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c subroutine regres.f
c
c source
c Bevington, pages 172-175.
c
c purpose
c make a mulitple linear regression fit to data with a specified
c function which is linear in coefficients
c
c usage
c call regres (x, y, sigmay, npts, nterms, m, mode, yfit,
c a0, a, sigma0, sigmaa, r, rmul, chisqr, ftest)
c
c description of parameters
c x - array of points for independent variable
c y - array of 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 coefficients
c m - array of inclusion/rejection criteria for fctn
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 yfit - array of calculated values of y
c a0 - constant term
c a - array of coefficients
c sigma0 - standard deviation of a0
c sigmaa - array of standard deviations for coefficients
c r - array of linear correlation coefficients
c rmul - multiple linear correlation coefficient
c chisqr - reduced chi square for fit
c ftest - value of f for test of fit
c
c subroutines and function subprograms required
c fctn (x, i, j, m)
c evaluates the function for the jth term and the ith data point
c using the array m to specify terms in the function
c matinv (array, nterms, det)
c inverts a symmetric two-dimensional matrix of degree nterms
c and calculates its determinant
c
c comments
c (dim npts changed 100->1000 21-may-84 dct)
c dimension statement valid for npts up to 100 and nterms up to 10
c sigmaag changed to sigmaa in statement following statement 132
c
subroutine regres (x,y,sigmay,npts,nterms,m,mode,yfit,
*a0,a,sigma0,sigmaa,r,rmul,chisqr,ftest)
double precision array,sum,ymean,sigma,chisq,xmean,sigmax
dimension x(1),y(1),sigmay(1),m(1),yfit(1),a(1),sigmaa(1),
*r(1)
dimension weight(1000),xmean(10),sigmax(10),array(10,10)
REAL FCTN
EXTERNAL FCTN
c
c initialize sums and arrays
c
11 sum=0.
ymean=0.
sigma=0.
chisq=0.
rmul=0.
do 17 i=1,npts
17 yfit(i)=0.
21 do 28 j=1,nterms
xmean(j)=0.
sigmax(j)=0.
r(j)=0.
a(j)=0.
sigmaa(j)=0.
do 28 k=1,nterms
28 array(j,k)=0.
c
c accumulate weighted sums
c
30 do 50 i=1,npts
31 if (mode) 32,37,39
32 if (y(i)) 35,37,33
33 weight(i)=1./y(i)
goto 41
35 weight(i)=1./(-y(i))
goto 41
37 weight(i)=1.
goto 41
39 weight(i)=1./sigmay(i)**2
41 sum=sum+weight(i)
ymean=ymean+weight(i)*y(i)
do 44 j=1,nterms
44 xmean(j)=xmean(j)+weight(i)*fctn(x,i,j,m)
50 continue
51 ymean=ymean/sum
do 53 j=1,nterms
53 xmean(j)=xmean(j)/sum
fnpts=npts
wmean=sum/fnpts
do 57 i=1,npts
57 weight(i)=weight(i)/wmean
c
c accumulate matrices r and array
c
61 do 67 i=1,npts
sigma=sigma+weight(i)*(y(i)-ymean)**2
do 67 j=1,nterms
sigmax(j)=sigmax(j)+weight(i)*(fctn(x,i,j,m)-xmean(j))**2
r(j)=r(j)+weight(i)*(fctn(x,i,j,m)-xmean(j))*(y(i)-ymean)
do 67 k=1,j
67 array(j,k)=array(j,k)+weight(i)*(fctn(x,i,j,m)-xmean(j))*
*(fctn(x,i,k,m)-xmean(k))
71 free1=npts-1
72 sigma=dsqrt(sigma/free1)
do 78 j=1,nterms
74 sigmax(j)=dsqrt(sigmax(j)/free1)
r(j)=r(j)/(free1*sigmax(j)*sigma)
do 78 k=1,j
array(j,k)=array(j,k)/(free1*sigmax(j)*sigmax(k))
78 array(k,j)=array(j,k)
c
c invert symmetric matrix
c
81 call matinv (array,nterms,det)
if (det) 101,91,101
91 a0=0.
sigma0=0.
rmul=0.
chisqr=0.
ftest=0.
goto 150
c
c calculate coefficients, fit, and chi square
c
101 a0=ymean
102 do 108 j=1,nterms
do 104 k=1,nterms
104 a(j)=a(j)+r(k)*array(j,k)
105 a(j)=a(j)*sigma/sigmax(j)
106 a0=a0-a(j)*xmean(j)
107 do 108 i=1,npts
108 yfit(i)=yfit(i)+a(j)*fctn(x,i,j,m)
111 do 113 i=1,npts
yfit(i)=yfit(i)+a0
113 chisq=chisq+weight(i)*(y(i)-yfit(i))**2
freen=npts-nterms-1
115 chisqr=chisq*wmean/freen
c
c calculate uncertainties
c
121 if (mode) 122,124,122
122 varnce=1./wmean
goto 131
124 varnce=chisqr
131 do 133 j=1,nterms
132 sigmaa(j)=array(j,j)*varnce/(free1*sigmax(j)**2)
sigmaa(j)=sqrt(sigmaa(j))
133 rmul=rmul+a(j)*r(j)*sigmax(j)/sigma
freej=nterms
c +noao: When rmul = 1, the following division (stmt 135) would blow up.
c It has been changed so ftest is set to -99999. in this case.
if (1. - rmul) 135, 935, 135
135 ftest=(rmul/freej)/((1.-rmul)/freen)
goto 136
935 ftest = -99999.
c -noao
136 rmul=sqrt(rmul)
141 sigma0=varnce/fnpts
do 145 j=1,nterms
do 145 k=1,nterms
145 sigma0=sigma0+varnce*xmean(j)*xmean(k)*array(j,k)/
*(free1*sigmax(j)*sigmax(k))
146 sigma0=sqrt(sigma0)
150 return
end
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