+++ /dev/null
-*DECK TQLRAT
- SUBROUTINE TQLRAT (N, D, E2, IERR)
-C***BEGIN PROLOGUE TQLRAT
-C***PURPOSE Compute the eigenvalues of symmetric tridiagonal matrix
-C using a rational variant of the QL method.
-C***LIBRARY SLATEC (EISPACK)
-C***CATEGORY D4A5, D4C2A
-C***TYPE SINGLE PRECISION (TQLRAT-S)
-C***KEYWORDS EIGENVALUES OF A SYMMETRIC TRIDIAGONAL MATRIX, EISPACK,
-C QL METHOD
-C***AUTHOR Smith, B. T., et al.
-C***DESCRIPTION
-C
-C This subroutine is a translation of the ALGOL procedure TQLRAT.
-C
-C This subroutine finds the eigenvalues of a SYMMETRIC
-C TRIDIAGONAL matrix by the rational QL method.
-C
-C On Input
-C
-C N is the order of the matrix. N is an INTEGER variable.
-C
-C D contains the diagonal elements of the symmetric tridiagonal
-C matrix. D is a one-dimensional REAL array, dimensioned D(N).
-C
-C E2 contains the squares of the subdiagonal elements of the
-C symmetric tridiagonal matrix in its last N-1 positions.
-C E2(1) is arbitrary. E2 is a one-dimensional REAL array,
-C dimensioned E2(N).
-C
-C On Output
-C
-C D contains the eigenvalues in ascending order. If an
-C error exit is made, the eigenvalues are correct and
-C ordered for indices 1, 2, ..., IERR-1, but may not be
-C the smallest eigenvalues.
-C
-C E2 has been destroyed.
-C
-C IERR is an INTEGER flag set to
-C Zero for normal return,
-C J if the J-th eigenvalue has not been
-C determined after 30 iterations.
-C
-C Calls PYTHAG(A,B) for sqrt(A**2 + B**2).
-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 C. H. Reinsch, Eigenvalues of a real, symmetric, tri-
-C diagonal matrix, Algorithm 464, Communications of the
-C ACM 16, 11 (November 1973), pp. 689.
-C***ROUTINES CALLED PYTHAG, R1MACH
-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 TQLRAT
-C
- INTEGER I,J,L,M,N,II,L1,MML,IERR
- REAL D(*),E2(*)
- REAL B,C,F,G,H,P,R,S,MACHEP
- REAL PYTHAG
- LOGICAL FIRST
-C
- SAVE FIRST, MACHEP
- DATA FIRST /.TRUE./
-C***FIRST EXECUTABLE STATEMENT TQLRAT
- IF (FIRST) THEN
- MACHEP = R1MACH(4)
- ENDIF
- FIRST = .FALSE.
-C
- IERR = 0
- IF (N .EQ. 1) GO TO 1001
-C
- DO 100 I = 2, N
- 100 E2(I-1) = E2(I)
-C
- F = 0.0E0
- B = 0.0E0
- E2(N) = 0.0E0
-C
- DO 290 L = 1, N
- J = 0
- H = MACHEP * (ABS(D(L)) + SQRT(E2(L)))
- IF (B .GT. H) GO TO 105
- B = H
- C = B * B
-C .......... LOOK FOR SMALL SQUARED SUB-DIAGONAL ELEMENT ..........
- 105 DO 110 M = L, N
- IF (E2(M) .LE. C) GO TO 120
-C .......... E2(N) IS ALWAYS ZERO, SO THERE IS NO EXIT
-C THROUGH THE BOTTOM OF THE LOOP ..........
- 110 CONTINUE
-C
- 120 IF (M .EQ. L) GO TO 210
- 130 IF (J .EQ. 30) GO TO 1000
- J = J + 1
-C .......... FORM SHIFT ..........
- L1 = L + 1
- S = SQRT(E2(L))
- G = D(L)
- P = (D(L1) - G) / (2.0E0 * S)
- R = PYTHAG(P,1.0E0)
- D(L) = S / (P + SIGN(R,P))
- H = G - D(L)
-C
- DO 140 I = L1, N
- 140 D(I) = D(I) - H
-C
- F = F + H
-C .......... RATIONAL QL TRANSFORMATION ..........
- G = D(M)
- IF (G .EQ. 0.0E0) G = B
- H = G
- S = 0.0E0
- MML = M - L
-C .......... FOR I=M-1 STEP -1 UNTIL L DO -- ..........
- DO 200 II = 1, MML
- I = M - II
- P = G * H
- R = P + E2(I)
- E2(I+1) = S * R
- S = E2(I) / R
- D(I+1) = H + S * (H + D(I))
- G = D(I) - E2(I) / G
- IF (G .EQ. 0.0E0) G = B
- H = G * P / R
- 200 CONTINUE
-C
- E2(L) = S * G
- D(L) = H
-C .......... GUARD AGAINST UNDERFLOW IN CONVERGENCE TEST ..........
- IF (H .EQ. 0.0E0) GO TO 210
- IF (ABS(E2(L)) .LE. ABS(C/H)) GO TO 210
- E2(L) = H * E2(L)
- IF (E2(L) .NE. 0.0E0) GO TO 130
- 210 P = D(L) + F
-C .......... ORDER EIGENVALUES ..........
- IF (L .EQ. 1) GO TO 250
-C .......... FOR I=L STEP -1 UNTIL 2 DO -- ..........
- DO 230 II = 2, L
- I = L + 2 - II
- IF (P .GE. D(I-1)) GO TO 270
- D(I) = D(I-1)
- 230 CONTINUE
-C
- 250 I = 1
- 270 D(I) = P
- 290 CONTINUE
-C
- GO TO 1001
-C .......... SET ERROR -- NO CONVERGENCE TO AN
-C EIGENVALUE AFTER 30 ITERATIONS ..........
- 1000 IERR = L
- 1001 RETURN
- END
git://source.jalview.org / jabaws.git / blobdiff