@@ -23,11 +23,11 @@ PROJECT := PDS_homework_1 | |||
# Excecutable's name | |||
TARGET := knnsearch | |||
# Source directories list(space seperated). Makefile-relative path, UNDER current directory. | |||
SRC_DIR_LIST := src | |||
SRC_DIR_LIST := src gtest | |||
# Include directories list(space seperated). Makefile-relative path. | |||
INC_DIR_LIST := inc \ | |||
src \ | |||
Libs/matrix/include/ \ | |||
gtest \ | |||
/usr/include/hdf5/serial/ | |||
# Libs/MATLAB/R2019b/include/ \ | |||
@@ -56,7 +56,6 @@ PRE_DEFS := | |||
LDFLAGS := -pthread -lopenblas \ | |||
-L/usr/lib/x86_64-linux-gnu/hdf5/serial -lhdf5 | |||
# -LLibs/MATLAB/R2019b/bin/ -lmat -lmx -Wl,-rpath,Libs/MATLAB/R2019b/bin/ \ | |||
# -Wl,-rpath,Libs/unwind/bin/ | |||
# Map output file | |||
MAP_FILE := output.map | |||
@@ -198,8 +197,8 @@ local_v0_opt: TARGET := local_v0_opt | |||
local_v0_opt: $(BUILD_DIR)/$(TARGET) | |||
cp $(BUILD_DIR)/$(TARGET) out/$(TARGET) | |||
local_v1: CFLAGS := $(DEB_CFLAGS) -DCODE_VERSION=4 | |||
local_v1: CXXFLAGS := $(DEB_CXXFLAGS) -DCODE_VERSION=4 | |||
local_v1: CFLAGS := $(DEB_CFLAGS) -DCODE_VERSION=1 | |||
local_v1: CXXFLAGS := $(DEB_CXXFLAGS) -DCODE_VERSION=1 | |||
local_v1: TARGET := local_v1 | |||
local_v1: $(BUILD_DIR)/$(TARGET) | |||
cp $(BUILD_DIR)/$(TARGET) out/$(TARGET) | |||
@@ -235,7 +234,13 @@ v1: TARGET := knnsearch_v1 | |||
v1: $(BUILD_DIR)/$(TARGET) | |||
cp $(BUILD_DIR)/$(TARGET) out/$(TARGET) | |||
tests: CFLAGS := $(DEB_CFLAGS) -DCODE_VERSION=0 -DTESTING | |||
tests: CXXFLAGS := $(DEB_CXXFLAGS) -DCODE_VERSION=0 -DTESTING | |||
tests: TARGET := tests | |||
tests: $(BUILD_DIR)/$(TARGET) | |||
cp $(BUILD_DIR)/$(TARGET) out/$(TARGET) | |||
# | |||
# ========= Inside CSAL Image build rules =========== | |||
# | |||
@@ -280,6 +285,6 @@ csal_v1: $(BUILD_DIR)/$(TARGET) | |||
# make IMAGE=hpcimage EXEC=knnsearch_v1 run | |||
# make IMAGE=hpcimage EXEC=knnsearch_v1 run | |||
# | |||
run: DOCKER := $(DOCKER_CMD) | |||
run: | |||
$(DOCKER) ./out/$(EXEC) |
@@ -13,7 +13,7 @@ | |||
#include <iostream> | |||
#include <string> | |||
#include <matrix.hpp> | |||
#include "matrix.hpp" | |||
// HDF5 supported types | |||
enum class HDF5_type { | |||
@@ -32,21 +32,11 @@ enum class HDF5_type { | |||
#define CODE_VERSION V1 | |||
#endif | |||
// matrix alias template dispatcher based on pre-define flag from compiler (see Makefile) | |||
#if CODE_VERSION == V0 | |||
#define NAMESPACE_VERSION using namespace v0 | |||
using MatrixDst = mtx::Matrix<double>; | |||
using MatrixIdx = mtx::Matrix<uint32_t>; | |||
static constexpr HDF5_type DstHDF5Type = HDF5_type::DOUBLE; | |||
static constexpr HDF5_type IdxHDF5Type = HDF5_type::INT; | |||
#elif CODE_VERSION == V1 | |||
#define NAMESPACE_VERSION using namespace v1 | |||
using MatrixDst = mtx::Matrix<double>; | |||
using MatrixIdx = mtx::Matrix<uint32_t>; | |||
static constexpr HDF5_type DstHDF5Type = HDF5_type::DOUBLE; | |||
static constexpr HDF5_type IdxHDF5Type = HDF5_type::INT; | |||
#endif | |||
// matrix alias template dispatcher | |||
using MatrixDst = mtx::Matrix<double>; | |||
using MatrixIdx = mtx::Matrix<uint32_t>; | |||
static constexpr HDF5_type DstHDF5Type = HDF5_type::DOUBLE; | |||
static constexpr HDF5_type IdxHDF5Type = HDF5_type::INT; | |||
//! enumerator for output handling | |||
@@ -83,25 +83,49 @@ struct Matrix { | |||
static constexpr MatrixOrder matrixOrder = Order; //!< meta:export of array order | |||
static constexpr MatrixType matrixType = Type; //!< meta:export of array type | |||
static constexpr bool symmetric = Symmetric; //!< meta:export symmetric flag | |||
/*! | |||
* \name Obj lifetime | |||
*/ | |||
//! @{ | |||
//! Construct an empty matrix with dimensions rows x columns | |||
Matrix(IndexType rows = IndexType{}, IndexType columns = IndexType{}) noexcept : | |||
m_(capacity(rows, columns)), rows_(rows), cols_(columns) { } | |||
Matrix(IndexType rows = IndexType{}, IndexType columns = IndexType{}) noexcept | |||
: vector_storage_(capacity(rows, columns)), | |||
raw_storage_(nullptr), | |||
use_vector_(true), | |||
rows_(rows), | |||
cols_(columns) { | |||
data_ = vector_storage_.data(); | |||
} | |||
//! Construct a matrix by copying existing data with dimensions rows x columns | |||
Matrix(DataType* data, IndexType rows, IndexType columns) noexcept : | |||
m_(data, data + capacity(rows, columns)), rows_(rows), cols_(columns) { } | |||
Matrix(DataType* data, IndexType major_start, IndexType major_length, IndexType minor_length) noexcept | |||
: vector_storage_(), | |||
raw_storage_ (data + major_start * minor_length), | |||
use_vector_ (false) { | |||
if constexpr (Order == MatrixOrder::ROWMAJOR) { | |||
rows_ = major_length; | |||
cols_ = minor_length; | |||
} | |||
else { | |||
rows_ = minor_length; | |||
cols_ = major_length; | |||
} | |||
data_ = raw_storage_; | |||
} | |||
//! Construct a matrix using an initializer list | |||
Matrix(IndexType rows, IndexType columns, std::initializer_list<DataType> list) | |||
: m_(list), rows_(rows), cols_(columns) { | |||
: vector_storage_(list), | |||
raw_storage_(nullptr), | |||
use_vector_(true), | |||
rows_(rows), | |||
cols_(columns) { | |||
if (list.size() != capacity(rows, columns)) { | |||
throw std::invalid_argument("Matrix initializer list size does not match matrix dimensions."); | |||
throw std::invalid_argument("Matrix initializer list size does not match matrix dimensions."); | |||
} | |||
data_ = vector_storage_.data(); | |||
} | |||
//! move ctor | |||
@@ -126,9 +150,12 @@ struct Matrix { | |||
} | |||
//! Set the interface size of the Matrix (what appears to be the size) | |||
IndexType resize(IndexType rows, IndexType columns) { | |||
rows_ = rows; | |||
cols_ = columns; | |||
m_.reserve(capacity(rows_, cols_)); | |||
if (use_vector_) { | |||
rows_ = rows; | |||
cols_ = columns; | |||
vector_storage_.resize(capacity(rows_, cols_)); | |||
data_ = vector_storage_.data(); | |||
} | |||
return capacity(rows_, cols_); | |||
} | |||
@@ -148,42 +175,49 @@ struct Matrix { | |||
auto T = [](size_t i)->size_t { return i*(i+1)/2; }; // Triangular number of i | |||
if constexpr (Order == MatrixOrder::COLMAJOR) { | |||
// In column major we use the lower triangle of the matrix | |||
if (i>=j) return m_[j*rows_ - T(j) + i]; // Lower, use our notation | |||
else return m_[i*rows_ - T(i) + j]; // Upper, use opposite index | |||
if (i>=j) return data_[j*rows_ - T(j) + i]; // Lower, use our notation | |||
else return data_[i*rows_ - T(i) + j]; // Upper, use opposite index | |||
} | |||
else { | |||
// In row major we use the upper triangle of the matrix | |||
if (i<=j) return m_[i*cols_ - T(i) + j]; // Upper, use our notation | |||
else return m_[j*cols_ - T(j) + i]; // Lower, use opposite index | |||
if (i<=j) return data_[i*cols_ - T(i) + j]; // Upper, use our notation | |||
else return data_[j*cols_ - T(j) + i]; // Lower, use opposite index | |||
} | |||
} | |||
else { | |||
if constexpr (Order == MatrixOrder::COLMAJOR) | |||
return m_[i + j*rows_]; | |||
return data_[i + j*rows_]; | |||
else | |||
return m_[i*cols_ + j]; | |||
return data_[i*cols_ + j]; | |||
} | |||
} | |||
/*! | |||
* \fn DataType set(DataType, IndexType, IndexType) | |||
* \param v | |||
* \param i | |||
* \param j | |||
* \return | |||
*/ | |||
DataType set (DataType v, IndexType i, IndexType j) { | |||
if constexpr (Symmetric) { | |||
auto T = [](size_t i)->size_t { return i*(i+1)/2; }; // Triangular number of i | |||
if constexpr (Order == MatrixOrder::COLMAJOR) { | |||
// In column major we use the lower triangle of the matrix | |||
if (i>=j) return m_[j*rows_ - T(j) + i] = v; // Lower, use our notation | |||
else return m_[i*rows_ - T(i) + j] = v; // Upper, use opposite index | |||
if (i>=j) return data_[j*rows_ - T(j) + i] = v; // Lower, use our notation | |||
else return data_[i*rows_ - T(i) + j] = v; // Upper, use opposite index | |||
} | |||
else { | |||
// In row major we use the upper triangle of the matrix | |||
if (i<=j) return m_[i*cols_ - T(i) + j] = v; // Upper, use our notation | |||
else return m_[j*cols_ - T(j) + i] = v; // Lower, use opposite index | |||
if (i<=j) return data_[i*cols_ - T(i) + j] = v; // Upper, use our notation | |||
else return data_[j*cols_ - T(j) + i] = v; // Lower, use opposite index | |||
} | |||
} | |||
else { | |||
if constexpr (Order == MatrixOrder::COLMAJOR) | |||
return m_[i + j*rows_] = v; | |||
return data_[i + j*rows_] = v; | |||
else | |||
return m_[i*cols_ + j] = v; | |||
return data_[i*cols_ + j] = v; | |||
} | |||
} | |||
// DataType operator()(IndexType i, IndexType j) { return get(i, j); } | |||
@@ -198,11 +232,11 @@ struct Matrix { | |||
} | |||
// a basic serial iterator support | |||
DataType* data() noexcept { return m_.data(); } | |||
DataType* data() noexcept { return data_; } | |||
// IndexType begin_idx() noexcept { return 0; } | |||
// IndexType end_idx() noexcept { return capacity(rows_, cols_); } | |||
const DataType* data() const noexcept { return m_.data(); } | |||
const DataType* data() const noexcept { return data_; } | |||
const IndexType begin_idx() const noexcept { return 0; } | |||
const IndexType end_idx() const noexcept { return capacity(rows_, cols_); } | |||
//! @} | |||
@@ -224,19 +258,29 @@ struct Matrix { | |||
// | |||
void swap(Matrix& src) noexcept { | |||
std::swap(m_, src.m_); | |||
std::swap(vector_storage_, src.vector_storage_); | |||
std::swap(raw_storage_, src.raw_storage_); | |||
std::swap(data_, src.data_); | |||
std::swap(use_vector_, src.use_vector_); | |||
std::swap(rows_, src.rows_); | |||
std::swap(cols_, src.cols_); | |||
} | |||
private: | |||
//! move helper | |||
void moves(Matrix&& src) noexcept { | |||
m_ = std::move(src.m_); | |||
data_ = std::move(src.vector_storage_); | |||
data_ = std::move(src.raw_storage_); | |||
data_ = std::move(src.data_); | |||
data_ = std::move(src.use_vector_); | |||
rows_ = std::move(src.rows_); | |||
cols_ = std::move(src.cols_); | |||
} | |||
std::vector<DataType> m_ {}; //!< Pointer to actual data. | |||
std::vector<DataType> | |||
vector_storage_; //!< Internal storage (if used). | |||
DataType* raw_storage_; //!< External storage (if used). | |||
DataType* data_; //!< Pointer to active storage. | |||
bool use_vector_; //!< True if using vector storage, false for raw pointer. | |||
IndexType rows_{}; //!< the virtual size of rows. | |||
IndexType cols_{}; //!< the virtual size of columns. | |||
}; | |||
@@ -484,6 +528,125 @@ private: | |||
}; | |||
template<typename ...> struct Matrix_view { }; | |||
/*! | |||
* @struct Matrix_view | |||
* @tparam MatrixType | |||
*/ | |||
template<template <typename, typename, MatrixType, MatrixOrder, bool> class Matrix, | |||
typename DataType, | |||
typename IndexType, | |||
MatrixType Type, | |||
MatrixOrder Order> | |||
struct Matrix_view<Matrix<DataType, IndexType, Type, Order, false>> { | |||
using owner_t = Matrix<DataType, IndexType, Type, Order, false>; | |||
using dataType = DataType; //!< meta:export of underling data type | |||
using indexType = IndexType; //!< meta:export of underling index type | |||
static constexpr MatrixOrder matrixOrder = Order; //!< meta:export of array order | |||
static constexpr MatrixType matrixType = Type; //!< meta:export of array type | |||
/*! | |||
* \name Obj lifetime | |||
*/ | |||
//! @{ | |||
//! Construct a matrix view to entire matrix | |||
Matrix_view(const owner_t* owner) noexcept : | |||
owner_(owner), m_(owner->data()), rows_(owner->rows()), cols_(owner->columns()) { } | |||
Matrix_view(const owner_t* owner, IndexType begin, IndexType end) noexcept : | |||
owner_(owner) { | |||
if constexpr (Order == MatrixOrder::ROWMAJOR) { | |||
m_ = owner->data() + begin * owner->columns(); | |||
rows_ = end - begin; | |||
cols_ = owner->columns(); | |||
} else if (Order == MatrixOrder::COLMAJOR) { | |||
m_ = owner->data() + begin * owner->rows(); | |||
rows_ = owner->rows(); | |||
cols_ = end - begin; | |||
} | |||
} | |||
Matrix_view(Matrix_view&& m) = delete; //! No move | |||
Matrix_view& operator=(Matrix_view&& m) = delete; | |||
Matrix_view(const Matrix_view& m) = delete; //!< No copy | |||
Matrix_view& operator=(const Matrix_view& m) = delete; | |||
//! @} | |||
//! Get/Set the size of each dimension | |||
const IndexType rows() const noexcept { return rows_; } | |||
const IndexType columns() const noexcept { return cols_; } | |||
//! Get the interface size of the Matrix (what appears to be the size) | |||
IndexType size() const { | |||
return rows_ * cols_; | |||
} | |||
//! Actual memory capacity of the symmetric matrix | |||
static constexpr IndexType capacity(IndexType M, IndexType N) { | |||
return M*N; | |||
} | |||
/* | |||
* virtual 2D accessors | |||
*/ | |||
const DataType get (IndexType i, IndexType j) const { | |||
if constexpr (Order == MatrixOrder::COLMAJOR) | |||
return m_[i + j*rows_]; | |||
else | |||
return m_[i*cols_ + j]; | |||
} | |||
DataType set (DataType v, IndexType i, IndexType j) { | |||
if constexpr (Order == MatrixOrder::COLMAJOR) | |||
return m_[i + j*rows_] = v; | |||
else | |||
return m_[i*cols_ + j] = v; | |||
} | |||
// DataType operator()(IndexType i, IndexType j) { return get(i, j); } | |||
/*! | |||
* Return a proxy MatVal object with read and write capabilities. | |||
* @param i The row number | |||
* @param j The column number | |||
* @return tHE MatVal object | |||
*/ | |||
MatVal<Matrix_view> operator()(IndexType i, IndexType j) noexcept { | |||
return MatVal<Matrix_view>(this, get(i, j), i, j); | |||
} | |||
// a basic serial iterator support | |||
DataType* data() noexcept { return m_.data(); } | |||
// IndexType begin_idx() noexcept { return 0; } | |||
// IndexType end_idx() noexcept { return capacity(rows_, cols_); } | |||
const DataType* data() const noexcept { return m_; } | |||
const IndexType begin_idx() const noexcept { return 0; } | |||
const IndexType end_idx() const noexcept { return capacity(rows_, cols_); } | |||
//! @} | |||
/*! | |||
* \name Safe iteration API | |||
* | |||
* This api automates the iteration over the array based on | |||
* MatrixType | |||
*/ | |||
//! @{ | |||
template<typename F, typename... Args> | |||
void for_each_in (IndexType begin, IndexType end, F&& lambda, Args&&... args) { | |||
for (IndexType it=begin ; it<end ; ++it) { | |||
std::forward<F>(lambda)(std::forward<Args>(args)..., it); | |||
} | |||
} | |||
//! @} | |||
//! | |||
private: | |||
const owner_t* owner_ {nullptr}; //!< Pointer to Matrix | |||
DataType* m_ {nullptr}; //!< Starting address of the slice/view | |||
IndexType rows_{}; //!< the virtual size of rows. | |||
IndexType cols_{}; //!< the virtual size of columns. | |||
}; | |||
/*! | |||
* A view/iterator hybrid object for Matrix columns. | |||
* |
@@ -14,8 +14,8 @@ | |||
#include <unistd.h> | |||
#include <hdf5.h> | |||
#include <matrix.hpp> | |||
#include <config.h> | |||
#include "matrix.hpp" | |||
#include "config.h" | |||
/*! | |||
* A Logger for entire program. | |||
@@ -14,8 +14,8 @@ | |||
#include <vector> | |||
#include <algorithm> | |||
#include <matrix.hpp> | |||
#include <config.h> | |||
#include "matrix.hpp" | |||
#include "config.h" | |||
namespace v0 { | |||
@@ -30,8 +30,10 @@ namespace v0 { | |||
* \param n number of rows in Y | |||
* \param d number of columns in both X and Y | |||
*/ | |||
template<typename DataType> | |||
void pdist2(const mtx::Matrix<DataType>& X, const mtx::Matrix<DataType>& Y, mtx::Matrix<DataType>& D2) { | |||
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(); | |||
@@ -79,26 +81,24 @@ void quickselect(std::vector<std::pair<DataType, IndexType>>& vec, int k) { | |||
* \param dst Is the Nxk matrix with the k distances to the C points of the nth | |||
* point of Q | |||
*/ | |||
template<typename DataType, typename IndexType> | |||
void knnsearch(const mtx::Matrix<DataType>& C, const mtx::Matrix<DataType>& Q, int k, | |||
mtx::Matrix<IndexType>& idx, | |||
mtx::Matrix<DataType>& dst) { | |||
template<typename MatrixD, typename MatrixI> | |||
void knnsearch(const MatrixD& C, const MatrixD& Q, size_t idx_offset, size_t k, size_t m, MatrixI& idx, MatrixD& dst) { | |||
int M = C.rows(); | |||
int N = Q.rows(); | |||
using DstType = typename MatrixD::dataType; | |||
using IdxType = typename MatrixI::dataType; | |||
mtx::Matrix<DataType> D(M, N); | |||
size_t M = C.rows(); | |||
size_t N = Q.rows(); | |||
pdist2(C, Q, D); | |||
mtx::Matrix<DstType> D(M, N); | |||
idx.resize(N, k); | |||
dst.resize(N, k); | |||
pdist2(C, Q, D); | |||
for (int j = 0; j < N; ++j) { | |||
for (size_t j = 0; j < N; ++j) { | |||
// Create a vector of pairs (distance, index) for the j-th query | |||
std::vector<std::pair<DataType, IndexType>> dst_idx(M); | |||
for (int i = 0; i < M; ++i) { | |||
dst_idx[i] = {D.data()[i * N + j], i}; | |||
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); | |||
@@ -107,9 +107,9 @@ void knnsearch(const mtx::Matrix<DataType>& C, const mtx::Matrix<DataType>& Q, i | |||
std::sort(dst_idx.begin(), dst_idx.end()); | |||
// Store the indices and distances | |||
for (int i = 0; i < k; ++i) { | |||
idx(j, i) = dst_idx[i].second; | |||
dst(j, i) = dst_idx[i].first; | |||
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); | |||
} | |||
} | |||
} | |||
@@ -9,8 +9,100 @@ | |||
#ifndef V1_HPP_ | |||
#define V1_HPP_ | |||
#include <vector> | |||
#include <algorithm> | |||
#include "matrix.hpp" | |||
#include "v0.hpp" | |||
#include "config.h" | |||
namespace v1 { | |||
template <typename DataType, typename IndexType> | |||
void mergeResultsWithM(mtx::Matrix<IndexType>& N1, mtx::Matrix<DataType>& D1, | |||
mtx::Matrix<IndexType>& N2, mtx::Matrix<DataType>& D2, | |||
size_t k, size_t m, | |||
mtx::Matrix<IndexType>& N, mtx::Matrix<DataType>& D) { | |||
size_t numQueries = N1.rows(); | |||
size_t maxCandidates = std::min((IndexType)m, (IndexType)(N1.columns() + N2.columns())); | |||
for (size_t q = 0; q < numQueries; ++q) { | |||
// Combine distances and neighbors | |||
std::vector<std::pair<DataType, IndexType>> candidates(N1.columns() + N2.columns()); | |||
// Concatenate N1 and N2 rows | |||
for (size_t i = 0; i < N1.columns(); ++i) { | |||
candidates[i] = {D1.get(q, i), N1.get(q, i)}; | |||
} | |||
for (size_t i = 0; i < N2.columns(); ++i) { | |||
candidates[i + N1.columns()] = {D2.get(q, i), N2.get(q, i)}; | |||
} | |||
// Keep only the top-m candidates | |||
v0::quickselect(candidates, maxCandidates); | |||
// Sort the top-m candidates | |||
std::sort(candidates.begin(), candidates.begin() + maxCandidates); | |||
// If m < k, pad the remaining slots with invalid values | |||
for (size_t i = 0; i < k; ++i) { | |||
if (i < maxCandidates) { | |||
D.set(candidates[i].first, q, i); | |||
N.set(candidates[i].second, q, i); | |||
} else { | |||
D.set(std::numeric_limits<DataType>::infinity(), q, i); | |||
N.set(static_cast<IndexType>(-1), q, i); // Invalid index (end) | |||
} | |||
} | |||
} | |||
} | |||
template<typename MatrixD, typename MatrixI> | |||
void knnsearch(const MatrixD& C, const 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; | |||
if (C.rows() <= 8 || Q.rows() <= 4) { | |||
// Base case: Call knnsearch directly | |||
v0::knnsearch(C, Q, idx_offset, k, m, idx, dst); | |||
return; | |||
} | |||
// Divide Corpus and Query into subsets | |||
IdxType midC = C.rows() / 2; | |||
IdxType midQ = Q.rows() / 2; | |||
// Slice corpus and query matrixes | |||
MatrixD C1((DstType*)C.data(), 0, midC, C.columns()); | |||
MatrixD C2((DstType*)C.data(), midC, midC, C.columns()); | |||
MatrixD Q1((DstType*)Q.data(), 0, midQ, Q.columns()); | |||
MatrixD Q2((DstType*)Q.data(), midQ, midQ, Q.columns()); | |||
// Allocate temporary matrixes for all permutations | |||
MatrixI N1_1(midQ, k), N1_2(midQ, k), N2_1(midQ, k), N2_2(midQ, k); | |||
MatrixD D1_1(midQ, k), D1_2(midQ, k), D2_1(midQ, k), D2_2(midQ, k); | |||
// Recursive calls | |||
knnsearch(C1, Q1, idx_offset, k, m, N1_1, D1_1); | |||
knnsearch(C2, Q1, idx_offset + midC, k, m, N1_2, D1_2); | |||
knnsearch(C1, Q2, idx_offset, k, m, N2_1, D2_1); | |||
knnsearch(C2, Q2, idx_offset + midC, k, m, N2_2, D2_2); | |||
// slice output matrixes | |||
MatrixI N1((IdxType*)idx.data(), 0, midQ, k); | |||
MatrixI N2((IdxType*)idx.data(), midQ, midQ, k); | |||
MatrixD D1((DstType*)dst.data(), 0, midQ, k); | |||
MatrixD D2((DstType*)dst.data(), midQ, midQ, k); | |||
// Merge results in place | |||
mergeResultsWithM(N1_1, D1_1, N1_2, D1_2, k, m, N1, D1); | |||
mergeResultsWithM(N2_1, D2_1, N2_2, D2_2, k, m, N2, D2); | |||
} | |||
} // namespace v1 | |||
#endif /* V1_HPP_ */ |
@@ -0,0 +1,11 @@ | |||
function [N, D] = mergeReducedResultsWithMink(N_sub, D_sub, C_sub, k, ~) | |||
% Merge reduced results for one subset of queries using mink | |||
numQueries = size(N_sub, 1); % Number of queries | |||
% Find the k smallest distances and their indices using mink | |||
[D, idx] = mink(D_sub, k, 2); | |||
% Select the corresponding neighbors based on the indices | |||
N = N_sub(sub2ind(size(N_sub), ... | |||
repmat((1:numQueries)', 1, k), idx)); | |||
end |
@@ -0,0 +1,19 @@ | |||
function [N, D] = mergeResults(N1, D1, N2, D2, C1, C2, k, ~) | |||
% Merge neighbors from two sources for a specific subset of queries | |||
numQueries = size(N1, 1); % Queries corresponding to N1 (or N2) | |||
N_combined = [N1, N2 + size(C1, 1)]; % Adjust indices for C2 | |||
D_combined = [D1, D2]; | |||
% Sort distances and select top-k for each query | |||
[D_sorted, idx] = sort(D_combined, 2); % Sort by distance for each query | |||
idx = idx(:, 1:k); % Top-k indices | |||
% Select corresponding neighbors | |||
N = zeros(numQueries, k); | |||
for i = 1:numQueries | |||
N(i, :) = N_combined(i, idx(i, :)); | |||
end | |||
% Select corresponding distances | |||
D = D_sorted(:, 1:k); | |||
end |
@@ -0,0 +1,46 @@ | |||
function [N, D] = mergeResultsWithM(N1, D1, N2, D2, C1, C2, k, m) | |||
% Merge neighbors from two sources with a limit on candidate neighbors (m) | |||
numQueries = size(N1, 1); % Number of queries in this subset | |||
maxCandidates = min(m, size(N1, 2) + size(N2, 2)); % Maximum candidates to consider | |||
% Combine distances and neighbors | |||
N_combined = [N1, N2 + size(C1, 1)]; % Adjust indices for C2 | |||
D_combined = [D1, D2]; | |||
% Sort distances and keep only top-m candidates for each query | |||
[D_sorted, idx] = sort(D_combined, 2, 'ascend'); | |||
D_sorted = D_sorted(:, 1:maxCandidates); % Keep only top-m distances | |||
idx = idx(:, 1:maxCandidates); % Keep indices corresponding to top-m distances | |||
% Select the corresponding neighbors | |||
%N_sorted = N_combined(sub2ind(size(N_combined), ... | |||
% repmat((1:numQueries)', 1, maxCandidates), idx)); | |||
N_sorted = zeros(numQueries, maxCandidates); % Initialize output | |||
for i = 1:numQueries | |||
for j = 1:maxCandidates | |||
N_sorted(i, j) = N_combined(i, idx(i, j)); | |||
end | |||
end | |||
% Handle cases where m < k | |||
if maxCandidates < k | |||
% Pad with Inf distances and invalid indices | |||
D_sorted = [D_sorted, Inf(numQueries, k - maxCandidates)]; | |||
N_sorted = [N_sorted, zeros(numQueries, k - maxCandidates)]; | |||
end | |||
% Extract top-k from the reduced set of candidates | |||
[D, idx_final] = sort(D_sorted, 2, 'ascend'); | |||
D = D(:, 1:k); % Final top-k distances | |||
%N = N_sorted(sub2ind(size(N_sorted), ... | |||
% repmat((1:numQueries)', 1, k), idx_final(:, 1:k))); | |||
% Extract top-k neighbors using a loop | |||
N = zeros(numQueries, k); % Initialize output | |||
for i = 1:numQueries | |||
for j = 1:k | |||
N(i, j) = N_sorted(i, idx_final(i, j)); | |||
end | |||
end | |||
end |
@@ -0,0 +1,32 @@ | |||
function [neighbors, distances] = recursiveKNN(C, Q, k, m) | |||
% Recursive break, call knnsearch | |||
if size(C, 1) <= 1000 || size(Q, 1) <= 500 % Adjastable limit | |||
[neighbors, distances] = knnsearch(C, Q, 'K', k); | |||
return; | |||
end | |||
% Divide into subsets | |||
midC = floor(size(C, 1) / 2); | |||
midQ = floor(size(Q, 1) / 2); | |||
C1 = C(1:midC, :); | |||
C2 = C(midC+1:end, :); | |||
Q1 = Q(1:midQ, :); | |||
Q2 = Q(midQ+1:end, :); | |||
% Recursive calls | |||
[N1_1, D1_1] = recursiveKNN(C1, Q1, k, m); | |||
[N1_2, D1_2] = recursiveKNN(C2, Q1, k, m); | |||
[N2_1, D2_1] = recursiveKNN(C1, Q2, k, m); | |||
[N2_2, D2_2] = recursiveKNN(C2, Q2, k, m); | |||
% Merge | |||
[N1, D1] = mergeResultsWithM(N1_1, D1_1, N1_2, D1_2, C1, C2, k, m); | |||
[N2, D2] = mergeResultsWithM(N2_1, D2_1, N2_2, D2_2, C1, C2, k, m); | |||
% Combine results for Q1 and Q2 | |||
neighbors = [N1; N2]; | |||
distances = [D1; D2]; | |||
end | |||
@@ -0,0 +1,23 @@ | |||
% | |||
% | |||
% | |||
%C = rand(10000, 2); % Corpus | |||
%Q = rand(10000, 2); % Queries | |||
C = rand(20000, 2); % Δύο clusters | |||
Q = C; | |||
%Q = rand(10000, 2); % Queries κοντά στο μέσο | |||
k = 100; % Number of neighbors | |||
m = 100; % Max candidates per query | |||
global count; | |||
count =0; | |||
tic; [pi, pd] = recursiveKNN(C, Q, k, m); toc | |||
count | |||
tic; [si, sd] = knnsearch(C, Q, 'k', k); toc | |||
[a,b] = size(si); | |||
all_neighbors = a*b | |||
accuracy = 1 - nnz(si-pi)/all_neighbors | |||
false_neighbors = nnz(sd-pd) | |||
@@ -1,24 +0,0 @@ | |||
% | |||
% | |||
% | |||
C = rand(40000,4); | |||
Q = rand(4000,4); | |||
disp ('C-Q'); | |||
disp ('build-in') | |||
tic; [i1, d1] = knnsearch(C, Q, 'k', 4); toc | |||
disp ('mine') | |||
tic; [i2, d2] = knnsearch2(C, Q, 4); toc | |||
sum(i1-i2) | |||
sum(d1-d2) | |||
disp (' '); | |||
disp (' '); | |||
disp ('C-C'); | |||
disp ('build-in') | |||
tic; [i1, d1] = knnsearch(C, C, 'k', 4); toc | |||
disp ('mine') | |||
tic; [i2, d2] = knnsearch2(C, C, 4); toc | |||
sum(i1-i2) | |||
sum(d1-d2) |
@@ -13,11 +13,12 @@ | |||
#include <unistd.h> | |||
#include <cstdio> | |||
#include <v0.hpp> | |||
#include <v1.hpp> | |||
#include <matrix.hpp> | |||
#include <utils.hpp> | |||
#include <config.h> | |||
#include "matrix.hpp" | |||
#include "v0.hpp" | |||
#include "v1.hpp" | |||
#include "utils.hpp" | |||
#include "config.h" | |||
// Global session data | |||
session_t session; | |||
@@ -108,8 +109,7 @@ bool get_options(int argc, char* argv[]){ | |||
return status; | |||
} | |||
NAMESPACE_VERSION; | |||
#ifndef TESTING | |||
int main(int argc, char* argv[]) try { | |||
// Instantiate matrixes | |||
MatrixDst Corpus; | |||
@@ -117,6 +117,12 @@ int main(int argc, char* argv[]) try { | |||
MatrixIdx Idx; | |||
MatrixDst Dst; | |||
#if CODE_VERSION == V0 | |||
using namespace v0; | |||
#else | |||
using namespace v1; | |||
#endif | |||
// try to read command line | |||
if (!get_options(argc, argv)) | |||
exit(1); | |||
@@ -132,17 +138,21 @@ int main(int argc, char* argv[]) try { | |||
timer.stop(); | |||
timer.print_dt("Load hdf5 files"); | |||
// Prepare output memory | |||
Idx.resize(Query.rows(), session.k); | |||
Dst.resize(Query.rows(), session.k); | |||
// Do the search | |||
logger << "Start knnsearch ..."; | |||
timer.start(); | |||
if (session.queryMtx) | |||
knnsearch(Corpus, Query, session.k, Idx, Dst); | |||
knnsearch(Corpus, Query, 0, session.k, session.k, Idx, Dst); | |||
else | |||
knnsearch(Corpus, Corpus, session.k, Idx, Dst); | |||
knnsearch(Corpus, Corpus, 0, session.k, session.k, Idx, Dst); | |||
timer.stop(); | |||
logger << " Done" << logger.endl; | |||
timer.print_dt("knnsearch"); | |||
// Store data | |||
timer.start(); | |||
Mtx::store<MatrixIdx, IdxHDF5Type>(session.outMtxFile, session.outMtxIdxDataSet, Idx); | |||
@@ -158,4 +168,17 @@ catch (std::exception& e) { | |||
exit(1); | |||
} | |||
#elif defined TESTING | |||
#include <gtest/gtest.h> | |||
#include <exception> | |||
GTEST_API_ int main(int argc, char **argv) try { | |||
testing::InitGoogleTest(&argc, argv); | |||
return RUN_ALL_TESTS(); | |||
} | |||
catch (std::exception& e) { | |||
std::cout << "Exception: " << e.what() << '\n'; | |||
} | |||
#endif |
@@ -0,0 +1,317 @@ | |||
/** | |||
* \file tests.cpp | |||
* \brief PDS homework_1 tests | |||
* | |||
* \author | |||
* Christos Choutouridis AEM:8997 | |||
* <cchoutou@ece.auth.gr> | |||
*/ | |||
#include <gtest/gtest.h> | |||
#include "matrix.hpp" | |||
#include "v0.hpp" | |||
#include "v1.hpp" | |||
#include "utils.hpp" | |||
#include "config.h" | |||
using matrix_t = mtx::Matrix<int>; | |||
// ===================================== | |||
// C1, Q1 | |||
mtx::Matrix<double> C1(10,2, { | |||
0.8147, 0.1576, | |||
0.9058, 0.9706, | |||
0.1270, 0.9572, | |||
0.9134, 0.4854, | |||
0.6324, 0.8003, | |||
0.0975, 0.1419, | |||
0.2785, 0.4218, | |||
0.5469, 0.9157, | |||
0.9575, 0.7922, | |||
0.9649, 0.9595 | |||
}); | |||
mtx::Matrix<double> Q1(5,2, { | |||
0.6557, 0.7577, | |||
0.0357, 0.7431, | |||
0.8491, 0.3922, | |||
0.9340, 0.6555, | |||
0.6787, 0.1712 | |||
}); | |||
// ===================================== | |||
// C2, Q2 | |||
mtx::Matrix<double> C2(16,4, { | |||
0.7060, 0.4456, 0.5060, 0.6160, | |||
0.0318, 0.6463, 0.6991, 0.4733, | |||
0.2769, 0.7094, 0.8909, 0.3517, | |||
0.0462, 0.7547, 0.9593, 0.8308, | |||
0.0971, 0.2760, 0.5472, 0.5853, | |||
0.8235, 0.6797, 0.1386, 0.5497, | |||
0.6948, 0.6551, 0.1493, 0.9172, | |||
0.3171, 0.1626, 0.2575, 0.2858, | |||
0.9502, 0.1190, 0.8407, 0.7572, | |||
0.0344, 0.4984, 0.2543, 0.7537, | |||
0.4387, 0.9597, 0.8143, 0.3804, | |||
0.3816, 0.3404, 0.2435, 0.5678, | |||
0.7655, 0.5853, 0.9293, 0.0759, | |||
0.7952, 0.2238, 0.3500, 0.0540, | |||
0.1869, 0.7513, 0.1966, 0.5308, | |||
0.4898, 0.2551, 0.2511, 0.7792 | |||
}); | |||
mtx::Matrix<double> Q2(8,4, { | |||
0.9340, 0.3112, 0.4505, 0.0782, | |||
0.1299, 0.5285, 0.0838, 0.4427, | |||
0.5688, 0.1656, 0.2290, 0.1067, | |||
0.4694, 0.6020, 0.9133, 0.9619, | |||
0.0119, 0.2630, 0.1524, 0.0046, | |||
0.3371, 0.6541, 0.8258, 0.7749, | |||
0.1622, 0.6892, 0.5383, 0.8173, | |||
0.7943, 0.7482, 0.9961, 0.8687 | |||
}); | |||
/* | |||
* ========================================== | |||
* pdist2 | |||
*/ | |||
TEST(Tv0_UT, pdist2_test1) { | |||
mtx::Matrix<double> D1_exp(10, 5, { | |||
0.6208, 0.9745, 0.2371, 0.5120, 0.1367, | |||
0.3284, 0.8993, 0.5811, 0.3164, 0.8310, | |||
0.5651, 0.2327, 0.9169, 0.8616, 0.9603, | |||
0.3749, 0.9147, 0.1132, 0.1713, 0.3921, | |||
0.0485, 0.5994, 0.4621, 0.3346, 0.6308, | |||
0.8312, 0.6044, 0.7922, 0.9815, 0.5819, | |||
0.5052, 0.4028, 0.5714, 0.6959, 0.4722, | |||
0.1919, 0.5395, 0.6045, 0.4665, 0.7561, | |||
0.3037, 0.9231, 0.4144, 0.1387, 0.6807, | |||
0.3692, 0.9540, 0.5790, 0.3056, 0.8386 | |||
}); | |||
mtx::Matrix<double> D (10,5); | |||
v0::pdist2(C1, Q1, D); | |||
for (size_t i = 0 ; i< D.rows() ; ++i) | |||
for (size_t j = 0 ; j<D.columns() ; ++j) { | |||
EXPECT_EQ (D1_exp.get(i ,j) + 0.01 > D(i, j), true); | |||
EXPECT_EQ (D1_exp.get(i ,j) - 0.01 < D(i, j), true); | |||
} | |||
} | |||
TEST(Tv0_UT, pdist2_test2) { | |||
mtx::Matrix<double> D2_exp(16, 8, { | |||
0.6020, 0.7396, 0.6583, 0.6050, 1.0070, 0.5542, 0.6298, 0.6352, | |||
1.0696, 0.6348, 0.9353, 0.6914, 0.8160, 0.4475, 0.4037, 0.9145, | |||
0.9268, 0.8450, 0.9376, 0.6492, 0.9671, 0.4360, 0.5956, 0.7400, | |||
1.3455, 0.9876, 1.2953, 0.4709, 1.2557, 0.3402, 0.4417, 0.7500, | |||
0.9839, 0.5476, 0.7517, 0.7216, 0.7074, 0.5605, 0.4784, 0.9954, | |||
0.6839, 0.7200, 0.7305, 0.9495, 1.0628, 0.8718, 0.8178, 0.9179, | |||
0.9850, 0.7514, 0.9585, 0.7996, 1.2054, 0.7784, 0.6680, 0.8591, | |||
0.6950, 0.4730, 0.3103, 1.0504, 0.4397, 0.8967, 0.8140, 1.2066, | |||
0.8065, 1.2298, 0.9722, 0.7153, 1.3933, 0.8141, 1.0204, 0.6758, | |||
1.1572, 0.3686, 0.9031, 0.8232, 0.7921, 0.6656, 0.3708, 1.0970, | |||
0.9432, 0.9049, 1.0320, 0.6905, 1.1167, 0.5094, 0.6455, 0.6653, | |||
0.7672, 0.3740, 0.5277, 0.8247, 0.6842, 0.6945, 0.5648, 0.9968, | |||
0.5768, 1.1210, 0.8403, 0.9345, 1.1316, 0.8292, 1.0380, 0.8127, | |||
0.1939, 0.8703, 0.2684, 1.1794, 0.8103, 1.0683, 1.1115, 1.1646, | |||
1.0106, 0.2708, 0.8184, 0.8954, 0.7402, 0.6982, 0.4509, 1.0594, | |||
0.8554, 0.5878, 0.6834, 0.7699, 0.9155, 0.7161, 0.6162, 0.9481 | |||
}); | |||
mtx::Matrix<double> D (16,8); | |||
v0::pdist2(C2, Q2, D); | |||
for (size_t i = 0 ; i< D.rows() ; ++i) | |||
for (size_t j = 0 ; j<D.columns() ; ++j) { | |||
EXPECT_EQ (D2_exp.get(i ,j) + 0.01 > D(i, j), true); | |||
EXPECT_EQ (D2_exp.get(i ,j) - 0.01 < D(i, j), true); | |||
} | |||
} | |||
/* | |||
* ========================================== | |||
* v0::knn | |||
*/ | |||
TEST(Tv0_UT, knn_test1) { | |||
size_t k = 3; | |||
mtx::Matrix<uint32_t> Idx_exp(5, k, { | |||
5, 8, 9, | |||
3, 7, 8, | |||
4, 1, 9, | |||
9, 4, 10, | |||
1, 4, 7 | |||
}); | |||
mtx::Matrix<double> Dst_exp(5, k, { | |||
0.0485, 0.1919, 0.3037, | |||
0.2327, 0.4028, 0.5395, | |||
0.1132, 0.2371, 0.4144, | |||
0.1387, 0.1713, 0.3056, | |||
0.1367, 0.3921, 0.4722 | |||
}); | |||
mtx::Matrix<uint32_t> Idx(5, k); | |||
mtx::Matrix<double> Dst(5, k); | |||
v0::knnsearch(C1, Q1, 0, k, 0, Idx, Dst); | |||
for (size_t i = 0 ; i< Idx.rows() ; ++i) | |||
for (size_t j = 0 ; j<Idx.columns() ; ++j) { | |||
EXPECT_EQ (Idx_exp(i ,j) == Idx(i, j) + 1, true); // matlab starts from 1 | |||
EXPECT_EQ (Dst_exp.get(i ,j) + 0.01 > Dst(i, j), true); | |||
EXPECT_EQ (Dst_exp.get(i ,j) - 0.01 < Dst(i, j), true); | |||
} | |||
} | |||
TEST(Tv0_UT, knn_test2) { | |||
size_t k = 3; | |||
mtx::Matrix<uint32_t> Idx_exp(8, k, { | |||
14, 13, 1, | |||
15, 10, 12, | |||
14, 8, 12, | |||
4, 1, 3, | |||
8, 12, 5, | |||
4, 3, 2, | |||
10, 2, 4, | |||
1, 11, 9 | |||
}); | |||
mtx::Matrix<double> Dst_exp(8, k, { | |||
0.1939, 0.5768, 0.6020, | |||
0.2708, 0.3686, 0.3740, | |||
0.2684, 0.3103, 0.5277, | |||
0.4709, 0.6050, 0.6492, | |||
0.4397, 0.6842, 0.7074, | |||
0.3402, 0.4360, 0.4475, | |||
0.3708, 0.4037, 0.4417, | |||
0.6352, 0.6653, 0.6758 | |||
}); | |||
mtx::Matrix<uint32_t> Idx(8, k); | |||
mtx::Matrix<double> Dst(8, k); | |||
v0::knnsearch(C2, Q2, 0, k, 0, Idx, Dst); | |||
for (size_t i = 0 ; i< Idx.rows() ; ++i) | |||
for (size_t j = 0 ; j<Idx.columns() ; ++j) { | |||
EXPECT_EQ (Idx_exp(i ,j) == Idx(i, j) + 1, true); // matlab starts from 1 | |||
EXPECT_EQ (Dst_exp.get(i ,j) + 0.01 > Dst(i, j), true); | |||
EXPECT_EQ (Dst_exp.get(i ,j) - 0.01 < Dst(i, j), true); | |||
} | |||
} | |||
/* | |||
* ========================================== | |||
* v1::knn | |||
*/ | |||
TEST(Tv1_UT, knn_test1) { | |||
size_t k = 3; | |||
mtx::Matrix<uint32_t> Idx_exp(8, k, { | |||
14, 13, 1, | |||
15, 10, 12, | |||
14, 8, 12, | |||
4, 1, 3, | |||
8, 12, 5, | |||
4, 3, 2, | |||
10, 2, 4, | |||
1, 11, 9 | |||
}); | |||
mtx::Matrix<double> Dst_exp(8, k, { | |||
0.1939, 0.5768, 0.6020, | |||
0.2708, 0.3686, 0.3740, | |||
0.2684, 0.3103, 0.5277, | |||
0.4709, 0.6050, 0.6492, | |||
0.4397, 0.6842, 0.7074, | |||
0.3402, 0.4360, 0.4475, | |||
0.3708, 0.4037, 0.4417, | |||
0.6352, 0.6653, 0.6758 | |||
}); | |||
mtx::Matrix<uint32_t> Idx(8, k); | |||
mtx::Matrix<double> Dst(8, k); | |||
v1::knnsearch(C2, Q2, 0, k, k, Idx, Dst); | |||
for (size_t i = 0 ; i< Idx.rows() ; ++i) | |||
for (size_t j = 0 ; j<Idx.columns() ; ++j) { | |||
EXPECT_EQ (Idx_exp(i ,j) == Idx(i, j) + 1, true); // matlab starts from 1 | |||
EXPECT_EQ (Dst_exp.get(i ,j) + 0.01 > Dst(i, j), true); | |||
EXPECT_EQ (Dst_exp.get(i ,j) - 0.01 < Dst(i, j), true); | |||
} | |||
} | |||
// all-to-all | |||
TEST(Tv1_UT, knn_test2) { | |||
size_t k = 3; | |||
mtx::Matrix<uint32_t> Idx_exp(16, k, { | |||
1, 16, 12, | |||
2, 3, 5, | |||
3, 11, 2, | |||
4, 2, 3, | |||
5, 10, 2, | |||
6, 7, 1, | |||
7, 6, 16, | |||
8, 12, 5, | |||
9, 1, 16, | |||
10, 15, 5, | |||
11, 3, 2, | |||
12, 16, 8, | |||
13, 3, 11, | |||
14, 8, 1, | |||
15, 10, 12, | |||
16, 12, 1 | |||
}); | |||
mtx::Matrix<double> Dst_exp(16, k, { | |||
0, 0.4179, 0.4331, | |||
0, 0.3401, 0.4207, | |||
0, 0.3092, 0.3401, | |||
0, 0.4555, 0.5381, | |||
0, 0.4093, 0.4207, | |||
0, 0.3903, 0.4560, | |||
0, 0.3903, 0.4811, | |||
0, 0.3398, 0.4846, | |||
0, 0.5461, 0.7607, | |||
0, 0.3745, 0.4093, | |||
0, 0.3092, 0.5345, | |||
0, 0.2524, 0.3398, | |||
0, 0.5759, 0.5941, | |||
0, 0.5428, 0.6304, | |||
0, 0.3745, 0.4586, | |||
0, 0.2524, 0.4179 | |||
}); | |||
mtx::Matrix<uint32_t> Idx(16, k); | |||
mtx::Matrix<double> Dst(16, k); | |||
v1::knnsearch(C2, C2, 0, k, k, Idx, Dst); | |||
for (size_t i = 0 ; i< Idx.rows() ; ++i) | |||
for (size_t j = 0 ; j<Idx.columns() ; ++j) { | |||
EXPECT_EQ (Idx_exp(i ,j) == Idx(i, j) + 1, true); // matlab starts from 1 | |||
EXPECT_EQ (Dst_exp.get(i ,j) + 0.01 > Dst(i, j), true); | |||
EXPECT_EQ (Dst_exp.get(i ,j) - 0.01 < Dst(i, j), true); | |||
} | |||
} | |||