MATLAB Homework Problem: "Incorrect use of '=' operator" in a for loop

Hi, everyone - I'm hoping to touch up some old homework, but I'm running into a smidge of a problem. The title is more or less the crux of the issue - the program throws an error at me whenever I try to use a for loop.

Below should be all of the relevant code, I'd appreciate any and all assistance with this.

HW5_MEE380.mlx

% plot minimum launch speed (fplot)
% seperate plot launch angle as a function of coordinates (fplot)

nd = (15-2)/0.5;
hd = (11+2)/0.5;

[X,Y] = meshgrid(2:0.5:15,-2:0.5:12)

Z1 = [];
Z2 = [];

for (i = 2:0.5:15 && j = -2:0.5:12)
    [v0,theta] = calcMinSpeedShot(i,j);
    Z1 = [Z1 v0];
    Z2 = [Z2 theta];
end

calcMinSpeedShot.mlx

function [v0,theta] = calcMinSpeedShot(xT,yT)
g = 9.81; % acceleration of gravity (m/s^2)
syms x_s y_s theta_s;

if(xT < 0)
    error('calcMinSpeedShot: xT must be positive.')
end
% x must be a positive value

if(atand(yT/xT) >= 85)
    error('calcMinSpeedShot: angle to hit target is too steep.')
end
% >85deg is too steep

f_v0 = sqrt((g*x_s^2) ./ (2*(cos(theta_s)).^2.*(x_s*tan(theta_s) - y_s))); % original v0 eqn
f_dv0 = diff(f_v0); % derivative of v0 wrt to theta
f_dv0_num = subs(f_dv0,[x_s,y_s],[xT,yT]); % substituting in given values
f_dv0_num_rootfind = @(theta) double(subs(f_dv0_num,theta_s,theta)); % substituting symbolic theta for testable theta


theta = findRootBisect(f_dv0_num_rootfind,atan(yT/xT),(atan(yT/xT)+1),0.0001); % findRootBisect to find appropriate theta
f_v0_ans = subs(f_v0,[x_s,y_s,theta_s],[xT,yT,theta]);
v0 = f_v0_ans(theta);

% same steps from 1 - 4 now in a function
end

findRootBisect.mlx

function [r,counter] = findRootBisect(f,x1,x2,err)
x_test = 0.0; %x_test will be our floating midpoint of each interval
counter = 0.0;
found = false;

if(f(x1)*f(x2) > 0.0)
    error('findRootBisect: Root not bracketed.')
end

if(err <= 0.0)
    error('findRootBisect: Error must be positive.')
end

while (found == false)
    x_test = (x1 + x2) / 2;
    
    if(f(x_test) == 0 || (x2 - x1) < err)
        r = x_test;
        found = true;
        counter = counter + 1;
    else
        if(f(x_test)*f(x1) < 0)
            x2 = x_test;
            counter = counter + 1;
        else
            x1 = x_test;
            counter = counter + 1;
        end
    end
end

[Daniel O'Dette]

Quick clarification, the error is with the for loop in HW5_MEE380.mlx

Answer 1

[James Tursa]

This:

for (i = 2:0.5:15 && j = -2:0.5:12)

Needs to be two nested loops:

for i = 2:0.5:15 
    for j = -2:0.5:12

[Daniel O'Dette]

I appreciate the quick answer! Unfortunately now I'm getting a battery of new errors...

Error using symengine

Division by zero.

Error in sym/subs>mupadsubs (line 160)

G = mupadmex('symobj::fullsubs',F.s,X2,Y2);

Error in sym/subs (line 145)

G = mupadsubs(F,X,Y);

Error in calcMinSpeedShot>@(theta)double(subs(f_dv0_num,theta_s,theta)) (line 18)

f_dv0_num_rootfind = @(theta) double(subs(f_dv0_num,theta_s,theta)); % substituting symbolic theta for testable theta

Error in findRootBisect (line 6)

if(f(x1)*f(x2) > 0.0)

Error in calcMinSpeedShot (line 21)

theta = findRootBisect(f_dv0_num_rootfind,atan(yT/xT),(atan(yT/xT)+1),0.0001); % findRootBisect to find appropriate theta

Answer 2

[Walter Roberson]

for (i = 2:0.5:15 && j = -2:0.5:12)

You need to use a nested loop instead, such as

for i = 2:0.5:15
    for j = -2:0.5:12
        code goes here
    end
end

[Daniel O'Dette]

I appreciate the quick answer! Unfortunately now I'm getting a battery of new errors...

Error using symengine

Division by zero.

Error in sym/subs>mupadsubs (line 160)

G = mupadmex('symobj::fullsubs',F.s,X2,Y2);

Error in sym/subs (line 145)

G = mupadsubs(F,X,Y);

Error in calcMinSpeedShot>@(theta)double(subs(f_dv0_num,theta_s,theta)) (line 18)

f_dv0_num_rootfind = @(theta) double(subs(f_dv0_num,theta_s,theta)); % substituting symbolic theta for testable theta

Error in findRootBisect (line 6)

if(f(x1)*f(x2) > 0.0)

Error in calcMinSpeedShot (line 21)

theta = findRootBisect(f_dv0_num_rootfind,atan(yT/xT),(atan(yT/xT)+1),0.0001); % findRootBisect to find appropriate theta

[Walter Roberson]

f_v0 = sqrt((g*x_s^2) ./ (2*(cos(theta_s)).^2.*(x_s*tan(theta_s) - y_s))); % original v0 eqn

theta = findRootBisect(f_dv0_num_rootfind,atan(yT/xT),(atan(yT/xT)+1),0.0001); % findRootBisect to find appropriate theta

so you are passing in atan(yT/xT) as the second parameter, to become theta_s . Now look inside f_v0 to the denominator:

(x_s*tan(theta_s) - y_s)

substitute theta_s = atan(yT/xT) and by definition of atan(), atan(tan(yT/xT)) is going to be yT/xT . Substitute that into the expression:

(x_s*yT/xT - y_s)

now let x_s = xT and y_s = yT and xT*yT/xT - yT = yT - yT = 0. So that term would come out as 0. It is being multipled by something, so no matter what that other thing is (provided it is not infinite) the result would be 0 for the denominator, which gives you a divide by 0.

[Daniel O'Dette]

Ah, I see now. But I'm not sure how to go about resolving that. I was given a few base equations to work off of, namely the ones that I wrote out in the code. I'm going to need to email my professor about this, I suppose - but thank you for all of the debugging help!

[Walter Roberson]

Start from atan(yT/xT) plus something small instead of from atan(yT/xT) exactly.

[Daniel O'Dette]

The good news is that that no longer derives a "divide by zero" error.

The bad news is that the program now ends spitting out my own error and stopping on rotation one.