// backward substitution on the linear system U*X = B, filling in an existing Matrix X
int BackSub(const Matrix& U, Matrix& X, const Matrix& B) {
// check that matrix sizes match
if (U.Rows() != B.Rows() || U.Rows() != U.Cols() ||
B.Cols() != X.Cols() || X.Rows() != U.Rows()) {
cerr << "BackSub error, incompatible matrix/vector dimensions\n";
cerr << " Matrix is " << U.Rows() << " x " << U.Cols()
<< ", rhs is " << B.Rows() << " x " << B.Cols()
<< ", solution is " << X.Rows() << " x " << X.Cols() << endl;
return 1;
}
// copy B into X
X.Copy(B);
// analyze matrix for magnitude
double Umax = InfNorm(U);
// perform column-oriented Backward Substitution algorithm
for (long int j=U.Rows()-1; j>=0; j--) {
// check for nonzero matrix diagonal
if (fabs(U.data[j][j]) < STOL*Umax) {
cerr << "BackSub error: numerically singular matrix!\n";
return 1;
}
// solve for this row of solution
for (long int k=0; k<X.Cols(); k++)
X.data[k][j] /= U.data[j][j];
// update all remaining rhs
for (long int k=0; k<X.Cols(); k++)
for (long int i=0; i<j; i++)
X.data[k][i] -= U.data[j][i]*X.data[k][j];
}
// return success
return 0;
}
// forward substitution on the linear system L*X = B, filling in the input Matrix X
// L and B remain unchanged in this operation; X holds the result
// B and X may have multiple columns
int FwdSub(const Matrix& L, Matrix& X, const Matrix& B) {
// check that matrix sizes match
if (L.Rows() != B.Rows() || L.Rows() != L.Cols() ||
B.Cols() != X.Cols() || X.Rows() != L.Rows()) {
cerr << "FwdSub error, illegal matrix/vector dimensions\n";
cerr << " Matrix is " << L.Rows() << " x " << L.Cols()
<< ", rhs is " << B.Rows() << " x " << B.Cols()
<< ", solution is " << X.Rows() << " x " << X.Cols() << endl;
return 1;
}
// copy B into X
X.Copy(B);
// analyze matrix magnitude
double Lmax = InfNorm(L);
// perform column-oriented Forwards Substitution algorithm
for (long int j=0; j<L.Rows(); j++) {
// check for nonzero matrix diagonal
if (fabs(L.data[j][j]) < STOL*Lmax) {
cerr << "FwdSub error: singular matrix!\n";
return 1;
}
// solve for this row of solution
for (long int k=0; k<X.Cols(); k++)
X.data[k][j] /= L.data[j][j];
// update all remaining rhs
for (long int k=0; k<X.Cols(); k++)
for (long int i=j+1; i<L.Rows(); i++)
X.data[k][i] -= L.data[j][i]*X.data[k][j];
}
// return success
return 0;
}
int main( int argc, char** argv ) {
if ( argc == 6 || argc == 7 ) {
const char* config = argv[1];
const char* model = argv[2];
const char* data = argv[3];
int order = atoi( argv[4] );
int batch = atoi( argv[5] );
float lnZ = 0.0f;
if ( argc > 6 ) {
lnZ = atof( argv[6] );
ASSERT( lnZ > 0.0f );
}
BatchConstructor bc( data, order, batch, 0, false );
Network network( config );
network.LoadParam( model );
Matrix placeholder;
Matrix buffer;
double loss = 0.0;
int nExample = 0;
while( bc.HasNext() ) {
bc.PrepareNext();
const SubMatrix input = bc.GetInput();
const SubMatrix target = bc.GetTarget();
ExtraInfo info( input.Rows(),
bc.GetSentenceLength(),
false,
target, // actually not used
placeholder ); // not used either
network.Prepare( info );
const MatrixBase& output = network.Compute( input );
if ( lnZ == 0.0f ) {
loss += output.Xent( target );
nExample += output.Rows();
}
else {
buffer.Reshape( output.Rows(), output.Columns() );
buffer.Copy( output );
buffer.Shift( -lnZ );
buffer.Exp( buffer );
loss += buffer.Xent( target );
nExample += output.Rows();
}
}
double avgLoss = loss / (double)nExample;
double ppl = exp(avgLoss);
cout << right
<< CurrentTime() << ") average cross-entropy loss of " << nExample
<< " examples: " << KGRN << avgLoss << KNRM << " or "
<< KGRN << ppl << KNRM << " in PPL " << endl;
return EXIT_SUCCESS;
}
else {
cerr << KRED;
cerr << "Usag: " << argv[0] << " <config> <model> <numeric-data> <order> <batch-size> [lnZ]" << endl;
cerr << " <config> : network configuration" << endl;
cerr << " <model> : trained model corresponding to config" << endl;
cerr << " <numeric-data> : data set to be evaluated, in numeric form" << endl;
cerr << " <order> : length of context window" << endl;
cerr << " <batch-size> : mini-batch size" << endl;
cerr << " [lnZ] : optional, if set, softmax is not applied" << endl;
cerr << KNRM;
exit( EXIT_FAILURE );
}
}