Finding maximum values for one 2D matrix in a loop but then finding the minimum value of that remaining vector? Help please!

Hello! This is a very simple question but I'm a third year mechanical student trying to optimize the geometry of a crane, varying values of phi and theta. Look at my code so far.

%List of Design Constraints

L = 4;          %units in metres
SF = 1;         %chosen due to the danger of failure for lifting heavy objects
m = 4000;       %units in kg
g = 9.81;       %units ms^-2
P = SF*m*g;     %total force units in Newtons
rmin = 1.2;     %units in metres
rmax = 2.2;     %units metres
thetamax = 80;  %units in degrees
thetamin = -20; %units in degrees %CHANGE TO RADIANS?

%-------------------------------------------------------------------------

%LOOP PROCESSES TO VARY PHI AND THETA TO FIND MINIMUM RAM FORCE

% Use i and j to set up the following variables as vectors
i = 1;
k = 1;

for phi=0:5:180;

    j = 1;

    y(i)=20+phi;
    c2(i)=((rmax^2)-(rmin^2))/((cosd(y(i)+thetamin))-(cosd(y(i)+thetamax)));
    c1(i)=(rmax^2)+c2(i)*(cosd(y(i)+thetamax));
    a(i)=(((c1(i)+c2(i))^0.5)+((c1(i)-c2(i))^0.5))/2;
    b(i)=((c2(i))/(2*a(i)));

    for theta=(thetamin):5:(thetamax);

        r(i,j)=sqrt(((a(i))^2)+(b(i)^2)-(2*a(i)*b(i)*cosd(y(i)+theta)));
        F(i,j)=(r(i,j)*P*L*cosd(theta))/(b(i)*a(i)*sind(y(i) + theta));
       Fmax(k)=max(F(i,j));
        j=j+1;
        k=k+1;
    end
   Fminmax=min(Fmax(i))

    i=1+i;

end

Essentially, F(i,j) is a large matrix of all possible values of force. I need to find the maximum force values for each value of phi and then the minimum based on the remaining vector? Sounds simple enough but i keep getting tied up!

Thank you! Emily

Answer 1

[Adam]

This looks identical to a question I have just been answering.

Unless you really need to, don't keep track of maxima within the loop.

Just get the maxima out of F at the end of the loop. Then get the minimum out of that vector using:

doc min
doc max

Note the second output argument from these that will allow you to track the index of the row or column that yielded the min or max.

[Emily]

I need the maximum values of the horizontal rows in my 37X21 matrix for force as a vector, not sure how to do that outside the loop! then i can find the minimum value for the 1X21 vector

Thanks! Emily

[Adam]

r = rand(37,21);

maxRowValus = max( r, [], 2 );

gives you the maximum values of along each horizontal row (37 of them), but there are 37 rows, 21 columns, so if you need a 1x21 vector I assume you mean you want the maximum of each column:

maxColValues = max( r );