Implement following matrix using for loop

Tipu Sultan

2019 5 15

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I want implement the following matrix and expression:

%Big_lambda

where theta,r,t are 1*3 matrix and a,b,p,q are 1*1 matrix.

My approach:

theta = [ 45 46 48] ;
t= [ 1 2 3 ];
r= [200 210 220];
for i=1:3
     dif_x = [(-cos(theta(i))) (r(i).*sin(theta(i))) (2*a.*t(i)+b);...
         (-sin(theta(i))) (-r(i).*cos(theta(i))) (2*p.*t(i)+q)]
     
     W = dif_x(i)*Big_lambda(i)*dif_x(i)'
end

Is the approach correct or if it is wrong what should be done!

Thanks in advance.

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Tipu Sultan 2019-5-15

编辑：Tipu Sultan 2019-5-15

在 MATLAB Online 中打开

I want to implement the following expression:

the expression contains partial derivative and big lambda which are basically the following expression:

where big lamda in the above can be taken as a identity matrix of 3*3.

W having index means it it will be inside a loop,I have implemented as follows:

theta = [ 45 46 48] ;
t= [ 1 2 3 ];
r= [200 210 220];
x = [ r; theta ; t];
Big_lambda = eye(2);
dif_x = zeros(2, 3, 3);  % Pre-allocation
for i=1:3
     dif_x(:, :, i) = [-cos(theta(i)), r(i).*sin(theta(i)),  2*a.*t(i)+b;...
                       -sin(theta(i)), -r(i).*cos(theta(i)), 2*p.*t(i)+q];
     W = dif_x(:,:,i)*Big_lambda(i)*dif_x(:,:,i)'
end

I want to know I am going in the correct direction or I need to change some thing.

Bob Thompson 2019-5-15

编辑：Bob Thompson 2019-5-15

As far as I can tell you are going in the correct direction. I am not a SME on your specific problem, but for the code aspect it seems to be functional.

I noticed you adjusted your indexing on dif_x. Don't forget to index W as well if you want to retain the results from each loop, instead of just the final loop.

W(i) = dif_x(:,:,i)*Big_lambda(i)*dif_x(:,:,i)'

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