regress.inp is for trying to deduce spectra of amino acids inprotein from spectra of known composition.
It is input for svdb.exe, and uses function 9,2 of that to multiply spectra as a matrix by a matrix to generate linear combo.

x4.mat is a matrix with the amino acid composition of each protein in (rows? columns?)
x4.lsi is the LS-inverse (in case of 4, maybe regular inverse)

regress.inp is multiplying the proteins spectra by x4.lsi to generate the putative control spectra,
then multiplying them by x4.mat to regenerate the protein spectra

Wouldn't this need to know the exact concentration of each protein?
Apparently we tried to do that. X4.mat looks like:
2
4
4
0.000  0.264  0.132  0.176
0.312  0.156  0.234  0.078
0.012  0.087  0.124  0.070
0.089  0.030  0.059  0.015

To also fit the concentration of each protein would make it nonlinear, since depends on product of conc and ext coeff, both of which are parameters. But we could do that like the tanh-fit program, alternately fitting linear and non-linear param.