To solve the matrix equation Ay = b where A is a square matrix of equation coefficients, y is a column vector of values to be solved for, and b is a column vector, use the code
int n = something Matrix A(n,n); ColumnVector b(n); ... put values in A and b ColumnVector y = A.i() * b; // solves matrix equationThe following notes are for the case where you want to solve more than one matrix equation with different values of b but the same A. Or where you want to solve a matrix equation and also find the determinant of A. In these cases you probably want to avoid repeating the LU decomposition of A for each solve or determinant calculation.
If A is a square or symmetric matrix use
CroutMatrix X = A; // carries out LU decomposition Matrix AP = X.i()*P; Matrix AQ = X.i()*Q; LogAndSign ld = X.LogDeterminant();rather than
Matrix AP = A.i()*P; Matrix AQ = A.i()*Q; LogAndSign ld = A.LogDeterminant();since each operation will repeat the LU decomposition.
If A is a BandMatrix or a SymmetricBandMatrix begin with
BandLUMatrix X = A; // carries out LU decompositionA CroutMatrix or a BandLUMatrix can't be manipulated or copied. Use references as an alternative to copying.
Alternatively use
LinearEquationSolver X = A;This will choose the most appropriate decomposition of A. That is, the band form if A is banded; the Crout decomposition if A is square or symmetric and no decomposition if A is triangular or diagonal. If you want to use the LinearEquationSolver #include newmatap.h.