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c subroutine integ.f
c
c source
c Bevington, page 274.
c
c purpose
c integrate the area beneath two data points
c
c usage
c call integ (x, y, nterms, i1, x1, x2, sum)
c
c description of parameters
c x - array of data points for independent variable
c y - array of data points for dependent variable
c nterms - number of terms in fitting polymonial
c i1 - first data point for fitting polynomial
c x1 - first value of x for integration
c x2 - final value of x for integration
c
c subroutines and function subprograms required
c none
c
c comments
c dimension statement valid for nterms up to 10
c
subroutine integ (x,y,nterms,i1,x1,x2,sum)
double precision xjk,array,a,denom,deltax,sum
dimension x(1),y(1)
dimension array(10,10)
c
c construct square matrix and invert
c
11 do 17 j=1,nterms
i=j+i1-1
deltax=x(i)-x(i1)
xjk=1.
do 17 k=1,nterms
array(j,k)=xjk
17 xjk=xjk*deltax
21 call matinv (array,nterms,det)
if (det) 31,23,31
23 imid=i1+nterms/2
sum=sum+y(imid)*(x2-x1)
goto 40
c
c evaluate coefficients and integrate
c
31 dx1=x1-x(i1)
dx2=x2-x(i1)
33 do 39 j=1,nterms
i=j+i1-1
a=0.
do 37 k=1,nterms
37 a=a+y(i)*array(j,k)
denom=j
39 sum=sum+(a/denom)*(dx2**j-dx1**j)
40 return
end
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