This is a least squares solver for general linear systems. Inspired by the solution of magnetic fields in rotationally symmetric gyrotrons.
The input is written in ascii text, e.g.:
# the name of the unknown vector (only consist of letters)
I
# arbitrary number of name for the Y components of the linear system
# only consist of letters
Bz Br Psi
# the numerical coefficient matrix M
# Bz0 = M00*I0 + M01*I1 + ...
# Br0 = M10*I0 + M11*I1 + ...
# Psi0 = M20*I0 + M21*I1 + ...
# Bz1 = M30*I0 + M31*I1 + ...
# ....
1 2 3
2 3.3 4
5 6 7
4 4 3e8
# each line contains an equation, can include several ='s
Br0 = 0 = Br1
Bz1 + 5 = Bz0 * 2 + (2 + 4)*Bz3 = (Psi3 + Bz1*2) * 6 = (Bz0 + Bz2)
2*I1 + 1 = (1+2) * 3
After solving the equation of [M][I] = [B], the unknown vector will be
given, in the above case the vector I.