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+c subroutine fderiv.f (non-analytical)
+c
+c source
+c   Bevington, page 242.
+c
+c purpose
+c   evaluate derivatives of function for least-squares search
+c      for arbitrary function given by functn
+c
+c usage
+c   call fderiv (x, i, a, deltaa, nterms, deriv)
+c
+c description of parameters
+c   x	   - array of data points for independent variable
+c   i	   - index of data points
+c   a	   - array of parameters
+c   deltaa - array of parameter increments
+c   nterms - number of parameters
+c   deriv  - derivatives of function
+c
+c subroutines and function subprograms required
+c   functn (x, i, a)
+c      evaluates the fitting function for the ith term
+c
+	subroutine fderiv (x,i,a,deltaa,nterms,deriv)
+	dimension x(1),a(1),deltaa(1),deriv(1)
+        real FUNCTN
+        external FUNCTN
+
+11	do 18 j=1,nterms
+	aj=a(j)
+	delta=deltaa(j)
+	a(j)=aj+delta
+	yfit=functn(x,i,a)
+	a(j)=aj-delta
+	deriv(j)=(yfit-functn(x,i,a))/(2.*delta)
+18	a(j)=aj
+	return
+	end