/*! solve overdetermined or underdetermined A*x=y using dgels
with the sum of residual squares output\n
The residual is set as the sum of residual squares
for overdetermined problems
while it is always zero for underdetermined problems.
*/
inline long dgematrix::dgels(dcovector& vec, double& residual)
{
#ifdef CPPL_VERBOSE
std::cerr << "# [MARK] dgematrix::dgels(dcovector&, double&)"
<< std::endl;
#endif//CPPL_VERBOSE
#ifdef CPPL_DEBUG
if(M!=vec.L){
std::cerr << "[ERROR] dgematrix::dgels(dcovector&, double&) " << std::endl
<< "These matrix and vector cannot be solved." << std::endl
<< "Your input was (" << M << "x" << N << ") and ("
<< vec.L << ")." << std::endl;
exit(1);
}
#endif//CPPL_DEBUG
residual=0.0;
if(M<N){ //underdetermined
dcovector tmp(N);
for(long i=0; i<vec.L; i++){ tmp(i)=vec(i); }
vec.clear();
swap(vec,tmp);
}
char TRANS('N');
long NRHS(1), LDA(M), LDB(vec.L),
LWORK(min(M,N)+max(min(M,N),NRHS)), INFO(1);
double *WORK(new double[LWORK]);
dgels_(TRANS, M, N, NRHS, Array, LDA, vec.Array, LDB, WORK, LWORK, INFO);
delete [] WORK;
if(M>N){ //overdetermined
for(long i=0; i<M-N; i++){ residual+=std::pow(vec(N+i),2.0); }
dcovector tmp(N);
for(long i=0; i<tmp.L; i++){ tmp(i)=vec(i); }
vec.clear();
swap(vec,tmp);
}
if(INFO!=0){
std::cerr << "[WARNING] dgematrix::dgels(dcovector&, double&) "
<< "Serious trouble happend. INFO = " << INFO << "."
<< std::endl;
}
return INFO;
}
/*! calculate the least-squares-least-norm solution for overdetermined or
underdetermined A*x=y using dgelss\n
*/
inline long dgematrix::dgelss(dcovector& B, dcovector& S, long& RANK,
const double RCOND =-1. )
{
#ifdef CPPL_VERBOSE
std::cerr << "# [MARK] dgematrix::dgelss(dcovector&, dcovector&, long&, const double)"
<< std::endl;
#endif//CPPL_VERBOSE
#ifdef CPPL_DEBUG
if(M!=B.L){
std::cerr << "[ERROR] dgematrix::dgelss"
<< "(dcovector&, dcovector&, long, double) " << std::endl
<< "These matrix and vector cannot be solved." << std::endl
<< "Your input was (" << M << "x" << N << ") and ("
<< B.L << ")." << std::endl;
exit(1);
}
#endif//CPPL_DEBUG
if(M<N){ //underdetermined
dcovector tmp(N);
for(long i=0; i<B.L; i++){ tmp(i)=B(i); }
B.clear();
swap(B,tmp);
}
S.resize(min(M,N));
long NRHS(1), LDA(M), LDB(B.L),
LWORK(3*min(M,N)+max(max(2*min(M,N),max(M,N)), NRHS)), INFO(1);
double *WORK(new double[LWORK]);
dgelss_(M, N, NRHS, Array, LDA, B.Array, LDB, S.Array,
RCOND, RANK, WORK, LWORK, INFO);
delete [] WORK;
if(INFO!=0){
std::cerr << "[WARNING] dgematrix::dgelss"
<< "(dcovector&, docvector&, long, const double) "
<< "Serious trouble happend. INFO = " << INFO << "."
<< std::endl;
}
return INFO;
}