How to use 'if else' in this case?

I have the following variance-covariance matrix which is not positive definite:

 x = [183.5310   -0.4098    8.0035   -0.0333   -0.1818   -0.9685    0.2681    0.1241   -8.3334;
   -0.4098    2.5004    0.7254    0.0150    0.2729    0.0262    0.0390   -0.0128   -0.5049;
    8.0035    0.7254  163.7246   -0.0541   -1.1285    0.8830   -0.0161   -0.2604   -0.5571;
   -0.0333    0.0150   -0.0541    0.0060   -1.4514   -2.4601    0.0049   -0.0071   -0.0297;
   -0.1818    0.2729   -1.1285   -1.4514 -318.8469 -607.2140   -0.0163   -1.7903   -1.4473;
   -0.9685    0.0262    0.8830   -2.4601 -607.2140 -924.7691   -0.1620   -2.8692   -1.1332;
    0.2681    0.0390   -0.0161    0.0049   -0.0163   -0.1620    0.0772   -0.0070   -0.0476;
    0.1241   -0.0128   -0.2604   -0.0071   -1.7903   -2.8692   -0.0070    0.0076   -0.0175;
   -8.3334   -0.5049   -0.5571   -0.0297   -1.4473   -1.1332   -0.0476   -0.0175   21.2720]
 

I can correct it and make it positive definite in this way:

[V,D] = eig(x);  % Calculate the eigendecomposition of your matrix (A = V*D*V') 
                        % where "D" is a diagonal matrix holding the eigenvalues of your matrix "A"
d= diag(D);           % Get the eigenvalues in a vector "d" 
d(d <= 1e-7) = 1e-7;  % Set any eigenvalues that are lower than threshold "TH" ("TH" here being 
                        % equal to 1e-7) to a fixed non-zero "small" value (here assumed equal to 1e-7)
D_c = diag(d);        % Built the "corrected" diagonal matrix "D_c"
PphiTilde = V*D_c*V';  % Recalculate your matrix "A" in its PD variant "A_PD"

Yet, I would like to write a code that says: if the matrix is not positive definite then do what I did above. I tried unsuccessfully:

if chol(x) == 'Matrix must be positive definite.' 
    
[V,D] = eig(x);  % Calculate the eigendecomposition of your matrix (A = V*D*V') 
                        % where "D" is a diagonal matrix holding the eigenvalues of your matrix "A"
d= diag(D);           % Get the eigenvalues in a vector "d" 
d(d <= 1e-7) = 1e-7;  % Set any eigenvalues that are lower than threshold "TH" ("TH" here being 
                        % equal to 1e-7) to a fixed non-zero "small" value (here assumed equal to 1e-7)
D_c = diag(d);        % Built the "corrected" diagonal matrix "D_c"
PphiTilde = V*D_c*V';  % Recalculate your matrix "A" in its PD variant "A_PD"
  else x
      
end

Can anyone help me?

Thanks!

Answer 1

[Steven Lord]

See the description of the second output from the chol function on its documentation page.

[madhan ravi]

help chol

 CHOL   Cholesky factorization.
    R = CHOL(A) calculates the Cholesky factor of full or sparse A using
    the diagonal and upper triangle of A, such that A = R'*R. A must be
    positive definite, and the lower triangle is assumed to be the (complex
    conjugate) transpose of the upper triangle.
 
    R = CHOL(A,TRIANGLE) specifies which triangle of A to use. For example,
    if TRIANGLE is 'lower', then CHOL uses only the diagonal and lower
    triangle of A to produce a lower triangular R such that A = R*R'. The
    default value of TRIANGLE is 'upper'. Using the 'lower' option is
    equivalent to calling CHOL with the 'upper' option and the transpose of
    A, and then transposing the output matrix R. In the following syntaxes,
    the output R is described only for the case when TRIANGLE is 'upper'.
 
    [R,FLAG] = CHOL(___) also returns the output FLAG indicating whether A
    is positive definite. Use this syntax to suppress errors produced when
    A is not positive definite.
    * If A is positive definite, then FLAG is 0 and R is the same as above.
    * If A is not positive definite, then FLAG is a positive integer. 
        - If A is full, then R is an upper triangular matrix of size
          q = FLAG-1 such that R'*R = A(1:q,1:q). 
        - If A is sparse, then R is an upper triangular matrix of size
          q-by-n such that the L-shaped region of the first q rows and
          first q columns of R'*R agree with those of A.
 
    [R,FLAG,P] = CHOL(S), for sparse S, additionally returns a permutation
    matrix P, which is a preordering of S obtained by AMD. The Cholesky
    factor of P'*S*P tends to be sparser than that of S.
    If FLAG = 0, then R is an upper triangular matrix such that R'*R = P'*S*P.
 
    [R,FLAG,p] = CHOL(___,OUTPUTFORM) specifies whether to return the
    permutation information as a vector p or matrix P. With this syntax you
    must specify a sparse input matrix S, and you optionally can specify
    TRIANGLE. For example, if OUTPUTFORM is 'vector' and FLAG = 0, then
    S(p,p) = R'*R. The default value of OUTPUTFORM is 'matrix' such that
    P'*S*P = R'*R.
 
    See also CHOLUPDATE, ICHOL, LDL, LU.

    Documentation for chol
       doc chol

    Other functions named chol

       codistributed/chol    gpuArray/chol    sym/chol

[Armando MAROZZI]

thanks a lot! sorted!