void test(Matrix& A, const char* name)
{
using mtl::irange;
A= 0.0;
A[0][0]= 1.0;
hessian_setup(A, 1.0);
A[irange(0, 8)][irange(0, 8)];
mtl::matrix::recursator<Matrix> rec(A);
std::cout << "\n" << name << "\n";
std::cout << "A:\n" << A << '\n';
std::cout << "A[irange(0, 8)][irange(0, 8)]:\n" << A[irange(0, 8)][irange(0, 8)] << '\n';
std::cout << "*rec:\n" << *rec << '\n';
mtl::matrix::recursator<Matrix> nw= north_west(rec);
std::cout << "north_west:\n" << *nw << '\n';
std::cout << "north_west of north_west:\n" << *north_west(nw) << '\n';
MTL_THROW_IF((*north_west(nw))[0][0] != 0.0, mtl::runtime_error("(*north_west(nw))[0][0] != 0.0"));
(*north_west(nw))[0][0]= 2.0;
std::cout << "south_east of north_west:\n" << *south_east(nw) << '\n';
MTL_THROW_IF((*south_east(nw))[0][0] != 4.0, mtl::runtime_error("(*south_east(nw))[0][0] != 4.0"));
std::cout << "north_west of north_west:\n" << *north_west(nw) << '\n';
MTL_THROW_IF((*north_west(nw))[0][0] != 2.0, mtl::runtime_error("(*north_west(nw))[0][0] != 2.0"));
std::cout << "south_east of north_west:\n" << *south_east(nw) << '\n';
MTL_THROW_IF((*south_east(nw))[0][0] != 4.0, mtl::runtime_error("(*south_east(nw))[0][0] != 4.0"));
std::cout << "nw.first_address() == " << nw.first_address()
<< ", &(*nw)[0][0] == " << &(*nw)[0][0] << '\n';
MTL_THROW_IF(nw.first_address() != &(*nw)[0][0], mtl::runtime_error("Inconsistency in address calculation"));
}
dense2D<typename mtl::Collection
<typename mtl::Collection<VVector>::value_type
>::value_type, parameters<> >
inline orthogonalize_factors(VVector& v, tag::vector)
{
using ::mtl::two_norm;
using math::zero;
using mtl::size1D;
typedef typename mtl::Collection<VVector>::size_type Size;
typedef typename mtl::Collection<VVector>::value_type Vector;
typedef typename mtl::Collection<Vector>::value_type Scalar;
dense2D<Scalar, parameters<> > tau(size1D(v), size1D(v));
tau= zero(Scalar());
for (Size j= 0; j < size1D(v); ++j) {
for (Size i= 0; i < j; ++i) {
Scalar t= dot(entry1D(v, i), entry1D(v, j)) / tau[i][i];
tau[i][j]= t;
entry1D(v, j)-= t * entry1D(v, i);
}
tau[j][j]= dot(entry1D(v, j), entry1D(v, j));
}
return tau;
}
void test2(Matrix& A, const char* name)
{
using mtl::irange; using mtl::imax; using mtl::iall;
A= 0.0;
A[1][1]= 1.0;
hessian_setup(A, 1.0);
std::cout << "\n" << name << "\nA == \n" << A;
cout << "A[irange(2, 4)][irange(2, imax)] == \n"
<< A[irange(2, 4)][irange(2, imax)] << "\n";
Matrix B(A[irange(2, 4)][irange(2, imax)]);
MTL_THROW_IF(B[0][0] != 4.0, mtl::runtime_error("Wrong value in B"));
MTL_THROW_IF(A[irange(2, 4)][irange(2, imax)][0][0] != 4.0, mtl::runtime_error("Wrong value in A[][]"));
Matrix C(A[irange(4, imax)][irange(0, imax)]);
std::cout << "\n" << name << "\nA[irange(4, imax)][irange(0, imax)] == \n" << C;
MTL_THROW_IF(C[0][1] != 5.0, mtl::runtime_error("Wrong value in C"));
Matrix D(A[irange(4, imax)][iall]);
std::cout << "\n" << name << "\nA[irange(4, imax)][iall] == \n" << C;
MTL_THROW_IF(D[0][1] != 5.0, mtl::runtime_error("Wrong value in D"));
}
inline void orth(VVector& v, typename mtl::Collection<VVector>::size_type j, tag::vector)
{
using mtl::two_norm;
using mtl::size1D;
MTL_DEBUG_THROW_IF(j < 0 || j >= size1D(v), index_out_of_range());
typedef typename mtl::Collection<VVector>::size_type Size;
for (Size i= 0; i < j; ++i)
entry1D(v, j)-= dot(entry1D(v, i), entry1D(v, j)) * entry1D(v, i);
entry1D(v, j)/= two_norm(entry1D(v, j));
}
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"));
}
int main(int, char**)
{
using namespace std;
using mtl::lazy; using mtl::io::tout;
typedef mtl::dense_vector<double> vt;
vt v(60);
iota(v);
tout << "v is " << v << endl;
mtl::mat::identity2D I(60);
vt w1(I * v);
tout << "I * v is " << w1 << endl;
if (one_norm(vt(w1 - v)) > 0.001) throw "Wrong result with square identity";
w1-= I * v;
tout << "w1-= I * v is " << w1 << endl;
if (one_norm(w1) > 0.001) throw "Wrong result";
w1+= I * v;
tout << "w1+= I * v is " << w1 << endl;
if (one_norm(vt(w1 - v)) > 0.001) throw "Wrong result with square identity";
vt w2( w1 - I * v );
double alpha;
(lazy(w2)= I * v) || (lazy(alpha)= lazy_dot(w2, v));
vt w3(30), w4(90);
mtl::mat::identity2D I3(30, 60), I4(90, 60);
w3= I3 * v;
tout << "I3 * v is " << w3 << endl;
if (one_norm(vt(w3 - v[mtl::irange(30)])) > 0.001) throw "Wrong result with broad identity";
w4= I4 * v;
tout << "I4 * v is " << w4 << endl;
if (one_norm(vt(w4[mtl::irange(60)] - v)) > 0.001) throw "Wrong result with long identity";
if (one_norm(w4[mtl::irange(60, 90)]) > 0.001) throw "Wrong result with long identity";
#if 0
mtl::dense2D<double> A(60,60);
A=2;
A+= A*I;
std::cout<< "A=\n" << A << "\n";
#endif
return 0;
}
inline void orth(VVector& v, tag::vector)
{
typedef typename mtl::Collection<VVector>::size_type Size;
using mtl::size1D;
for (Size j= 0; j < size1D(v); ++j)
orth(v, j, tag::vector());
}
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();
}
void test(Matrix& matrix, const char* name)
{
cout << "\n" << name << "\n";
using mtl::matrix::inserter; using mtl::element_array;
typedef typename mtl::Collection<Matrix>::value_type value_type;
mtl::dense2D<double> m1(2, 2);
m1[0][0]= 1.0; m1[0][1]= 2.0;
m1[1][0]= 3.0; m1[1][1]= 4.0;
std::vector<int> row1, col1;
row1.push_back(1); row1.push_back(2);
col1.push_back(0); col1.push_back(2);
double a2[2][2]= {{11., 12.},{13., 14.}};
std::vector<int> ind2;
ind2.push_back(2); ind2.push_back(4);
std::vector<int> ind3;
ind3.push_back(3); ind3.push_back(1);
set_to_zero(matrix); // dense matrices are not automatically set to zero
{
inserter<Matrix, mtl::operations::update_plus<value_type> > ins(matrix);
ins << element_matrix(m1, row1, col1)
<< element_array(a2, ind2);
ins << element_array(a2, ind3);
}
cout << "Filled matrix:\n" << matrix << "\n";
MTL_THROW_IF(matrix[0][0] != 0.0, mtl::runtime_error("wrong zero-element"));
MTL_THROW_IF(matrix[1][0] != 1.0, mtl::runtime_error("wrong insertion (single value)"));
MTL_THROW_IF(matrix[2][2] != 15.0, mtl::runtime_error("wrong summation"));
MTL_THROW_IF(matrix[1][1] != 14.0, mtl::runtime_error("wrong insertion (single value)"));
}
int main(int, char**)
{
using namespace std;
using mtl::lazy;
using mtl::io::tout;
typedef mtl::vector::dense_vector<double> vt;
mtl::compressed2D<double> A0;
laplacian_setup(A0, 4, 15);
tout << "A0 is\n" << A0 << endl;
vt v(60);
iota(v);
tout << "v is " << v << endl;
vt w1(A0 * v);
tout << "A0 * v is " << w1 << endl;
mtl::matrix::poisson2D_dirichlet A(4, 15);
vt w2(60);
w2= A * v;
tout << "A * v is " << w2 << endl;
if (one_norm(vt(w1 - w2)) > 0.001) throw "Wrong result";
w2+= A * v;
tout << "w2+= A * v is " << w2 << endl;
if (one_norm(vt(w1 + w1 - w2)) > 0.001) throw "Wrong result";
w2-= A * v;
tout << "w2-= A * v is " << w2 << endl;
if (one_norm(vt(w1 - w2)) > 0.001) throw "Wrong result";
vt w3( w2 - A * v );
double alpha;
(lazy(w3)= A * v) || (lazy(alpha)= lazy_dot(w3, v));
return 0;
}
int main(int, char**)
{
using mtl::max; using std::pow; // to avoid possible ambiguity with ARPREC
mtl::dense_vector<double> v(100);
for (unsigned i= 0; i < size(v); i++)
v[i]= double(i+1) * pow(-1.0, int(i)); // Amb. in MSVC
std::cout << "max(v) is " << max(v)<< "\n";
std::cout << "min(v) is " << min(v)<< "\n";
std::cout << "max<6>(v) is " << max<6>(v)<< "\n";
return 0;
}
void test(VectorU& u, VectorV& v, VectorW& w, const char* name)
{
using mtl::dot;
// test right scale
u= 3.0; v= 4.0; w= 5.0;
std::cout << name << " --- v= u*3 + w*4;:\n"; std::cout.flush();
v= u*3 + w*4;
cout << "v: " << v << "\n"; std::cout.flush();
MTL_THROW_IF(v[0] != 29.0, mtl::runtime_error("v wrong"));
std::cout << name << " --- u= 3; v= 4; u+= v+= (w= 5) * 3.0;:\n"; std::cout.flush();
u= 3; v= 4;
u+= v+= (w= 5.0) * 3.0;
cout << "u: " << u << "v: " << v << "\n"; std::cout.flush();
MTL_THROW_IF(v[0] != 19.0, mtl::runtime_error("v wrong"));
MTL_THROW_IF(u[0] != 22.0, mtl::runtime_error("u wrong"));
std::cout << name << " --- u= 3; v= 4; w=5; u+= w * dot(v, w);:\n"; std::cout.flush();
u= 3; v= 4; w=5; u+= w * dot(v, w);
cout << "u: " << u << "v: " << v << "w: " << w << "\n"; std::cout.flush();
MTL_THROW_IF(u[0] != 503.0, mtl::runtime_error("u wrong"));
std::cout << name << " --- u+= w * dot<12>(v, w);:\n"; std::cout.flush();
u+= w * dot<12>(v, w);
cout << "u: " << u << "v: " << v << "w: " << w << "\n"; std::cout.flush();
MTL_THROW_IF(u[0] != 1003.0, mtl::runtime_error("u wrong"));
// test divide by scalar
u= 3.0; v= 4.0; w= 5.0;
std::cout << name << " --- v= u/3 + w/5;:\n"; std::cout.flush();
v= u/3 + w/5;
cout << "v: " << v << "\n"; std::cout.flush();
MTL_THROW_IF(v[0] != 2.0, mtl::runtime_error("v wrong"));
std::cout << name << " --- u= 3; v= 4; u+= v+= (w= 6.0) / 3.0;:\n"; std::cout.flush();
u= 3; v= 4;
u+= v+= (w= 6.0) / 3.0;
cout << "u: " << u << "v: " << v << "\n"; std::cout.flush();
MTL_THROW_IF(v[0] != 6.0, mtl::runtime_error("v wrong"));
MTL_THROW_IF(u[0] != 9.0, mtl::runtime_error("u wrong"));
}
void test(Vector& v, const char* name)
{
using mtl::size; using mtl::num_rows; using mtl::num_cols;
cout << "\n" << name << "\n";
cout << "size(v) = " << size(v) << "\n";
// Value is less critical main purpose of the test is to check compilibilit
MTL_THROW_IF(size(v) != 3, mtl::runtime_error("Vector size should be 3"));
cout << "num_rows(v) = " << num_rows(v) << "\n";
// Value is less critical main purpose of the test is to check compilibilit
MTL_THROW_IF(num_rows(v) != 3, mtl::runtime_error("Vector number of rows should be 3"));
cout << "num_cols(v) = " << num_cols(v) << "\n";
// Value is less critical main purpose of the test is to check compilibilit
MTL_THROW_IF(num_cols(v) != 1, mtl::runtime_error("Vector number of columns should be 1"));
}
type lower_bound(Matrix const& c, size_type position) const
{
using mtl::num_cols;
return type(std::min(num_cols(c), position), c);
}
typename traits::permutation<Value>::type
inline permutation(const PermutationVector& v)
{
using mtl::size;
return reorder(v, size(v));
}
static inline void update(Value& value, const Element& x)
{
using mtl::squared_abs;
value+= squared_abs(x);
}
int bicgstab_ell(const LinearOperator &A, Vector &x, const Vector &b,
const LeftPreconditioner &L, const RightPreconditioner &R,
Iteration& iter, size_t l)
{
mtl::vampir_trace<7006> tracer;
using mtl::size; using mtl::irange; using mtl::imax; using mtl::matrix::strict_upper;
typedef typename mtl::Collection<Vector>::value_type Scalar;
typedef typename mtl::Collection<Vector>::size_type Size;
if (size(b) == 0) throw mtl::logic_error("empty rhs vector");
const Scalar zero= math::zero(Scalar()), one= math::one(Scalar());
Vector x0(resource(x)), y(resource(x));
mtl::vector::dense_vector<Vector> r_hat(l+1,Vector(resource(x))), u_hat(l+1,Vector(resource(x)));
// shift problem
x0= zero;
r_hat[0]= b;
if (two_norm(x) != zero) {
r_hat[0]-= A * x;
x0= x;
x= zero;
}
Vector r0_tilde(r_hat[0]/two_norm(r_hat[0]));
y= solve(L, r_hat[0]);
r_hat[0]= y;
u_hat[0]= zero;
Scalar rho_0(one), rho_1(zero), alpha(zero), Gamma(zero), beta(zero), omega(one);
mtl::matrix::dense2D<Scalar> tau(l+1, l+1);
mtl::vector::dense_vector<Scalar> sigma(l+1), gamma(l+1), gamma_a(l+1), gamma_aa(l+1);
while (! iter.finished(r_hat[0])) {
++iter;
rho_0= -omega * rho_0;
for (Size j= 0; j < l; ++j) {
rho_1= dot(r0_tilde, r_hat[j]);
beta= alpha * rho_1/rho_0; rho_0= rho_1;
for (Size i= 0; i <= j; ++i)
u_hat[i]= r_hat[i] - beta * u_hat[i];
y= A * Vector(solve(R, u_hat[j]));
u_hat[j+1]= solve(L, y);
Gamma= dot(r0_tilde, u_hat[j+1]);
alpha= rho_0 / Gamma;
for (Size i= 0; i <= j; ++i)
r_hat[i]-= alpha * u_hat[i+1];
if (iter.finished(r_hat[j])) {
x= solve(R, x);
x+= x0;
return iter;
}
r_hat[j+1]= solve(R, r_hat[j]);
y= A * r_hat[j+1];
r_hat[j+1]= solve(L, y);
x+= alpha * u_hat[0];
}
// mod GS (MR part)
irange i1m(1, imax);
mtl::vector::dense_vector<Vector> r_hat_tail(r_hat[i1m]);
tau[i1m][i1m]= orthogonalize_factors(r_hat_tail);
for (Size j= 1; j <= l; ++j)
gamma_a[j]= dot(r_hat[j], r_hat[0]) / tau[j][j];
gamma[l]= gamma_a[l]; omega= gamma[l];
if (omega == zero) return iter.fail(3, "bicg breakdown #2");
// is this something like a tri-solve?
for (Size j= l-1; j > 0; --j) {
Scalar sum= zero;
for (Size i=j+1;i<=l;++i)
sum += tau[j][i] * gamma[i];
gamma[j] = gamma_a[j] - sum;
}
gamma_aa[irange(1, l)]= strict_upper(tau[irange(1, l)][irange(1, l)]) * gamma[irange(2, l+1)] + gamma[irange(2, l+1)];
x+= gamma[1] * r_hat[0];
r_hat[0]-= gamma_a[l] * r_hat[l];
u_hat[0]-= gamma[l] * u_hat[l];
for (Size j=1; j < l; ++j) {
u_hat[0] -= gamma[j] * u_hat[j];
x+= gamma_aa[j] * r_hat[j];
r_hat[0] -= gamma_a[j] * r_hat[j];
}
}
x= solve(R, x); x+= x0; // convert to real solution and undo shift
return iter;
}
type end(Matrix const& c) const
{
using mtl::num_rows; using mtl::matrix::num_rows;
return type(num_rows(c), c); //return type(c.end_row(), c);
}
type end(Cursor const& c) const { using mtl::num_cols; return type(c.ref, *c, num_cols(c.ref)); }
type end(Matrix const& c) const
{
using mtl::num_cols;
return type(num_cols(c), c); // return type(c.end_col(), c);
}
type end(Cursor const& c) const { using mtl::num_rows; return type(c.ref, num_rows(c.ref), *c); }
type end(Ref& c)
{
using mtl::size;
return type(c.address_data() + size(c) + c.stride(), c.stride());
}
type lower_bound(Cursor const& c, size_type position) const
{
using mtl::num_rows;
return type(c.ref, std::min(num_rows(c.ref), position), *c);
}