*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