void SolveGEIP(const Matrix& A, Vector &x, const Vector& b)
{
// Verify that the system is well-formed
const int size = A.Rows();
if ((A.Cols() != size) || (b.Size() != size)) {
throw NonconformableShapesError();
}
// Prepare the augmented matrix
Matrix aug(size, size+1, NaN());
for (int i = 0; i < size; ++i) {
aug.Col(i) = A.Col(i);
}
aug.Col(size) = b;
// Go to town...
eliminate(aug, size, fabs(1e-14));
back_substitute(aug, size);
x = aug.Col(size);
}
void lin_alg::Gauss_Solve(double **A, double *b, double *x, int size, bool pivoting, bool printing)
{
// This is a function that performs a row reduction on an augmented matrix followed by
// backsubstitution to find the solution of A.x=b
// R. Sheehan 28 - 2 - 2013
// the argument pivoting has been defaulted to be set to true
// so that pivoting is always applied unless otherwise specified
// Create an array to aid with the simulated row-interchanges
// new is equivalent to malloc
int *nrow = new (int [size+1]);
double **Aug = matrix(size, size+1); // create an array to hold the augmented matrix
// perform the row reduction
row_reduce( A, b, Aug, nrow, size, pivoting);
if(printing){
cout<<"Row reduced system\n";
print_matrix(Aug, size, size+1);
}
// compute x by back-substitution on the row-reduced augmented matrix
back_substitute(x,Aug,nrow,size);
if(printing){
cout<<"Computed solution\n";
print_vector(x, size);
}
// Delete memory that is no longer required
delete[] nrow;
delete[] Aug;
}