void testDatasetEquality(LabeledData<int, int> const& set1, LabeledData<int, int> const& set2){
BOOST_REQUIRE_EQUAL(set1.numberOfBatches(),set2.numberOfBatches());
BOOST_REQUIRE_EQUAL(set1.numberOfElements(),set2.numberOfElements());
for(std::size_t i = 0; i != set1.numberOfBatches(); ++i){
BOOST_REQUIRE_EQUAL(set1.batch(i).input.size(),set1.batch(i).label.size());
BOOST_REQUIRE_EQUAL(set2.batch(i).input.size(),set2.batch(i).label.size());
}
testSetEquality(set1.inputs(),set2.inputs());
testSetEquality(set1.labels(),set2.labels());
}
void LinearRegression::train(LinearModel<>& model, LabeledData<RealVector, RealVector> const& dataset){
std::size_t inputDim = inputDimension(dataset);
std::size_t outputDim = labelDimension(dataset);
std::size_t numInputs = dataset.numberOfElements();
std::size_t numBatches = dataset.numberOfBatches();
//Let P be the matrix of points with n rows and X=(P|1). the 1 rpresents the bias weight
//Let A = X^T X + lambda * I
//than whe have (for lambda = 0)
//A = ( P^T P P^T 1)
// ( 1^T P 1^T1)
RealMatrix matA(inputDim+1,inputDim+1,0.0);
blas::Blocking<RealMatrix> Ablocks(matA,inputDim,inputDim);
//compute A and the label matrix batchwise
typedef LabeledData<RealVector, RealVector>::const_batch_reference BatchRef;
for (std::size_t b=0; b != numBatches; b++){
BatchRef batch = dataset.batch(b);
symm_prod(trans(batch.input),Ablocks.upperLeft(),false);
noalias(column(Ablocks.upperRight(),0))+=sum_rows(batch.input);
}
row(Ablocks.lowerLeft(),0) = column(Ablocks.upperRight(),0);
matA(inputDim,inputDim) = numInputs;
//X^TX+=lambda* I
diag(Ablocks.upperLeft())+= blas::repeat(m_regularization,inputDim);
//we also need to compute X^T L= (P^TL, 1^T L) where L is the matrix of labels
RealMatrix XTL(inputDim + 1,outputDim,0.0);
for (std::size_t b=0; b != numBatches; b++){
BatchRef batch = dataset.batch(b);
RealSubMatrix PTL = subrange(XTL,0,inputDim,0,outputDim);
axpy_prod(trans(batch.input),batch.label,PTL,false);
noalias(row(XTL,inputDim))+=sum_rows(batch.label);
}
//we solve the system A Beta = X^T L
//usually this is solved via the moore penrose inverse:
//Beta = A^-1 T
//but it is faster und numerically more stable, if we solve it as a symmetric system
//w can use in-place solve
RealMatrix& beta = XTL;
blas::solveSymmSemiDefiniteSystemInPlace<blas::SolveAXB>(matA,beta);
RealMatrix matrix = subrange(trans(beta), 0, outputDim, 0, inputDim);
RealVector offset = row(beta,inputDim);
// write parameters into the model
model.setStructure(matrix, offset);
}