Implimentation of linear regression without intercept using SVD in c++

I have code for linear regression using normal algebraic equations but I am working on the code using SVD ( which is more accurate relative to normal equations) without intercept. I don't know how to do.

https://github.com/sequinstandards/Anaquin/blob/master/src/stats/ss/regression/linear.hpp

this is the link which has already code for linear regression using SVD but I need the linear fit without intercept. Any help would be great.

Thanks in advance!