*DECK FIGI2
SUBROUTINE FIGI2 (NM, N, T, D, E, Z, IERR)
C***BEGIN PROLOGUE FIGI2
C***PURPOSE Transforms certain real non-symmetric tridiagonal matrix
C to symmetric tridiagonal matrix.
C***LIBRARY SLATEC (EISPACK)
C***CATEGORY D4C1C
C***TYPE SINGLE PRECISION (FIGI2-S)
C***KEYWORDS EIGENVALUES, EIGENVECTORS, EISPACK
C***AUTHOR Smith, B. T., et al.
C***DESCRIPTION
C
C Given a NONSYMMETRIC TRIDIAGONAL matrix such that the products
C of corresponding pairs of off-diagonal elements are all
C non-negative, and zero only when both factors are zero, this
C subroutine reduces it to a SYMMETRIC TRIDIAGONAL matrix
C using and accumulating diagonal similarity transformations.
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 On OUTPUT
C
C T is unaltered.
C
C D contains the diagonal elements of the tridiagonal symmetric
C matrix. D is a one-dimensional REAL array, dimensioned D(N).
C
C E contains the subdiagonal elements of the tridiagonal
C symmetric matrix in its last N-1 positions. E(1) is not set.
C E is a one-dimensional REAL array, dimensioned E(N).
C
C Z contains the diagonal transformation matrix produced in the
C symmetrization. Z is a two-dimensional REAL array,
C dimensioned Z(NM,N).
C
C IERR is an INTEGER flag set to
C Zero for normal return,
C N+I if T(I,1)*T(I-1,3) is negative,
C 2*N+I if T(I,1)*T(I-1,3) is zero with one factor
C non-zero. In these cases, there does not exist
C a symmetrizing similarity transformation which
C is essential for the validity of the later
C eigenvector computation.
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 FIGI2
C
INTEGER I,J,N,NM,IERR
REAL T(NM,3),D(*),E(*),Z(NM,*)
REAL H
C
C***FIRST EXECUTABLE STATEMENT FIGI2
IERR = 0
C
DO 100 I = 1, N
C
DO 50 J = 1, N
50 Z(I,J) = 0.0E0
C
IF (I .EQ. 1) GO TO 70
H = T(I,1) * T(I-1,3)
IF (H) 900, 60, 80
60 IF (T(I,1) .NE. 0.0E0 .OR. T(I-1,3) .NE. 0.0E0) GO TO 1000
E(I) = 0.0E0
70 Z(I,I) = 1.0E0
GO TO 90
80 E(I) = SQRT(H)
Z(I,I) = Z(I-1,I-1) * E(I) / T(I-1,3)
90 D(I) = T(I,2)
100 CONTINUE
C
GO TO 1001
C .......... SET ERROR -- PRODUCT OF SOME PAIR OF OFF-DIAGONAL
C ELEMENTS IS NEGATIVE ..........
900 IERR = N + I
GO TO 1001
C .......... SET ERROR -- PRODUCT OF SOME PAIR OF OFF-DIAGONAL
C ELEMENTS IS ZERO WITH ONE MEMBER NON-ZERO ..........
1000 IERR = 2 * N + I
1001 RETURN
END