REAL array, dimensioned E(N).
C
C M is the number of eigenvectors to be back transformed.
C M is an INTEGER variable.
C
C Z contains the eigenvectors to be back transformed
C in its first M columns. Z is a two-dimensional REAL
C array, dimensioned Z(NM,M).
C
C On OUTPUT
C
C T is unaltered.
C
C E is destroyed.
C
C Z contains the transformed eigenvectors in its first M columns.
C
C IERR is an INTEGER flag 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 B. S. Garbow,
C APPLIED MATHEMATICS DIVISION, ARGONNE NATIONAL LABORATORY
C ------------------------------------------------------------------
C
C***REFERENCES B. T. Smith, J. M. Boyle, J. J. Dongarra, B. S. Garbow,
C Y. Ikebe, V. C. Klema and C. B. Moler, Matrix Eigen-
C system Routines - EISPACK Guide, Springer-Verlag,
C 1976.
C***ROUTINES CALLED (NONE)
C***REVISION HISTORY (YYMMDD)
C 760101 DATE WRITTEN
C 890831 Modified array declarations. (WRB)
C 890831 REVISION DATE from Version 3.2
C 891214 Prologue converted to Version 4.0 format. (BAB)
C 920501 Reformatted the REFERENCES section. (WRB)
C***END PROLOGUE BAKVEC
C
INTEGER I,J,M,N,NM,IERR
REAL T(NM,3),E(*),Z(NM,*)
C
C***FIRST EXECUTABLE STATEMENT BAKVEC
IERR = 0
IF (M .EQ. 0) GO TO 1001
E(1) = 1.0E0
IF (N .EQ. 1) GO TO 1001
C
DO 100 I = 2, N
IF (E(I) .NE. 0.0E0) GO TO 80
IF (T(I,1) .NE. 0.0E0 .OR. T(I-1,3) .NE. 0.0E0) GO TO 1000
E(I) = 1.0E0
GO TO 100
80 E(I) = E(I-1) * E(I) / T(I-1,3)
100 CONTINUE
C
DO 120 J = 1, M
C
DO 120 I = 2, N
Z(I,J) = Z(I,J) * E(I)
120 CONTINUE
C
GO TO 1001
C .......... SET ERROR -- EIGENVECTORS CANNOT BE
C FOUND BY THIS PROGRAM ..........
1000 IERR = 2 * N + I
1001 RETURN
END