WSJT-X/map65/libm65/polfit.f90

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subroutine polfit(y,npts,a)
! Input: y(npts) !Expect npts=4
! Output: a(1) = baseline
! a(2) = amplitude
! a(3) = theta (deg)
real y(npts)
real a(3)
real deltaa(3)
integer ipk(1)
save
! Set starting values:
a(1)=minval(y)
a(2)=maxval(y)-a(1)
ipk=maxloc(y)
a(3)=(ipk(1)-1)*45.0
deltaa(1:2)=0.1*(a(2)-a(1))
deltaa(3)=10.0
nterms=3
! Start the iteration
chisqr=0.
chisqr0=1.e6
iters=10
do iter=1,iters
do j=1,nterms
chisq1=fchisq_pol(y,npts,a)
fn=0.
delta=deltaa(j)
10 a(j)=a(j)+delta
chisq2=fchisq_pol(y,npts,a)
if(chisq2.eq.chisq1) go to 10
if(chisq2.gt.chisq1) then
delta=-delta !Reverse direction
a(j)=a(j)+delta
tmp=chisq1
chisq1=chisq2
chisq2=tmp
endif
20 fn=fn+1.0
a(j)=a(j)+delta
chisq3=fchisq_pol(y,npts,a)
if(chisq3.lt.chisq2) then
chisq1=chisq2
chisq2=chisq3
go to 20
endif
! Find minimum of parabola defined by last three points
delta=delta*(1./(1.+(chisq1-chisq2)/(chisq3-chisq2))+0.5)
a(j)=a(j)-delta
deltaa(j)=deltaa(j)*fn/3.
! write(*,4000) iter,j,a,deltaa,chisq2
!4000 format(2i2,2(2x,3f8.2),f12.5)
enddo ! j=1,nterms
chisqr=fchisq_pol(y,npts,a)
! write(*,4000) 0,0,a,chisqr
if(chisqr.lt.1.0) exit
if(deltaa(1).lt.0.01*(a(2)-a(1)) .and. deltaa(2).lt.0.01*(a(2)-a(1)) &
.and. deltaa(3).lt.1.0) exit
if(chisqr/chisqr0.gt.0.99) exit
chisqr0=chisqr
enddo ! iter
a(3)=mod(a(3)+360.0,180.0)
return
end subroutine polfit
real function fchisq_pol(y,npts,a)
real y(npts),a(3)
data rad/57.2957795/
chisq = 0.
do i=1,npts
theta=(i-1)*45.0
yfit=a(1) + a(2)*cos((theta-a(3))/rad)**2
chisq=chisq + (y(i) - yfit)**2
enddo
fchisq_pol=chisq
return
end function fchisq_pol