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************************************************************************* |
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* |
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* Subroutine tricircle.f |
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* |
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* - find the best circle passing through npoints: compute the circle |
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* passing through every combination of 3 of them and average the |
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* resulting centres and radii |
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* |
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* output variables: |
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* - angle(npoints) angle of the tangent in the input points, in degrees, range -90..+90 |
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* - residual(npoints) residuals |
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* - chi sum of squared residuals |
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* - xc,zc,radius circle parameters |
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* - eflag error flag |
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* |
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* to be called inside ./fitxy.f |
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* |
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************************************************************************* |
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subroutine tricircle(npoints,dep,indep,angle,residual,chi |
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$ ,xc,zc,radius,eflag) |
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c------------------------------------------------------------------------ |
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c |
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c local variables |
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c |
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c------------------------------------------------------------------------ |
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|
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integer npoints !fit number of points |
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real dep(npoints),indep(npoints) !dependent and independent variables |
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real angle(npoints) !angle between the tangent line in the input points and |
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! the independent variable axis |
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real residual(npoints) !residuals |
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real chi !sum of squared residuals |
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real xc,zc,radius !circle parameters |
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integer eflag !error flag =1 if the procedure fails |
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c integer nloops !number of combinations of 3 points out of npoints |
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integer index(3) !indexes of the 3 chosen points |
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|
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parameter(scale=1000.) |
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double precision z(3),x(3),unit(3),zzxx(3) !temp variables |
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double precision a(3,3),d(3,3),e(3,3),f(3,3) |
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double precision ir(3) |
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double precision deta,detd,dete,detf !determinants |
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integer ifail !=-1 if singular matrix error, =0 if not singular |
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integer jfail !=0 if determinant can be evaluated, =-1 if determinat is probably too small, =+1 if too large |
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parameter (ibig=1.e4) !just a number greater than C(npoints,3) |
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double precision xxc(ibig),zzc(ibig),rrr(ibig) !centres and radii to be averaged |
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double precision tmp1,tmp2,tmp(npoints) !temp variables |
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logical DEBUG |
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real pigr !3.1415... |
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pigr=ACOS(-1.) |
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DEBUG = .false. |
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if(eflag.eq.1)DEBUG = .true. |
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eflag = 0 |
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|
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c------------------------------------------------------------------------ |
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c choose 3 points out of npoints |
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c------------------------------------------------------------------------ |
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c nloops = fact(npoints) / (fact(3) * fact(npoints-3)) |
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|
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k=0 |
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do i1=1,npoints-2 |
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index(1)=i1 |
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do i2=i1+1,npoints-1 |
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index(2)=i2 |
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do i3=i2+1,npoints |
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index(3)=i3 |
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|
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k=k+1 !number of combinations |
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c$$$ print*,' ' !??? |
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c$$$ print*,'k =',k,' index =',index |
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|
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c------------------------------------------------------------------------ |
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c build temp vectors |
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c------------------------------------------------------------------------ |
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do i=1,3 |
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z(i)=indep(index(i))/scale !to avoid too big numbers in matrix computation |
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x(i)=dep(index(i))/scale |
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unit(i)=1. |
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zzxx(i)=z(i)**2.+x(i)**2. |
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enddo |
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c$$$ print*,'z =',z,' x =',x !??? |
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c$$$ print*,'unit =',unit,' zzxx =',zzxx |
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|
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c------------------------------------------------------------------------ |
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c build the matrixes |
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c------------------------------------------------------------------------ |
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do i=1,3 |
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a(i,1)=z(i) !A has (z x 1) as columns |
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a(i,2)=x(i) |
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a(i,3)=unit(i) |
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d(i,1)=zzxx(i) !D has (zzxx x 1) as columns |
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d(i,2)=x(i) |
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d(i,3)=unit(i) |
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e(i,1)=zzxx(i) !E has (zzxx z 1) as columns |
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e(i,2)=z(i) |
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e(i,3)=unit(i) |
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f(i,1)=zzxx(i) !F has (zzxx z x) as columns |
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f(i,2)=z(i) |
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f(i,3)=x(i) |
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enddo |
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|
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c$$$ print*,'matrix A:' !??? |
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c$$$ do i=1,3 |
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c$$$ print*,(a(i,j),j=1,3) |
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c$$$ enddo |
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c$$$ print*,'matrix D:' !??? |
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c$$$ do i=1,3 |
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c$$$ print*,(d(i,j),j=1,3) |
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c$$$ enddo |
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c$$$ print*,'matrix E:' !??? |
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c$$$ do i=1,3 |
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c$$$ print*,(e(i,j),j=1,3) |
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c$$$ enddo |
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c$$$ print*,'matrix F:' !??? |
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c$$$ do i=1,3 |
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c$$$ print*,(f(i,j),j=1,3) |
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c$$$ enddo |
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|
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c------------------------------------------------------------------------ |
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c compute the determinants of A, D, E and F matrixes |
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c using DFACT (http://wwwasdoc.web.cern.ch/wwwasdoc/shortwrupsdir/f011/top.html) |
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c------------------------------------------------------------------------ |
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|
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ifail=0 |
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jfail=0 |
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call DFACT(3,a,3,ir,ifail,deta,jfail) |
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if(ifail.eq.-1) then |
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if(DEBUG)then |
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print*,'tricircle: ERROR: singular matrix A:' |
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do i=1,3 |
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print*,(a(i,j),j=1,3) |
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enddo |
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endif |
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eflag=1 |
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endif |
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if(jfail.eq.-1) then |
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if(DEBUG)then |
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print* |
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$ ,'tricircle: ERROR: matrix A: determinant too small?' |
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do i=1,3 |
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print*,(d(i,j),j=1,3) |
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enddo |
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endif |
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eflag=1 |
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elseif(jfail.eq.1) then |
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if(DEBUG)then |
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print* |
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$ ,'tricircle: ERROR: matrix A: determinant too large?' |
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do i=1,3 |
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print*,(d(i,j),j=1,3) |
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enddo |
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endif |
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eflag=1 |
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endif |
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|
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ifail=0 |
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jfail=0 |
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call DFACT(3,d,3,ir,ifail,detd,jfail) |
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if(ifail.eq.-1) then |
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if(DEBUG)then |
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print*,'tricircle: ERROR: singular matrix D:' |
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do i=1,3 |
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print*,(d(i,j),j=1,3) |
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enddo |
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endif |
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eflag=1 |
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endif |
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if(jfail.eq.-1) then |
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if(DEBUG)then |
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print* |
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$ ,'tricircle: ERROR: matrix D: determinant too small?' |
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do i=1,3 |
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print*,(d(i,j),j=1,3) |
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enddo |
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endif |
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eflag=1 |
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elseif(jfail.eq.1) then |
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if(DEBUG)then |
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print* |
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$ ,'tricircle: ERROR: matrix D: determinant too large?' |
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do i=1,3 |
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print*,(d(i,j),j=1,3) |
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enddo |
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endif |
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eflag=1 |
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endif |
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|
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ifail=0 |
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jfail=0 |
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call DFACT(3,e,3,ir,ifail,dete,jfail) |
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if(ifail.eq.-1) then |
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if(DEBUG)then |
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print*,'tricircle: ERROR: singular matrix E:' |
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do i=1,3 |
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print*,(e(i,j),j=1,3) |
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enddo |
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endif |
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eflag=1 |
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endif |
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if(jfail.eq.-1) then |
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if(DEBUG)then |
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print* |
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$ ,'tricircle: ERROR: matrix E: determinant too small?' |
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do i=1,3 |
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print*,(e(i,j),j=1,3) |
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enddo |
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endif |
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eflag=1 |
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elseif(jfail.eq.1) then |
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if(DEBUG)then |
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print* |
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$ ,'tricircle: ERROR: matrix E: determinant too large?' |
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do i=1,3 |
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print*,(e(i,j),j=1,3) |
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enddo |
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endif |
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eflag=1 |
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endif |
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|
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ifail=0 |
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jfail=0 |
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call DFACT(3,f,3,ir,ifail,detf,jfail) |
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c ifail=-1 !??? |
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if(ifail.eq.-1) then |
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if(DEBUG)then |
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print*,'tricircle: ERROR: singular matrix F:' |
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do i=1,3 |
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print*,(f(i,j),j=1,3) |
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enddo |
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endif |
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eflag=1 |
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endif |
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if(jfail.eq.-1) then |
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if(DEBUG)then |
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print* |
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$ ,'tricircle: ERROR: matrix F: determinant too small?' |
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do i=1,3 |
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print*,(f(i,j),j=1,3) |
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enddo |
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endif |
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eflag=1 |
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elseif(jfail.eq.1) then |
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if(DEBUG)then |
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print* |
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$ ,'tricircle: ERROR: matrix F: determinant too large?' |
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do i=1,3 |
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print*,(f(i,j),j=1,3) |
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enddo |
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endif |
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eflag=1 |
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endif |
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|
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c------------------------------------------------------------------------ |
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c compute the centre and radius |
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c------------------------------------------------------------------------ |
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detd=-detd |
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detf=-detf |
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|
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c xxc(k)=-detd/(2.*deta) |
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c zzc(k)=-dete/(2.*deta) |
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xxc(k)=-dete/(2.*deta) |
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zzc(k)=-detd/(2.*deta) |
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rrr(k)=SQRT((detd**2+dete**2)/(4.*deta**2.)-detf/deta) |
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|
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c$$$ write(30,*) xxc(k)*scale !??? |
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c$$$ write(31,*) zzc(k)*scale !??? |
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c$$$ write(32,*) rrr(k)*scale !??? |
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c$$$ print*,'xxc =',xxc(k)*scale,' zzc =',zzc(k)*scale |
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c$$$ $ ,' rrr =',rrr(k)*scale !??? |
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|
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enddo !index loops |
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enddo |
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enddo |
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|
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c------------------------------------------------------------------------ |
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c averages the centres and the radii |
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c------------------------------------------------------------------------ |
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xc=0. |
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zc=0. |
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radius=0. |
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do i=1,k |
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xc=xc+xxc(i) |
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zc=zc+zzc(i) |
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radius=radius+rrr(i) |
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enddo |
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xc=xc/k * scale !back to micrometers |
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zc=zc/k * scale |
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radius=radius/k * scale |
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|
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c$$$ c------------------------------------------------------------------------ |
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c$$$ c check for small radius...!??? |
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c$$$ c------------------------------------------------------------------------ |
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c$$$ num=200 |
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c$$$ height=ABS(indep(1)-indep(6)) |
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c$$$ if(radius.lt.(num*height)) then |
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c$$$ xc=0. |
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c$$$ zc=0. |
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c$$$ radius=0. |
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c$$$ print*,'tricircle: ERROR: bad circle' |
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c$$$ print*,'radius' ,radius,' < ', num,' x',height |
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c$$$ c$$$ print*,dep !??? |
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c$$$ c$$$ print*,indep !??? |
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c$$$ eflag=1 |
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c$$$ endif |
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|
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|
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c------------------------------------------------------------------------ |
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c computes residuals and chi-squared |
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c------------------------------------------------------------------------ |
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chi=0. |
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|
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c print*,xc,zc,radius !??? |
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do i=1,npoints |
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tmp1 = SQRT(radius**2.-(indep(i)-zc)**2.) |
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tmp2 = dep(i)-xc |
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if(ABS(tmp2-tmp1).le.ABS(tmp2+tmp1)) then !it chooses the right sign |
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tmp(i)=tmp1 !according to residuals |
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else |
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tmp(i)=-tmp1 |
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endif |
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residual(i)=tmp2 - tmp(i) |
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chi=chi + residual(i)**2. |
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c print*,dep(i) !??? |
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c print*,indep(i) !??? |
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c print*,tmp1,tmp2,tmp(i),residual(i) !??? |
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enddo |
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|
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c------------------------------------------------------------------------ |
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c it computes the angle between the tangent to the circumference and the |
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c independent variable axis |
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c------------------------------------------------------------------------ |
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do i=1,npoints |
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angle(i)=(zc-indep(i)) / tmp(i) |
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angle(i)=ATAN(angle(i)) !-pi/2 <= angle <= pi/2 |
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angle(i)=angle(i)/pigr*180. |
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enddo |
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|
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return |
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end |
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c------------------------------------------------------------------------ |
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c------------------------------------------------------------------------ |
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c------------------------------------------------------------------------ |
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c$$$c------------------------------------------------------------------------ |
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c$$$c Function to find the factorial value |
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c$$$c------------------------------------------------------------------------ |
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c$$$ |
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c$$$c from http://www.digitalcoding.com/programming/fortran/tutorial/ftute10.htm |
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c$$$ |
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c$$$ |
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c$$$ FUNCTION FACT(N) |
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c$$$ FACT=1 |
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c$$$ DO 10 J=2,N |
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c$$$ FACT=FACT*J |
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c$$$10 CONTINUE |
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c$$$ RETURN |
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c$$$ END |
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c$$$ |
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c$$$c------------------------------------------------------------------------ |
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