int CLapack::syev(char jobz,char uplo,CFortranMatrix& a,CVector& w)
{
int info = 0;
int nrows = a.GetNumberOfRows();
int nwork = -1;
double twork[1];
// query workspace length
dsyev_(&jobz,&uplo,&nrows,a.GetRawDataField(),&nrows,w.GetRawDataField(),
twork,&nwork,&info);
if( info != 0 ){
CSmallString error;
error << "unable to determine lwork, info = " << info;
INVALID_ARGUMENT(error);
}
// allocate work space
CVector work;
nwork = static_cast<int>(twork[0]) + 1;
work.CreateVector(nwork);
// run again
dsyev_(&jobz,&uplo,&nrows,a.GetRawDataField(),&nrows,w.GetRawDataField(),
work.GetRawDataField(),&nwork,&info);
return(info);
}
int CLapack::gelsd(CFortranMatrix& a,CVector& rhs,double rcond,int& rank)
{
int m = a.GetNumberOfRows();
int n = a.GetNumberOfColumns();
int nrhs = 1;
int lda = m;
int ldb = std::max(m,n);
CVector s;
int ns = std::min(m,n);
s.CreateVector(ns);
int info = 0;
// query work size
int lwork = -1;
double twork[1];
// printf("lwork = %d\n",lwork);
CSimpleVector<int> iwork;
int li = 3*std::min(m,n)*std::min(m,n) + 11*std::min(m,n);
iwork.CreateVector(li);
dgelsd_(&m,&n,&nrhs,a.GetRawDataField(),&lda,rhs.GetRawDataField(),&ldb,s.GetRawDataField(),
&rcond,&rank,twork,&lwork,iwork.GetRawDataField(),&info);
if( info != 0 ){
CSmallString error;
error << "unable to determine lwork, info = " << info;
INVALID_ARGUMENT(error);
}
lwork = static_cast<int>(twork[0]) + 1;
// printf("lwork = %d\n",lwork);
CSimpleVector<double> work;
work.CreateVector(lwork);
// run svd
dgelsd_(&m,&n,&nrhs,a.GetRawDataField(),&lda,rhs.GetRawDataField(),&ldb,s.GetRawDataField(),
&rcond,&rank,work.GetRawDataField(),&lwork,iwork.GetRawDataField(),&info);
return(info);
}
bool CABFIntegratorRBF::IntegrateByLS(CVerboseStr& vout)
{
vout << " Creating A and rhs ..." << endl;
// number of equations
int neq = Accumulator->GetNumberOfBins()*NumOfCVs;
CSimpleVector<double> spos; // best sampled bin
spos.CreateVector(NumOfCVs);
CSimpleVector<double> ipos; // best sampled bin
ipos.CreateVector(NumOfCVs);
CSimpleVector<double> lpos; // best sampled bin
lpos.CreateVector(NumOfCVs);
vout << " Dim: " << neq << " x " << NumOfRBFs << endl;
CFortranMatrix A;
A.CreateMatrix(neq,NumOfRBFs);
CVector rhs;
int nrhs = std::max(neq,NumOfRBFs);
rhs.CreateVector(nrhs);
// calculate A and rhs
int j=0;
for(int i=0; i < Accumulator->GetNumberOfBins(); i++){
Accumulator->GetPoint(i,ipos);
// A
for(int l=0; l < NumOfRBFs; l++){
GetRBFPosition(l,lpos);
// cout << lpos[0] << " " << lpos[1] << endl;
double av = 1.0;
for(int k=0; k < NumOfCVs; k++){
double dvc = Accumulator->GetCoordinate(k)->GetDifference(ipos[k],lpos[k]);
double sig = Sigmas[k];
av *= exp( - dvc*dvc/(2.0*sig*sig) );
}
for(int k=0; k < NumOfCVs; k++){
double dvc = Accumulator->GetCoordinate(k)->GetDifference(ipos[k],lpos[k]);
double sig = Sigmas[k];
double fc = -dvc/(sig*sig); // switch to derivatives
A[j+k][l] = av * fc;
}
}
// rhs
for(int k=0; k < NumOfCVs; k++){
rhs[j+k] = Accumulator->GetABFForceSum(k,i);
}
j += NumOfCVs;
}
int result = 0;
switch(Method){
case EARBF_SVD:{
vout << " Solving least square problem by SVD ..." << endl;
// solve least square problem via GELSD
int rank = 0;
result = CLapack::gelsd(A,rhs,RCond,rank);
vout << " Rank = " << rank << "; Info = " << result << endl;
if( result != 0 ) return(false);
}
break;
case EARBF_QRLQ:{
vout << " Solving least square problem by QRLQ ..." << endl;
// solve least square problem via GELS
result = CLapack::gels(A,rhs);
if( result != 0 ) return(false);
}
break;
default:
INVALID_ARGUMENT("unsupported method");
}
// copy results to Weights
for(int l=0; l < NumOfRBFs; l++){
Weights[l] = rhs[l];
}
cout << Weights[0] << endl;
return( true );
}