bool NnlsHals(const MatrixType<T>& A,
DenseMatrix<T>& W,
DenseMatrix<T>& H,
const T tol,
const bool verbose,
const unsigned int max_iter)
{
unsigned int n = A.Width();
unsigned int k = W.Width();
if (static_cast<unsigned int>(W.Height()) != static_cast<unsigned int>(A.Height()))
throw std::logic_error("NnlsHals: W and A must have identical height");
if (static_cast<unsigned int>(H.Width()) != static_cast<unsigned int>(A.Width()))
throw std::logic_error("NnlsHals: H and A must have identical width");
if (H.Height() != W.Width())
throw std::logic_error("NnlsHals: non-conformant W and H");
DenseMatrix<T> WtW(k, k), WtA(k, n), WtWH_r(1, n), gradH(k, n);
if (verbose)
std::cout << "\nRunning NNLS solver..." << std::endl;
// compute W'W and W'A for the normal equations
Gemm(TRANSPOSE, NORMAL, T(1.0), W, W, T(0.0), WtW);
Gemm(TRANSPOSE, NORMAL, T(1.0), W, A, T(0.0), WtA);
bool success = false;
T pg0 = T(0), pg;
for (unsigned int i=0; i<max_iter; ++i)
{
// compute the new matrix H
UpdateH_Hals(H, WtWH_r, WtW, WtA);
// compute gradH = WtW*H - WtA
Gemm(NORMAL, NORMAL, T(1.0), WtW, H, T(0.0), gradH);
Axpy( T(-1.0), WtA, gradH);
// compute progress metric
if (0 == i)
{
pg0 = ProjectedGradientNorm(gradH, H);
if (verbose)
ReportProgress(i+1, T(1.0));
continue;
}
else
{
pg = ProjectedGradientNorm(gradH, H);
}
if (verbose)
ReportProgress(i+1, pg/pg0);
// check progress vs. desired tolerance
if (pg < tol * pg0)
{
success = true;
NormalizeAndScale<T>(W, H);
break;
}
}
if (!success)
std::cerr << "NNLS solver reached iteration limit." << std::endl;
return success;
}
mat nnls_solver_with_missing(const mat & A, const mat & W, const mat & W1, const mat & H2, const umat & mask,
const double & eta, const double & beta, int max_iter, double rel_tol, int n_threads)
{
// A = [W, W1, W2] [H, H1, H2]^T.
// Where A may have missing values
// Note that here in the input W = [W, W2]
// compute x = [H, H1]^T given W, W2
// A0 = W2*H2 is empty when H2 is empty (no partial info in H)
// Return: x = [H, H1]
int n = A.n_rows, m = A.n_cols;
int k = W.n_cols - H2.n_cols;
int kW = W1.n_cols;
int nH = k+kW;
mat x(nH, m, fill::zeros);
if (n_threads < 0) n_threads = 0;
bool is_masked = !mask.empty();
#pragma omp parallel for num_threads(n_threads) schedule(dynamic)
for (int j = 0; j < m; j++)
{
// break if all entries of col_j are masked
if (is_masked && arma::all(mask.col(j)))
continue;
uvec non_missing = find_finite(A.col(j));
mat WtW(nH, nH); // WtW
update_WtW(WtW, W.rows(non_missing), W1.rows(non_missing), H2);
if (beta > 0) WtW += beta;
if (eta > 0) WtW.diag() += eta;
mat mu(nH, 1); // -WtA
uvec jv(1);
jv(0) = j;
//non_missing.t().print("non_missing = ");
//std::cout << "1.1" << std::endl;
if (H2.empty())
update_WtA(mu, W.rows(non_missing), W1.rows(non_missing), H2, A.submat(non_missing, jv));
else
update_WtA(mu, W.rows(non_missing), W1.rows(non_missing), H2.rows(j, j), A.submat(non_missing, jv));
//std::cout << "1.5" << std::endl;
vec x0(nH);
double tmp;
int i = 0;
double err1, err2 = 9999;
do {
x0 = x.col(j);
err1 = err2;
err2 = 0;
for (int l = 0; l < nH; l++)
{
if (is_masked && mask(l,j) > 0) continue;
tmp = x(l,j) - mu(l,0) / WtW(l,l);
if (tmp < 0) tmp = 0;
if (tmp != x(l,j))
{
mu.col(0) += (tmp - x(l,j)) * WtW.col(l);
}
x(l,j) = tmp;
tmp = std::abs(x(l,j) - x0(l));
if (tmp > err2) err2 = tmp;
}
} while(++i < max_iter && std::abs(err1 - err2) / (err1 + 1e-9) > rel_tol);
}
return x;
}
