void YAPCAReduce<eltype>::reconstruct_error(const ya_type1 &input,
const ya_type2 &output,
const ya_type3 &dims,
ya_type4 &rmsd_vec) {
YA_DEBUG_ERROR(input.cols()==this->high_dim() &&
output.cols()==this->low_dim(),
"Dimensions in input matrix do not match map");
YA_DEBUG_ERROR(maximum(dims)<=this->low_dim() && minimum(dims)>0,
"A reconstruction dimensionality is greater than map");
YA_DEBUG_ERROR(eigen_vectors.rows()==this->high_dim() &&
eigen_vectors.cols()>=this->low_dim(),
"Map does not match high and low dimensions");
YA_MatT new_coords=rowrep(column_means,input.rows());
rmsd_vec.setup(dims.numel());
ya_sizet dim=0;
ya_sizet dN=dims.numel();
for (ya_sizet i=0; i<dN; i++) {
while (dim<dims(i)) {
new_coords+=output(":",dim)*transpose(eigen_vectors(":",dim));
dim++;
}
rmsd_vec(i)=rmsd(input,new_coords);
}
}
void YAPCAReduce<eltype>::reverse_map(const ya_type1 &input,
ya_type2 &output) const {
YA_DEBUG_ERROR(input.cols()==this->low_dim(),
"Dimensions in input matrix do not match map");
YA_DEBUG_ERROR(eigen_vectors.rows()==this->high_dim() &&
eigen_vectors.cols()==this->low_dim(),
"Map does not match high and low dimensionalities");
output=input*transpose(eigen_vectors)+rowrep(column_means,input.rows());
}
void YAPCAReduce<eltype>::forward_map(const ya_type1 &input,
ya_type2 &output) const {
YA_DEBUG_ERROR(input.cols()==this->high_dim(),
"Dimensions in input matrix do not match map");
YA_DEBUG_ERROR(eigen_vectors.rows()==this->high_dim() &&
eigen_vectors.cols()==this->low_dim(),
"Map does not match high and low dimensionalities");
output=YA_MatT(input-rowrep(column_means,input.rows()))*eigen_vectors;
}
void point_pca_ep(const YA_BaseT &input, const eltype epsilon,
const ya_type2 &dims, EigenOptions &eigopts, YA_RowD &vmean,
YA_RowD &vmin, YA_RowD &vmax, YA_RowD &vstd,
const int verbose) {
YA_DEBUG_ERROR(epsilon>0,
"Epsilon must be greater than 0 for point_pca");
int me, num_procs;
ya_mpi_info(me,num_procs);
YA_ColI counts, starts;
ya_mpi_counts(input.rows(),num_procs,counts,starts);
eigopts.dim(input.cols());
YA_MatT output;
_point_pca_ep(input,epsilon,eigopts,output,true,verbose,me,num_procs,
counts,starts);
if (input.cols()!=dims.numel() && counts[me]>0)
output=YA_MatT(output(":",dims-1));
#ifdef YA_MPI
if (num_procs>1)
mpi_vstat(output,dims.numel(),vmin,vmax,vmean,vstd);
else
#endif
vstat(output,vmin,vmax,vmean,vstd);
}
void point_pca_ep(const YA_BaseT &input, const eltype epsilon,
const ya_type2 &dims, EigenOptions &eigopts,
ya_type3 &output, const int verbose_out) {
YA_DEBUG_ERROR(epsilon>0,
"Epsilon must be greater than 0 for point_pca");
int me, num_procs;
ya_mpi_info(me,num_procs);
YA_ColI counts, starts;
ya_mpi_counts(input.rows(),num_procs,counts,starts);
eigopts.dim(input.cols());
_point_pca_ep(input,epsilon,eigopts,output,true,verbose_out,me,num_procs,
counts,starts);
if (num_procs>1) {
YA_MatRMT piece_t;
#ifdef YA_MPI
if (counts[me]>0)
piece_t=output(":",dims-1);
ya_mpi_concat_rows(piece_t,output,dims.numel(),me,num_procs,counts,starts);
#endif
} else if (input.cols()!=dims.numel())
output=YA_MatT(output(":",dims-1));
}
int YAPCAReduce<eltype>::find_map(const ya_type1 &input,
ya_type2 &output, ya_sizet dim,
EigenOptions &eigopts) {
// Target dimensionality
YA_DEBUG_ERROR(dim<=input.cols(),
"Not enough dimensions in input matrix");
eigopts.dim(dim);
this->_high_dim=input.cols();
this->_low_dim=dim;
// Column center the matrix
column_means=sum(input)/static_cast<eltype>(input.rows());
YA_MatT input_cen(input.rows(),input.cols());
ya_sizet iC=input.cols();
for (ya_sizet i=0; i<iC; i++)
input_cen(":",i)=input(":",i)-column_means(i);
// Calculate covarience matrix
#ifdef YA_PROGMETER
YA_TimeKeeper tk;
YA_ProgMeter pm;
if (this->_verbose) {
pm.start("Computing Forward and Reverse Maps:", 70, 0, false);
tk.start();
}
#endif
VM_SymMat covmat=input_cen.T()*input_cen;
eigs(covmat,eigen_vectors,this->eigen_values,eigopts);
#ifdef YA_PROGMETER
if (this->_verbose) {
pm.finish();
tk.end();
cerr << "Done. " << tk << ".\n";
}
#endif
// Calculate the reduced output
output=input_cen*eigen_vectors;
return 0;
}
void _point_pca(const YA_BaseT &input, const ya_sizet k,
EigenOptions &eigopts, ya_type2 &output, const bool residual,
const int verbose_out, const int me, const int num_procs,
const YA_ColI &counts, const YA_ColI &starts) {
YA_DEBUG_ERROR(k>=0 && k<input.rows(),
"More neighbors than datapoints for point_pca");
int verbose=verbose_out;
#ifdef YA_MPI
if (me!=0)
verbose=0;
else if (num_procs>1 && verbose>1)
verbose=1;
#ifdef YA_PROGMETER
if (verbose)
cout << "Performing point-PCA on " << num_procs << " processors.\n";
#endif
#endif
YA_MatI neighbors;
YA_MatD dists;
if (num_procs==1) {
kneighbors(input,k,neighbors,dists,verbose);
neighbors=YA_MatI(concat(vm_cast<ya_sizet>::sc(vmcount(input.rows()).T()),
neighbors));
} else if (counts[me]>0)
kneighbors(input(vmcount(starts[me],":",starts[me]+counts[me]-1),":"),
input,k+1,neighbors,dists,verbose);
#ifdef YA_MPI
if (num_procs>1 && verbose_out>1) {
#ifdef YA_PROGMETER
YA_TimeKeeper mtk;
if (verbose>0) {
cerr << "Waiting on other procs...";
mtk.start();
}
MPI_Barrier(MPI_COMM_WORLD);
if (verbose>0) {
mtk.end();
cerr << "Done. " << mtk << endl;
}
#endif
if (me==0) cerr << "Neighbor Distance Stats:\n";
eltype dmin, dmax, dmean, dstd;
mpi_vstat(dists(":",vmcount(k)+1),dmin,dmax,dmean,dstd);
if (me==0)
cerr << " Min: " << dmin << " Max: " << dmax << endl
<< " Mean: " << dmean << " Std: " << dstd << endl << endl;
}
#endif
dists.clear();
output.setup(counts[me],input.cols());
#ifdef YA_PROGMETER
YA_TimeKeeper tk;
YA_ProgMeter pm;
if (verbose) {
tk.start();
pm.start("Performing Point PCA:",70,counts[0],false);
}
#endif
#pragma omp parallel
{
YA_RowT column_means;
YA_MatT input_cen;
VM_SymMat covmat;
YA_RowT eigens;
#pragma omp for
for (ya_sizet i=0; i<counts[me]; i++) {
// Column center the matrix
column_means=sum(input(neighbors(i,":"),":")/static_cast<eltype>(k+1));
input_cen=input(neighbors(i,":"),":")-rowrep(column_means,k+1);
covmat=input_cen.T()*input_cen;
eigs(covmat,eigens,eigopts);
output(i,":")=eigens;
#ifdef YA_PROGMETER
if (verbose)
pm.iterate();
#endif
}
}
neighbors.clear();
#ifdef YA_PROGMETER
if (verbose) {
pm.finish();
tk.end();
cerr << "Done. " << tk << ".\n";
}
YA_TimeKeeper mtk;
if (num_procs>1)
if (verbose>0) {
cerr << "Waiting on other procs...";
mtk.start();
}
#endif
#ifdef YA_MPI
if (num_procs>1)
MPI_Barrier(MPI_COMM_WORLD);
#endif
#ifdef YA_PROGMETER
if (num_procs>1 && verbose>0) {
mtk.end();
cerr << "Done. " << mtk << endl;
}
#endif
if (residual && counts[me]>0) {
YA_VecT totals=sum(output.T());
output=output.dot_div(colrep(totals,output.cols()));
ya_sizet iC=output.cols();
for (ya_sizet i=1; i<iC-1; i++)
output(":",i)+=output(":",i-1);
output(":",iC-1)=1.0;
output=1.0-output;
}
}
void _point_pca_ep(const YA_BaseT &input, const eltype epsilon,
EigenOptions &eigopts, vmtype2 &output,
const bool residual, const int verbose_out, const int me,
const int num_procs, const YA_ColI &counts,
const YA_ColI &starts) {
YA_DEBUG_ERROR(epsilon>0,
"Epsilon must be greater than 0 for point_pca");
int verbose=verbose_out;
#ifdef YA_MPI
if (me!=0)
verbose=0;
else if (num_procs>1 && verbose>1)
verbose=1;
#ifdef YA_PROGMETER
if (verbose)
cout << "Performing point-PCA on " << num_procs << " processors.\n";
#endif
#endif
vector<YA_DynI> neighbors;
vector<YA_Dyn<eltype> > dists;
if (num_procs==1) {
eneighbors(input,epsilon,neighbors,dists,verbose);
int iR=input.rows();
for (ya_sizet i=0; i<iR; i++)
neighbors[i].push_back(i);
} else if (counts[me]>0)
eneighbors(input(vmcount(starts[me],":",starts[me]+counts[me]-1),":"),
input,epsilon,neighbors,dists,verbose);
dists.clear();
#ifdef YA_MPI
if (num_procs>1 && verbose_out>1) {
#ifdef YA_PROGMETER
YA_TimeKeeper mtk;
if (verbose>0) {
cerr << "Waiting on other procs...";
mtk.start();
}
MPI_Barrier(MPI_COMM_WORLD);
if (verbose>0) {
mtk.end();
cerr << "Done. " << mtk << endl;
}
#endif
if (me==0) cerr << "Neighbor Counts Stats:\n";
ya_sizet dmin, dmax;
eltype dmean, dstd;
ya_sizet n=neighbors.size();
YA_ColI ncounts;
if (n>0)
ncounts.setup(n);
for (ya_sizet i=0; i<n; i++)
ncounts(i)=neighbors[i].numel()-1;
mpi_vstat(ncounts,dmin,dmax,dmean,dstd);
if (me==0)
cerr << " Min: " << dmin << " Max: " << dmax << endl
<< " Mean: " << dmean << " Std: " << dstd << endl << endl;
}
#endif
output.setup(counts[me],input.cols());
#ifdef YA_PROGMETER
YA_TimeKeeper tk;
YA_ProgMeter pm;
if (verbose) {
tk.start();
pm.start("Performing Point PCA:",70,counts[0],false);
}
#endif
#pragma omp parallel
{
YA_RowT column_means;
YA_MatT input_cen;
VM_SymMat covmat;
YA_RowT eigens;
ya_sizet NN=counts[me];
#pragma omp for
for (ya_sizet i=0; i<NN; i++) {
ya_sizet k=neighbors[i].numel();
column_means=sum(input(neighbors[i],":")/static_cast<eltype>(k));
input_cen=input(neighbors[i],":")-rowrep(column_means,k);
covmat=input_cen.T()*input_cen;
eigs(covmat,eigens,eigopts);
output(i,":")=eigens;
#ifdef YA_PROGMETER
if (verbose)
pm.iterate();
#endif
}
}
neighbors.clear();
#ifdef YA_PROGMETER
if (verbose) {
pm.finish();
tk.end();
cerr << "Done. " << tk << ".\n";
}
YA_TimeKeeper mtk;
if (num_procs>1 && verbose) {
cerr << "Waiting on other procs...";
mtk.start();
}
#endif
#ifdef YA_MPI
if (num_procs>1)
MPI_Barrier(MPI_COMM_WORLD);
#endif
#ifdef YA_PROGMETER
if (num_procs>1 && verbose>0) {
mtk.end();
cerr << "Done. " << mtk << endl;
}
#endif
if (residual && counts[me]>0) {
YA_VecT totals=sum(output.T());
output=output.dot_div(colrep(totals,output.cols()));
ya_sizet iC=output.cols();
for (ya_sizet i=1; i<iC-1; i++)
output(":",i)+=output(":",i-1);
output(":",iC-1)=1.0;
output=1.0-output;
}
}
