MATLAB - singularity warning [closed] - matlab

Question

Closed. This question does not meet Stack Overflow guidelines. It is not currently accepting answers.
This question appears to be off-topic because it lacks sufficient information to diagnose the problem. Describe your problem in more detail or include a minimal example in the question itself.
Closed 8 years ago.
Improve this question
when my matlab code gets to the line:
vE(:,:,i)=(mY(:,:,i))\(-mA*(vIs-mG(:,:,i)*vVs));
The following warning comes up:
Warning: Matrix is close to singular or badly scaled. Results may be inaccurate.
RCOND = 1.682710e-16.
Whats wrong?
Full code:
function [ vE, vV_node, vI_node ] = ...
node_analysis( vIs, vVs, mA, mG, mY )
[A,B,N]=size(mY);
vE=zeros(4,1,N);
for i=1:N
vE(:,:,i)=(mY(:,:,i))\(-mA*(vIs-mG(:,:,i)*vVs));
vV_node(:,:,i)=mA'*vE(:,:,i);
vI_node(:,:,i)=mG(:,:,i)*vV_node(:,:,i)+(vIs-mG(:,:,i)*vVs);
end
end
vE=mY^-1 * (-mA*(cIs-mG*vVs))
vE is (4x1xN) size
mY(4x4xN)
mA(4x9)
vIs(9x1)
mG(9x9xN)
vVs(9x1)

Answer 1

When you use the \ operator with a matrix, MATLAB will try and solve the least squares problem to estimate x given y in the equation y = A*x. Depending on the size and shape of A, solving this equation might be easy, hard, or impossible without additional information. It just depends on your particular problem.
As Oli mentioned the comments, this is because your matrix is close to singular or its singular values are close to zero. MATLAB is properly informing you that the MATRIX likely has either unknown information that is going to screw up the answer or that some of the information in the MATRIX is so small compared to other pieces that the small part is going to make solving for x almost impossible and error prone.
Depending on your math background, you might consider the following cod where I create create a matrix with one value very small. This will reproduce your error:
%% Make some data:
randn('seed', 1982);
n = 3;
A = zeros(n);
for ind = 1:n-1
v = randn(n,1);
A = A + v*v';
end
% Last bit is very tiny compared to the others:
A = A + 1e-14*randn(n,1)*randn(1,n);
%% Try and solve Ax=y for x= 1,2,3...
x = (1:n)';
y = A*x
x_est = A \ y
There are various ways to start trying to fix this, usually by reformulating the problem and/or adding some kind of regularization term. A good first try, though, is so add a simple Tikhonov regularization which bumps up all the small values to something reasonable that MATLAB can work with. This may mess up your data but you can plat with it.
Roughly, try this:
tikk = 1e-12;
x_est2 = (A + tikk * eye(n)) \ y
For larger or smaller values of tikk and you will see the error goes away but the solution is to some degree wrong. You might find this acceptable or not.
Note that in my example the answer is quite wrong because I used n=3. As you increase the problem size n you will be better results.
Finally, to begin exploring what is wrong with your matrix A ((-mA*(vIs-mG(:,:,i)*vVs))), you might consider seeing how fast the values s in s=svd(A) decay. Some of them should be quite close to zero. Also, you might look at Tihkonov regularization and what you can do by actually decomposing the matrix into the SVD and scaling things better.