FOR loop with subs :: NEED HELP

Hi All,

I've been trying to implement a for loop to obtain different values of the following matrix (T_x_new), it's working perfect till obtaining normal T_x_new, so I just would like to add different theta for T_x_new to check different values but it's not working

Would any one mind helping me to run this code:

clear all;
 
syms l1 m1 n1 l2 m2 n2 l3 m3 n3 theta real;
T_x= [l1^2 m1^2 n1^2 2*m1*n1 2*l1*n1 2*l1*m1;
     l2^2 m2^2 n2^2 2*m2*n2 2*l2*n2 2*l2*m2;
     l3^2 m3^2 n3^2 2*m3*n3 2*l3*n3 2*l3*m3;
     l2*l3 m2*m3 n2*n3 m2*n3+n2*m3 l2*n3+n2*l3 l2*m3+m2*l3;
     l1*l3 m1*m3 n1*n3 m1*n3+n1*m3 l1*n3+n1*l3 l1*m3+m1*l3;
     l1*l2 m1*m2 n1*n2 m1*n2+n1*m2 l1*n2+n1*l2 l1*m2+m1*l2];
T_x_new=subs(T_x,{l1,m1,n1,l2,m2,n2,l3,m3,n3},{1,0,0,0,cos(theta),sin(theta),0,-sin(theta),cos(theta)});
for i=45:90;
    theta=i*(pi/180);
T_x_new(:,:,i)

end 

Answer 1

[Walter Roberson]

for i=45:90;
    theta=i*(pi/180);
    subs(T_x_new)
end

This will produce 46 matrices of output, so you may wish to reconsider using 45:90 rather than (say) 45:15:90

[Ali Tawfik]

Thanks, Walter it's working, but I wanna solve the matrix, I mean still the output written cos() and sin().... I wanna final answer with the theta angle also, with degrees, I mean I can remove (pi/180) but I got an error if I wrote cosd()....

Looking to hearing your answer !

Thanks again,

[Walter Roberson]

syms l1 m1 n1 l2 m2 n2 l3 m3 n3 theta real
syms pi
Cosd = @(theta) cos(theta*pi/180);
Sind = @(theta) sin(theta*pi/180);
T_x= [l1^2 m1^2 n1^2 2*m1*n1 2*l1*n1 2*l1*m1;
     l2^2 m2^2 n2^2 2*m2*n2 2*l2*n2 2*l2*m2;
     l3^2 m3^2 n3^2 2*m3*n3 2*l3*n3 2*l3*m3;
     l2*l3 m2*m3 n2*n3 m2*n3+n2*m3 l2*n3+n2*l3 l2*m3+m2*l3;
     l1*l3 m1*m3 n1*n3 m1*n3+n1*m3 l1*n3+n1*l3 l1*m3+m1*l3;
     l1*l2 m1*m2 n1*n2 m1*n2+n1*m2 l1*n2+n1*l2 l1*m2+m1*l2];
T_x_new=subs(T_x, {l1,m1,n1,l2,m2,n2,l3,m3,n3}, {1, 0, 0, 0, Cosd(theta), Sind(theta), 0, -Sind(theta), Cosd(theta)});
for Theta = 45 : 90
    subs(T_x_new, theta, Theta)
end

You need to define your own sind and cosd functions because the MATLAB sind and cosd are for numeric inputs only.

... but I am going to guess that what you mean is that you want

for Theta = 45 : 90
    double( subs(T_x_new, theta, Theta) )
end

These will only be decimal approximations of the answers.

[Ali Tawfik]

Thanks again... how smart you're .. I just do not understand excatly what do you mean by defining my own sind and cosd functions, `I thought the following two lines for that purpose

Cosd = @(theta) cos(theta*pi/180);

Sind = @(theta) sin(theta*pi/180);

May I ask you what shall I do if I wanna get the accurate answer with cosd and sind ?

Thank again

[Ali Tawfik]

What I am also trying to say: how it work normally when I calculate cosd(45) or something like that ?

[Walter Roberson]

cosd(45) works. But

syms Theta
subs( cosd(Theta), Theta, 45 )

does not work. This is because cosd is not defined for symbolic inputs.

If you must use cosd for some reason you will need to loop:

syms l1 m1 n1 l2 m2 n2 l3 m3 n3 theta real;
T_x= [l1^2 m1^2 n1^2 2*m1*n1 2*l1*n1 2*l1*m1;
     l2^2 m2^2 n2^2 2*m2*n2 2*l2*n2 2*l2*m2;
     l3^2 m3^2 n3^2 2*m3*n3 2*l3*n3 2*l3*m3;
     l2*l3 m2*m3 n2*n3 m2*n3+n2*m3 l2*n3+n2*l3 l2*m3+m2*l3;
     l1*l3 m1*m3 n1*n3 m1*n3+n1*m3 l1*n3+n1*l3 l1*m3+m1*l3;
     l1*l2 m1*m2 n1*n2 m1*n2+n1*m2 l1*n2+n1*l2 l1*m2+m1*l2];
for theta = 45:90;
    T_x_new = subs(T_x, {l1,m1,n1,l2,m2,n2,l3,m3,n3}, {1,0,0,0,cosd(theta),sind(theta),0,-sind(theta),cosd(theta)})
end

This evaluates cosd() and sind() with numeric inputs, giving floating point results, and then substitutes those floating point results into T_x after converting the floating point into algebraic numbers. You will get out results such as

[ 1,                                                                   0,                                                                  0,                                                                      0,                                  0,                                  0]
[ 0,  9860332038599659652432850501889/1298074214633706907132624082305024,  20128341915548551236140856573601/20282409603651670423947251286016,      14088013865473437438305199633233/81129638414606681695789005144064,                                  0,                                  0]
[ 0,   20128341915548551236140856573601/20282409603651670423947251286016, 9860332038599659652432850501889/1298074214633706907132624082305024,     -14088013865473437438305199633233/81129638414606681695789005144064,                                  0,                                  0]
[ 0, -14088013865473437438305199633233/162259276829213363391578010288128, 14088013865473437438305199633233/162259276829213363391578010288128, -1278353550556507619460581970208575/1298074214633706907132624082305024,                                  0,                                  0]
[ 0,                                                                   0,                                                                  0,                                                                      0, 3140116564492417/36028797018963968, -4486462071114449/4503599627370496]
[ 0,                                                                   0,                                                                  0,                                                                      0,  4486462071114449/4503599627370496, 3140116564492417/36028797018963968]
 

[Ali Tawfik]

I understood what you mean by cosd not defined for symbolic inputs. Therefore, I will explain you what excatly I am looking for:

• First to obtain the transformation matrix with symbloic inputs (T_x_new) (already done)
• Then I wanna a final result with different angles (in degree ) variation (e.g. 0, 45, 30, 20, and 90).
• So may you have a look about the following code, my result should be a normal 6*6,but I have no idea why it's 18*6

syms l1 m1 n1 l2 m2 n2 l3 m3 n3 theta real
syms pi
Cosd = @(theta) cos(theta*pi/180);  % May I ask, is it a function or ?
Sind = @(theta) sin(theta*pi/180);
T_x= [l1^2 m1^2 n1^2 2*m1*n1 2*l1*n1 2*l1*m1;
     l2^2 m2^2 n2^2 2*m2*n2 2*l2*n2 2*l2*m2;
     l3^2 m3^2 n3^2 2*m3*n3 2*l3*n3 2*l3*m3;
     l2*l3 m2*m3 n2*n3 m2*n3+n2*m3 l2*n3+n2*l3 l2*m3+m2*l3;
     l1*l3 m1*m3 n1*n3 m1*n3+n1*m3 l1*n3+n1*l3 l1*m3+m1*l3;
     l1*l2 m1*m2 n1*n2 m1*n2+n1*m2 l1*n2+n1*l2 l1*m2+m1*l2];
T_x_new=subs(T_x, {l1,m1,n1,l2,m2,n2,l3,m3,n3}, {1, 0, 0, 0, Cosd(theta), Sind(theta), 0, -Sind(theta), Cosd(theta)});
angle(1,:)=0;
angle(2,:)=45;
angle(3,:)=90;
num=size(angle,1); 
 
for i=1:num;
    w(:,:,i)=double( subs(T_x_new, theta, angle) ); 
% I wanna here, to sub. every theta with 0, 45, and 90.. and wanna 6*6 % matrix (w) for each trial.. Hope you understand what I mean now
end

But anyway, thank you so much.. I really appericate your kind help.. & hope you can find a solution for what I mentioned.

[Ali Tawfik]

Maybe I have to add angle(i)?, and I think I can get the result without the problem of sind and cosd..

[Walter Roberson]

angle = [0 45 30 20 90];
num = length(angle); 
 
for i=1:num;
    w(:,:,i)=double( subs(T_x_new, theta, angle(i)) ); 
end

Or alternately,

angle = [0 45 30 20 90];
w = double(subs(T_x_new, theta, reshape(angle, 1, 1, [])));