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tql2.f
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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
SUBROUTINE eigsrtnico(d,v,n,np)
INTEGER n,np
REAL*16 d(np), v(np)
INTEGER i,j,k
REAL*16 p,q
! do i=1,n
! write(*,*)i,d(i)
! enddo
! stop
do 13 i=1,n-1
k=i
p=d(i)
q=v(i)
do 11 j=i+1,n
if(d(j).le.p)then
k=j
p=d(j)
q=v(j)
endif
11 continue
if(k.ne.i)then
d(k)=d(i)
d(i)=p
v(k)=v(i)
v(i)=q
endif
13 continue
return
END SUBROUTINE eigsrtnico
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
SUBROUTINE TQL2(NM,N,D,E,Z,IERR)
C
INTEGER I,J,K,L,M,N,II,L1,L2,NM,MML,IERR
REAL*16 D(N),E(N),Z(NM,N)
REAL*16 C,C2,C3,DL1,EL1,F,G,H,P,R,S,S2,TST1,TST2,PYTHAG
C
C THIS SUBROUTINE IS A TRANSLATION OF THE ALGOL PROCEDURE TQL2,
C NUM. MATH. 11, 293-306(1968) BY BOWDLER, MARTIN, REINSCH, AND
C WILKINSON.
C HANDBOOK FOR AUTO. COMP., VOL.II-LINEAR ALGEBRA, 227-240(1971).
C
C THIS SUBROUTINE FINDS THE EIGENVALUES AND EIGENVECTORS
C OF A SYMMETRIC TRIDIAGONAL MATRIX BY THE QL METHOD.
C THE EIGENVECTORS OF A FULL SYMMETRIC MATRIX CAN ALSO
C BE FOUND IF TRED2 HAS BEEN USED TO REDUCE THIS
C FULL MATRIX TO TRIDIAGONAL FORM.
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 D CONTAINS THE DIAGONAL ELEMENTS OF THE INPUT MATRIX.
C
C E CONTAINS THE SUBDIAGONAL ELEMENTS OF THE INPUT MATRIX
C IN ITS LAST N-1 POSITIONS. E(1) IS ARBITRARY.
C
C Z CONTAINS THE TRANSFORMATION MATRIX PRODUCED IN THE
C REDUCTION BY TRED2, IF PERFORMED. IF THE EIGENVECTORS
C OF THE TRIDIAGONAL MATRIX ARE DESIRED, Z MUST CONTAIN
C THE IDENTITY MATRIX.
C
C ON OUTPUT
C
C D CONTAINS THE EIGENVALUES IN ASCENDING ORDER. IF AN
C ERROR EXIT IS MADE, THE EIGENVALUES ARE CORRECT BUT
C UNORDERED FOR INDICES 1,2,...,IERR-1.
C
C E HAS BEEN DESTROYED.
C
C Z CONTAINS ORTHONORMAL EIGENVECTORS OF THE SYMMETRIC
C TRIDIAGONAL (OR FULL) MATRIX. IF AN ERROR EXIT IS MADE,
C Z CONTAINS THE EIGENVECTORS ASSOCIATED WITH THE STORED
C EIGENVALUES.
C
C IERR IS 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 FOR DSQRT(A*A + B*B) .
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
IERR = 0
IF (N .EQ. 1) GO TO 1001
C
DO 100 I = 2, N
100 E(I-1) = E(I)
C
F = 0.0Q0
TST1 = 0.0Q0
E(N) = 0.0Q0
C
DO 240 L = 1, N
J = 0
H = QABS(D(L)) + QABS(E(L))
IF (TST1 .LT. H) TST1 = H
C .......... LOOK FOR SMALL SUB-DIAGONAL ELEMENT ..........
DO 110 M = L, N
TST2 = TST1 + QABS(E(M))
IF (TST2 .EQ. TST1) GO TO 120
C .......... E(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 220
130 IF (J .EQ. 30) GO TO 1000
J = J + 1
C .......... FORM SHIFT ..........
L1 = L + 1
L2 = L1 + 1
G = D(L)
P = (D(L1) - G) / (2.0Q0 * E(L))
R = PYTHAG(P,1.0Q0)
D(L) = E(L) / (P + QSIGN(R,P))
D(L1) = E(L) * (P + QSIGN(R,P))
DL1 = D(L1)
H = G - D(L)
IF (L2 .GT. N) GO TO 145
C
DO 140 I = L2, N
140 D(I) = D(I) - H
C
145 F = F + H
C .......... QL TRANSFORMATION ..........
P = D(M)
C = 1.0Q0
C2 = C
EL1 = E(L1)
S = 0.0Q0
MML = M - L
C .......... FOR I=M-1 STEP -1 UNTIL L DO -- ..........
DO 200 II = 1, MML
C3 = C2
C2 = C
S2 = S
I = M - II
G = C * E(I)
H = C * P
R = PYTHAG(P,E(I))
E(I+1) = S * R
S = E(I) / R
C = P / R
P = C * D(I) - S * G
D(I+1) = H + S * (C * G + S * D(I))
C .......... FORM VECTOR ..........
DO 180 K = 1, N
H = Z(K,I+1)
Z(K,I+1) = S * Z(K,I) + C * H
Z(K,I) = C * Z(K,I) - S * H
180 CONTINUE
C
200 CONTINUE
C
P = -S * S2 * C3 * EL1 * E(L) / DL1
E(L) = S * P
D(L) = C * P
TST2 = TST1 + QABS(E(L))
IF (TST2 .GT. TST1) GO TO 130
220 D(L) = D(L) + F
240 CONTINUE
C .......... ORDER EIGENVALUES AND EIGENVECTORS ..........
DO 300 II = 2, N
I = II - 1
K = I
P = D(I)
C
DO 260 J = II, N
IF (D(J) .GE. P) GO TO 260
K = J
P = D(J)
260 CONTINUE
C
IF (K .EQ. I) GO TO 300
D(K) = D(I)
D(I) = P
C
DO 280 J = 1, N
P = Z(J,I)
Z(J,I) = Z(J,K)
Z(J,K) = P
280 CONTINUE
C
300 CONTINUE
C
GO TO 1001
C .......... SET ERROR -- NO CONVERGENCE TO AN
C EIGENVALUE AFTER 30 ITERATIONS ..........
1000 IERR = L
1001 RETURN
END