How to call columns of matrices using 'for loop' ?

Hello,

I am new to MATLAB, can anyone tell me how can I use for loop for the following formulas?

Approx1=U(:,1)*S(1)*V(:,1)';

Approx2=U(:,1)*S(1)*V(:,1)'+ U(:,2)*S(2)*V(:,2)';

Approx3=U(:,1)*S(1)*V(:,1)'+ U(:,2)*S(2)*V(:,2)'+ UU(:,3)*S(3)*V(:,3)';

where U is 6 x 3, S is diagonal (3 x 3) and V is a 3 x 3 matrix. 1, 2 3 are being the columns of respective matrices.

Thank you

[Matt J]

Approx3=U(:,1)*S(1)*V(:,1)'+ U(:,2)*S(2)*V(:,2)'+ UU(:,3)*S(3)*V(:,3)';

This looks mistyped. Since S is diagonal S(2) and S(3) will always be zero so the 2nd and 3rd terms will contribute nothing. Are you sure you do not mean,

Approx3 = U(:,1)*S(1,1)*V(:,1)'+ U(:,2)*S(2,2)*V(:,2)'+ UU(:,3)*S(3,3)*V(:,3)';

[Khan]

here is the full code. Could you please run it. and compare Approx1, Approx2, Approx2 results with the for loop results, Thanks

clear all;

clc;

X = [1 2 4; 0 4 1; 0 20 1;0.3449 -0.9776 0.8097; 0.8156 -0.1027 0.3482; 0.3285 -0.4102 0.7213];

V=[1 2 4; 0 4 1; 0 20 1];

S= [1 0 0; 0 4 0; 0 0 1];

Approx1=X(:,1)*S(1)*V(:,1)'

Approx2=X(:,1)*S(1)*V(:,1)'+ X(:,2)*S(2)*V(:,2)'

Approx3=X(:,1)*S(1)*V(:,1)'+ X(:,2)*S(2)*V(:,2)'+ X(:,3)*S(3)*V(:,3)'

[Matt J]

Forget about the loop for a moment. Running your code as you've written it, you can see that Approx1, Approx2 and Approx3 all give the same result, so something is clearly wrong

clear all;
clc;
X = [1 2 4; 0 4 1; 0 20 1;0.3449   -0.9776    0.8097; 0.8156   -0.1027    0.3482; 0.3285   -0.4102    0.7213];
V=[1 2 4; 0 4 1; 0 20 1];
S= [1 0 0; 0 4 0; 0 0 1];
Approx1=X(:,1)*S(1)*V(:,1)'

Approx1 = 6×3

1.0000 0 0 0 0 0 0 0 0 0.3449 0 0 0.8156 0 0 0.3285 0 0

Approx2=X(:,1)*S(1)*V(:,1)'+ X(:,2)*S(2)*V(:,2)'

Approx2 = 6×3

1.0000 0 0 0 0 0 0 0 0 0.3449 0 0 0.8156 0 0 0.3285 0 0

Approx3=X(:,1)*S(1)*V(:,1)'+ X(:,2)*S(2)*V(:,2)'+ X(:,3)*S(3)*V(:,3)'

Approx3 = 6×3

1.0000 0 0 0 0 0 0 0 0 0.3449 0 0 0.8156 0 0 0.3285 0 0

[Khan]

Dear these are just random numbers. you can chose any numbers. My origiona U matrix is 2000 by 2000. S matrix is 2000 by 20 and V matrix is 20 by 20. the approxmation matrices should be 2000 by 20. i want three different approximations matricres using for loop. I can get it by using above simple formulas, but I dont know how to calculate it by loop.

[Matt J]

Dear these are just random numbers.

That doesn't matter. You will see the same issue I'm talking about for any data with diagonal S.

[Khan]

Ok thanks, however, My question is, can we get three different aproximations? [[[in the first Approximation I want to Multiply, first coulmns of U, S and V' matrices. In the Second approximatrion, I want to Multiply first coulmn of U, S and V' matrices and then multiply second coulms of U, S and V' matrices, and then add them. Simillarly for the last approximation. I want to get three different approximations.]]]]

[Matt J]

I want to Multiply first coulmn of U, S and V' matrices and then multiply second coulms of U, S and V' matrices

No, you can't because the columns of all these matrices have different lengths. You therefore cannot multiply their columns together.

Aren't you simply doing KL-transforms with different truncations? If so, that is what my answer below gives you, (and you should Accept-click it).

[Khan]

Thank you

Answer 1

[Matt J]

for i=1:3
 
    Approx{i}= U(:,1:i)*S(1:i,1:i)*V(:,1:i).';
   
end

[Khan]

dear, it is not working. actually in the first Approximation I want to Multiply, first coulmns of U, S and V' matrices. In the Second approximatrion, I want to Multiply first coulmn of U, S and V' matrices and then multiply second coulms of U, S and V' matrices, and then add them. Simillarly for the last approximation. I want to get three different approximations.

Answer 2

[David Hill]

s=diag(S);
for i=1:3
  Approx(:,:,i)=U(:,i)*V(:,i)'*s(i);%I am assuming this is what you want, s(i) being scalar along the diagonal
end
Approx=cumsum(Approx,3);

[Khan]

dear, actually in the first Approximation I want to multiply, first coulmns of U, S and V' matrices. In the Second approximatrion, I want to Multiply first coulmn of U, S and V' matrices and then multiply second coulms of U, S and V' matrices, and then add them. Simillarly for the last approximation.

[David Hill]

You will have to explain further. You cannot multiply 6x1 by a 3x1. This should be very easy if you could accurately describe what you want.

[Khan]

here is the full code. Could you please run it. and compare Approx1, Approx2, Approx2 results with the for loop results, Thanks

clear all;

clc;

X = [1 2 4; 0 4 1; 0 20 1;0.3449 -0.9776 0.8097; 0.8156 -0.1027 0.3482; 0.3285 -0.4102 0.7213];

V=[1 2 4; 0 4 1; 0 20 1];

S= [1 0 0; 0 4 0; 0 0 1];

Approx1=X(:,1)*S(1)*V(:,1)'

Approx2=X(:,1)*S(1)*V(:,1)'+ X(:,2)*S(2)*V(:,2)'

Approx3=X(:,1)*S(1)*V(:,1)'+ X(:,2)*S(2)*V(:,2)'+ X(:,3)*S(3)*V(:,3)'

[Khan]

Dear these are just random numbers. you can chose any numbers. My origiona U matrix is 2000 by 2000. S matrix is 2000 by 20 and V matrix is 20 by 20. the approxmation matrices should be 2000 by 20. i want three different approximations matricres using for loop. I can get it by using above simple formulas, but I dont know how to calculate it by loop.

[David Hill]

Hopefully you realize that S(1) is scalar and the first element in the diagonal matrix, S(2) will be zero, and S(3) will be zero. You are not multiplying by the column of S. The below produces the same result as expected.

for i=1:3
  Approx(:,:,i)=U(:,i)*V(:,i)'*S(i);
end
Approx=cumsum(Approx,3);

[Khan]

Thank you