In a linear system Ax=b where A is a matrix and x,b are (column) vectors,
in case the unknowns are not all on one side, i.e. some x are known and others
unknown, and the same for b, this function program allows to calculate the
unknown ones.
The syntax is: [y,c]=linear(A,sigma_x,x,sigma_b,b) where
sigma_x is a d-components column vector of the indices of the given x''s
sigma_b is a (n-d)-components column vector of the indices of the given b''s
x is a d-components column vector of the actual value of the given x''s
b is a (n-d)-components column vector of the actual value of the given b''s
Then [y,c] are the wanted solutions (the values of x,b which were unknown).
PS: the usual inversion of a linear system is recovered by
[y,c]=linear(A,[],[],[1:n]'',[b1;b2....;bn])