How to find the maximum value

Below is a 3D graph.

   T=600:1:850;
    t=0.2:0.1:20;
    [tm,Tm] = meshgrid(t, T);
    k1 = 10^7.*exp(-12700./Tm);
    k2 = 5*10^4.*exp(-10800./Tm);
    k3 = 7*10^7.*exp(-15000./Tm);
    Y_B = (k1.*tm)./(((k2.*tm)+1).*(1+(tm.*(k1+k3))));
    mesh(t,T,Y_B)
    view(40, 45)
    grid on

How do I find the maximum value of Y_B for t=0.2:0.1:20 over the range of T from 600 to 850 and plots on a double y-axis graph the value of T and Y_Bmax with t?

Answer 1

[Jan]

   t = 0.2:0.1:20;
   T = 600:50:850;
   for i = 1:numel(T)
      k1 = 1e7 .* exp(-12700 ./ T(i));
      k2 = 5e4 .* exp(-10800 ./ T(i));
      k3 = 7e7 .* exp(-15000 ./ T(i));
      for j = 1:numel(t)
         Y_B(i,j) = (k1.*t(j)) ./ (((k2.*t(j))+1).*(1+(t(j).*(k1+k3))));
         % Prefer:
         % Y_B(i,j) = k1 .* t(j) ./ ((k2 .* t(j) + 1) .* (1 + t(j) .* (k1 + k3)));
      end
  end
  plot(t, max(Y_B, [], 1), '.-');

k1, k2, k3 are not changed inside the inner loop, so move them to the outer one. I would not overdo it with the parentheses.

By the way, you can even omit the loops:

t   = 0.2:0.1:20;
T   = (600:50:850).';
k1  = 1e7 .* exp(-12700 ./ T);
k2  = 5e4 .* exp(-10800 ./ T);
k3  = 7e7 .* exp(-15000 ./ T);
Y_B = k1 .* t ./ ((k2 .* t + 1) .* (1 + t .* (k1 + k3)));  % >= R2016
plot(t, max(Y_B, [], 1), '.-');

This uses auto expanding, which was introduced in Matlab R2016b. Your meshgrid approach was fine also, while the loops suggested by Birdman have no advantage here.

[sophp]

HI Jan thank you for this, it works perfectly! I am trying to plot a graph to show the relationship between residence time t and the operating temperature T(y_B max). However, one is row vector where as the other is a column vector. HOw do I do this?

[Jan]

@sophp: By transposing one of the two vectors?

Answer 2

[Rik]

You can specify the dimension max should operate on, so you can insert your matrix. See the documentation for instructions.

For a double y-axis, see yyaxis, or search the File Exchange for one of many examples.

[sophp]

Hi Rik,

I should have been more specific with my question. But, I am new to MATLAB and cannot find anything that tells me to find the maximum for each loop of i, form an array and plot a graph. This is the code I have

t = [0.2:0.1:20];
T = [600:50:850];
hold on;
for i=1:numel(T)
    for j=1:numel(t)
        k1(i) = 1e7 .* exp(-12700 ./ T(i));
        k2(i) = 5e4 .* exp(-10800 ./ T(i));
        k3(i) = 7e7 .* exp(-15000 ./ T(i));
        Y_B(i,j) = (k1(i).*t(j))./(((k2(i).*t(j))+1).*(1+(t(j).*(k1(i)+k3(i)))));
    end
   [val,idt] = max(Y_B(i,j))
end 
hold on
plot(t(idt),Y_B(idt))

However the correct graph does not appear.