Pseudo inverse (SVD) of a singular complex square matrix in C/C++ -

singular complex matrix 2ⁿ x 2ⁿ n 3; 4 or 5. how calculate singular value decomposition in c/c++?

input matrix r in form y*y' ()' transjugate.

eigenvectors in u main output. consider following matlab code:

[u,d,v]=svd(r); en=u(:,n+1:m); % first few eigenvectors out enen = en*en'; 

most of c/c++ libraries (e.g. opencv) support matrix inversion , svd real matrices. in non-singular case

r = re(r) + j*im(r) 

resolution helps. upper half of inverted

[re(r) -im(r); im(r) re(r)] 

gives r^-1 when complex. numerical method key here, many suggested armadillo , eigen instead of implementing custom error prone solution.

what think? choice , why?

let a matrix , a* conjugate transpose. matrix a.a* hermitian. positive semi-definite https://en.wikipedia.org/wiki/conjugate_transpose

in case, there no fundamental difference between svd , eigenvalue decomposition. http://cims.nyu.edu/~donev/teaching/nmi-fall2010/lecture5.handout.pdf

hence, routines of lapack can prove useful zheevd() , zheev().

you can call these function c lapacke interface. these functions wrapped libraries armadillo , eigen c++.

take @ answer of mine example of how call these functions using lapacke: low ram consuming c++ eigen solver .