Initial commit

dataassim/math/othersupmath/autocorr.f

@@ -0,0 +1,75 @@
+c autocorrelation function
+c
+      subroutine autocorr(nsamp,xvar,yvar,step,rcorr,ncorr)
+      implicit none
+      integer nsamp,ncorr
+      double precision xvar(nsamp),yvar(nsamp),step(nsamp),
+     &                 rcorr(nsamp)
+      
+      double precision ymean,sum,hmin,sig0,crit
+      integer i,j,k,n
+      
+      sum=0.0d0
+      do i=1,nsamp
+        sum=sum+yvar(i)
+      enddo
+      ymean=sum/dble(nsamp)
+      
+      step(1)=0.0d0
+      rcorr(1)=1.0d0
+      sum=0.0d0
+      do i=1,nsamp
+        sum=sum+(yvar(i)-ymean)*(yvar(i)-ymean)
+      enddo
+      sig0=sum/dble(nsamp)
+      if(sig0.eq.0.0d0)then
+        do i=1,nsamp
+          step(i)=-9999.0d0
+          rcorr(i)=-9999.0d0
+        enddo
+        return
+      endif
+            
+      hmin=xvar(2)-xvar(1)
+      do i=2,nsamp-1
+        if((xvar(i+1)-xvar(i)).lt.hmin)then
+          hmin=xvar(i+1)-xvar(i)
+        endif
+      enddo
+      crit=0.01d0*hmin
+ 
+      
+      i=2
+      step(i)=hmin
+           
+            
+10    j=1
+      n=0
+      sum=0.0d0
+100   do k=j+1,nsamp
+        if((xvar(k)-xvar(j)).lt.(step(i)+crit).and.
+     &     (xvar(k)-xvar(j)).gt.(step(i)-crit))then
+          n=n+1
+          sum=sum+(yvar(k)-ymean)*(yvar(j)-ymean)
+        endif
+      enddo
+      if(j.lt.nsamp-1)then
+        j=j+1
+        goto 100
+      endif
+      if(n.le.1)then
+        step(i)=step(i)+hmin
+      else
+! this form of autocorrelation has less bias
+        rcorr(i)=sum/(dble(n)*sig0)
+     
+! but this form is more common in statistic literature because it has certain
+! desirable properties
+!        rcorr(i)=sum/(dble(nsamp)*sig0)
+        i=i+1    
+        step(i)=step(i-1)+hmin     
+      endif
+      if((xvar(1)+step(i)).lt.xvar(nsamp))goto 10
+      ncorr=i-1
+      return
+      end