Display rotation matrix with s1, c1, etc. in place of sind(theta1), cosd(theta1), etc. respectively.

How can I easily display rotation matrix results by s1, c1, etc. in place of sind(theta1), cosd(theta1), etc. respectively. [theta1, theta2 are defined by syms]

Answer 1

[Paul]

Use subs:

>> doc subs
>> syms theta1 s1 c1
>> A=[cos(theta1) sin(theta1);-sin(theta1) cos(theta1)]
 
A =
 
[  cos(theta1), sin(theta1)]
[ -sin(theta1), cos(theta1)]
 
>> subs(subs(A,cos(theta1),c1),sin(theta1),s1)
 
ans =
 
[  c1, s1]
[ -s1, c1]

[Sourabh Karmakar]

Thank you Paul, it worked. But this looks like not a good way, becuase if I have upto theta6, I have to create 6 nested subs for each replacements.

[Paul]

Use subs() combined with sym() if the variables are named theta1, theta2, etc.

>> syms theta1 theta2 theta3
>> A=[cos(theta1) sin(theta1);-sin(theta1) cos(theta1)];
>> B=[cos(theta2) sin(theta2);-sin(theta2) cos(theta2)];
>> C=[cos(theta3) sin(theta3);-sin(theta3) cos(theta3)];
>> D=A*B*C
 
D =
 
[   cos(theta3)*(cos(theta1)*cos(theta2) - sin(theta1)*sin(theta2)) - sin(theta3)*(cos(theta1)*sin(theta2) + cos(theta2)*sin(theta1)), cos(theta3)*(cos(theta1)*sin(theta2) + cos(theta2)*sin(theta1)) + sin(theta3)*(cos(theta1)*cos(theta2) - sin(theta1)*sin(theta2))]
[ - cos(theta3)*(cos(theta1)*sin(theta2) + cos(theta2)*sin(theta1)) - sin(theta3)*(cos(theta1)*cos(theta2) - sin(theta1)*sin(theta2)), cos(theta3)*(cos(theta1)*cos(theta2) - sin(theta1)*sin(theta2)) - sin(theta3)*(cos(theta1)*sin(theta2) + cos(theta2)*sin(theta1))]
 
 
>> subs(D,[cos(sym('theta',[1 3])) sin(sym('theta',[1 3]))],[sym('c',[1 3]) sym('s',[1 3])])
 
ans =
 
[   c3*(c1*c2 - s1*s2) - s3*(c1*s2 + c2*s1), c3*(c1*s2 + c2*s1) + s3*(c1*c2 - s1*s2)]
[ - c3*(c1*s2 + c2*s1) - s3*(c1*c2 - s1*s2), c3*(c1*c2 - s1*s2) - s3*(c1*s2 + c2*s1)]
 

[Sourabh Karmakar]

Fantastic! this is a great solution. Thank you very much.