void SparseMatrixTemplate_RM<T>::mulTranspose(const MatrixT& a,MatrixT& x) const
{
if(a.m != n) {
FatalError("A matrix has incorrect # of rows");
}
if(x.isEmpty()) x.resize(n,a.n);
if(n != x.m) {
FatalError("X matrix has incorrect # of rows");
}
if(a.n != x.n) {
FatalError("X matrix has incorrect # of columns");
}
for(int i=0;i<a.n;i++) {
VectorT ai,xi;
a.getColRef(i,ai);
x.getColRef(i,xi);
mulTranspose(ai,xi);
}
}
void RowEchelon<T>::getAllSolutions(VectorT& x0,MatrixT& N) const
{
getNullspace(N);
VectorT* N0 = new VectorT[N.n];
for(int i=0;i<N.n;i++) N.getColRef(i,N0[i]);
backSub(x0);
Orthogonalize(x0,N0,N.n);
delete [] N0;
}
void DiagonalMatrixTemplate<T>::postMultiplyTranspose(const MatrixT& a,MatrixT& x) const
{
Assert(this->n == a.m);
x.resize(a.n,this->n);
MyT xrow,acol;
for(int i=0;i<a.n;i++) {
x.getRowRef(i,xrow);
a.getColRef(i,acol);
xrow.componentMul(acol,*this);
}
}
void CholeskyDecomposition<T>::getInverse(MatrixT& Ainv) const
{
Ainv.resize(L.n,L.n);
VectorT temp(L.n,Zero),y,x;
for(int i=0;i<L.n;i++) {
Ainv.getColRef(i,x); //x &= col i of A
temp(i)=One;
LBackSub(temp,y);
LTBackSub(y,x);
temp(i)=Zero;
}
}
void DiagonalMatrixTemplate<T>::preMultiplyTranspose(const MatrixT& a,MatrixT& x) const
{
Assert(this->n == a.n);
x.resize(this->n,a.m);
ItT v=this->begin();
MyT xrow,acol;
for(int i=0;i<this->n;i++,v++) {
x.getRowRef(i,xrow);
a.getColRef(i,acol);
xrow.mul(acol,*v);
}
}
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;
}