PDS/homework_1/inc/v0.hpp

/**
 * \file    v0.hpp
 * \brief
 *
 * \author
 *    Christos Choutouridis AEM:8997
 *    <cchoutou@ece.auth.gr>
 */
#ifndef V0_HPP_
#define V0_HPP_

#include <cblas.h>
#include <cmath>
#include <vector>
#include <algorithm>

#include "matrix.hpp"
#include "config.h"

namespace v0 {

/*!
 * Function to compute squared Euclidean distances
 *
 * \fn void pdist2(const double*, const double*, double*, int, int, int)
 * \param X    m x d matrix (Column major)
 * \param Y    n x d matrix (Column major)
 * \param D2   m x n matrix to store distances (Column major)
 * \param m    number of rows in X
 * \param n    number of rows in Y
 * \param d    number of columns in both X and Y
 */
template<typename Matrix>
void pdist2(const Matrix& X, const Matrix& Y, Matrix& D2) {
   using DataType = typename Matrix::dataType;

   int M = X.rows();
   int N = Y.rows();
   int d = X.columns();

   // Compute the squared norms of each row in X and Y
   std::vector<DataType> X_norms(M), Y_norms(N);
   for (int i = 0; i < M ; ++i) {
      X_norms[i] = cblas_ddot(d, X.data() + i * d, 1, X.data() + i * d, 1);
   }
   for (int j = 0; j < N ; ++j) {
      Y_norms[j] = cblas_ddot(d, Y.data() + j * d, 1, Y.data() + j * d, 1);
   }

   // Compute -2 * X * Y'
   cblas_dgemm(CblasRowMajor, CblasNoTrans, CblasTrans, M, N, d, -2.0, X.data(), d, Y.data(), d, 0.0, D2.data(), N);

   // Step 3: Add the squared norms to each entry in D2
   for (int i = 0; i < M ; ++i) {
      for (int j = 0; j < N; ++j) {
         D2.set(D2.get(i, j) + X_norms[i] + Y_norms[j], i, j);
         D2.set(std::max(D2.get(i, j), 0.0),            i, j); // Ensure non-negative
         D2.set(std::sqrt(D2.get(i, j)),                i, j); // Take the square root of each
      }
   }
   M++;
}

/*!
 * Quick select implementation
 * \fn void quickselect(std::vector<std::pair<DataType,IndexType>>&, int)
 * \tparam DataType
 * \tparam IndexType
 * \param vec  Vector of paire(distance, index) to partially sort over distance
 * \param k    The number of elements to sort-select
 */
template<typename DataType, typename IndexType>
void quickselect(std::vector<std::pair<DataType, IndexType>>& vec, int k) {
   std::nth_element(
      vec.begin(),
      vec.begin() + k,
      vec.end(),
      [](const std::pair<DataType, IndexType>& a, const std::pair<DataType, IndexType>& b) {
         return a.first < b.first;
   });
   vec.resize(k);  // Keep only the k smallest elements
}

/*!
 * \param C    Is a MxD matrix (Corpus)
 * \param Q    Is a NxD matrix (Query)
 * \param idx_offset The offset of the indexes for output (to match with the actual Corpus indexes)
 * \param k    The number of nearest neighbors needed
 * \param idx  Is the Nxk matrix with the k indexes of the C points, that are
 *             neighbors of the nth point of Q
 * \param dst  Is the Nxk matrix with the k distances to the C points of the nth
 *             point of Q
 */
template<typename MatrixD, typename MatrixI>
void knnsearch(MatrixD& C, MatrixD& Q, size_t idx_offset, size_t k, size_t m, MatrixI& idx, MatrixD& dst) {

   using DstType = typename MatrixD::dataType;
   using IdxType = typename MatrixI::dataType;

   size_t M = C.rows();
   size_t N = Q.rows();

   mtx::Matrix<DstType> D(M, N);

   pdist2(C, Q, D);

   for (size_t j = 0; j < N; ++j) {
      // Create a vector of pairs (distance, index) for the j-th query
      std::vector<std::pair<DstType, IdxType>> dst_idx(M);
      for (size_t i = 0; i < M; ++i) {
         dst_idx[i] = {D.data()[i * N + j], i};
      }
      // Find the k smallest distances using quickSelectKSmallest
      quickselect(dst_idx, k);

      // Sort the k smallest results by distance for consistency
      std::sort(dst_idx.begin(), dst_idx.end());

      // Store the indices and distances
      for (size_t i = 0; i < k; ++i) {
         dst.set(dst_idx[i].first, j, i);
         idx.set(dst_idx[i].second + idx_offset, j, i);
      }
   }
}

}

#endif /* V0_HPP_ */