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");
}
}
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);
}
}