How can I use the "diff" function instead of a for loop?

Dear altruists,

How can I get the similar result from this few lines of code using the MATLAB built in "diff" function instead of using the for loop?

g = 9.807;
for i=2:size(lon,1)-1
    for j=2:size(lat,2)-1
        dx=double(m_lldist([lon(i+1) lon(i-1)],[lat(j) lat(j)]))*1000;
        dy=double(m_lldist([lon(i) lon(i)],[lat(j+1) lat(j-1)]))*1000;
        f=2*(omega)*sin((lat(j)*(pi/180)));
        u(i,j)=-g/f*(ssh(i,j+1)-ssh(i,j-1))/dy;
        v(i,j)= g/f*(ssh(i+1,j)-ssh(i-1,j))/dx;        
    end
end

the size of the variables: lat, lon, and ssh is the same. (size:71*294)

Any feedback from you will be highly appreciated. Happy new year all!

Answer 1

[Matt J]

[m,n]=size(ssh);
zm=zeros(m,1);
zn=zeros(1,n);

gf=g./(2*omega*sind( lat ) );

Du=diff(ssh(:,2:end),1,2)+diff(ssh(:,1:end-1),1,2); 
   Du=-gf.*[zm,Du,zm];

Dv=diff(ssh(2:end,:),1,1)+diff(ssh(1:end-1,:),1,1);
   Dv=gf.*[zn;Dv;zn];

 [dx,dy]=deal(ones(size(Du)));
   
for i=2:size(lon,1)-1
    for j=2:size(lat,2)-1
        
        dx(i,j)=double(m_lldist([lon(i+1) lon(i-1)],[lat(j) lat(j)]))*1000;
        dy(i,j)=double(m_lldist([lon(i) lon(i)],[lat(j+1) lat(j-1)]))*1000;

    end
end

u=Du./dy;
v=Dv./dx;

[Ashfaq Ahmed]

Hi Matt,

Thank you so much for your effort on my question. Unfortunately, I fogrot to include that, the g in my code is a variable with a constant value.

g = 9.807;

I ran your code and it is not giving me the values that I am expecting. Do you think it was because of the g?

[Matt J]

No, I assumed g to be a scalar constant.