inline void decomr(double fac1,MatrixReal& Jac)
{
if(calhes)
{
int ilo=1,ihi=n,lda=n,info;
int k=-1;
//find the optimum size for array work/
int nn=n;
dgehrd_(&nn,&ilo,&ihi,&Jac,&lda,tau,work,&k,&info);
k=work[0];
if(lwork<k)
{
if(work!=0) delete[] work;
lwork=k;
work=new double[lwork];
}
dgehrd_(&nn,&ilo,&ihi,&Jac,&lda,tau,work,&k,&info);
if(info!=0)
throw OdesException("odes::Matrices::Matrices, decomr: info=",
info);
calhes=false;
}
E1.equal_minus(Jac);
E1.addDiag(fac1);
int info=dech<n>(E1,ipr);
if(info!=0)
throw OdesException("odes::Matrices::Matrices, decomr (dech): ",
info);
}
void DualityDiagram::check_(
const MatrixReal& matrix,
const std::vector<double>& rowWeights,
const std::vector<double>& colWeights,
unsigned int nbAxes) throw (RbException)
{
size_t rowNb = matrix.getNumberOfRows();
size_t colNb = matrix.getNumberOfColumns();
if (rowWeights.size() != rowNb)
throw RbException("DualityDiagram::check_. The number of row weigths has to be equal to the number of rows!");
if (colWeights.size() != colNb)
throw RbException("DualityDiagram::check_. The number of column weigths has to be equal to the number of columns!");
// All row weigths have to be positive
for (std::vector<double>::const_iterator it = rowWeights.begin(); it != rowWeights.end(); it++)
{
if (*it < 0.)
throw RbException("DualityDiagram::check_. All row weights have to be positive");
}
// All column weigths have to be positive
for (std::vector<double>::const_iterator it = colWeights.begin(); it != colWeights.end(); it++)
{
if (*it < 0.)
throw RbException("DualityDiagram::check_. All column weights have to be positive");
}
}
//! build and factorize "real" matrix
//! \param fac1 : we add fac1*I to the Jacobian.
//! \param Jac the jacobian.
inline void decomr(double fac1,MatrixReal& Jac)
{
E1.equal_minus(Jac);
E1.addDiag(fac1);
int nn=n,info;
dgetrf_(&nn,&nn,&E1,&nn,&(ipivr[0]),&info);
if(info!=0)
throw OdesException("odes::Matrices::decomr dgetrf,info=",info);
}
//! see full matrix case.
inline void decomr(double fac1,const MatrixReal& Jac)
{
E1.equal_minus(Jac);
E1.addDiag(fac1);
int nn=n,knsub=nsub,knsup=nsup,lldab=ldab,info;
dgbtrf_(&nn,&nn,&knsub,&knsup,&E1,&lldab,&(ipivr[0]),&info);
if(info!=0)
throw OdesException("odes::Matrices::decomr dgbtrf,info=",info);
}
double RbStatistics::DecomposedInverseWishart::lnPdf(double nu, const MatrixReal &r) {
size_t k = r.getDim();
if ( r.isPositive() == false )
{
return RbConstants::Double::neginf;
}
double lnP = (0.5 * (k - 1.0) * (nu - 1.0) - 1.0);
lnP += r.getLogDet();
MatrixReal submatrix(k-1);
for (size_t i=0; i<k; i++)
{
size_t ai = 0;
for (size_t a=0; a<k; a++)
{
if (a != i)
{
size_t bi = 0;
for (size_t b=0; b<k; b++)
{
if ( b != i )
{
submatrix[ai][bi] = r[a][b];
bi++;
}
}
ai++;
}
}
lnP += submatrix.getLogDet();
std::cout << "logdet=" << submatrix.getLogDet() << std::endl;
}
return lnP;
}
PrecisionMatrix::PrecisionMatrix(const MatrixReal& from) : MatrixReal(from), eigensystem(this), eigenflag(false), inverse(from.getNumberOfColumns(), from.getNumberOfColumns(), 0) {
if (getNumberOfRows() != getNumberOfColumns()) {
std::cerr << "error in PrecisionMatrix: copy constructor from a non-square matrix\n";
throw(NULL);
}
}
void Tree::trainTree(const MatrixReal& featMat, const VectorInteger& labels)
{
// We work with a queue of nodes, initially containing only the root node.
// We process the queue until it becomes empty.
std::queue<int> toTrain;
int size,numClasses,numVars,dims;
size = labels.size();
dims = featMat.cols();
numClasses = labels.maxCoeff();
classWts = VectorReal::Zero(numClasses+1);
for(int i = 0; i < labels.size(); ++i)
classWts(labels(i)) += 1.0;
classWts /= size;
for(int i = 0; i < size; ++i)
nodeix.push_back(i);
std::cout<<"Training tree, dimensions set\n";
numVars = (int)((double)sqrt((double)dims)) + 1;
int cur;
// The relevant indices for the root node is the entire set of training data
nodes[0].start = 0;
nodes[0].end = size-1;
// Initialise the queue with just the root node
toTrain.push(0);
// Stores the relevant features.
VectorReal relFeat;
// Resize our boolean array, more on this later.
indices.resize(size);
std::cout<<"Starting the queue\n";
int lpoints,rpoints;
// While the queue isn't empty, continue processing.
while(!toTrain.empty())
{
int featNum;
double threshold;
lpoints = rpoints = 0;
cur = toTrain.front();
// std::cout<<"In queue, node being processed is d :"<<cur.depth<<"\n";
// There are two ways for a node to get out of the queue trivially,
// a) it doesn't have enough data to be a non-trivial split, or
// b) it has hit the maximum permissible depth
if((nodes[cur].end - nodes[cur].start < DATA_MIN) || (nodes[cur].depth == depth))
{
// Tell ourselves that this is a leaf node, and remove the node
// from the queue.
// std::cout<<"Popping a leaf node\n";
nodes[cur].setType(true);
// Initialize the histogram and set it to zero
nodes[cur].hist = VectorReal::Zero(numClasses+1);
// The below code should give the histogram of all the elements
for(int i = nodes[cur].start; i <= nodes[cur].end; ++i)
{
nodes[cur].hist[labels(nodeix[i])] += 1.0;
}
for(int i = 0 ; i < classWts.size(); ++i)
nodes[cur].hist[i] = nodes[cur].hist[i] / classWts[i];
toTrain.pop();
continue;
}
double infoGain(-100.0);
relFeat.resize(size);
// In case this isn't a trivial node, we need to process it.
for(int i = 0; i < numVars; ++i)
{
// std::cout<<"Choosing a random variable\n";
// Randomly select a feature
featNum = rand()%dims;
// std::cout<<"Feat: "<<featNum<<std::endl;
// Extract the relevant feature set from the training data
relFeat = featMat.col(featNum);
double tmax,tmin,curInfo;
tmax = relFeat.maxCoeff();
tmin = relFeat.minCoeff();
// infoGain = -100;
//std::cout<<"Min "<<tmin<<"Max: "<<tmax<<std::endl;
// NUM_CHECKS is a macro defined at the start
for(int j = 0; j < NUM_CHECKS; ++j)
{
// std::cout<<"Choosing a random threshold\n";
// Generate a random threshold
threshold = ((rand()%100)/100.0)*(tmax - tmin) + tmin;
//std::cout<<"Thresh: "<<threshold<<std::endl;
for(int k = nodes[cur].start; k <= nodes[cur].end ; ++k)
indices[k] = (relFeat(k) < threshold);
// Check if we have enough information gain
curInfo = informationGain(nodes[cur].start,nodes[cur].end, labels);
// std::cout<<"Info gain : "<<curInfo<<"\n";
// curInfo = (double) ((rand()%10)/10.0);
if(curInfo > infoGain)
{
infoGain = curInfo;
nodes[cur].x = featNum;
nodes[cur].threshold = threshold;
}
}
}
// We have selected a feature and a threshold for it that maximises the information gain.
relFeat = featMat.col(nodes[cur].x);
// We just set the indices depending on whether the features are greater or lesser.
// Conventions followed : greater goes to the right.
for(int k = nodes[cur].start; k <= nodes[cur].end; ++k)
{
// If relfeat is lesser, indices[k] will be true, which will put it in the
// left side of the partition.
indices[k] = relFeat(k) < nodes[cur].threshold;
// indices[k] = (bool)(rand()%2);
if(indices[k])
lpoints++;
else
rpoints++;
}
if( (lpoints < DATA_MIN) || (rpoints < DATA_MIN) )
{
// Tell ourselves that this is a leaf node, and remove the node
// from the queue.
// std::cout<<"Popping a leaf node\n";
nodes[cur].setType(true);
// Initialize the histogram and set it to zero
nodes[cur].hist.resize(numClasses+1);
nodes[cur].hist = VectorReal::Zero(numClasses+1);
// The below code should give the histogram of all the elements
for(int i = nodes[cur].start; i <= nodes[cur].end; ++i)
{
nodes[cur].hist[labels(nodeix[i])] += 1.0;
}
toTrain.pop();
continue;
}
int part;
// Use the prebuilt function to linearly partition our data
part = partition(nodes[cur].start,nodes[cur].end);
Node right, left;
// Increase the depth of the children
right.depth = left.depth = nodes[cur].depth + 1;
// Correctly assign the partitions
left.start = nodes[cur].start;
left.end = part -1;
// Push back into the relevant places and also link the parent and the child
nodes.push_back(left);
nodes[cur].leftChild = nodes.size()-1;
toTrain.push(nodes[cur].leftChild);
// Ditto with the right node.
right.start = part;
right.end = nodes[cur].end;
nodes.push_back(right);
nodes[cur].rightChild = nodes.size()-1;
toTrain.push(nodes[cur].rightChild);
// Finally remove our node from the queue.
toTrain.pop();
}
}
void DualityDiagram::compute_(const MatrixReal& matrix, double tol)
{
size_t rowNb = matrix.getNumberOfRows();
size_t colNb = matrix.getNumberOfColumns();
// If there are less rows than columns, the variance-covariance or correlation matrix is obtain differently (see below)
bool transpose = (rowNb < colNb);
// The initial matrix is multiplied by the square root of the row weigths.
std::vector<double> rW(rowWeights_);
for (size_t i = 0; i < rowWeights_.size(); i++)
{
rW[i] = sqrt(rowWeights_[i]);
}
MatrixReal M1(rowNb, colNb);
RbMath::hadamardMult(matrix, rW, M1, true);
// The resulting matrix is then multiplied by the square root of the column weigths.
std::vector<double> cW(colWeights_);
for (unsigned int i = 0; i < colWeights_.size(); i++)
{
cW[i] = sqrt(colWeights_[i]);
}
MatrixReal M2(rowNb,colNb);
RbMath::hadamardMult(M1, cW, M2, false);
// The variance-covariance (if the data is centered) or the correlation (if the data is centered and normalized) matrix is calculated
MatrixReal tM2(M2.getNumberOfColumns(),M2.getNumberOfRows());
RbMath::transposeMatrix(M2, tM2);
MatrixReal *M3 = new MatrixReal(0,0);
if (!transpose)
(*M3) = tM2 * M2;
else
(*M3) = M2 * tM2;
EigenSystem eigen(M3);
eigen.update();
// @todo: This may be implemented some time ... (Sebastian)
// if (!eigen.isSymmetric())
// throw RbException("DualityDiagram (constructor). The variance-covariance or correlation matrix should be symmetric...");
eigenValues_ = eigen.getRealEigenvalues();
eigenVectors_ = eigen.getEigenvectors();
// How many significant axes have to be conserved?
size_t rank = 0;
for (size_t i = eigenValues_.size(); i > 0; i--)
{
if ((eigenValues_[i - 1] / eigenValues_[eigenValues_.size() - 1]) > tol)
rank++;
}
if (nbAxes_ <=0)
{
throw RbException("DualityDiagram (constructor). The number of axes to keep must be positive.");
}
if (nbAxes_ > rank)
{
nbAxes_ = rank;
}
/*The eigen values are initially sorted into ascending order by the 'eigen' function. Here the significant values are sorted
in the other way around.*/
std::vector<double> tmpEigenValues(nbAxes_);
size_t cpt = 0;
for (size_t i = eigenValues_.size(); i > (eigenValues_.size() - nbAxes_); i--)
{
tmpEigenValues[cpt] = eigenValues_[i-1];
cpt++;
}
eigenValues_ = tmpEigenValues;
for (std::vector<double>::iterator it = rowWeights_.begin(); it != rowWeights_.end(); it++)
{
if (*it == 0.)
*it = 1.;
}
for (std::vector<double>::iterator it = colWeights_.begin(); it != colWeights_.end(); it++)
{
if (*it == 0.)
*it = 1.;
}
std::vector<double> dval(nbAxes_);
for (size_t i = 0; i < dval.size(); i++)
{
dval[i] = sqrt(eigenValues_[i]);
}
std::vector<double> invDval(nbAxes_);
for (size_t i = 0; i < invDval.size(); i++)
{
invDval[i] = 1. / sqrt(eigenValues_[i]);
}
// Calculation of the row and column coordinates as well as the principal axes and components:
if (!transpose)
{
std::vector<double> tmpColWeights(colNb);
for (unsigned int i = 0; i < colWeights_.size(); i++)
{
tmpColWeights[i] = 1. / sqrt(colWeights_[i]);
}
// The eigen vectors are placed in the same order as their corresponding eigen value in eigenValues_.
MatrixReal tmpEigenVectors(0,0);
tmpEigenVectors.resize(eigenVectors_.getNumberOfRows(), nbAxes_);
size_t cpt2 = 0;
for (size_t i = eigenVectors_.getNumberOfColumns(); i > (eigenVectors_.getNumberOfColumns() - nbAxes_); i--)
{
for (unsigned int j = 0; j < eigenVectors_.getNumberOfRows(); j++)
{
tmpEigenVectors[j][cpt2] = eigenVectors_[j][i-1];
}
cpt2++;
}
// matrix of principal axes
RbMath::hadamardMult(tmpEigenVectors, tmpColWeights, ppalAxes_, true);
// matrix of row coordinates
MatrixReal tmpRowCoord_(0,0);
tmpRowCoord_.resize(rowNb, nbAxes_);
RbMath::hadamardMult(matrix, colWeights_, tmpRowCoord_, false);
rowCoord_ = tmpRowCoord_ * ppalAxes_;
// matrix of column coordinates
RbMath::hadamardMult(ppalAxes_, dval, colCoord_, false);
// matrix of principal components
RbMath::hadamardMult(rowCoord_, invDval, ppalComponents_, false);
}
else
{
std::vector<double> tmpRowWeights(rowNb);
for (unsigned int i = 0; i < rowWeights_.size(); i++)
{
tmpRowWeights[i] = 1. / sqrt(rowWeights_[i]);
}
// The eigen vectors are placed in the same order as their corresponding eigen value in eigenValues_.
MatrixReal tmpEigenVectors(0,0);
tmpEigenVectors.resize(eigenVectors_.getNumberOfRows(), nbAxes_);
size_t cpt2 = 0;
for (size_t i = eigenVectors_.getNumberOfColumns(); i > (eigenVectors_.getNumberOfColumns() - nbAxes_); i--)
{
for (size_t j = 0; j < eigenVectors_.getNumberOfRows(); j++)
{
tmpEigenVectors[j][cpt2] = eigenVectors_[j][i-1];
}
cpt2++;
}
// matrix of principal components
RbMath::hadamardMult(tmpEigenVectors, tmpRowWeights, ppalComponents_, true);
// matrix of column coordinates
MatrixReal tmpColCoord_(colNb, nbAxes_);
RbMath::hadamardMult(matrix, rowWeights_, tmpColCoord_, true);
MatrixReal tTmpColCoord_(tmpColCoord_.getNumberOfColumns(),tmpColCoord_.getNumberOfRows());
RbMath::transposeMatrix(tmpColCoord_, tTmpColCoord_);
colCoord_ = tTmpColCoord_ * ppalComponents_;
// matrix of row coordinates
RbMath::hadamardMult(ppalComponents_, dval, rowCoord_, false);
// matrix of principal axes
RbMath::hadamardMult(colCoord_, invDval, ppalAxes_, false);
}
}