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//////////////////////////////////////////////////////////////////
// //
// PLINK (c) 2005-2009 Shaun Purcell //
// //
// This file is distributed under the GNU General Public //
// License, Version 2. Please see the file COPYING for more //
// details //
// //
//////////////////////////////////////////////////////////////////
#include <iostream>
#include <iomanip>
#include <fstream>
#include <cmath>
#include "plink.h"
#include "options.h"
#include "helper.h"
#include "stats.h"
#ifdef WITH_LAPACK
#include "lapackf.h"
#endif
void Plink::generateMDS()
{
// Take this solution, (i)
// 1) Average clusters to generate points
// 2) Perform multidimensional scaling
// 3) Dump information into Haploview-friendly file for visualisation
string f = par::output_file_name + ".mds";
printLOG("Writing MDS solution to [ " + f + " ] \n");
if (par::mds_by_individual)
printLOG("MDS plot of individuals (not clusters)\n");
else
printLOG("MDS plot of clusters (not individuals)\n");
vector< vector<int> > cl;
// Re-Populate the cl cluster information list, if need be
if ( ! par::mds_by_individual )
{
set<int> clnum;
for (int i=0; i<n; i++)
{
if ( sample[i]->sol >= 0 )
clnum.insert( sample[i]->sol );
}
cl.resize( clnum.size() );
for (int i=0; i<n; i++)
{
if ( sample[i]->sol >= 0 )
cl[ sample[i]->sol ].push_back(i);
}
}
int nc;
if (par::mds_by_individual)
nc = n;
else
nc = cl.size();
// Now we have built the between-cluster distance matrix (which will
// typically be smaller than the between-individual matrix, we
// should be able to apply visualisation (note: for samples of under
// 5000 individuals, should be okay to apply standard per-individual
// clustering
// B = - 1/2 Z D^2 Z
//
// where Z = I - 1/n U
//
// I identity matrix (n x n)
// U is unit matix (n x n)
// A double-centered matrix B
// b_ij = -1/2 [ d^2_ij - d^2_.j - d^2_i. + d^2_.. ]
#ifdef WITH_LAPACK
// Full, symm matrix (1D format)
vector_t D(nc*nc,0);
for (int c1 = 0 ; c1 < nc ; c1++)
for (int c2 = c1 ; c2 < nc ; c2++)
{
if (c1==c2) D[ c1 + c2*nc ]=0;
else
{
if (par::mds_by_individual)
{
if (c1>c2)
D[c1 + c2*nc] = D[ c2 + c1*nc ] = (1-mdist[c1][c2]) * (1-mdist[c1][c2]);
else
D[c1 + c2*nc] = D[ c2 + c1*nc ] = (1-mdist[c2][c1]) * (1-mdist[c2][c1]);
}
else
{
// Average over all pairs between cluster
double avg = 0;
for (int i1=0; i1<cl[c1].size(); i1++)
for (int i2=0; i2<cl[c2].size(); i2++)
{
if ( cl[c1][i1] > cl[c2][i2] )
avg += 1-mdist[cl[c1][i1]][cl[c2][i2]];
else
avg += 1-mdist[cl[c2][i2]][cl[c1][i1]];
}
avg /= cl[c1].size() * cl[c2].size();
// Symmetric matrix of squared distances
D[c1 + c2*nc] = D[c2 + c1*nc] = avg * avg;
}
}
}
double mean = 0;
vector_t M(nc,0);
for (int c1 = 0 ; c1 < nc ; c1++)
{
for (int c2 = 0 ; c2 < nc ; c2++)
{
M[c1] += D[c1 + c2*nc];
}
M[c1] /= (double)nc;
mean += M[c1];
}
mean /= (double)nc;
// For each element for D, double center
for (int c1 = 0 ; c1 < nc ; c1++)
for (int c2 = c1 ; c2 < nc ; c2++)
D[c1 + c2*nc] = D[c2 + c1*nc] = - 0.5 * ( D[c1 + c2*nc] - M[c1] - M[c2] + mean );
// Calculate only required eigen-vectors
vector_t eigenvalue(nc);
matrix_t eigenvector;
sizeMatrix(eigenvector,nc,nc);
//svd_lapack(n,D,eigenvalue,eigenvector);
eigen_lapack(n,D,eigenvalue,eigenvector);
// cout << "EVAL = \n";
// display(eigenvalue);
// cout << "EVEC = \n";
// display(eigenvector);
#else
// Not using LAPACK
matrix_t D;
sizeMatrix(D,nc,nc);
for (int c1 = 0 ; c1 < nc ; c1++)
for (int c2 = c1 ; c2 < nc ; c2++)
{
if (c1==c2) D[c1][c2]=0;
else
{
if (par::mds_by_individual)
{
if (c1>c2)
D[c1][c2] = D[c2][c1] = (1-mdist[c1][c2]) * (1-mdist[c1][c2]);
else
D[c1][c2] = D[c2][c1] = (1-mdist[c2][c1]) * (1-mdist[c2][c1]);
}
else
{
// Average over all pairs between cluster
double avg = 0;
for (int i1=0; i1<cl[c1].size(); i1++)
for (int i2=0; i2<cl[c2].size(); i2++)
{
if ( cl[c1][i1] > cl[c2][i2] )
avg += 1-mdist[cl[c1][i1]][cl[c2][i2]];
else
avg += 1-mdist[cl[c2][i2]][cl[c1][i1]];
}
avg /= cl[c1].size() * cl[c2].size();
// Symmetric matrix of squared distances
D[c1][c2] = D[c2][c1] = avg * avg;
}
}
}
double mean = 0;
vector_t M(nc,0);
for (int c1 = 0 ; c1 < nc ; c1++)
{
for (int c2 = 0 ; c2 < nc ; c2++)
{
M[c1] += D[c1][c2];
}
M[c1] /= (double)nc;
mean += M[c1];
}
mean /= (double)nc;
// For each element for D, double center
for (int c1 = 0 ; c1 < nc ; c1++)
for (int c2 = c1 ; c2 < nc ; c2++)
D[c1][c2] = D[c2][c1] = - 0.5 * ( D[c1][c2] - M[c1] - M[c2] + mean );
vector_t eigenvalue(nc);
matrix_t eigenvector;
sizeMatrix(eigenvector,nc,nc);
// cout << "*---------\n";
// for (int i=0; i<nc; i++)
// {
// for (int j=0; j<nc; j++)
// cout << D[i][j] << " ";
// cout << "\n";
// }
// cout << "*---------\n";
bool flag = svd(D,eigenvalue,eigenvector);
// cout << "EVAL = \n";
// display(eigenvalue);
// cout << "EVEC = \n";
// display(eigenvector);
#endif
/////////////////////////////////////////////////////
// Done all SVD calculation, return to normal code
// Take the e largest eignevectors
map<double,int> emap;
for (int i=0; i<nc; i++)
emap.insert(make_pair( eigenvalue[i] , i ) );
map<double,int>::reverse_iterator e = emap.rbegin();
int inc = par::cluster_mds_dim;
vector<int> elist;
while ( e != emap.rend() && inc > 0 )
{
elist.push_back(e->second);
inc--;
e++;
}
if (par::cluster_mds_dim < 1)
par::cluster_mds_dim = 1;
if (par::cluster_mds_dim > nc)
par::cluster_mds_dim = nc;
if ( elist.size() != par::cluster_mds_dim )
{
error("Internal problem extracting MDS solution\n");
elist.resize(par::cluster_mds_dim);
}
// Sqrt(D)
for (int i=0; i<nc; i++)
eigenvalue[i] = eigenvalue[i] >= 0 ? sqrt(eigenvalue[i]) : 0 ;
// Make solution
// EVEC * sqrt(EVAL) but filter on rows that are in solution
// with EVAL as diagonal matrix
matrix_t mds;
sizeMatrix(mds,nc,par::cluster_mds_dim);
for (int c1=0; c1<nc; c1++)
for (int c2=0; c2<par::cluster_mds_dim; c2++)
// ERROR: *** in 1.02 and below was *** for (int c3=0; c3<nc; c3++)
for (int c3=0; c3<par::cluster_mds_dim; c3++)
{
int i2 = elist[c2];
int i3 = elist[c3];
if ( i3 == i2 )
mds[c1][c2] += eigenvector[c1][i3] * eigenvalue[i2];
}
// Display solution
ofstream MDS(f.c_str(),ios::out);
MDS.precision(6);
MDS << setw(par::pp_maxfid) << "FID" << " "
<< setw(par::pp_maxiid) << "IID" << " "
<< setw(6) << "SOL" << " ";
for (int c=0; c<par::cluster_mds_dim; c++)
MDS << setw(12) << "C"+int2str(c+1) << " ";
MDS << "\n";
for (int i=0; i<n; i++)
{
MDS << setw(par::pp_maxfid) << sample[i]->fid << " "
<< setw(par::pp_maxiid) << sample[i]->iid << " "
<< setw(6) << sample[i]->sol << " ";
for (int c=0; c<par::cluster_mds_dim; c++)
{
if ( par::mds_by_individual )
MDS << setw(12) << mds[i][c] << " ";
else
{
if ( sample[i]->sol >= 0 )
MDS << setw(12) << mds[ sample[i]->sol ][c] << " ";
else
MDS << setw(12) << "NA" << " ";
}
}
MDS << "\n";
}
MDS.close();
}
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