void test(Matrix& matrix, const char* name)
{
using mtl::conj;
set_to_zero(matrix);
typename Matrix::value_type ref(0);
{
mtl::matrix::inserter<Matrix> ins(matrix);
ins(2, 3) << value(ref);
ins(4, 3) << value(ref) + 1.0;
ins(2, 5) << value(ref) + 2.0;
}
cout << "\n\n" << name << "\n";
cout << "Original matrix:\n" << matrix << "\n";
mtl::matrix::scaled_view<double, Matrix> scaled_matrix(2.0, matrix);
cout << "matrix scaled with 2.0\n" << scaled_matrix << "\n";
MTL_THROW_IF(scaled_matrix(2, 3) != svalue(ref), mtl::runtime_error("scaling wrong"));
cout << "matrix scaled with 2.0 (as operator)\n" << 2.0 * matrix << "\n";
MTL_THROW_IF((2.0 * matrix)(2, 3) != svalue(ref), mtl::runtime_error("scaling wrong"));
mtl::matrix::conj_view<Matrix> conj_matrix(matrix);
cout << "conjugated matrix\n" << conj_matrix << "\n";
MTL_THROW_IF(conj_matrix(2, 3) != cvalue(ref), mtl::runtime_error(" wrong"));
mtl::matrix::scaled_view<ct, Matrix> cscaled_matrix(ct(0.0, 1.0), matrix);
cout << "matrix scaled with i (complex(0, 1))\n" << cscaled_matrix << "\n";
MTL_THROW_IF(cscaled_matrix(2, 3) != csvalue(ref), mtl::runtime_error("complex scaling wrong"));
mtl::matrix::hermitian_view<Matrix> hermitian_matrix(matrix);
cout << "Hermitian matrix (conjugate transposed)\n" << hermitian_matrix << "\n";
MTL_THROW_IF(hermitian_matrix(3, 2) != cvalue(ref), mtl::runtime_error("conjugate transposing wrong"));
cout << "matrix scaled with 2.0 (free function)\n" << scale(2.0, matrix) << "\n";
MTL_THROW_IF(scale(2.0, matrix)(2, 3) != svalue(ref), mtl::runtime_error("scaling wrong"));
cout << "matrix scaled with 2.0 (free function as mtl::scale)\n" << mtl::scale(2.0, matrix) << "\n";
cout << "conjugated matrix (free function) \n" << conj(matrix) << "\n";
MTL_THROW_IF(conj(matrix)(2, 3) != cvalue(ref), mtl::runtime_error("conjugating wrong"));
cout << "matrix scaled with i (complex(0, 1)) (free function)\n" << scale(ct(0.0, 1.0), matrix) << "\n";
MTL_THROW_IF(scale(ct(0.0, 1.0), matrix)(2, 3) != csvalue(ref), mtl::runtime_error("complex scaling wrong"));
cout << "Hermitian matrix (conjugate transposed) (free function)\n" << hermitian(matrix) << "\n";
MTL_THROW_IF(hermitian(matrix)(3, 2) != cvalue(ref), mtl::runtime_error("conjugate transposing wrong"));
}
void adjoint_solve(const VectorIn& x, VectorOut& y) const
{
using mtl::conj;
y.checked_change_resource(x);
MTL_THROW_IF(size(x) != size(inv_diag), mtl::incompatible_size());
for (size_type i= 0; i < size(inv_diag); ++i)
y[i]= conj(inv_diag[i]) * x[i];
}
int bicg(const LinearOperator &A, Vector &x, const Vector &b,
const Preconditioner &M, Iteration& iter)
{
using mtl::conj;
typedef typename mtl::Collection<Vector>::value_type Scalar;
Scalar rho_1(0), rho_2(0), alpha(0), beta(0);
Vector r(b - A * x), z(size(x)), p(size(x)), q(size(x)),
r_tilde(r), z_tilde(size(x)), p_tilde(size(x)), q_tilde(size(x));
while (! iter.finished(r)) {
z= solve(M, r);
z_tilde= adjoint_solve(M, r_tilde);
rho_1= dot(z_tilde, z);
if (rho_1 == 0.) {
iter.fail(2, "bicg breakdown");
break;
}
if (iter.first()) {
p= z;
p_tilde= z_tilde;
} else {
beta= rho_1 / rho_2;
p= z + beta * p;
p_tilde= z_tilde + conj(beta) * p_tilde;
}
q= A * p;
q_tilde= adjoint(A) * p_tilde;
alpha= rho_1 / dot(p_tilde, q);
x+= alpha * p;
r-= alpha * q;
r_tilde-= conj(alpha) * q_tilde;
rho_2= rho_1;
++iter;
}
return iter.error_code();
}