bool LtBackSubstitute(const MatrixTemplate<T>& a, const VectorTemplate<T>& b, VectorTemplate<T>& x)
{
Assert(a.isSquare());
Assert(a.n == b.n);
if(x.empty()) x.resize(a.n);
else Assert(a.n == x.n);
int n=a.n;
T aii,sum;
for(int i=n-1; i>=0; i--) {
aii=a(i,i);
sum=b[i];
for(int j=i+1; j<n; j++)
sum-=a(j,i)*x[j];
if(aii == 0) {
if(!FuzzyZero(sum,(T)kBackSubZeroTolerance)) {
//LOG4CXX_ERROR(KrisLibrary::logger(),"LtBackSubstitute: dividing by zero: "<<sum<<"/"<<aii);
return false;
}
x[i]=0;
}
else
x[i]=sum/aii;
}
return true;
}
bool LBackSubstitute(const MatrixTemplate<T>& a, const VectorTemplate<T>& b, VectorTemplate<T>& x)
{
Assert(a.isSquare());
Assert(a.n == b.n);
if(x.empty()) x.resize(a.n);
else Assert(a.n == x.n);
int n=a.n;
T aii,sum;
for(int i=0; i<n; i++) {
aii=a(i,i);
sum=b[i];
for(int j=0; j<i; j++)
sum-=a(i,j)*x[j];
if(aii == 0) {
if(!FuzzyZero(sum,(T)kBackSubZeroTolerance)) {
//cerr<<"LBackSubstitute: dividing by zero: "<<sum<<"/"<<aii<<endl;
//cerr<<MatrixPrinter(a)<<endl;
return false;
}
x[i]=0;
}
else
x[i]=sum/aii;
}
return true;
}
void U1BackSubstitute(const MatrixTemplate<T>& a, const VectorTemplate<T>& b, VectorTemplate<T>& x)
{
Assert(a.isSquare());
Assert(a.n == b.n);
if(x.empty()) x.resize(a.n);
else Assert(a.n == x.n);
int n=a.n;
T sum;
for(int i=n-1; i>=0; i--) {
sum=b(i);
for(int j=i+1; j<n; j++)
sum-=a(i,j)*x[j];
x[i]=sum;
}
}
void L1BackSubstitute(const MatrixTemplate<T>& a, const VectorTemplate<T>& b, VectorTemplate<T>& x)
{
Assert(a.isSquare());
Assert(a.n == b.n);
if(x.empty()) x.resize(a.n);
else Assert(a.n == x.n);
int n=a.n;
T sum;
for(int i=0; i<n; i++) {
sum=b[i];
for(int j=0; j<i; j++)
sum-=a(i,j)*x[j];
x[i]=sum;
}
}
void VectorTemplate<T>::copy(const VectorTemplate<T2>& a)
{
CHECKRESIZE(a.n);
VectorIterator<T> k=begin();
VectorIterator<T2> ak=a.begin();
for(int i=0;i<n;i++,k++,ak++)
*k = (T)*ak;
}
T HouseholderTransform(VectorTemplate<T>& v)
{
Assert(v.n != 0);
if (v.n == 1) return 0;
T alpha, beta, tau ;
VectorTemplate<T> x; x.setRef(v,1);
T xnorm = x.norm();
if (xnorm == 0) {
return 0;
}
alpha = v(0);
beta = - (alpha >= 0.0 ? 1 : -1) * pythag(alpha, xnorm);
tau = (beta - alpha) / beta ;
x.inplaceDiv(alpha-beta);
v(0)=beta;
return tau;
}
