commit cc78e036b2cb2898d052cf09979518da388da9d9 Author: David Holzmüller Date: Mon Mar 18 22:26:59 2019 +0100 initial commit with a working interpolation code diff --git a/.clang-format b/.clang-format new file mode 100644 index 0000000..d79fba4 --- /dev/null +++ b/.clang-format @@ -0,0 +1,2 @@ +BasedOnStyle: Google +ColumnLimit: 100 \ No newline at end of file diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..3b23940 --- /dev/null +++ b/.gitignore @@ -0,0 +1,36 @@ +*~ +*.pdf +*.synctex.gz +*.log +*.aux +*.toc +*.out +*.dvi +*.bbl +*.blg +*.nav +*.snm +*.auxlock +*.dpth +*.md5 + +build/* +TexCode/* +!TexCode/info.txt +measurements/* + +*.hi +!references/*.pdf +.cproject +.project +.settings + +Debug +Release + +*.pyc +*.os +*.o +*.so +*.jar +*.pydevproject diff --git a/CMakeLists.txt b/CMakeLists.txt new file mode 100644 index 0000000..b21f246 --- /dev/null +++ b/CMakeLists.txt @@ -0,0 +1,40 @@ +cmake_minimum_required(VERSION 2.8) +project(fast_sparse_interpolation CXX) + +set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -Wall -Wextra -fmessage-length=0 -std=c++11 -D_GNU_SOURCE=1 -D_REENTRANT -Dlinux -D__linux__ -Dx86_64 -D__x86_64__") +set(CMAKE_CXX_FLAGS_DEBUG "${CMAKE_CXX_FLAGS_DEBUG} -g3 -O0") +set(CMAKE_CXX_FLAGS_RELEASE "${CMAKE_CXX_FLAGS_RELEASE} -O2") #-mtune=native -march=native +set(CMAKE_LD_FLAGS "${CMAKE_LD_FLAGS} -L/usr/local/lib") + +link_directories(/usr/local/lib) + +file(GLOB SRC "src/*.cpp") + +file(GLOB INC "src/*.hpp") +file(GLOB INC_TEST "test/*.hpp") + +option(BUILD_TEST ON) + +## Build application +add_library(fast_sparse_interpolation ${SRC}) +include_directories("${PROJECT_SOURCE_DIR}/src") + +if(BUILD_TEST) + if(BUILD_TEST STREQUAL "ON") + file(GLOB SRC_TEST "test/*.cpp") + add_executable(fsi-test ${SRC_TEST}) + include_directories("${PROJECT_SOURCE_DIR}/src") + target_link_libraries(fast_sparse_interpolation) + endif() +endif() + + + +install(TARGETS fast_sparse_interpolation DESTINATION lib) +install(FILES ${INC} DESTINATION include/sfcpp) + + + + + + diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..8dada3e --- /dev/null +++ b/LICENSE @@ -0,0 +1,201 @@ + Apache License + Version 2.0, January 2004 + http://www.apache.org/licenses/ + + TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION + + 1. 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Bachelor Thesis (2017) + + +The following files contain code taken from the SG++ project: +src/files/files.cpp +src/files/files.hpp +src/time/Stopwatch.hpp +src/time/Stopwatch.cpp + +======================================================================== +SG++ copyright notice (BSD License): +======================================================================== + +The software SG++ is developed by The SG++ Project which is the +owner of the software. + +According to good scientific practice, publications on results +achieved in whole or in part due to SG++ have to cite at least one +paper presenting the SG++ software. + +The owner wishes to make the software available to all users to use, +reproduce, modify, distribute and redistribute also for commercial +purposes under the following conditions of the original BSD +license. Linking the SG++ module statically or dynamically with other +modules is making a combined work based on SG++. Thus, the terms and +conditions of this license cover the whole combination. As a special +exception, the copyright holders of SG++ give you permission to link +it with independent modules or to instantiate templates and macros +from SG++'s source files to produce an executable, regardless of the +license terms of these independent modules, and to copy and distribute +the resulting executable under terms of your choice, provided that you +also meet, for each linked independent module, the terms and +conditions of this license of that module. + + +Copyright (c) 2008-today The SG++ Project + +All rights reserved. + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are +met: + + Redistributions of source code must retain the above copyright notice, this + list of conditions and the following disclaimer. + Redistributions in binary form must reproduce the above copyright notice, + this list of conditions and the following disclaimer in the documentation + and/or other materials provided with the distribution. + All advertising materials mentioning features or use of this software must + display the following acknowledgement: "This product includes the software + SG++ developed 2008-today by The SG++ Project and its contributors." + Neither the name of The SG++ Project nor the names of its contributors + may be used to endorse or promote products derived from this software + without specific prior written permission. + +THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT +LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR +A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT +HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, +SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT +LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, +DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY +THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT +(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE +OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. diff --git a/README.md b/README.md new file mode 100644 index 0000000..69b32cc --- /dev/null +++ b/README.md @@ -0,0 +1,47 @@ +The sfcpp library is published under an Apache 2.0 license. The sfc part of this library is described in my bachelor thesis (https://arxiv.org/abs/1710.06384). If you use the sfc part of this project for research purposes, please cite one of the following publications: +- David Holzmüller: Efficient Neighbor-Finding on Space-Filling Curves. Bachelor Thesis (2017). + +The sfcpp library can be compiled by executing the top-level Makefile (make debug / make release). This Makefile executes cmake on CMakeLists.txt to generate a Makefile in the build folder, which is then automatically executed using make to compile the library. +The modules img, sfc and the test code can be excluded from the build process. The test code requires all modules to be built and the img module requires the OpenCV libraries to be installed. The modules latex and sfc use the Color class of the img module. +The sfcpp library requires the libraries Eigen3 and boost. It has only been tested on an Ubuntu system but contains very little platform-dependent code and should be rather easy to port to other systems. + + +The sfcpp library contains the following modules: + +cpp - currently unimplemented, contains some class stubs for C++ code generation + +data - contains data structures + +files - contains miscellaneous functions for file handling + +geo - contains geometric functions: +- ConvexPolytope represents the face structure of a convex polytope +- QuickHullAlgorithm can compute such a polytope as the convex hull of a list of vertices +- coordinate system, point and vector classes for conversion between different coordinate systems and representation of 3D points and vectors + +img - contains OpenCV wrappers for image processing + +latex - contains classes for generation of LaTeX code and a submodule latex::tikz for generation of TikZ code + +math - contains mathematical functions and classes representing mathematical objects + +sfc - contains code for computations around space-filling curves: +- The KDCurveSpecification and CurveSpecification classes can be used to specify a curve +- The CurveInformation class computes informations about a CurveSpecification +- The CurveRenderer class can be used to generate TikZ graphics visualizing curves +- Several Algorithms classes provide optimized algorithms for different curves +- Some of the remaining classes are currently unimplemented because they were intended for code generation + +strings - contains string helper functions + +time - contains a Stopwatch class + +A separate folder called "test" contains code that is compiled for execution and linked against the library. Currently, it contains code for rendering and analyzing space-filling curves and making performance tests. The code there can also be used as an example of how to use the sfc module. + + + +To run the script ./prepend_header.sh, modify it to only prepend the header in files that do not contain one and run +shopt -s globstar +beforehand + + diff --git a/header.txt b/header.txt new file mode 100644 index 0000000..4cb4aea --- /dev/null +++ b/header.txt @@ -0,0 +1,16 @@ +/* Copyright 2017 The sfcpp Authors. All Rights Reserved. + +Licensed under the Apache License, Version 2.0 (the "License"); +you may not use this file except in compliance with the License. +You may obtain a copy of the License at + + http://www.apache.org/licenses/LICENSE-2.0 + +Unless required by applicable law or agreed to in writing, software +distributed under the License is distributed on an "AS IS" BASIS, +WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +See the License for the specific language governing permissions and +limitations under the License. +==============================================================================*/ + + diff --git a/prepend_header.sh b/prepend_header.sh new file mode 100644 index 0000000..ebf034d --- /dev/null +++ b/prepend_header.sh @@ -0,0 +1,11 @@ +for f in **/*.hpp; do + cat ./header.txt $f > $f.new + mv $f.new $f +done + +for f in **/*.cpp; do + cat ./header.txt $f > $f.new + mv $f.new $f +done + + diff --git a/src/Interpolation.cpp b/src/Interpolation.cpp new file mode 100644 index 0000000..736cb9b --- /dev/null +++ b/src/Interpolation.cpp @@ -0,0 +1,8 @@ +// Copyright (C) 2008-today The SG++ project +// This file is part of the SG++ project. For conditions of distribution and +// use, please see the copyright notice provided with SG++ or at +// sgpp.sparsegrids.org + +#include "Interpolation.hpp" + +namespace fsi {} /* namespace fsi */ diff --git a/src/Interpolation.hpp b/src/Interpolation.hpp new file mode 100644 index 0000000..ae9de0c --- /dev/null +++ b/src/Interpolation.hpp @@ -0,0 +1,325 @@ +// Copyright (C) 2008-today The SG++ project +// This file is part of the SG++ project. For conditions of distribution and +// use, please see the copyright notice provided with SG++ or at +// sgpp.sparsegrids.org + +#pragma once + +#include +#include +#include +#include + +namespace fsi { + +class BoundedSumIterator { + size_t d; + size_t bound; + std::vector index_head; // contains all entries of the index except the last one + size_t index_head_sum; + bool is_done; + + public: + BoundedSumIterator(size_t d, size_t bound) + : d(d), bound(bound), index_head(d - 1, 0), index_head_sum(0), is_done(false){}; + + /** + * At the current multi-index (i_1, ..., i_{d-1}, 0), return how many multi-indices starting with + * (i_1, ..., i_{d-1}) are contained in the multi-index set, then advance to the next multi-index + * that ends with a zero. + */ + size_t lastDimensionCount() { return bound - index_head_sum + 1; } + + void next() { + if (bound > index_head_sum) { + index_head_sum += 1; + index_head[d - 2] += 1; + } else { + int dim = d - 2; + + for (; dim >= 0 && index_head[dim] == 0; --dim) { + // reduce dimension until entry is nonzero + } + + if (dim > 0) { + index_head_sum -= (index_head[dim] - 1); + index_head[dim] = 0; + index_head[dim - 1] += 1; + } else if (dim == 0) { + index_head[dim] = 0; + index_head_sum = 0; + is_done = true; + } + } + } + + size_t firstIndex() { return index_head[0]; } + + size_t indexAt(size_t dim) { return index_head[dim]; } + + bool done() { return is_done; } + + void reset() { + index_head = std::vector(d - 1, 0); + index_head_sum = 0; + is_done = false; + } + + size_t dim() { return d; } + + std::vector indexBounds() { return std::vector(d, bound + 1); } +}; + +class StandardBoundedSumIterator { + size_t d; + size_t bound; + std::vector index; // contains all entries of the index except the last one + size_t index_sum; + bool is_done; + + public: + StandardBoundedSumIterator(size_t d, size_t bound) + : d(d), bound(bound), index(d, 0), index_sum(0), is_done(false){}; + + /** + * At the current multi-index (i_1, ..., i_{d-1}, 0), return how many multi-indices starting with + * (i_1, ..., i_{d-1}) are contained in the multi-index set, then advance to the next multi-index + * that ends with a zero. + */ + bool next() { + if (bound > index_sum) { + index_sum += 1; + index[d - 1] += 1; + } else { + int dim = d - 1; + + for (; dim >= 0 && index[dim] == 0; --dim) { + // reduce dimension until entry is nonzero + } + + if (dim > 0) { + index_sum -= index[dim]; + index[dim] = 0; + index[dim - 1] += 1; + } else if (dim == 0) { + index[dim] = 0; + index_sum = 0; + is_done = true; + } + } + return is_done; + } + + size_t firstIndex() { return index[0]; } + + size_t indexSum() { return index_sum; } + + bool done() { return is_done; } + + void reset() { + index = std::vector(d - 1, 0); + index_sum = 0; + is_done = false; + } +}; + +// class FastSparseInterpolation { +// public: +// FastSparseInterpolation(std::function)> const &f, +// BoundedSumIterator it, std::vector> phi); +//}; + +class MultiDimVector { + public: + // put the first dimension into an outer vector for processing reasons + std::vector> data; + MultiDimVector(size_t n) : data(n){}; + + void swap(MultiDimVector &other) { data.swap(other.data); } + + void clear() { + for (size_t dim = 0; dim < data.size(); ++dim) { + data[dim].clear(); + } + } +}; + +inline std::ostream &operator<<(std::ostream &os, boost::numeric::ublas::matrix matrix) { + os << "["; + for (size_t i = 0; i < matrix.size1(); ++i) { + for (size_t j = 0; j < matrix.size2(); ++j) { + os << matrix(i, j) << " "; + } + os << "\n"; + } + os << " ]"; + return os; +} + +template +inline std::ostream &operator<<(std::ostream &os, const std::vector &v) { + os << "["; + for (auto ii = v.begin(); ii != v.end(); ++ii) { + os << " " << *ii; + } + os << " ]"; + return os; +} + +template +MultiDimVector interpolate(Func f, It it, Phi phi, X x) { + auto n = it.indexBounds(); + size_t d = it.dim(); + + namespace ublas = boost::numeric::ublas; + typedef ublas::matrix Matrix; + + std::vector Linv, Uinv; + + // create matrices and inverted LU decompositions + for (size_t k = 0; k < d; ++k) { + // std::cout << "Matrix creation loop\n"; + Matrix Mk(n[k], n[k]); + for (size_t i = 0; i < n[k]; ++i) { + for (size_t j = 0; j < n[k]; ++j) { + Mk(i, j) = phi[k](j)(x[k](i)); + } + } + + // std::cout << "Matrices:\n"; + + // std::cout << Mk << "\n"; + + ublas::lu_factorize(Mk); + + // std::cout << Mk << "\n"; + + Matrix Lkinv = ublas::identity_matrix(n[k]); + Matrix Ukinv = ublas::identity_matrix(n[k]); + ublas::inplace_solve(Mk, Lkinv, ublas::unit_lower_tag()); + ublas::inplace_solve(Mk, Ukinv, ublas::upper_tag()); + + // std::cout << Lkinv << "\n"; + + // std::cout << Ukinv << "\n"; + + Linv.push_back(Lkinv); + Uinv.push_back(Ukinv); + } + + MultiDimVector v(n[0]); + + std::cout << "Compute function values\n"; + + // compute function values + it.reset(); + std::vector point(d); + while (not it.done()) { + size_t last_dim_count = it.lastDimensionCount(); + for (size_t dim = 0; dim < d - 1; ++dim) { + point[dim] = x[dim](it.indexAt(dim)); + } + + for (size_t last_dim_idx = 0; last_dim_idx < last_dim_count; ++last_dim_idx) { + point[d - 1] = x[d - 1](last_dim_idx); + + double function_value = f(point); + + v.data[it.firstIndex()].push_back(function_value); + } + + it.next(); + } + + size_t number = 0; + for (size_t dim = 0; dim < n[0]; ++dim) { + number += v.data[dim].size(); + } + std::cout << "number of points: " << number << "\n"; + + // for (size_t i = 0; i < v.data.size(); ++i) { + // std::cout << v.data[i] << "\n\n"; + // } + + std::cout << "First matrix multiplication\n"; + + // multiply by L^{-1} + // the multiplication is based on a cyclic permutation of the indices: the last index of v becomes + // the first index of w + + for (int k = d - 1; k >= 0; --k) { + MultiDimVector w(n[k]); + auto &Lkinv = Linv[k]; + it.reset(); + + size_t first_v_index = 0; + size_t second_v_index = 0; + + while (not it.done()) { + size_t last_dim_count = it.lastDimensionCount(); + for (size_t i = 0; i < last_dim_count; ++i) { + double sum = 0.0; + for (size_t j = 0; j <= i; ++j) { + // std::cout << Lkinv(i, j) << " * " << v.data[first_v_index][second_v_index + j] << "\n"; + sum += Lkinv(i, j) * v.data[first_v_index][second_v_index + j]; + } + w.data[i].push_back(sum); + } + second_v_index += last_dim_count; + if (second_v_index >= v.data[first_v_index].size()) { + second_v_index = 0; + first_v_index += 1; + } + it.next(); + } + + v.swap(w); + + // for (size_t i = 0; i < v.data.size(); ++i) { + // std::cout << v.data[i] << "\n\n"; + // } + } + + std::cout << "Second matrix multiplication\n"; + + // multiply by U^{-1} + // the multiplication is based on a cyclic permutation of the indices: the last index of v becomes + // the first index of w + + for (int k = d - 1; k >= 0; --k) { + MultiDimVector w(n[k]); + auto &Ukinv = Uinv[k]; + it.reset(); + + size_t first_v_index = 0; + size_t second_v_index = 0; + + while (not it.done()) { + size_t last_dim_count = it.lastDimensionCount(); + for (size_t i = 0; i < last_dim_count; ++i) { + double sum = 0.0; + for (size_t j = i; j < last_dim_count; ++j) { + sum += Ukinv(i, j) * v.data[first_v_index][second_v_index + j]; + } + w.data[i].push_back(sum); + } + second_v_index += last_dim_count; + if (second_v_index >= v.data[first_v_index].size()) { + second_v_index = 0; + first_v_index += 1; + } + + it.next(); + } + + v.swap(w); + + // for (size_t i = 0; i < v.data.size(); ++i) { + // std::cout << v.data[i] << "\n\n"; + // } + } + + return v; +} + +} /* namespace fsi */ diff --git a/test/main.cpp b/test/main.cpp new file mode 100644 index 0000000..d6fddca --- /dev/null +++ b/test/main.cpp @@ -0,0 +1,71 @@ + +#include +#include +#include +#include + +double f(std::vector point) { + double prod = 1.0; + for (size_t dim = 0; dim < point.size(); ++dim) { + prod *= point[dim]; + } + return prod; +} + +class GoldenPointDistribution { + static constexpr double golden_ratio = 0.5 * (1.0 + sqrt(5)); + + public: + double operator()(size_t idx) { + double value = (idx + 1) * golden_ratio; + return value - int(value); + } +}; + +class SimplePointDistribution { + public: + double operator()(size_t idx) { + if (idx == 0) { + return 0.0; + } else if (idx == 1) { + return 1.0; + } else { + return 0.5; + } + } +}; + +class MonomialFunctions { + public: + std::function operator()(size_t idx) { + return [=](double x) { return pow(x, idx); }; + } +}; + +template +inline std::ostream &operator<<(std::ostream &os, const std::vector &v) { + os << "["; + for (auto ii = v.begin(); ii != v.end(); ++ii) { + os << " " << *ii; + } + os << " ]"; + return os; +} + +// using namespace fsi; +int main() { + size_t d = 12; + size_t bound = 16; + fsi::BoundedSumIterator it(d, bound); + std::vector phi(d); + std::vector x(d); + auto start = std::chrono::high_resolution_clock::now(); + auto result = fsi::interpolate(f, it, phi, x); + auto finish = std::chrono::high_resolution_clock::now(); + std::chrono::duration elapsed = finish - start; + std::cout << "Elapsed time: " << elapsed.count() << " s\n"; + + // for (size_t i = 0; i < result.data.size(); ++i) { + // std::cout << result.data[i] << "\n\n"; + // } +}