sub_matrix_type constructor_helper(transposed_view<MatrixType> const& view)
{
typedef typename boost::remove_const<MatrixType>::type tmp_type;
typedef typename sub_matrix_t<tmp_type>::sub_matrix_type ref_sub_type;
typedef boost::shared_ptr<ref_sub_type> pointer_type;
typedef typename transposed_view<MatrixType>::other ref_type;
// Submatrix of referred matrix, colums and rows interchanged
// Create a submatrix, whos address will be kept by transposed_view
pointer_type p(new ref_sub_type(sub_matrix(const_cast<ref_type&>(view.ref), view.begin_col(), view.end_col(),
view.begin_row(), view.end_row())));
return sub_matrix_type(p);
}
void abcd::aijAugmentMatrix(std::vector<CompCol_Mat_double> &M)
{
int nbcols = A.dim(1);
std::map<int,std::vector<CompCol_Mat_double> > C;
std::map<int,std::vector<int> > stCols;
#ifdef WIP
double filter_c = dcntl[Controls::aug_filter];
#endif //WIP
stC.assign(M.size(), -1);
for( size_t i = 0; i < M.size() - 1; i++ ){
for ( size_t j = i+1; j < M.size(); j++ ) {
std::vector<int> intersect;
std::set_intersection(column_index[i].begin(),
column_index[i].end(),
column_index[j].begin(),
column_index[j].end(),
std::back_inserter(intersect));
if (intersect.empty()) continue;
CompCol_Mat_double A_ij(sub_matrix(M[i], intersect));
CompCol_Mat_double A_ji(sub_matrix(M[j], intersect));
double *jv = A_ji.val_ptr();
for (int k = 0; k < A_ji.NumNonzeros(); k++) {
jv[k] *= -1.0;
}
#ifdef WIP
if(filter_c != 0 || icntl[Controls::aug_iterative] != 0) {
std::vector<int> selected_cols;
std::vector<double> frob_ij, mu;
frob_ij.reserve(A_ij.dim(1));
mu.reserve(A_ij.dim(1));
double card_max = 0;
double frob_sum = 0;
double nu;
for (int k = 0; k < A_ij.dim(1); ++k){
VECTOR_int A_ij_k_ind, A_ji_k_ind;
VECTOR_double A_ij_k = middleCol(A_ij, k, A_ij_k_ind);
VECTOR_double A_ji_k = middleCol(A_ji, k, A_ji_k_ind);
double card_current = A_ij_k_ind.size() * A_ji_k_ind.size();
// exploit the sparcity of the vectors!
frob_ij.push_back(sqrt( squaredNorm(A_ij_k, A_ij_k_ind) * squaredNorm(A_ji_k, A_ji_k_ind)));
frob_sum += frob_ij[k];
card_max = card_max > card_current ? card_max : card_current;
}
nu = (frob_sum / frob_ij.size()) / sqrt(card_max);
for (int k = 0; k < A_ij.dim(1); ++k){
VECTOR_int A_ij_k_ind, A_ji_k_ind;
VECTOR_double A_ij_k = middleCol(A_ij, k, A_ij_k_ind);
VECTOR_double A_ji_k = middleCol(A_ji, k, A_ji_k_ind);
double inf_ij = infNorm(A_ij_k);
double inf_ji = infNorm(A_ji_k);
double p = 0, q = 0;
for (int l = 0; l < A_ij_k_ind.size(); ++l){
if (abs(A_ij_k(A_ij_k_ind(l))) >= nu/inf_ji) p++;
}
for (int l = 0; l < A_ji_k_ind.size(); ++l){
if (abs(A_ji_k(A_ji_k_ind(l))) >= nu/inf_ij) q++;
}
p = ( p==0 ? A_ij_k_ind.size() : p );
q = ( q==0 ? A_ji_k_ind.size() : q );
double mu_ij_k = frob_ij[k] / sqrt(p*q);
mu.push_back(mu_ij_k);
if(mu_ij_k >= filter_c){
selected_cols.push_back(k);
}
if(icntl[Controls::aug_iterative] != 0){
if (dcntl[Controls::aug_precond] < 0) {
if ((nbcols + k - n_o) % abs((int)dcntl[Controls::aug_precond]) == 0)
selected_S_columns.push_back( nbcols + k - n_o);
else
skipped_S_columns.push_back( nbcols + k - n_o);
} else {
if (mu_ij_k >= dcntl[Controls::aug_precond])
selected_S_columns.push_back( nbcols + k - n_o);
else
skipped_S_columns.push_back( nbcols + k - n_o);
}
}
}
if (selected_cols.empty()) continue;
if( icntl[Controls::aug_iterative] != 2 ) { // don't reduce the A_ij/A_ji, we just need the selected columns!
A_ij = sub_matrix(A_ij, selected_cols);
A_ji = sub_matrix(A_ji, selected_cols);
}
}
#endif //WIP
stCols[i].push_back(nbcols);
stCols[j].push_back(nbcols);
C[i].push_back(A_ij);
C[j].push_back(A_ji);
nbcols += A_ij.dim(1);
}
}
size_c = nbcols - A.dim(1);
n = nbcols;
LINFO << "Size of C : " << size_c;
#ifdef WIP
if(icntl[Controls::aug_analysis] != 0) return;
#endif // WIP
// Augment the matrices
for(size_t k = 0; k < M.size(); k++){
if(stCols[k].size() == 0) continue;
// now augment each partition!
stC[k] = stCols[k][0];
M[k] = concat_columns(M[k], C[k], stCols[k]);
M[k] = resize_columns(M[k], nbcols);
}
}
// -----------------------------------------------------------------
// Given matrix in = P.u, calculate the unitary matrix u = [1 / P].in
// and the positive P = sqrt[in.in^dag]
// We diagonalize PSq = in.in^dag using LAPACK,
// then project out its inverse square root
void polar(matrix *in, matrix *u, matrix *P) {
char V = 'V'; // Ask LAPACK for both eigenvalues and eigenvectors
char U = 'U'; // Have LAPACK store upper triangle of U.Ubar
int row, col, Npt = NCOL, stat = 0, Nwork = 2 * NCOL;
matrix PSq, Pinv, tmat;
// Convert PSq to column-major double array used by LAPACK
mult_na(in, in, &PSq);
for (row = 0; row < NCOL; row++) {
for (col = 0; col < NCOL; col++) {
store[2 * (col * NCOL + row)] = PSq.e[row][col].real;
store[2 * (col * NCOL + row) + 1] = PSq.e[row][col].imag;
}
}
// Compute eigenvalues and eigenvectors of PSq
zheev_(&V, &U, &Npt, store, &Npt, eigs, work, &Nwork, Rwork, &stat);
// Check for degenerate eigenvalues (broke previous Jacobi algorithm)
for (row = 0; row < NCOL; row++) {
for (col = row + 1; col < NCOL; col++) {
if (fabs(eigs[row] - eigs[col]) < IMAG_TOL)
printf("WARNING: w[%d] = w[%d] = %.8g\n", row, col, eigs[row]);
}
}
// Move the results back into matrix structures
// Overwrite PSq to hold the eigenvectors for projection
for (row = 0; row < NCOL; row++) {
for (col = 0; col < NCOL; col++) {
PSq.e[row][col].real = store[2 * (col * NCOL + row)];
PSq.e[row][col].imag = store[2 * (col * NCOL + row) + 1];
P->e[row][col] = cmplx(0.0, 0.0);
Pinv.e[row][col] = cmplx(0.0, 0.0);
}
P->e[row][row].real = sqrt(eigs[row]);
Pinv.e[row][row].real = 1.0 / sqrt(eigs[row]);
}
mult_na(P, &PSq, &tmat);
mult_nn(&PSq, &tmat, P);
// Now project out 1 / sqrt[in.in^dag] to find u = [1 / P].in
mult_na(&Pinv, &PSq, &tmat);
mult_nn(&PSq, &tmat, &Pinv);
mult_nn(&Pinv, in, u);
#ifdef DEBUG_CHECK
// Check unitarity of u
mult_na(u, u, &PSq);
c_scalar_add_diag(&PSq, &minus1);
for (row = 0; row < NCOL; row++) {
for (col = 0; col < NCOL; col++) {
if (cabs_sq(&(PSq.e[row][col])) > SQ_TOL) {
printf("Error getting unitary piece: ");
printf("%.4g > %.4g for [%d, %d]\n",
cabs(&(PSq.e[row][col])), IMAG_TOL, row, col);
dumpmat(in);
dumpmat(u);
dumpmat(P);
return;
}
}
}
#endif
#ifdef DEBUG_CHECK
// Check hermiticity of P
adjoint(P, &tmat);
sub_matrix(P, &tmat, &PSq);
for (row = 0; row < NCOL; row++) {
for (col = 0; col < NCOL; col++) {
if (cabs_sq(&(PSq.e[row][col])) > SQ_TOL) {
printf("Error getting hermitian piece: ");
printf("%.4g > %.4g for [%d, %d]\n",
cabs(&(PSq.e[row][col])), IMAG_TOL, row, col);
dumpmat(in);
dumpmat(u);
dumpmat(P);
return;
}
}
}
#endif
#ifdef DEBUG_CHECK
// Check that in = P.u
mult_nn(P, u, &tmat);
sub_matrix(in, &tmat, &PSq);
for (row = 0; row < NCOL; row++) {
for (col = 0; col < NCOL; col++) {
if (cabs_sq(&(PSq.e[row][col])) > SQ_TOL) {
printf("Error reconstructing initial matrix: ");
printf("%.4g > %.4g for [%d, %d]\n",
cabs(&(PSq.e[row][col])), IMAG_TOL, row, col);
dumpmat(in);
dumpmat(u);
dumpmat(P);
return;
}
}
}
#endif
}
sub_matrix_type constructor_helper(MatrixType const& matrix)
{
return sub_matrix(matrix, matrix.begin_row(), matrix.end_row(),
matrix.begin_col(), matrix.end_col());
}