MATLAB: Problem with rref function

solving linear equation

Hi All,

I was trying to solve a set of linear equations by using rref function. My matrix is a rectangular positive definite and the explicit form of the matrices are attached with this message. However, the rref works fine with matrix1 but it doesn't work for matrix2. The only change between the two matrices is at (13,23) element (68.4900 vs 61.6410). the matrix2 only gives bunch of 0.0s as solution. But my interest to get the numbers from the matrix2. How should i proceed? or where is my wrong.

Any comments will be highly appreciated

Thanks in advance

Sudipta

Best Answer

You should be using mldivide(), not rref().

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MATLAB: How to store value of for loop in a array

"some how it stops after 3 itrations at z = 0.03"

That's actually not true. In your script, z contains 4 values and the loop has 4 iterations

% First 7 values of A from your version
>> A(1:7)
ans =
            1      0.99998       0.9999      0.99978            0            0            0

You're initializeing A as a 1x31 vector of zeros which is why there are extra value in the output.

There's nothing wrong with your loop but I find it more intuitive to loop over intergers 1:n rather than looping over elements of a vector directly. Consider this version,

z= 0:0.01:0.03;
A = zeros(size(z));
aes = 2;
counter= 1;
for i= 1:numel(z)
    A(i) = 1/(1+((z(i)/aes)^2));
end

Result:

>> A
A =
            1      0.99998       0.9999      0.99978

If you intended to have 31 iterations, define z in the first line of my version as

z = linspace(0,.03,31)
% or 
z = 0 : 0.001: 0.03;

and then run the rest of my version.

Result:

A =
  Columns 1 through 11
            1            1            1            1            1      0.99999      0.99999      0.99999      0.99998      0.99998      0.99998
  Columns 12 through 22
      0.99997      0.99996      0.99996      0.99995      0.99994      0.99994      0.99993      0.99992      0.99991       0.9999      0.99989
  Columns 23 through 31
      0.99988      0.99987      0.99986      0.99984      0.99983      0.99982       0.9998      0.99979      0.99978

MATLAB: Chol() Error with Real, Symmetric, Positive Definite, 3-by-3 Matrix

Hi Matthias,

I understand that you are trying to use the 'chol' function to find the upper/lower triangular Cholesky factor of a certain 3x3 matrix. You are getting an error that the matrix 'must be positive definite', even though it looks like the matrix is already positive definite.

Unfortunately, it seems that the matrix X is not actually positive definite. To explain, the 'svd' function returns the singular values of the input matrix, not the eigenvalues. These two are not the same, and in particular, the singular values will always be nonnegative; therefore, they will not help in determining whether the eigenvalues are nonnegative. To obtain the eigenvalues, you can use the 'eig' function, as follows:

>> eig(X)
ans =
   -0.1885
    1.3032
    4.8853

Note that when you use the 'eig' function to obtain the eigenvalues, one of the values is -0.1885; therefore, the eigenvalues are not strictly positive, and the matrix is not positive definite.

For more information, see the documentation on singular values and eigenvalues:

http://www.mathworks.com/help/matlab/math/singular-values.html

http://www.mathworks.com/help/matlab/math/eigenvalues.html

Best Answer

Related Solutions

MATLAB: How to store value of for loop in a array

MATLAB: Chol() Error with Real, Symmetric, Positive Definite, 3-by-3 Matrix

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