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// $Id: PowerEigenSolver.cpp 1528 2010-09-26 17:04:37Z glandrum $
//
// Copyright (C) 2004-2008 Greg Landrum and Rational Discovery LLC
//
// @@ All Rights Reserved @@
// This file is part of the RDKit.
// The contents are covered by the terms of the BSD license
// which is included in the file license.txt, found at the root
// of the RDKit source tree.
//
#include "PowerEigenSolver.h"
#include <Numerics/Vector.h>
#include <Numerics/Matrix.h>
#include <Numerics/SymmMatrix.h>
#include <RDGeneral/Invariant.h>
#include <time.h>
#define MAX_ITERATIONS 1000
#define TOLERANCE 0.001
#define HUGE_EIGVAL 1.0e10
#define TINY_EIGVAL 1.0e-10
namespace RDNumeric {
namespace EigenSolvers {
bool powerEigenSolver(unsigned int numEig, DoubleSymmMatrix &mat,
DoubleVector &eigenValues, DoubleMatrix *eigenVectors, int seed) {
// first check all the sizes
unsigned int N = mat.numRows();
CHECK_INVARIANT(eigenValues.size() >= numEig, "");
CHECK_INVARIANT(numEig <= N, "");
if(eigenVectors){
unsigned int evRows, evCols;
evRows = eigenVectors->numRows();
evCols = eigenVectors->numCols();
CHECK_INVARIANT(evCols >= N, "");
CHECK_INVARIANT(evRows >= numEig, "");
}
unsigned int ei;
double eigVal, prevVal, maxEval;
bool converged=false;
unsigned int i, j, id, iter, evalId;
DoubleVector v(N), z(N);
if(seed<=0) seed = clock();
for (ei = 0; ei < numEig; ei++) {
eigVal = -HUGE_EIGVAL;
seed += ei;
v.setToRandom(seed);
converged = false;
for (iter = 0; iter < MAX_ITERATIONS; iter++) {
// z = mat*v
multiply(mat, v, z);
prevVal = eigVal;
maxEval = -1.0;
evalId = z.largestAbsValId();
eigVal = z.getVal(evalId);
if (fabs(eigVal) < TINY_EIGVAL) {
break;
}
// compute the next estimate for the eigen vector
v.assign(z);
v /= eigVal;
if (fabs(eigVal - prevVal) < TOLERANCE) {
converged = true;
break;
}
}
if (!converged) {
break;
}
v.normalize();
// save this is a eigen vector and value
// directly access the data instead of setVal so that we save time
double *vdata = v.getData();
if(eigenVectors){
id = ei*eigenVectors->numCols();
double *eigVecData = eigenVectors->getData();
for (i = 0; i < N; i++) {
eigVecData[id + i] = vdata[i];
}
}
eigenValues[ei]=eigVal;
// now remove this eigen vector space out of the matrix
double *matData = mat.getData();
for (i = 0; i < N; i++) {
id = i*(i+1)/2;
for (j = 0; j < i+1; j++) {
matData[id+j] -= (eigVal*vdata[i]*vdata[j]);
}
}
}
return converged;
}
}
}
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