T OneNorm(const SparseMatrix<T>& A)
{
// compute the max absolute column sum
const unsigned int* cols_a = A.LockedColBuffer();
const T* data_a = A.LockedDataBuffer();
const unsigned int width_a = A.Width();
T max_col_sum = T(0), col_sum;
for (unsigned int c=0; c != width_a; ++c)
{
unsigned int start = cols_a[c];
unsigned int end = cols_a[c+1];
col_sum = T(0);
for (unsigned int offset=start; offset != end; ++offset)
{
T val = fabs(data_a[offset]);
col_sum += val;
}
if (col_sum > max_col_sum)
max_col_sum = col_sum;
}
return max_col_sum;
}
T FrobeniusNorm(const SparseMatrix<T>& A)
{
// compute the sum of the absolute value squared of each element
const T* data_a = A.LockedDataBuffer();
const unsigned int size_a = A.Size();
T sum = T(0);
for (unsigned int i=0; i != size_a; ++i)
{
T val = fabs(data_a[i]);
sum += val*val;
}
return sqrt(sum);
}
T MaxNorm(const SparseMatrix<T>& A)
{
// find max( |A_ij| )
const T* data_a = A.LockedDataBuffer();
const unsigned int size_a = A.Size();
T max_norm = T(0);
for (unsigned int i=0; i != size_a; ++i)
{
T val = fabs(data_a[i]);
if (val > max_norm)
max_norm = val;
}
return max_norm;
}
bool WriteMatrixMarketFile(const std::string& file_path,
const SparseMatrix<T>& A,
const unsigned int precision)
{
// Write a MatrixMarket file with no comments. Note that the
// MatrixMarket format uses 1-based indexing for rows and columns.
std::ofstream outfile(file_path);
if (!outfile)
return false;
unsigned int height = A.Height();
unsigned int width = A.Width();
unsigned int nnz = A.Size();
// write the 'banner'
outfile << MM_BANNER << " matrix coordinate real general" << std::endl;
// write matrix dimensions and number of nonzeros
outfile << height << " " << width << " " << nnz << std::endl;
outfile << std::fixed;
outfile.precision(precision);
const unsigned int* cols_a = A.LockedColBuffer();
const unsigned int* rows_a = A.LockedRowBuffer();
const T* data_a = A.LockedDataBuffer();
unsigned int width_a = A.Width();
for (unsigned int c=0; c != width_a; ++c)
{
unsigned int start = cols_a[c];
unsigned int end = cols_a[c+1];
for (unsigned int offset=start; offset != end; ++offset)
{
unsigned int r = rows_a[offset];
T val = data_a[offset];
outfile << r+1 << " " << c+1 << " " << val << std::endl;
}
}
outfile.close();
return true;
}
void Print(const SparseMatrix<T>& M)
{
// Print a SparseMatrix to the screen.
const unsigned int* col_buf = M.LockedColBuffer();
const unsigned int* row_buf = M.LockedRowBuffer();
const T* buf = M.LockedDataBuffer();
if (0 == M.Size())
{
std::cout << "Matrix is empty." << std::endl;
return;
}
for (unsigned int c=0; c != M.Width(); ++c)
{
unsigned int start = col_buf[c];
unsigned int end = col_buf[c+1];
for (unsigned int offset=start; offset != end; ++offset)
{
assert(offset >= 0);
assert(offset < M.Size());
unsigned int row_index = row_buf[offset];
T data = buf[offset];
std::cout << "(" << row_index << ", " << c << "): " << data << std::endl;
}
}
std::cout << "Col indices: "; std::cout.flush();
for (unsigned int i=0; i != M.Width(); ++i)
std::cout << col_buf[i] << ", ";
std::cout << col_buf[M.Width()] << std::endl;
std::cout << "Row indices: "; std::cout.flush();
for (unsigned int i=0; i != M.Size(); ++i)
std::cout << row_buf[i] << ", ";
std::cout << std::endl;
std::cout << "Data: "; std::cout.flush();
for (unsigned int i=0; i != M.Size(); ++i)
std::cout << buf[i] << ", ";
std::cout << std::endl;
}
//-----------------------------------------------------------------------------
void Nmf(const unsigned int kval,
const Algorithm algorithm,
const std::string& csv_file_w,
const std::string& csv_file_h)
{
if (!matrix_loaded)
throw std::logic_error("smallk error (NMF): no matrix has been loaded.");
if (max_iter < min_iter)
throw std::logic_error("smallk error (NMF): min_iterations exceeds max_iterations.");
if (0 == kval)
throw std::logic_error("smallk error (NMF): k must be greater than 0.");
// Check the sizes of matrix W(m, k) and matrix H(k, n) and make sure
// they don't overflow Elemental's default signed int index type.
if (!SizeCheck<int>(m, kval))
throw std::logic_error("smallk error (Nmf): mxk matrix W is too large.");
if (!SizeCheck<int>(kval, n))
throw std::logic_error("smallk error (Nmf): kxn matrix H is too large.");
k = kval;
// convert to the 'NmfAlgorithm' type in nmf.hpp
switch (algorithm)
{
case Algorithm::MU:
nmf_opts.algorithm = NmfAlgorithm::MU;
break;
case Algorithm::HALS:
nmf_opts.algorithm = NmfAlgorithm::HALS;
break;
case Algorithm::RANK2:
nmf_opts.algorithm = NmfAlgorithm::RANK2;
break;
case Algorithm::BPP:
nmf_opts.algorithm = NmfAlgorithm::BPP;
break;
default:
throw std::logic_error("smallk error (NMF): unknown NMF algorithm.");
}
// set k == 2 for Rank2 algorithm
if (NmfAlgorithm::RANK2 == nmf_opts.algorithm)
k = 2;
ldim_w = m;
ldim_h = k;
if (buf_w.size() < m*k)
buf_w.resize(m*k);
if (buf_h.size() < k*n)
buf_h.resize(k*n);
// initialize matrices W and H
bool ok;
unsigned int height_w = m, width_w = k, height_h = k, width_h = n;
cout << "Initializing matrix W..." << endl;
if (csv_file_w.empty())
ok = RandomMatrix(&buf_w[0], ldim_w, m, k, rng);
else
ok = LoadDelimitedFile(buf_w, height_w, width_w, csv_file_w);
if (!ok)
{
std::ostringstream msg;
msg << "smallk error (Nmf): load failed for file ";
msg << "\"" << csv_file_w << "\"";
throw std::runtime_error(msg.str());
}
if ( (height_w != m) || (width_w != k))
{
cerr << "\tdimensions of matrix W are " << height_w
<< " x " << width_w << endl;
cerr << "\texpected " << m << " x " << k << endl;
throw std::logic_error("smallk error (Nmf): non-conformant matrix W.");
}
cout << "Initializing matrix H..." << endl;
if (csv_file_h.empty())
ok = RandomMatrix(&buf_h[0], ldim_h, k, n, rng);
else
ok = LoadDelimitedFile(buf_h, height_h, width_h, csv_file_h);
if (!ok)
{
std::ostringstream msg;
msg << "smallk error (Nmf): load failed for file ";
msg << "\"" << csv_file_h << "\"";
throw std::runtime_error(msg.str());
}
if ( (height_h != k) || (width_h != n))
{
cerr << "\tdimensions of matrix H are " << height_h
<< " x " << width_h << endl;
cerr << "\texpected " << k << " x " << n << endl;
throw std::logic_error("smallk error (Nmf): non-conformant matrix H.");
}
// The ratio of projected gradient norms doesn't seem to work very well
// with MU. We frequently observe a 'leveling off' behavior and the
// convergence is even slower than usual. So for MU use the relative
// change in the Frobenius norm of W as the stopping criterion, which
// always seems to behave well, even though it is on shaky theoretical
// ground.
if (NmfAlgorithm::MU == nmf_opts.algorithm)
nmf_opts.prog_est_algorithm = NmfProgressAlgorithm::DELTA_FNORM;
else
nmf_opts.prog_est_algorithm = NmfProgressAlgorithm::PG_RATIO;
nmf_opts.tol = nmf_tolerance;
nmf_opts.height = m;
nmf_opts.width = n;
nmf_opts.k = k;
nmf_opts.min_iter = min_iter;
nmf_opts.max_iter = max_iter;
nmf_opts.tolcount = 1;
nmf_opts.max_threads = max_threads;
nmf_opts.verbose = true;
nmf_opts.normalize = true;
// display all params to user
PrintNmfOpts(nmf_opts);
NmfStats stats;
Result result;
if (is_sparse)
{
result = NmfSparse(nmf_opts,
A.Height(), A.Width(), A.Size(),
A.LockedColBuffer(),
A.LockedRowBuffer(),
A.LockedDataBuffer(),
&buf_w[0], ldim_w,
&buf_h[0], ldim_h,
stats);
}
else
{
result = Nmf(nmf_opts,
&buf_a[0], ldim_a,
&buf_w[0], ldim_w,
&buf_h[0], ldim_h,
stats);
}
cout << "Elapsed wall clock time: ";
cout << ElapsedTime(stats.elapsed_us) << endl;
cout << endl;
if (Result::OK != result)
throw std::runtime_error("smallk error (Nmf): NMF solver failure.");
// write the computed W and H factors to disk
std::string outfile_w, outfile_h;
if (outdir.empty())
{
outfile_w = DEFAULT_FILENAME_W;
outfile_h = DEFAULT_FILENAME_H;
}
else
{
outfile_w = outdir + DEFAULT_FILENAME_W;
outfile_h = outdir + DEFAULT_FILENAME_H;
}
cout << "Writing output files..." << endl;
if (!WriteDelimitedFile(&buf_w[0], ldim_w, m, k, outfile_w, outprecision))
throw std::runtime_error("smallk error (Nmf): could not write W result.");
if (!WriteDelimitedFile(&buf_h[0], ldim_h, k, n, outfile_h, outprecision))
throw std::runtime_error("smallk error (Nmf): could not write H result.");
}