void RowEchelon<T>::backSub(VectorT& x) const
{
Assert(EB.n == 1);
Assert(EB.m == R.m);
x.resize(R.n);
VectorT b;
EB.getColRef(0,b);
Assert((int)firstEntry.size() == R.m+1);
x.setZero();
int m=R.m,n=R.n;
for(int i=m-1;i>=0;i--) {
VectorT ri; R.getRowRef(i,ri);
//solve to set R*x = b[i]
//calculate alpha = dot between rest of x[>ji] and R[i]
int ji=firstEntry[i];
if(ji == n) continue;
int ji2=firstEntry[i+1]; //(i+1==m?n:firstEntry[i+1]);
T alpha;
if(ji2 == n) alpha = Zero;
else {
VectorT rji2; rji2.setRef(ri,ji2,1,R.n-ji2);
VectorT xji2; xji2.setRef(x,ji2,1,R.n-ji2);
alpha = xji2.dot(rji2);
}
x[ji] = (b[i]-alpha)/ri[ji];
}
}
void SparseMatrixTemplate_RM<T>::mulTranspose(const VectorT& a,VectorT& x) const
{
if(x.n == 0) x.resize(n);
if(x.n != n) {
FatalError("Destination vector has incorrect dimensions");
}
if(a.n != m) {
FatalError("Source vector has incorrect dimensions");
}
x.setZero();
for(int i=0;i<m;i++) {
for(ConstRowIterator it=rows[i].begin();it!=rows[i].end();it++)
x(it->first) += it->second*a(i);
}
}
void QRDecomposition<T>::leastSquares(const VectorT& b, VectorT& x, VectorT& residual) const
{
if(x.n == 0) x.resize(QR.n);
Assert(QR.m >= QR.n);
Assert(QR.m == b.n);
Assert(QR.n == x.n);
Assert(QR.m == residual.n);
MatrixT R;
R.setRef(QR,0,0,1,1,QR.n,QR.n);
VectorT c;
c.setRef(residual,0,1,QR.n);
/* compute rhs = Q^T b */
QtMul(b,residual);
/* Solve R x = rhs */
UBackSubstitute(R,c,x);
/* Compute residual = b - A x = Q (Q^T b - R x) */
c.setZero();
QMul(residual,residual);
}
void RowEchelon<T>::getNullspace(MatrixT& N) const
{
if(R.isEmpty()) {
N.clear();
return;
}
Assert((int)firstEntry.size() == R.m+1);
int nullspace_dims=getNull();
N.resize(R.n,nullspace_dims);
//first get nullspace vectors from 0 to firstEntry[0]
int i,j,numVecs=0;
int m=R.m,n=R.n;
for(j=0;j<firstEntry[0];j++) {
N.setCol(numVecs,0); N(j,numVecs)=1;
numVecs++;
}
for(i=0;i<m;i++) {
//cancel out the i'th entry
for(j=firstEntry[i]+1;j<firstEntry[i+1];j++) {
if(numVecs >= N.n) {
LOG4CXX_INFO(KrisLibrary::logger(),"Num nullspace vectors "<<numVecs);
LOG4CXX_INFO(KrisLibrary::logger(),"Found more nullspace vectors than found dims, row "<<i);
LOG4CXX_INFO(KrisLibrary::logger(),MatrixPrinter(R));
}
Assert(numVecs < N.n);
VectorT xn; N.getColRef(numVecs,xn);
xn.setZero();
xn[firstEntry[i]] = R(i,j);
xn[j] = -R(i,firstEntry[i]);
//cancel out all the entries prior to i
int isave=i;
i--;
for(;i>=0;i--) {
VectorT ri; R.getRowRef(i,ri);
//calculate alpha
int ji=firstEntry[i];
Assert(ji != n);
int ji2=firstEntry[i+1]; //(i+1==m?n:firstEntry[i+1]);
T alpha;
if(ji2 == n) alpha = Zero;
else {
VectorT rji2; rji2.setRef(ri,ji2,1,R.n-ji2);
VectorT xji2; xji2.setRef(xn,ji2,1,R.n-ji2);
alpha = xji2.dot(rji2);
}
xn[ji] = -alpha/ri[ji];
}
i=isave;
numVecs++;
}
}
if(numVecs != nullspace_dims) {
LOG4CXX_ERROR(KrisLibrary::logger(),"Error in counting rank in row-eschelon decomposition");
LOG4CXX_INFO(KrisLibrary::logger(),"Num nullspace vectors "<<numVecs);
LOG4CXX_INFO(KrisLibrary::logger(),MatrixPrinter(R));
}
Assert(numVecs == nullspace_dims);
/*
VectorT temp;
for(int i=0;i<numVecs;i++) {
VectorT xi; N.getColRef(i,xi);
xi.print();
R.mul(xi,temp);
if(temp.maxAbsElement() > 1e-4) {
LOG4CXX_INFO(KrisLibrary::logger(),"Nullspace vector "<<i<<" not in null space!");
xi.print();
LOG4CXX_INFO(KrisLibrary::logger(),"Result = "); temp.print();
KrisLibrary::loggerWait();
}
}
*/
VectorT* N0 = new VectorT[nullspace_dims];
for(int i=0;i<nullspace_dims;i++) N.getColRef(i,N0[i]);
int num=OrthonormalBasis(N0,N0,nullspace_dims);
Assert(num == nullspace_dims);
delete [] N0;
}