Multiplication of matrices with Multiple variables

I have 4 matrices, each with 4 different variables. i.e. Matrix 1 with variable x, 2 with y and so on. How do I multiply them for different values of each variable?

T1 = [cos(th1) 0 -sin(th1) 0; sin(th1) 0 -cos(th1) 0; 0 -1 0 0; 0 0 0 1];

T2 = [cos(th2) -sin(th2) 0 (260*cos(th2)); sin(th2) cos(th2) 0 (260*sin(th2)) ; 0 0 1 0; 0 0 0 1];

T3 = [cos(th3) 0 sin(th3) (-30*cos(th3)); sin(th3) 0 -cos(th3) (-30*sin(th3)) ; 0 1 0 0; 0 0 0 1];

T4 = [cos(th4) 0 sin(th4) 0; sin(th4) 0 -cos(th4) 0; 0 1 0 270; 0 0 0 1];

T5 = [cos(th5) 0 sin(th5) 0; sin(th5) 0 -cos(th5) 0; 0 1 0 0; 0 0 0 1];

T6 = [cos(th6) -sin(th6) 0 0; sin(th6) cos(th6) 0 0; 0 0 1 90; 0 0 0 1];

T = T1 * T2 * T3 * T4 * T5 * T6;

%case I

th1 = 0;

th2 = 0;

th3 = 0;

th4 = 0;

th5 = 0;

th6 = 0;

display("Case 1");

display(T);

%case II

th1 = pi/2;

th2 = 0;

th3 = pi;

th4 = 0;

th5 = 0;

th6 = 0;

display("Case 2");

display(T);

Returns the same value

[Raj]

Your problem statement is not clear. Can you elaborate possibly with data?

[Anush Karki]

Eg:

M1 = [ 0 0 1 x]

M2 = [0 1 0 y]

M3 = [0 0 1 z]

M4 = [ 1 1 1 w]

calculate M5= M1*M2*M3*M4 for 2 cases:

1. x = 1, y=2, z=3, w=4;
2. x = 0, y = 3, z = 3, w =5.

[Raj]

ok so what exactly is the problem here?

[Anush Karki]

T1 = [cos(th1) 0 -sin(th1) 0; sin(th1) 0 -cos(th1) 0; 0 -1 0 0; 0 0 0 1];

T2 = [cos(th2) -sin(th2) 0 (260*cos(th2)); sin(th2) cos(th2) 0 (260*sin(th2)) ; 0 0 1 0; 0 0 0 1];

T3 = [cos(th3) 0 sin(th3) (-30*cos(th3)); sin(th3) 0 -cos(th3) (-30*sin(th3)) ; 0 1 0 0; 0 0 0 1];

T4 = [cos(th4) 0 sin(th4) 0; sin(th4) 0 -cos(th4) 0; 0 1 0 270; 0 0 0 1];

T5 = [cos(th5) 0 sin(th5) 0; sin(th5) 0 -cos(th5) 0; 0 1 0 0; 0 0 0 1];

T6 = [cos(th6) -sin(th6) 0 0; sin(th6) cos(th6) 0 0; 0 0 1 90; 0 0 0 1];

T = T1 * T2 * T3 * T4 * T5 * T6;

%case I

th1 = 0;

th2 = 0;

th3 = 0;

th4 = 0;

th5 = 0;

th6 = 0;

display("Case 1");

display(T);

%case II

th1 = pi/2;

th2 = 0;

th3 = pi;

th4 = 0;

th5 = 0;

th6 = 0;

display("Case 2");

display(T);

Both the time command Returns the same value

Answer 1

[Raj]

Not sure how you are getting the 'same value'. Your code as it is will not run in the first place.

Try this:

%case I
th1 = 0;
th2 = 0;
th3 = 0;
th4 = 0;
th5 = 0;
th6 = 0;
display('Case 1');
T1 = [cos(th1) 0 -sin(th1) 0; sin(th1) 0 -cos(th1) 0; 0 -1 0 0; 0 0 0 1];
T2 = [cos(th2) -sin(th2) 0 (260*cos(th2)); sin(th2) cos(th2) 0 (260*sin(th2)) ; 0 0 1 0; 0 0 0 1];
T3 = [cos(th3) 0 sin(th3) (-30*cos(th3)); sin(th3) 0 -cos(th3) (-30*sin(th3)) ; 0 1 0 0; 0 0 0 1];
T4 = [cos(th4) 0 sin(th4) 0; sin(th4) 0 -cos(th4) 0; 0 1 0 270; 0 0 0 1];
T5 = [cos(th5) 0 sin(th5) 0; sin(th5) 0 -cos(th5) 0; 0 1 0 0; 0 0 0 1];
T6 = [cos(th6) -sin(th6) 0 0; sin(th6) cos(th6) 0 0; 0 0 1 90; 0 0 0 1];
T = T1 * T2 * T3 * T4 * T5 * T6;
display(T);
%case II
th1 = pi/2;
th2 = 0;
th3 = pi;
th4 = 0;
th5 = 0;
th6 = 0;
display('Case 2');
T1 = [cos(th1) 0 -sin(th1) 0; sin(th1) 0 -cos(th1) 0; 0 -1 0 0; 0 0 0 1];
T2 = [cos(th2) -sin(th2) 0 (260*cos(th2)); sin(th2) cos(th2) 0 (260*sin(th2)) ; 0 0 1 0; 0 0 0 1];
T3 = [cos(th3) 0 sin(th3) (-30*cos(th3)); sin(th3) 0 -cos(th3) (-30*sin(th3)) ; 0 1 0 0; 0 0 0 1];
T4 = [cos(th4) 0 sin(th4) 0; sin(th4) 0 -cos(th4) 0; 0 1 0 270; 0 0 0 1];
T5 = [cos(th5) 0 sin(th5) 0; sin(th5) 0 -cos(th5) 0; 0 1 0 0; 0 0 0 1];
T6 = [cos(th6) -sin(th6) 0 0; sin(th6) cos(th6) 0 0; 0 0 1 90; 0 0 0 1];
T = T1 * T2 * T3 * T4 * T5 * T6;
display(T);

Works fine. If you want an optimized code and dont want to repeat the T1 to T6 equations, you can write them in a function and just call the function multiple times.

[Anush Karki]

Thank you for your reply. I have already gotten the answer using the method you suggested. I actually want an optimised code. I am new to MATLAB. How do write them in function? I tried writing them in function but have no idea regarding the code to call them.

[Raj]

Open a new script and copy this:

function T= calculation(th1,th2,th3,th4,th5,th6)
T1 = [cos(th1) 0 -sin(th1) 0; sin(th1) 0 -cos(th1) 0; 0 -1 0 0; 0 0 0 1];
T2 = [cos(th2) -sin(th2) 0 (260*cos(th2)); sin(th2) cos(th2) 0 (260*sin(th2)) ; 0 0 1 0; 0 0 0 1];
T3 = [cos(th3) 0 sin(th3) (-30*cos(th3)); sin(th3) 0 -cos(th3) (-30*sin(th3)) ; 0 1 0 0; 0 0 0 1];
T4 = [cos(th4) 0 sin(th4) 0; sin(th4) 0 -cos(th4) 0; 0 1 0 270; 0 0 0 1];
T5 = [cos(th5) 0 sin(th5) 0; sin(th5) 0 -cos(th5) 0; 0 1 0 0; 0 0 0 1];
T6 = [cos(th6) -sin(th6) 0 0; sin(th6) cos(th6) 0 0; 0 0 1 90; 0 0 0 1];
T = T1 * T2 * T3 * T4 * T5 * T6;
end

Now save it with lets say 'calculation' itself as file name. This becomes your function.

Open a new script and copy this:

%case I
th1 = 0;
th2 = 0;
th3 = 0;
th4 = 0;
th5 = 0;
th6 = 0;
display('Case 1');
T = calculation(th1,th2,th3,th4,th5,th6);
display(T);
%case II
th1 = pi/2;
th2 = 0;
th3 = pi;
th4 = 0;
th5 = 0;
th6 = 0;
display('Case 2');
T = calculation(th1,th2,th3,th4,th5,th6);
display(T);

Now save this and run. This becomes your script which calls the "calculation" function.

Also read about basics of functions from here and here. Pretty useful stuff!!

[Anush Karki]

Thank you very much.