///
/// \brief Vespucci::Math::Quantification::FindBandwidthMat
/// \param X
/// \param abscissa
/// \param min
/// \param max
/// \param midlines
/// \param baselines
/// \return
/// Finds the bandwidth of every column of a arma::matrix.
arma::vec Vespucci::Math::Quantification::FindBandwidthMat(const arma::mat &X, arma::vec abscissa, double &min, double &max, arma::mat &midlines, arma::mat &baselines, arma::uvec &boundaries)
{
double delta = std::abs(abscissa(1) - abscissa(0));
arma::uvec left_bound = find(((min-delta) <= abscissa) && (abscissa <= (min+delta)));
arma::uvec right_bound = find(((max-delta) <= abscissa) && (abscissa <= (max+delta)));
arma::uword min_index = left_bound(0);
arma::uword max_index = right_bound(0);
boundaries << min_index << arma::endr << max_index;
min = abscissa(min_index);
max = abscissa(max_index);
arma::uword size = abscissa.subvec(min_index, max_index).n_elem;
arma::vec results(X.n_cols);
midlines.set_size(X.n_cols, size);
baselines.set_size(X.n_cols, size);
arma::vec midline;
arma::vec baseline;
for (arma::uword i = 0; i < X.n_cols; ++i){
results(i) = FindBandwidth(X.col(i), min_index, max_index, midline, baseline, delta);
midlines.row(i) = midline;
baselines.row(i) = baseline;
}
return results;
}
void FastMKS<KernelType, TreeType>::Search(TreeType* queryTree,
const size_t k,
arma::Mat<size_t>& indices,
arma::mat& kernels)
{
// If either naive mode or single mode is specified, this must fail.
if (naive || singleMode)
{
throw std::invalid_argument("can't call Search() with a query tree when "
"single mode or naive search is enabled");
}
// No remapping will be necessary because we are using the cover tree.
indices.set_size(k, queryTree->Dataset().n_cols);
kernels.set_size(k, queryTree->Dataset().n_cols);
kernels.fill(-DBL_MAX);
Timer::Start("computing_products");
typedef FastMKSRules<KernelType, TreeType> RuleType;
RuleType rules(referenceSet, queryTree->Dataset(), indices, kernels,
metric.Kernel());
typename TreeType::template DualTreeTraverser<RuleType> traverser(rules);
traverser.Traverse(*queryTree, *referenceTree);
Log::Info << rules.BaseCases() << " base cases." << std::endl;
Log::Info << rules.Scores() << " scores." << std::endl;
Timer::Stop("computing_products");
}
/**
* Create a Lovasz-Theta initial point.
*/
void CreateLovaszThetaInitialPoint(const arma::mat& edges,
arma::mat& coordinates)
{
// Get the number of vertices in the problem.
const size_t vertices = max(max(edges)) + 1;
const size_t m = edges.n_cols + 1;
float r = 0.5 + sqrt(0.25 + 2 * m);
if (ceil(r) > vertices)
r = vertices; // An upper bound on the dimension.
coordinates.set_size(vertices, ceil(r));
// Now we set the entries of the initial matrix according to the formula given
// in Section 4 of Monteiro and Burer.
for (size_t i = 0; i < vertices; ++i)
{
for (size_t j = 0; j < ceil(r); ++j)
{
if (i == j)
coordinates(i, j) = sqrt(1.0 / r) + sqrt(1.0 / (vertices * m));
else
coordinates(i, j) = sqrt(1.0 / (vertices * m));
}
}
}
arma::mat Vespucci::Math::Transform::cwtPeakAnalysis(const arma::mat &X,
std::string wavelet, arma::uword qscale,
double threshold, std::string threshold_method,
arma::mat &transform)
{
transform.set_size(X.n_rows, X.n_cols);
arma::uvec scales(1);
scales(0) = qscale;
arma::uword i;
arma::umat peak_positions;
arma::mat peak_extrema(X.n_rows, X.n_cols);
arma::vec spectrum, current_transform, dtransform, peak_magnitudes;
try{
for (i = 0; i < X.n_cols; ++i){
spectrum = X.col(i);
current_transform = Vespucci::Math::Transform::cwt(spectrum, wavelet, scales);
transform.col(i) = current_transform;
dtransform = Vespucci::Math::diff(transform, 1);
dtransform.insert_rows(0, 1, true); //dtransform(i) is derivative at transform(i)
peak_positions = Vespucci::Math::PeakFinding::FindPeakPositions(transform, dtransform,
threshold, threshold_method,
peak_magnitudes);
peak_extrema.col(i) = Vespucci::Math::PeakFinding::PeakExtrema(X.n_elem, peak_positions);
}
}
catch(std::exception e){
std::cerr << "CWTPeakAnalysis" << std::endl;
std::cerr << "i = " << i << std::endl;
throw(e);
}
return peak_extrema;
}
arma::mat Vespucci::Math::Transform::cwt_spdbc_mat(const arma::mat &X, std::string wavelet, arma::uword qscale,
double threshold, std::string threshold_method,
arma::uword window_size, arma::field<arma::umat> &peak_positions,
arma::mat &baselines)
{
baselines.set_size(X.n_rows, X.n_cols);
arma::vec baseline;
arma::vec spectrum;
arma::vec current_corrected;
arma::mat corrected(X.n_rows, X.n_cols);
arma::umat current_peakpos;
peak_positions.set_size(X.n_cols);
arma::uword i;
try{
for (i = 0; i < X.n_cols; ++i){
spectrum = X.col(i);
current_corrected = Vespucci::Math::Transform::cwt_spdbc(spectrum, wavelet,
qscale, threshold,
threshold_method, window_size,
current_peakpos, baseline);
peak_positions(i) = current_peakpos;
baselines.col(i) = baseline;
corrected.col(i) = current_corrected;
}
}catch(std::exception e){
std::cerr << std::endl << "exception! cwt_spdbc_mat" << std::endl;
std::cerr << "i = " << i << std::endl;
std::cerr << e.what();
throw(e);
}
return corrected;
}
/**
* Calculates and stores the gradient values given a set of parameters.
*/
void SoftmaxRegressionFunction::Gradient(const arma::mat& parameters,
arma::mat& gradient) const
{
// Calculate the class probabilities for each training example. The
// probabilities for each of the classes are given by:
// p_j = exp(theta_j' * x_i) / sum(exp(theta_k' * x_i))
// The sum is calculated over all the classes.
// x_i is the input vector for a particular training example.
// theta_j is the parameter vector associated with a particular class.
arma::mat probabilities;
GetProbabilitiesMatrix(parameters, probabilities);
// Calculate the parameter gradients.
gradient.set_size(parameters.n_rows, parameters.n_cols);
if (fitIntercept)
{
// Treating the intercept term parameters.col(0) seperately to avoid
// the cost of building matrix [1; data].
arma::mat inner = probabilities - groundTruth;
gradient.col(0) =
inner * arma::ones<arma::mat>(data.n_cols, 1) / data.n_cols +
lambda * parameters.col(0);
gradient.cols(1, parameters.n_cols - 1) =
inner * data.t() / data.n_cols +
lambda * parameters.cols(1, parameters.n_cols - 1);
}
else
{
gradient = (probabilities - groundTruth) * data.t() / data.n_cols +
lambda * parameters;
}
}
void AugLagrangianTestFunction::Gradient(const arma::mat& coordinates,
arma::mat& gradient)
{
// f'_x1(x) = 12 x_1 + 4 x_2
// f'_x2(x) = 4 x_1 + 6 x_2
gradient.set_size(2, 1);
gradient[0] = 12 * coordinates[0] + 4 * coordinates[1];
gradient[1] = 4 * coordinates[0] + 6 * coordinates[1];
}
void LogisticRegression<MatType>::Classify(const MatType& dataset,
arma::mat& probabilities) const
{
// Set correct size of output matrix.
probabilities.set_size(2, dataset.n_cols);
probabilities.row(1) = 1.0 / (1.0 + arma::exp(-parameters(0) - dataset.t() *
parameters.subvec(1, parameters.n_elem - 1))).t();
probabilities.row(0) = 1.0 - probabilities.row(1);
}
inline static void Cluster(const MatType& data,
const size_t clusters,
arma::mat& centroids)
{
centroids.set_size(data.n_rows, clusters);
for (size_t i = 0; i < clusters; ++i)
{
// Randomly sample a point.
const size_t index = math::RandInt(0, data.n_cols);
centroids.col(i) = data.col(index);
}
}
void GockenbachFunction::Gradient(const arma::mat& coordinates,
arma::mat& gradient)
{
// f'_x1(x) = 2 (x_1 - 1)
// f'_x2(x) = 4 (x_2 + 2)
// f'_x3(x) = 6 (x_3 + 3)
gradient.set_size(3, 1);
gradient[0] = 2 * (coordinates[0] - 1);
gradient[1] = 4 * (coordinates[1] + 2);
gradient[2] = 6 * (coordinates[2] + 3);
}
/**
* Remove a certain set of rows in a matrix while copying to a second matrix.
*
* @param input Input matrix to copy.
* @param rowsToRemove Vector containing indices of rows to be removed.
* @param output Matrix to copy non-removed rows into.
*/
void mlpack::math::RemoveRows(const arma::mat& input,
const std::vector<size_t>& rowsToRemove,
arma::mat& output)
{
const size_t nRemove = rowsToRemove.size();
const size_t nKeep = input.n_rows - nRemove;
if (nRemove == 0)
{
output = input; // Copy everything.
}
else
{
output.set_size(nKeep, input.n_cols);
size_t curRow = 0;
size_t removeInd = 0;
// First, check 0 to first row to remove.
if (rowsToRemove[0] > 0)
{
// Note that this implies that n_rows > 1.
output.rows(0, rowsToRemove[0] - 1) = input.rows(0, rowsToRemove[0] - 1);
curRow += rowsToRemove[0];
}
// Now, check i'th row to remove to (i + 1)'th row to remove, until i is the
// penultimate row.
while (removeInd < nRemove - 1)
{
const size_t height = rowsToRemove[removeInd + 1] -
rowsToRemove[removeInd] - 1;
if (height > 0)
{
output.rows(curRow, curRow + height - 1) =
input.rows(rowsToRemove[removeInd] + 1,
rowsToRemove[removeInd + 1] - 1);
curRow += height;
}
removeInd++;
}
// Now that i is the last row to remove, check last row to remove to last
// row.
if (rowsToRemove[removeInd] < input.n_rows - 1)
{
output.rows(curRow, nKeep - 1) = input.rows(rowsToRemove[removeInd] + 1,
input.n_rows - 1);
}
}
}
/**
* Calculate the gradient.
*/
void RosenbrockFunction::Gradient(const arma::mat& coordinates,
arma::mat& gradient)
{
// f'_{x1}(x) = -2 (1 - x1) + 400 (x1^3 - (x2 x1))
// f'_{x2}(x) = 200 (x2 - x1^2)
double x1 = coordinates[0];
double x2 = coordinates[1];
gradient.set_size(2, 1);
gradient[0] = -2 * (1 - x1) + 400 * (std::pow(x1, 3) - x2 * x1);
gradient[1] = 200 * (x2 - std::pow(x1, 2));
}
/***
* Calculate the gradient.
*/
void RosenbrockWoodFunction::Gradient(const arma::mat& coordinates,
arma::mat& gradient)
{
gradient.set_size(4, 2);
arma::vec grf(4);
arma::vec gwf(4);
rf.Gradient(coordinates.col(0), grf);
wf.Gradient(coordinates.col(1), gwf);
gradient.col(0) = grf;
gradient.col(1) = gwf;
}
void LogisticRegressionFunction<MatType>::Gradient(
const arma::mat& parameters,
arma::mat& gradient) const
{
// Regularization term.
arma::mat regularization;
regularization = lambda * parameters.tail_cols(parameters.n_elem - 1);
const arma::rowvec sigmoids = (1 / (1 + arma::exp(-parameters(0, 0)
- parameters.tail_cols(parameters.n_elem - 1) * predictors)));
gradient.set_size(arma::size(parameters));
gradient[0] = -arma::accu(responses - sigmoids);
gradient.tail_cols(parameters.n_elem - 1) = (sigmoids - responses) *
predictors.t() + regularization;
}
/**
* Calculate the gradient.
*/
void GeneralizedRosenbrockFunction::Gradient(const arma::mat& coordinates,
arma::mat& gradient) const
{
gradient.set_size(n);
for (int i = 0; i < (n - 1); i++)
{
gradient[i] = 400 * (std::pow(coordinates[i], 3) - coordinates[i] *
coordinates[i + 1]) + 2 * (coordinates[i] - 1);
if (i > 0)
gradient[i] += 200 * (coordinates[i] - std::pow(coordinates[i - 1], 2));
}
gradient[n - 1] = 200 * (coordinates[n - 1] -
std::pow(coordinates[n - 2], 2));
}
void NormalizeColByMax(const arma::mat &input,
arma::mat &output)
{
output.set_size(input.n_rows, input.n_cols);
for (arma::uword i = 0; i != input.n_cols; ++i)
{
const double max = arma::max(arma::abs(input.col(i)));
if (max != 0.0)
{
output.col(i) = input.col(i) / max;
}
else
{
output.col(i) = input.col(i);
}
}
}
void DualTreeBoruvka<MetricType, TreeType>::EmitResults(arma::mat& results)
{
// Sort the edges.
std::sort(edges.begin(), edges.end(), SortFun);
Log::Assert(edges.size() == data.n_cols - 1);
results.set_size(3, edges.size());
// Need to unpermute the point labels.
if (!naive && ownTree && tree::TreeTraits<TreeType>::RearrangesDataset)
{
for (size_t i = 0; i < (data.n_cols - 1); i++)
{
// Make sure the edge list stores the smaller index first to
// make checking correctness easier
size_t ind1 = oldFromNew[edges[i].Lesser()];
size_t ind2 = oldFromNew[edges[i].Greater()];
if (ind1 < ind2)
{
edges[i].Lesser() = ind1;
edges[i].Greater() = ind2;
}
else
{
edges[i].Lesser() = ind2;
edges[i].Greater() = ind1;
}
results(0, i) = edges[i].Lesser();
results(1, i) = edges[i].Greater();
results(2, i) = edges[i].Distance();
}
}
else
{
for (size_t i = 0; i < edges.size(); i++)
{
results(0, i) = edges[i].Lesser();
results(1, i) = edges[i].Greater();
results(2, i) = edges[i].Distance();
}
}
} // EmitResults
/**
* Initialize the dictionary by adding together three random observations from
* the data, and then normalizing the atom. This implementation is simple
* enough to be included with the definition.
*
* @param data Dataset to initialize the dictionary with.
* @param atoms Number of atoms in dictionary.
* @param dictionary Dictionary to initialize.
*/
static void Initialize(const arma::mat& data,
const size_t atoms,
arma::mat& dictionary)
{
// Set the size of the dictionary.
dictionary.set_size(data.n_rows, atoms);
// Create each atom.
for (size_t i = 0; i < atoms; ++i)
{
// Add three atoms together.
dictionary.col(i) = (data.col(math::RandInt(data.n_cols)) +
data.col(math::RandInt(data.n_cols)) +
data.col(math::RandInt(data.n_cols)));
// Now normalize the atom.
dictionary.col(i) /= norm(dictionary.col(i), 2);
}
}
void pca::read_armmat (const char * fname, arma::mat & cmtx)
{
int n, m;
std::ifstream myfilec(fname, std::ios::binary | std::ios::in);
myfilec.read((char *)&n, sizeof(n));
myfilec.read((char *)&m, sizeof(m));
cmtx.set_size(n, m);
for (int i=0; i<(int)cmtx.n_rows; i++)
{
for (int j=0; j<(int)cmtx.n_cols; j++)
{
double v;
myfilec.read((char *)&v, sizeof(v));
cmtx(i, j) = v;
}
}
myfilec.close();
}
void HMM<Distribution>::Generate(const size_t length,
arma::mat& dataSequence,
arma::Col<size_t>& stateSequence,
const size_t startState) const
{
// Set vectors to the right size.
stateSequence.set_size(length);
dataSequence.set_size(dimensionality, length);
// Set start state (default is 0).
stateSequence[0] = startState;
// Choose first emission state.
double randValue = math::Random();
// We just have to find where our random value sits in the probability
// distribution of emissions for our starting state.
dataSequence.col(0) = emission[startState].Random();
// Now choose the states and emissions for the rest of the sequence.
for (size_t t = 1; t < length; t++)
{
// First choose the hidden state.
randValue = math::Random();
// Now find where our random value sits in the probability distribution of
// state changes.
double probSum = 0;
for (size_t st = 0; st < transition.n_rows; st++)
{
probSum += transition(st, stateSequence[t - 1]);
if (randValue <= probSum)
{
stateSequence[t] = st;
break;
}
}
// Now choose the emission.
dataSequence.col(t) = emission[stateSequence[t]].Random();
}
}
void LSHSearch<SortPolicy>::
Search(const size_t k,
arma::Mat<size_t>& resultingNeighbors,
arma::mat& distances,
const size_t numTablesToSearch)
{
// Set the size of the neighbor and distance matrices.
resultingNeighbors.set_size(k, querySet.n_cols);
distances.set_size(k, querySet.n_cols);
distances.fill(SortPolicy::WorstDistance());
resultingNeighbors.fill(referenceSet.n_cols);
size_t avgIndicesReturned = 0;
Timer::Start("computing_neighbors");
// Go through every query point sequentially.
for (size_t i = 0; i < querySet.n_cols; i++)
{
// Hash every query into every hash table and eventually into the
// 'secondHashTable' to obtain the neighbor candidates.
arma::uvec refIndices;
ReturnIndicesFromTable(i, refIndices, numTablesToSearch);
// An informative book-keeping for the number of neighbor candidates
// returned on average.
avgIndicesReturned += refIndices.n_elem;
// Sequentially go through all the candidates and save the best 'k'
// candidates.
for (size_t j = 0; j < refIndices.n_elem; j++)
BaseCase(distances, resultingNeighbors, i, (size_t) refIndices[j]);
}
Timer::Stop("computing_neighbors");
distanceEvaluations += avgIndicesReturned;
avgIndicesReturned /= querySet.n_cols;
Log::Info << avgIndicesReturned << " distinct indices returned on average." <<
std::endl;
}
void CylindricalBirefringentMaterial::dielectricTensorInPrincCrdSyst( const meep::vec &r, arma::mat &eps, const BirefringentEps &biref ) const
{
eps.set_size(3,3);
arma::vec rTrans;
transformR(r,rTrans);
for ( unsigned int i=0;i<3;i++ )
{
eps(princAxis,i) = 0.0;
eps(i,princAxis) = 0.0;
}
eps(princAxis,princAxis) = biref.ordinary;
unsigned int indx1 = (princAxis+1)%3;
unsigned int indx2 = (princAxis+2)%3;
double R = sqrt( pow(rTrans(indx1),2) + pow(rTrans(indx2),2 ));
double cosTheta = rTrans(indx1)/R;
double sinTheta = rTrans(indx2)/R;
eps(indx1,indx1) = biref.extraOrdinary*cosTheta*cosTheta + biref.ordinary*sinTheta*sinTheta;
eps(indx2,indx2) = biref.extraOrdinary*sinTheta*sinTheta + biref.ordinary*cosTheta*cosTheta;
eps(indx1,indx2) = (biref.extraOrdinary - biref.ordinary)*sinTheta*cosTheta;
eps(indx2,indx1) = eps(indx1,indx2);
}
/**
* Calculate the gradient.
*/
void WoodFunction::Gradient(const arma::mat& coordinates,
arma::mat& gradient)
{
// For convenience; we assume these temporaries will be optimized out.
double x1 = coordinates[0];
double x2 = coordinates[1];
double x3 = coordinates[2];
double x4 = coordinates[3];
// f'_{x1}(x) = 400 (x1^3 - x2 x1) - 2 (1 - x1)
// f'_{x2}(x) = 200 (x2 - x1^2) + 20 (x2 + x4 - 2) + (1 / 5) (x2 - x4)
// f'_{x3}(x) = 360 (x3^3 - x4 x3) - 2 (1 - x3)
// f'_{x4}(x) = 180 (x4 - x3^2) + 20 (x2 + x4 - 2) - (1 / 5) (x2 - x4)
gradient.set_size(4, 1);
gradient[0] = 400 * (std::pow(x1, 3) - x2 * x1) - 2 * (1 - x1);
gradient[1] = 200 * (x2 - std::pow(x1, 2)) + 20 * (x2 + x4 - 2) +
(1.0 / 5.0) * (x2 - x4);
gradient[2] = 360 * (std::pow(x3, 3) - x4 * x3) - 2 * (1 - x3);
gradient[3] = 180 * (x4 - std::pow(x3, 2)) + 20 * (x2 + x4 - 2) -
(1.0 / 5.0) * (x2 - x4);
}
void SparseCoding::Encode(const arma::mat& data, arma::mat& codes)
{
// When using the Cholesky version of LARS, this is correct even if
// lambda2 > 0.
arma::mat matGram = trans(dictionary) * dictionary;
codes.set_size(atoms, data.n_cols);
for (size_t i = 0; i < data.n_cols; ++i)
{
// Report progress.
if ((i % 100) == 0)
Log::Debug << "Optimization at point " << i << "." << std::endl;
bool useCholesky = true;
regression::LARS lars(useCholesky, matGram, lambda1, lambda2);
// Create an alias of the code (using the same memory), and then LARS will
// place the result directly into that; then we will not need to have an
// extra copy.
arma::vec code = codes.unsafe_col(i);
lars.Train(dictionary, data.unsafe_col(i), code, false);
}
}
void RASearch<SortPolicy, MetricType, TreeType>::
Search(const size_t k,
arma::Mat<size_t>& resultingNeighbors,
arma::mat& distances,
const double tau,
const double alpha,
const bool sampleAtLeaves,
const bool firstLeafExact,
const size_t singleSampleLimit)
{
// If we have built the trees ourselves, then we will have to map all the
// indices back to their original indices when this computation is finished.
// To avoid an extra copy, we will store the neighbors and distances in a
// separate matrix.
arma::Mat<size_t>* neighborPtr = &resultingNeighbors;
arma::mat* distancePtr = &distances;
// Mapping is only required if this tree type rearranges points and we are not
// in naive mode.
if (tree::TreeTraits<TreeType>::RearrangesDataset)
{
if (treeOwner && !(singleMode && hasQuerySet))
distancePtr = new arma::mat; // Query indices need to be mapped.
if (treeOwner)
neighborPtr = new arma::Mat<size_t>; // All indices need mapping.
}
// Set the size of the neighbor and distance matrices.
neighborPtr->set_size(k, querySet.n_cols);
distancePtr->set_size(k, querySet.n_cols);
distancePtr->fill(SortPolicy::WorstDistance());
size_t numPrunes = 0;
if (naive)
{
// We don't need to run the base case on every possible combination of
// points; we can achieve the rank approximation guarantee with probability
// alpha by sampling the reference set.
typedef RASearchRules<SortPolicy, MetricType, TreeType> RuleType;
RuleType rules(referenceSet, querySet, *neighborPtr, *distancePtr,
metric, tau, alpha, naive, sampleAtLeaves, firstLeafExact,
singleSampleLimit);
// Find how many samples from the reference set we need and sample uniformly
// from the reference set without replacement.
const size_t numSamples = rules.MinimumSamplesReqd(referenceSet.n_cols, k,
tau, alpha);
arma::uvec distinctSamples;
rules.ObtainDistinctSamples(numSamples, referenceSet.n_cols,
distinctSamples);
// Run the base case on each combination of query point and sampled
// reference point.
for (size_t i = 0; i < querySet.n_cols; ++i)
for (size_t j = 0; j < distinctSamples.n_elem; ++j)
rules.BaseCase(i, (size_t) distinctSamples[j]);
}
else if (singleMode)
{
// Create the helper object for the tree traversal. Initialization of
// RASearchRules already implicitly performs the naive tree traversal.
typedef RASearchRules<SortPolicy, MetricType, TreeType> RuleType;
RuleType rules(referenceSet, querySet, *neighborPtr, *distancePtr,
metric, tau, alpha, naive, sampleAtLeaves, firstLeafExact,
singleSampleLimit);
// If the reference root node is a leaf, then the sampling has already been
// done in the RASearchRules constructor. This happens when naive = true.
if (!referenceTree->IsLeaf())
{
Rcpp::Rcout << "Performing single-tree traversal..." << std::endl;
// Create the traverser.
typename TreeType::template SingleTreeTraverser<RuleType>
traverser(rules);
// Now have it traverse for each point.
for (size_t i = 0; i < querySet.n_cols; ++i)
traverser.Traverse(i, *referenceTree);
numPrunes = traverser.NumPrunes();
Rcpp::Rcout << "Single-tree traversal complete." << std::endl;
Rcpp::Rcout << "Average number of distance calculations per query point: "
<< (rules.NumDistComputations() / querySet.n_cols) << "."
<< std::endl;
}
}
else // Dual-tree recursion.
{
Rcpp::Rcout << "Performing dual-tree traversal..." << std::endl;
typedef RASearchRules<SortPolicy, MetricType, TreeType> RuleType;
RuleType rules(referenceSet, querySet, *neighborPtr, *distancePtr,
metric, tau, alpha, sampleAtLeaves, firstLeafExact,
singleSampleLimit);
typename TreeType::template DualTreeTraverser<RuleType> traverser(rules);
if (queryTree)
{
Rcpp::Rcout << "Query statistic pre-search: "
<< queryTree->Stat().NumSamplesMade() << std::endl;
traverser.Traverse(*queryTree, *referenceTree);
}
else
{
Rcpp::Rcout << "Query statistic pre-search: "
<< referenceTree->Stat().NumSamplesMade() << std::endl;
traverser.Traverse(*referenceTree, *referenceTree);
}
numPrunes = traverser.NumPrunes();
Rcpp::Rcout << "Dual-tree traversal complete." << std::endl;
Rcpp::Rcout << "Average number of distance calculations per query point: "
<< (rules.NumDistComputations() / querySet.n_cols) << "." << std::endl;
}
Rcpp::Rcout << "Pruned " << numPrunes << " nodes." << std::endl;
// Now, do we need to do mapping of indices?
if (!treeOwner || !tree::TreeTraits<TreeType>::RearrangesDataset)
{
// No mapping needed. We are done.
return;
}
else if (treeOwner && hasQuerySet && !singleMode) // Map both sets.
{
// Set size of output matrices correctly.
resultingNeighbors.set_size(k, querySet.n_cols);
distances.set_size(k, querySet.n_cols);
for (size_t i = 0; i < distances.n_cols; i++)
{
// Map distances (copy a column).
distances.col(oldFromNewQueries[i]) = distancePtr->col(i);
// Map indices of neighbors.
for (size_t j = 0; j < distances.n_rows; j++)
{
resultingNeighbors(j, oldFromNewQueries[i]) =
oldFromNewReferences[(*neighborPtr)(j, i)];
}
}
// Finished with temporary matrices.
delete neighborPtr;
delete distancePtr;
}
else if (treeOwner && !hasQuerySet)
{
// No query tree -- map both references and queries.
resultingNeighbors.set_size(k, querySet.n_cols);
distances.set_size(k, querySet.n_cols);
for (size_t i = 0; i < distances.n_cols; i++)
{
// Map distances (copy a column).
distances.col(oldFromNewReferences[i]) = distancePtr->col(i);
// Map indices of neighbors.
for (size_t j = 0; j < distances.n_rows; j++)
{
resultingNeighbors(j, oldFromNewReferences[i]) =
oldFromNewReferences[(*neighborPtr)(j, i)];
}
}
}
else if (treeOwner && hasQuerySet && singleMode) // Map only references.
{
// Set size of neighbor indices matrix correctly.
resultingNeighbors.set_size(k, querySet.n_cols);
// Map indices of neighbors.
for (size_t i = 0; i < resultingNeighbors.n_cols; i++)
{
for (size_t j = 0; j < resultingNeighbors.n_rows; j++)
{
resultingNeighbors(j, i) = oldFromNewReferences[(*neighborPtr)(j, i)];
}
}
// Finished with temporary matrix.
delete neighborPtr;
}
} // Search
void FastMKS<KernelType, TreeType>::Search(const size_t k,
arma::Mat<size_t>& indices,
arma::mat& kernels)
{
// No remapping will be necessary because we are using the cover tree.
Timer::Start("computing_products");
indices.set_size(k, referenceSet.n_cols);
kernels.set_size(k, referenceSet.n_cols);
kernels.fill(-DBL_MAX);
// Naive implementation.
if (naive)
{
// Simple double loop. Stupid, slow, but a good benchmark.
for (size_t q = 0; q < referenceSet.n_cols; ++q)
{
for (size_t r = 0; r < referenceSet.n_cols; ++r)
{
if (q == r)
continue; // Don't return the point as its own candidate.
const double eval = metric.Kernel().Evaluate(referenceSet.col(q),
referenceSet.col(r));
size_t insertPosition;
for (insertPosition = 0; insertPosition < indices.n_rows;
++insertPosition)
if (eval > kernels(insertPosition, q))
break;
if (insertPosition < indices.n_rows)
InsertNeighbor(indices, kernels, q, insertPosition, r, eval);
}
}
Timer::Stop("computing_products");
return;
}
// Single-tree implementation.
if (singleMode)
{
// Create rules object (this will store the results). This constructor
// precalculates each self-kernel value.
typedef FastMKSRules<KernelType, TreeType> RuleType;
RuleType rules(referenceSet, referenceSet, indices, kernels,
metric.Kernel());
typename TreeType::template SingleTreeTraverser<RuleType> traverser(rules);
for (size_t i = 0; i < referenceSet.n_cols; ++i)
traverser.Traverse(i, *referenceTree);
// Save the number of pruned nodes.
const size_t numPrunes = traverser.NumPrunes();
Log::Info << "Pruned " << numPrunes << " nodes." << std::endl;
Log::Info << rules.BaseCases() << " base cases." << std::endl;
Log::Info << rules.Scores() << " scores." << std::endl;
Timer::Stop("computing_products");
return;
}
// Dual-tree implementation.
Timer::Stop("computing_products");
Search(referenceTree, k, indices, kernels);
}
void FastMKS<KernelType, TreeType>::Search(
const typename TreeType::Mat& querySet,
const size_t k,
arma::Mat<size_t>& indices,
arma::mat& kernels)
{
Timer::Start("computing_products");
// No remapping will be necessary because we are using the cover tree.
indices.set_size(k, querySet.n_cols);
kernels.set_size(k, querySet.n_cols);
// Naive implementation.
if (naive)
{
// Fill kernels.
kernels.fill(-DBL_MAX);
// Simple double loop. Stupid, slow, but a good benchmark.
for (size_t q = 0; q < querySet.n_cols; ++q)
{
for (size_t r = 0; r < referenceSet.n_cols; ++r)
{
const double eval = metric.Kernel().Evaluate(querySet.col(q),
referenceSet.col(r));
size_t insertPosition;
for (insertPosition = 0; insertPosition < indices.n_rows;
++insertPosition)
if (eval > kernels(insertPosition, q))
break;
if (insertPosition < indices.n_rows)
InsertNeighbor(indices, kernels, q, insertPosition, r, eval);
}
}
Timer::Stop("computing_products");
return;
}
// Single-tree implementation.
if (singleMode)
{
// Fill kernels.
kernels.fill(-DBL_MAX);
// Create rules object (this will store the results). This constructor
// precalculates each self-kernel value.
typedef FastMKSRules<KernelType, TreeType> RuleType;
RuleType rules(referenceSet, querySet, indices, kernels, metric.Kernel());
typename TreeType::template SingleTreeTraverser<RuleType> traverser(rules);
for (size_t i = 0; i < querySet.n_cols; ++i)
traverser.Traverse(i, *referenceTree);
Log::Info << rules.BaseCases() << " base cases." << std::endl;
Log::Info << rules.Scores() << " scores." << std::endl;
Timer::Stop("computing_products");
return;
}
// Dual-tree implementation. First, we need to build the query tree. We are
// assuming it doesn't map anything...
Timer::Stop("computing_products");
Timer::Start("tree_building");
TreeType queryTree(querySet);
Timer::Stop("tree_building");
Search(&queryTree, k, indices, kernels);
}
///
/// \brief Vespucci::MathDimensionReduction::plsregress PLS Regression Using SIMPLS algorithm.
/// This is essentially a line-for-line rewrite of plsregress from the Octave
/// statistics package.
/// Copyright (C) 2012 Fernando Damian Nieuwveldt <*****@*****.**>
/// This is an implementation of the SIMPLS algorithm:
/// Reference: SIMPLS: An alternative approach to partial least squares regression.
/// Chemometrics and Intelligent Laboratory Systems (1993)
/// \param x
/// \param y
/// \param components Number of PLS components
/// \param x_loadings "Output" values
/// \param y_loadings
/// \param x_scores
/// \param y_scores
/// \param coefficients
/// \param fitted_data
/// \return
///
bool Vespucci::Math::DimensionReduction::plsregress(arma::mat X, arma::mat Y,
int components, arma::mat &X_loadings,
arma::mat &Y_loadings,
arma::mat &X_scores,
arma::mat &Y_scores,
arma::mat &coefficients,
arma::mat &percent_variance,
arma::mat &fitted)
{
using namespace arma;
uword observations = X.n_rows;
uword predictors = X.n_cols;
uword responses = Y.n_cols;
//Mean centering
mat Xmeans = arma::mean(X);
mat Ymeans = arma::mean(Y);
//Octave does below with bsxfun. After optimization, this should hopefully not
// be slower.
X.each_row() -= Xmeans; //element-wise subtraction of mean
Y.each_row() -= Ymeans; //same
mat S = trans(X) * Y;
mat R = zeros(predictors, components);
mat P = R;
mat V = R;
mat T = zeros(observations, components);
mat U = T;
mat Q = zeros(responses, components);
mat eigvec;
vec eigval;
mat q;
mat r;
mat t;
mat nt;
mat p;
mat u;
mat v;
double max_eigval;
for (int i = 0; i < components; ++i){
eig_sym(eigval, eigvec, (trans(S) * S));
max_eigval = eigval.max();
uvec dom_index = find(eigval >= max_eigval);
uword dominant_index = dom_index(0);
q = eigvec.col(dominant_index);
r = S*q; //X block factor weights
t = X*r; //X block factor weights
t.each_row() -= mean(t); //center t
nt = arma::sqrt(t.t()*t); //compute norm (is arma::norm() the same?)
t.each_row() /= nt;
r.each_row() /= nt; //normalize
p = X.t()*t; //X block factor loadings
q = Y.t()*t; //Y block factor loadings
u = Y*q; //Y block factor scores
v = p;
//Ensure orthogonality
if (i > 0){
v = v - V*(V.t()*p);
u = u - T*(T.t()*u);
}
v.each_row() /= arma::sqrt(trans(v) * v); //normalize orthogonal loadings
S = S - v * (trans(v)*S); //deflate S wrt loadings
R.col(i) = r;
T.col(i) = t;
P.col(i) = p;
Q.col(i) = q;
U.col(i) = u;
V.col(i) = v;
}
//Regression coefficients
mat B = R*trans(Q);
fitted = T*trans(Q);
fitted.each_row() += Ymeans;
//Octave creates copies from inputs before sending to output. Doing same
//here just to be safe.
coefficients = B;
X_scores = T;
X_loadings = P;
Y_scores = U;
Y_loadings = Q;
//projection = R;
percent_variance.set_size(2, coefficients.n_cols);
percent_variance.row(0) = sum(arma::abs(P)%arma::abs(P)) / sum(sum(arma::abs(X)%arma::abs(X)));
percent_variance.row(1) = sum(arma::abs(Q)%arma::abs(Q)) / sum(sum(arma::abs(Y)%arma::abs(Y)));
return true;
}
void RAModel<SortPolicy>::Search(arma::mat&& querySet,
const size_t k,
arma::Mat<size_t>& neighbors,
arma::mat& distances)
{
// Apply the random basis if necessary.
if (randomBasis)
querySet = q * querySet;
Log::Info << "Searching for " << k << " approximate nearest neighbors with ";
if (!Naive() && !SingleMode())
Log::Info << "dual-tree rank-approximate " << TreeName() << " search...";
else if (!Naive())
Log::Info << "single-tree rank-approximate " << TreeName() << " search...";
else
Log::Info << "brute-force (naive) rank-approximate search...";
Log::Info << std::endl;
switch (treeType)
{
case KD_TREE:
if (!kdTreeRA->Naive() && !kdTreeRA->SingleMode())
{
// Build a second tree and search.
Timer::Start("tree_building");
Log::Info << "Building query tree..." << std::endl;
std::vector<size_t> oldFromNewQueries;
typename RAType<tree::KDTree>::Tree queryTree(std::move(querySet),
oldFromNewQueries, leafSize);
Log::Info << "Tree built." << std::endl;
Timer::Stop("tree_building");
arma::Mat<size_t> neighborsOut;
arma::mat distancesOut;
kdTreeRA->Search(&queryTree, k, neighborsOut, distancesOut);
// Unmap the query points.
distances.set_size(distancesOut.n_rows, distancesOut.n_cols);
neighbors.set_size(neighborsOut.n_rows, neighborsOut.n_cols);
for (size_t i = 0; i < neighborsOut.n_cols; ++i)
{
neighbors.col(oldFromNewQueries[i]) = neighborsOut.col(i);
distances.col(oldFromNewQueries[i]) = distancesOut.col(i);
}
}
else
{
// Search without building a second tree.
kdTreeRA->Search(querySet, k, neighbors, distances);
}
break;
case COVER_TREE:
// No mapping necessary.
coverTreeRA->Search(querySet, k, neighbors, distances);
break;
case R_TREE:
// No mapping necessary.
rTreeRA->Search(querySet, k, neighbors, distances);
break;
case R_STAR_TREE:
// No mapping necessary.
rStarTreeRA->Search(querySet, k, neighbors, distances);
break;
case X_TREE:
// No mapping necessary.
xTreeRA->Search(querySet, k, neighbors, distances);
break;
}
}
void NeighborSearch<SortPolicy, MetricType, TreeType>::Search(
const size_t k,
arma::Mat<size_t>& resultingNeighbors,
arma::mat& distances)
{
Timer::Start("computing_neighbors");
// If we have built the trees ourselves, then we will have to map all the
// indices back to their original indices when this computation is finished.
// To avoid an extra copy, we will store the neighbors and distances in a
// separate matrix.
arma::Mat<size_t>* neighborPtr = &resultingNeighbors;
arma::mat* distancePtr = &distances;
if (treeOwner && !(singleMode && hasQuerySet))
distancePtr = new arma::mat; // Query indices need to be mapped.
if (treeOwner)
neighborPtr = new arma::Mat<size_t>; // All indices need mapping.
// Set the size of the neighbor and distance matrices.
neighborPtr->set_size(k, querySet.n_cols);
distancePtr->set_size(k, querySet.n_cols);
distancePtr->fill(SortPolicy::WorstDistance());
size_t numPrunes = 0;
// Create the helper object for the tree traversal.
typedef NeighborSearchRules<SortPolicy, MetricType, TreeType> RuleType;
RuleType rules(referenceSet, querySet, *neighborPtr, *distancePtr, metric);
if (singleMode)
{
// Create the traverser.
typename TreeType::template SingleTreeTraverser<RuleType> traverser(rules);
// Now have it traverse for each point.
for (size_t i = 0; i < querySet.n_cols; ++i)
traverser.Traverse(i, *referenceTree);
}
else // Dual-tree recursion.
{
// Create the traverser.
typename TreeType::template DualTreeTraverser<RuleType> traverser(rules);
traverser.Traverse(*queryTree, *referenceTree);
Log::Info << traverser.NumVisited() << " node combinations were visited.\n";
Log::Info << traverser.NumScores() << " node combinations were scored.\n";
Log::Info << traverser.NumBaseCases() << " base cases were calculated.\n";
}
Timer::Stop("computing_neighbors");
// Now, do we need to do mapping of indices?
if (!treeOwner)
{
// No mapping needed. We are done.
return;
}
else if (treeOwner && hasQuerySet && !singleMode) // Map both sets.
{
// Set size of output matrices correctly.
resultingNeighbors.set_size(k, querySet.n_cols);
distances.set_size(k, querySet.n_cols);
for (size_t i = 0; i < distances.n_cols; i++)
{
// Map distances (copy a column).
distances.col(oldFromNewQueries[i]) = distancePtr->col(i);
// Map indices of neighbors.
for (size_t j = 0; j < distances.n_rows; j++)
{
resultingNeighbors(j, oldFromNewQueries[i]) =
oldFromNewReferences[(*neighborPtr)(j, i)];
}
}
// Finished with temporary matrices.
delete neighborPtr;
delete distancePtr;
}
else if (treeOwner && !hasQuerySet)
{
resultingNeighbors.set_size(k, querySet.n_cols);
distances.set_size(k, querySet.n_cols);
for (size_t i = 0; i < distances.n_cols; i++)
{
// Map distances (copy a column).
distances.col(oldFromNewReferences[i]) = distancePtr->col(i);
// Map indices of neighbors.
for (size_t j = 0; j < distances.n_rows; j++)
{
resultingNeighbors(j, oldFromNewReferences[i]) =
oldFromNewReferences[(*neighborPtr)(j, i)];
}
}
}
else if (treeOwner && hasQuerySet && singleMode) // Map only references.
{
// Set size of neighbor indices matrix correctly.
resultingNeighbors.set_size(k, querySet.n_cols);
// Map indices of neighbors.
for (size_t i = 0; i < resultingNeighbors.n_cols; i++)
{
for (size_t j = 0; j < resultingNeighbors.n_rows; j++)
{
resultingNeighbors(j, i) = oldFromNewReferences[(*neighborPtr)(j, i)];
}
}
// Finished with temporary matrix.
delete neighborPtr;
}
} // Search
