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SUBROUTINE NLCFIT(IM,INN,IN,INTA,XEPSI,XV,XYD)
C+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
C NONLINEAR LEAST SQUARES FITTING USING SIMPLEX
C METHOD AND QUADRATIC APPROXIMATION.
C WITH LINEAR PARAMETER ELIMINATION.
C-------------------------------------------------------------
INTEGER IM,INN,IN,INTA
REAL XEPSI,XV(IM),XYD(IM)
COMMON /NLC/ EPSI,IFLAG,IL,IQ,INDEX,F(15,120),M,N
COMMON /NLC/ SOLD,Y(20),YVAL,XF(11),X(11,11),V(120),YD(120,10)
COMMON /NLC/ GG(11,11),GINV(11,11),EM(15,120),BB(5),NT
COMMON /NLC/ GA(120,5),NN
COMMON /NLCOUT/ FF(120),PARS(10),BPARS(10)
DIMENSION SUMC(11),XC(11),XE(11),XCO(11),XR(11)
REAL LERROR
C-----
C RESET ERROR HANDLER
c...UNIX has general handler only!
c call trpfpe (0, 0d0)
C-----
C FLOAT OVERFLOW
c CALL ERRSET(72,.TRUE.,.FALSE.,.FALSE.,.FALSE.,15)
C FLOAT UNDERFLOW
c CALL ERRSET(74,.TRUE.,.FALSE.,.FALSE.,.FALSE.,15)
C EXP TOO SMALL
c CALL ERRSET(89,.TRUE.,.FALSE.,.FALSE.,.FALSE.,15)
C EXP TOO LRGE
c CALL ERRSET(88,.TRUE.,.FALSE.,.FALSE.,.FALSE.,15)
C-----
LERROR=1.E30
IFLAG=0
C COEFFICIENTS
C-----
C ASSIGN EXTERNAL PARAMETERS
M=IM
NN=INN
N=IN
NT=INTA
EPSI=XEPSI
DO 8100 I=1,M
V(I)=XV(I)
YD(I,1)=XYD(I)
8100 CONTINUE
C-----
T=1.0
A=1.0
B=0.5
G=2.0
ICOUNT=0
INDEX=1
IQ=3*N
DO 140 J=1,N
140 X(1,J)=1.0
160 DO 172 J=1,N
172 XF(J)=X(1,J)
CALL FVAL
Y(1)=YVAL
SOLD=YVAL
C---- CONSTRUCT SIMPLEX
EN=N
PN=(SQRT(EN+1.0)-1.0+EN)/(EN*SQRT(2.0))*T
QN=(SQRT(EN+1.0)-1.0)/(EN*SQRT(2.0))*T
NP1=N+1
DO 305 I=2,NP1
INDEX=I
DO 300 J=1,N
EJ=0.0
EI=0.0
IF(I-1.NE.J) EJ=1.0
IF(I-1.EQ.J) EI=1.0
X(I,J)=X(1,J)+EI*PN+EJ*QN
300 XF(J)=X(I,J)
CALL FVAL
305 Y(I)=YVAL
C---- DETERMINE MAX XH
310 IH=1
DO 350 J=1,NP1
IF(Y(IH).GE.Y(J)) GOTO 350
IH=J
350 CONTINUE
C---- DETERMINE SECOND MAX XS
IS=1
IF(IH.NE.1) GOTO 470
IS=2
470 CONTINUE
DO 420 J=1,NP1
IF(J.EQ.IH) GOTO 420
IF(Y(IS).GE.Y(J)) GOTO 420
IS=J
420 CONTINUE
C---- DETERMINE MIN XL
IL=1
DO 480 J=1,NP1
IF(Y(IL).LE.Y(J)) GOTO 480
IL=J
480 CONTINUE
C---- COMPUTE CENTROID
DO 510 J=1,N
510 SUMC(J)=0.0
EN=N
DO 570 J=1,N
DO 560 I=1,NP1
IF(I.EQ.IH) GOTO 560
SUMC(J)=SUMC(J)+X(I,J)
560 CONTINUE
570 XC(J)=1.0/EN*SUMC(J)
DO 573 J=1,N
573 XF(J)=XC(J)
CALL FVAL
YBAR=YVAL
SUM=0.0
DO 577 I=1,NP1
577 SUM = SUM + ((Y(I)-YBAR)/YBAR)**2
ICOUNT=ICOUNT+1
ERROR=SQRT(SUM/EN)
IQ=IQ-1
IF(IQ.EQ.-1) CALL QADFIT
IF(IFLAG.EQ.1) GOTO 1990
IF(ERROR.LE.EPSI) GOTO 1990
IF(ABS(LERROR-ERROR).LT.EPSI) GO TO 1990
LERROR=ERROR
C---- DO A REFLECTION
DO 600 J=1,N
600 XR(J)=(1.0+A)*XC(J)-A*X(IH,J)
DO 610 J=1,N
610 XF(J)=XR(J)
INDEX=N+2
CALL FVAL
YXR=YVAL
IF(YXR.GE.Y(IL)) GOTO 750
C---- DO A EXPANSION
DO 660 J=1,N
660 XE(J)=G*XR(J)+(1.0-G)*XC(J)
DO 680 J=1,N
680 XF(J)=XE(J)
INDEX=N+3
CALL FVAL
YXE=YVAL
IF(YXE.GT.Y(IL)) GOTO 760
DO 730 J=1,N
730 X(IH,J)=XE(J)
Y(IH)=YXE
NP3=N+3
DO 735 K=1,M
735 F(IH,K)=F(NP3,K)
GOTO 310
750 IF(YXR.GT.Y(IS)) GOTO 800
760 DO 780 J=1,N
780 X(IH,J)=XR(J)
Y(IH)=YXR
NP2=N+2
DO 785 K=1,M
785 F(IH,K)=F(NP2,K)
GOTO 310
800 IF(YXR.GT.Y(IH)) GOTO 830
DO 820 J=1,N
820 X(IH,J)=XR(J)
C---- DO A CONTRACTION
830 DO 840 J=1,N
840 XCO(J)=B*X(IH,J)+(1.0-B)*XC(J)
DO 860 J=1,N
860 XF(J)=XCO(J)
INDEX=N+2
CALL FVAL
YXCO=YVAL
IF(YXCO.GT.Y(IH)) GOTO 930
DO 910 J=1,N
910 X(IH,J)=XCO(J)
Y(IH)=YXCO
NP2=N+2
DO 915 K=1,M
915 F(IH,K)=F(NP2,K)
GOTO 310
930 DO 960 I=1,NP1
INDEX=I
DO 955 J=1,N
950 X(I,J)=0.5*(X(I,J)+X(IL,J))
955 XF(J)=X(I,J)
CALL FVAL
960 Y(I)=YVAL
C---- HAS A MIN BEEN REACHED?
GOTO 310
1990 DO 1594 J=1,N
PARS(J)=X(IL,J)
1594 XF(J)=X(IL,J)
CALL FVAL
DO 1595 I=1,NT
1595 BPARS(I)=BB(I)
CALL INDEXD
RETURN
END
C---------------------------------------------------------------------
SUBROUTINE MATIN
C---- DETERMINE INVERSE OF MATRIX
COMMON /NLC/ EPSI,IFLAG,IL,IQ,INDEX,F(15,120),M,N
COMMON /NLC/ SOLD,Y(20),YVAL,XF(11),X(11,11),V(120),YD(120,10)
COMMON /NLC/ GG(11,11),GINV(11,11),EM(15,120),BB(5),NT
COMMON /NLC/ GA(120,5),NN
DIMENSION E(15,120),EN(20),T(20),Z(11,11),YY(20)
EQUIVALENCE (EM(1,1),E(1,1))
DO 20 I=1,N
DO 20 J=1,N
IF(I.EQ.J) GOTO 10
Z(I,J)=0.0
GOTO 20
10 Z(I,J)=1.0
20 CONTINUE
DO 120 J0=1,N
I0=J0
DO 30 I=1,N
30 YY(I)=GG(I,J0)
DO 40 I=1,N
EN(I) = 0.
T(I)=0.0
DO 40 J=1,N
40 T(I)=T(I)+Z(I,J)*YY(J)
IF(T(J0).EQ.0.) GO TO 65
DO 60 J=1,N
IF(J.EQ.J0) GOTO 50
EN(J)=-T(J)/T(J0)
GOTO 60
50 EN(J)=1./T(J0)
60 CONTINUE
65 DO 80 I = 1,N
DO 80 J=1,N
IF (I.EQ.J) GOTO 70
E(I,J)=0.0
GOTO 80
70 E(I,J)=1.0
80 CONTINUE
DO 90 J=1,N
90 E(J,J0)=EN(J)
DO 100 K=1,N
DO 100 I=1,N
GINV(K,I)=0.0
DO 100 J=1,N
100 GINV(K,I)=GINV(K,I)+E(K,J)*Z(J,I)
DO 110 J=1,N
DO 110 I=1,N
110 Z(I,J)=GINV(I,J)
120 CONTINUE
RETURN
END
C-------------------------------------------------------------------------
SUBROUTINE QADFIT
COMMON /NLC/ EPSI,IFLAG,IL,IQ,INDEX,F(15,120),M,N
COMMON /NLC/ SOLD,Y(20),YVAL,XF(11),X(11,11),V(120),YD(120,10)
COMMON /NLC/ GG(11,11),GINV(11,11),EM(15,120),BB(5),NT
COMMON /NLC/ GA(120,5),NN
DIMENSION A(11,11),DELX(20),E(20),F0(20)
NP1=N+1
C---- QUADRATIC COEFFICIENTS
II=0
DO 30 K=1,M
II=0
DO 30 I=1,NP1
IF(I.EQ.IL) GOTO 30
II=II+1
EM(II,K)=F(I,K)-F(IL,K)
30 CONTINUE
DO 50 I=1,N
F0(I)=0.0
DO 50 K=1,M
50 F0(I)=F0(I)-F(IL,K)*EM(I,K)
C---- ELEMENTS OF THE MATRIX GAMMA,G
DO 70 I=1,N
DO 70 J=1,N
GG(I,J)=0.0
DO 70 K=1,M
70 GG(I,J)=GG(I,J)+EM(I,K)*EM(J,K)
CALL MATIN
DO 80 I=1,N
E(I)=0.0
DO 80 J=1,N
80 E(I)=E(I)+GINV(I,J)*F0(J)
C---- DEFINE THE SCALING MATRIX A
II=0
DO 101 I=1,NP1
IF(I.EQ.IL) GOTO 101
II=II+1
DO 100 J=1,N
A(II,J)=X(I,J)-X(IL,J)
100 CONTINUE
101 CONTINUE
C---- DETERMINE DEL X
DO 110 I=1,N
DELX(I)=0.0
DO 110 J=1,N
110 DELX(I)=DELX(I)+A(J,I)*E(J)
DO 120 J=1,N
120 XF(J)=X(IL,J)+DELX(J)
INDEX=N+2
CALL FVAL
IF(Y(IL).LT.YVAL) GOTO 140
TEMP=ABS(1-SOLD/YVAL)
IF(TEMP.EQ.1) GOTO 150
IF(TEMP.LE.EPSI) GOTO 150
SOLD=YVAL
DO 130 J=1,N
130 X(IL,J)=XF(J)
NP2=N+2
DO 135 K=1,M
135 F(IL,K)=F(NP2,K)
IFLAG=2
IQ=(3*N)/2
GOTO 160
140 IFLAG=2
IQ=3*N
GOTO 160
150 IFLAG=1
DO 155 J=1,N
155 X(IL,J)=XF(J)
Y(IL)=YVAL
160 RETURN
END
C----------------------------------------------------------------------
SUBROUTINE INDEXD
COMMON /NLC/ EPSI,IFLAG,IL,IQ,INDEX,F(15,120),M,N
COMMON /NLC/ SOLD,Y(20),YVAL,XF(11),X(11,11),V(120),YD(120,10)
COMMON /NLC/ GG(11,11),GINV(11,11),EM(15,120),BB(5),NT
COMMON /NLC/ GA(120,5),NN
COMMON /NLCOUT/ FF(120),PARS(10),BPARS(10)
SUM=0.0
DO 200 I=1,M
200 SUM=SUM+V(I)
XM=M
YBAR=SUM/XM
SST=0.0
DO 240 I=1,M
240 SST=SST+(V(I)-YBAR)**2
SSR=0.0
DO 280 I=1,M
FF(I)=0.0
DO 260 J=1,NT
260 FF(I)=BB(J)*GA(I,J)+FF(I)
280 SSR=SSR+(FF(I)-V(I))**2
XINDX=1-SSR/SST
SIGMAR=SQRT(SSR/XM)
DO 300 I=1,M
DIFF=FF(I)-V(I)
IF(V(I).EQ.0.) GO TO 295
DIFF = DIFF*100./V(I)
GO TO 300
295 DIFF=0.
300 CONTINUE
C
C---- WRITE(1) (FF(I),I=1,M)
C---- WRITE(1) (V(I),I=1,M)
RETURN
END
C---------------------------------------------------------------------------
SUBROUTINE FVAL
COMMON /NLC/ EPSI,IFLAG,IL,IQ,INDEX,F(15,120),M,N
COMMON /NLC/ SOLD,Y(20),YVAL,XF(11),X(11,11),V(120),YD(120,10)
COMMON /NLC/ GG(11,11),GINV(11,11),EM(15,120),BB(5),NT
COMMON /NLC/ GA(120,5),NN
DIMENSION GTGA(11,11),GT(5,120),GGG(5,120),B(5)
DIMENSION G(120,5),A(11),TR(5),XP(11)
EQUIVALENCE (GG(1,1),GTGA(1,1)),(BB(1),B(1)),(XF(1),A(1)),
*(G(1,1),GA(1,1))
DO 200 I=1,M
DO 100 J=1,NN
100 XP(J)=YD(I,J)
C
C---- LOCATION OF TRANSFORMS
CALL TRANS(TR,A,XP)
C
DO 110 J=1,NT
110 GA(I,J)=TR(J)
200 CONTINUE
DO 230 J=1,NT
DO 230 I=1,M
230 GT(J,I)=GA(I,J)
DO 280 K=1,NT
DO 280 I=1,NT
GTGA(K,I)=0.0
DO 280 J=1,M
280 GTGA(K,I)=GTGA(K,I)+GT(K,J)*GA(J,I)
HOLD=N
N=NT
CALL MATIN
N=HOLD
DO 350 K=1,NT
DO 350 I=1,M
GGG(K,I)=0.0
DO 350 J=1,NT
350 GGG(K,I)=GGG(K,I)+GINV(K,J)*GT(J,I)
DO 400 K=1,NT
B(K)=0.0
DO 400 J=1,M
400 B(K)=B(K)+GGG(K,J)*V(J)
YVAL=0.0
DO 460 I=1,M
FF=0.0
DO 240 J=1,NT
240 FF=B(J)*GA(I,J)+FF
F(INDEX,I)=V(I)-FF
460 YVAL=(V(I)-FF)**2+YVAL
RETURN
END
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