#Finite difference derivative on a nonuniform 1D grid
#Sundqwist and Veronis, Tellus, Vol. 22, Issuse 1, pp. 26-31 (1970).

#In: x - vector of coordinates, y - vector of function values on x
#Out: dydx - derivative at points 1:size(x)

dx = x(2:length(x)) - x(1:length(x)-1);
dydx=y;
dydx(1) = (y(2)-y(1))/(x(2)-x(1));
dydx(end) = (y(end)-y(end-1))/(x(end)-x(end-1));
for(i=2; i <= length(x)-1; i=i+1){
    dydx(i) = y(i+1) - (dx(i)/dx(i-1))^2*y(i-1) - (1-(dx(i)/dx(i-1))^2)*y(i);
    dydx(i) = dydx(i)/(dx(i)*(1+dx(i)/dx(i-1)));
}