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C SUBROUTINE GRIDLS.F
C
C SOURCE
C BEVINGTON, PAGES 212-213.
C
C PURPOSE
C MAKE A GRID-SEARCH LEAST-SQUARES FIT TO DATA WITH A SPECIFIED
C FUNCTION WHICH IS NOT LINEAR IN COEFFICIENTS
C
C USAGE
C CALL GRIDLS (X, Y, SIGMAY, NPTS, NTERMS, MODE, A, DELTAA,
C SIGMAA, YFIT, CHISQR)
C
C DESCRIPTION OF PARAMETERS
C X - ARRAY OF DATA POINTS FOR INDEPENDENT VARIABLE
C Y - ARRAY OF DATA POINTS FOR DEPENDENT VARIABLE
C SIGMAY - ARRAY OF STANDARD DEVIATIONS FOR Y DATA POINTS
C NPTS - NUMBER OF PAIRS OF DATA POINTS
C NTERMS - NUMBER OF PARAMETERS
C MODE - DETERMINES METHOD OF WEIGHTING LEAST-SQUARES FIT
C +1 (INSTRUMENTAL) WEIGHT(I) = 1./SIGMAY(I)**2
C 0 (NO WEIGHTING) WEIGHT(I) = 1.
C -1 (STATISTICAL) WEIGHT(I) = 1./Y(I)
C A - ARRAY OF PARAMETERS
C DELTAA - ARRAY OF INCREMENTS FOR PARAMETERS A
C SIGMAA - ARRAY OF STANDARD DEVIATIONS FOR PARAMETERS A
C YFIT - ARRAY OF CALCULATED VALUES OF Y
C CHISQR - REDUCED CHI SQUARE FOR FIT
C
C SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
C FUNCTN (X, I, A)
C EVALUATES THE FITTING FUNCTION FOR THE ITH TERM
C FCHISQ (Y, SIGMAY, NPTS, NFREE, MODE, YFIT)
C EVALUATES REDUCED CHI SQUARED FOR FIT TO DATA
C
C COMMENTS
C DELTAA VALUES ARE MODIFIED BY THE PROGRAM
C
SUBROUTINE GRIDLS (X,Y,SIGMAY,NPTS,NTERMS,MODE,A,DELTAA,
*SIGMAA,YFIT,CHISQR)
DIMENSION X(1),Y(1),SIGMAY(1),A(1),DELTAA(1),SIGMAA(1),
*YFIT(1)
REAL FUNCTN
EXTERNAL FUNCTN
C
11 NFREE=NPTS-NTERMS
FREE=NFREE
CHISQR=0.
IF (NFREE) 100,100,20
20 DO 90 J=1,NTERMS
C
C EVALUATE CHI SQUARE AT FIRST TWO SEARCH POINTS
C
21 DO 22 I=1,NPTS
22 YFIT(I)=FUNCTN (X,I,A)
23 CHISQ1=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
FN=0.
DELTA=DELTAA(J)
41 A(J)=A(J)+DELTA
DO 43 I=1,NPTS
43 YFIT(I)=FUNCTN (X,I,A)
44 CHISQ2=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
45 IF (CHISQ1-CHISQ2) 51,41,61
C
C REVERSE DIRECTION OF SEARCH IF CHI SQUARE IS INCREASING
C
51 DELTA=-DELTA
A(J)=A(J)+DELTA
DO 54 I=1,NPTS
54 YFIT(I)=FUNCTN (X,I,A)
SAVE=CHISQ1
CHISQ1=CHISQ2
57 CHISQ2=SAVE
C
C INCREMENT A(J) UNTIL CHI SQUARE INCREASES
C
61 FN=FN+1.
A(J)=A(J)+DELTA
DO 64 I=1,NPTS
64 YFIT(I)=FUNCTN (X,I,A)
CHISQ3=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
66 IF (CHISQ3-CHISQ2) 71,81,81
71 CHISQ1=CHISQ2
CHISQ2=CHISQ3
GOTO 61
C
C FIND MINIMUM OF PARABOLA DEFINED BY LAST THREE POINTS
C
81 DELTA=DELTA*(1./(1.+(CHISQ1-CHISQ2)/(CHISQ3-CHISQ2))+0.5)
82 A(J)=A(J)-DELTA
83 SIGMAA(J)=DELTAA(J)*SQRT(2./(FREE*(CHISQ3-2.*CHISQ2+CHISQ1)))
84 DELTAA(J)=DELTAA(J)*FN/3.
90 CONTINUE
C
C EVALUATE FIT AND CHI SQUARE FOR FINAL PARAMETERS
C
91 DO 92 I=1,NPTS
92 YFIT(I)=FUNCTN (X,I,A)
93 CHISQR=FCHISQ (Y,SIGMAY,NPTS,NFREE,MODE,YFIT)
100 RETURN
END
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