WSJT-X/lib/lorentzian.f90

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subroutine lorentzian(y,npts,a)
! Input: y(npts); assume x(i)=i, i=1,npts
! Output: a(5)
! a(1) = baseline
! a(2) = amplitude
! a(3) = x0
! a(4) = width
! a(5) = chisqr
real y(npts)
real a(5)
real deltaa(4)
a=0.
df=12000.0/8192.0 !df = 1.465 Hz
width=0.
ipk=0
ymax=-1.e30
do i=1,npts
if(y(i).gt.ymax) then
ymax=y(i)
ipk=i
endif
! write(50,3001) i,i*df,y(i)
!3001 format(i6,2f12.3)
enddo
! base=(sum(y(ipk-149:ipk-50)) + sum(y(ipk+51:ipk+150)))/200.0
base=(sum(y(1:20)) + sum(y(npts-19:npts)))/40.0
stest=ymax - 0.5*(ymax-base)
ssum=y(ipk)
do i=1,50
if(ipk+i.gt.npts) exit
if(y(ipk+i).lt.stest) exit
ssum=ssum + y(ipk+i)
enddo
do i=1,50
if(ipk-i.lt.1) exit
if(y(ipk-i).lt.stest) exit
ssum=ssum + y(ipk-i)
enddo
ww=ssum/y(ipk)
width=2
t=ww*ww - 5.67
if(t.gt.0.0) width=sqrt(t)
a(1)=base
a(2)=ymax-base
a(3)=ipk
a(4)=width
! Now find Lorentzian parameters
deltaa(1)=0.1
deltaa(2)=0.1
deltaa(3)=1.0
deltaa(4)=1.0
nterms=4
! Start the iteration
chisqr=0.
chisqr0=1.e6
do iter=1,5
do j=1,nterms
chisq1=fchisq0(y,npts,a)
fn=0.
delta=deltaa(j)
10 a(j)=a(j)+delta
chisq2=fchisq0(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=fchisq0(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,chisq2
!4000 format(i1,i2,4f10.4,f11.3)
enddo
chisqr=fchisq0(y,npts,a)
! write(*,4000) 0,0,a,chisqr
if(chisqr/chisqr0.gt.0.99) exit
chisqr0=chisqr
enddo
a(5)=chisqr
return
end subroutine lorentzian