void HouseMatrix(Matrix H,Vector v, int start, int end)
{
int i,j;
double a;
a = 2.0/xty(v,v,start,end);
MakeID(H);
for (i=start;i<=end;i++)
for (j=start;j<=end;j++)
H[i][j] -= a*v[i]*v[j];
}
double RM::Loglike(const Vector &sigsq_beta,
Vector &g, Matrix &h, uint nd)const{
const double log2pi = 1.83787706640935;
const double sigsq = sigsq_beta[0];
const Vector b(ConstVectorView(sigsq_beta, 1));
double n = suf()->n();
if(b.size()==0) return empty_loglike(g, h, nd);
double SSE = yty() - 2*b.dot(xty()) + xtx().Mdist(b);
double ans = -.5*(n * log2pi + n *log(sigsq)+ SSE/sigsq);
if(nd>0){ // sigsq derivs come first in CP2 vectorization
SpdMatrix xtx = this->xtx();
Vector gbeta = (xty() - xtx*b)/sigsq;
double sig4 = sigsq*sigsq;
double gsigsq = -n/(2*sigsq) + SSE/(2*sig4);
g = concat(gsigsq, gbeta);
if(nd>1){
double h11 = .5*n/sig4 - SSE/(sig4*sigsq);
h = unpartition(h11, (-1/sigsq)*gbeta, (-1/sigsq)*xtx);}}
return ans;
}
int main() {
auto b = genRandomVector(kDim);
Matrix xtx(kDim);
Vector xty(kDim);
{
Timer tGen("Generate");
constexpr u32 kVectorPoints = 4000 * kDim;
for (u32 iVectorPoint = 0; iVectorPoint < kVectorPoints; ++iVectorPoint) {
auto p = getRandomVectorPoint(b);
for (size_t i = 0; i < p.dimension(); ++i) {
for (size_t j = 0; j < p.dimension(); ++j) {
xtx.data_[i][j] += p.a_[i] * p.a_[j];
}
}
for (size_t i = 0; i < p.dimension(); ++i) {
xty[i] += p.a_[i] * p.b_;
}
}
}
{
Timer tSolve("Invert");
auto inv = xtx.invert();
tSolve.finish();
Vector bPrime = inv * xty;
LOG(INFO) << OUT(b) << OUT(length(b));
LOG(INFO) << OUT(bPrime) << OUT(length(bPrime));
auto err = b - bPrime;
LOG(INFO) << OUT(err) << OUT(length(err));
}
{
Timer tSolve("Cholesky");
auto chol = xtx.cholesky();
tSolve.finish();
Matrix xtx2 = chol*chol.transpose();
LOG(INFO) << OUT(xtx.norm2()) << OUT(xtx2.norm2()) << OUT((xtx - xtx2).norm2());
}
return 0;
}
DoubleVector linearRegression(const VectorPoints& points, double rigid) {
assert(!points.empty());
Matrix xtx(points[0].dimension());
Vector xty(points[0].dimension());
for (u32 iVectorPoint = 0; iVectorPoint < points.size(); ++iVectorPoint) {
const auto& p = points[iVectorPoint];
assert(p.dimension() == xty.size());
for (size_t i = 0; i < p.dimension(); ++i) {
for (size_t j = 0; j < p.dimension(); ++j) {
xtx.data_[i][j] += p.a_[i] * p.a_[j];
}
}
for (size_t i = 0; i < p.dimension(); ++i) {
xty[i] += p.a_[i] * p.b_;
}
}
for (size_t i = 0; i < xtx.dimension(); ++i) {
xtx.data_[i][i] += rigid;
}
xtx /= points.size();
for (auto& x : xty) {
x /= points.size();
}
auto b = xtx.invert() * xty;
// cout << OUT((xtx.invert() * xtx - Matrix::one(xtx.dimension())).norm2()) << endl;
/*
for (size_t i = 0; i < points.size(); ++i) {
const auto& p = points[i];
cout << OUT(p.b_) << OUT(dot(p.a_, b)) << OUT(p.a_[p.a_.size() - 2]) << endl;
}
*/
return b;
}
SpdMatrix MvRegSuf::SSE(const Matrix &B) const {
SpdMatrix ans = yty();
ans.add_inner2(B, xty(), -1);
ans += sandwich(B.transpose(), xtx());
return ans;
}
Vector RM::xty()const{ return xty( coef().inc() ) ;}
double NeRegSuf::SSE()const{
SpdMatrix ivar = xtx().inv();
return yty() - ivar.Mdist(xty()); }
ostream & QrRegSuf::print(ostream &out)const{
return out << "sumsqy = " << yty() << endl
<< "xty_ = " << xty() << endl
<< "xtx = " << endl << xtx();
}
Vector QrRegSuf::xty(const Selector &inc)const{
// if(!current) refresh_qr();
return inc.select(xty());
}
//======================================================================
ostream & RegSuf::print(ostream &out)const{
out << "sample size: " << n() << endl
<< "xty: " << xty() << endl
<< "xtx: " << endl << xtx();
return out;
}