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