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c function pcorre.f
c
c source
c Bevington, pages 124-125.
c
c purpose
c evaluate probability for no correlation between two variables
c
c usage
c result = pcorre (r, npts)
c
c description of parameters
c r - linear correlation coefficient
c npts - number of data points
c
c subroutines and function subprograms required
c gamma (x)
c calculates gamma function for integers and half-integers
c
function pcorre (r,npts)
double precision r2,term,sum,fi,fnum,denom
c
c evaluate number of degrees of freedom
c
11 nfree=npts-2
if (nfree) 13,13,15
13 pcorre=0.
goto 60
15 r2=r**2
if (1.-r2) 13,13,17
17 neven=2*(nfree/2)
if (nfree-neven) 21,21,41
c
c number of degrees of freedom is even
c
21 imax=(nfree-2)/2
free=nfree
23 term=abs(r)
sum=term
if (imax) 60,26,31
26 pcorre=1.-term
goto 60
31 do 36 i=1,imax
fi=i
fnum=imax-i+1
denom=2*i+1
term=-term*r2*fnum/fi
36 sum=sum+term/denom
pcorre=1.128379167*(gamma((free+1.)/2.)/gamma(free/2.))
pcorre=1.-pcorre*sum
goto 60
c
c number of degrees of freedom is odd
c
41 imax=(nfree-3)/2
42 term=abs(r)*dsqrt(1.-r2)
43 sum=datan(r2/term)
if (imax) 57,45,51
45 sum=sum+term
goto 57
51 sum=sum+term
52 do 56 i=1,imax
fnum=2*i
denom=2*i+1
term=term*(1.-r2)*fnum/denom
56 sum=sum+term
57 pcorre=1.-0.6366197724*sum
60 return
end
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