initial commit with a working interpolation code
This commit is contained in:
David Holzmüller
commit
cc78e036b2
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BasedOnStyle: Google
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ColumnLimit: 100
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*~
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*.pdf
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||||
*.synctex.gz
|
||||
*.log
|
||||
*.aux
|
||||
*.toc
|
||||
*.out
|
||||
*.dvi
|
||||
*.bbl
|
||||
*.blg
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||||
*.nav
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||||
*.snm
|
||||
*.auxlock
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||||
*.dpth
|
||||
*.md5
|
||||
|
||||
build/*
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||||
TexCode/*
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||||
!TexCode/info.txt
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measurements/*
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||||
|
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*.hi
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||||
!references/*.pdf
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||||
.cproject
|
||||
.project
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||||
.settings
|
||||
|
||||
Debug
|
||||
Release
|
||||
|
||||
*.pyc
|
||||
*.os
|
||||
*.o
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||||
*.so
|
||||
*.jar
|
||||
*.pydevproject
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cmake_minimum_required(VERSION 2.8)
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||||
project(fast_sparse_interpolation CXX)
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||||
|
||||
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")
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||||
file(GLOB INC_TEST "test/*.hpp")
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||||
|
||||
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)
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||||
install(FILES ${INC} DESTINATION include/sfcpp)
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||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
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@ -0,0 +1,201 @@
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@ -0,0 +1,13 @@
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all: release
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#.PHONY: release
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release:
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mkdir -p build
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cd build && cmake -DCMAKE_BUILD_TYPE=Release -DBUILD_TEST=ON .. && make -j4 VERBOSE=1
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debug:
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mkdir -p build
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@ -0,0 +1,67 @@
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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)
|
||||
|
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The following files contain code taken from the SG++ project:
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src/files/files.cpp
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src/files/files.hpp
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src/time/Stopwatch.hpp
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src/time/Stopwatch.cpp
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========================================================================
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Copyright (c) 2008-today The SG++ Project
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All rights reserved.
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Redistribution and use in source and binary forms, with or without
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@ -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
|
||||
|
||||
|
||||
|
|
@ -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.
|
||||
==============================================================================*/
|
||||
|
||||
|
||||
|
|
@ -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
|
||||
|
||||
|
||||
|
|
@ -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 */
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@ -0,0 +1,325 @@
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// 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
|
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|
||||
#pragma once
|
||||
|
||||
#include <boost/numeric/ublas/lu.hpp>
|
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#include <boost/numeric/ublas/matrix.hpp>
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||||
#include <iostream>
|
||||
#include <vector>
|
||||
|
||||
namespace fsi {
|
||||
|
||||
class BoundedSumIterator {
|
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size_t d;
|
||||
size_t bound;
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std::vector<size_t> index_head; // contains all entries of the index except the last one
|
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size_t index_head_sum;
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bool is_done;
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||||
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public:
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BoundedSumIterator(size_t d, size_t bound)
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: d(d), bound(bound), index_head(d - 1, 0), index_head_sum(0), is_done(false){};
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|
||||
/**
|
||||
* 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
|
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* that ends with a zero.
|
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*/
|
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size_t lastDimensionCount() { return bound - index_head_sum + 1; }
|
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|
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void next() {
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if (bound > index_head_sum) {
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||||
index_head_sum += 1;
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index_head[d - 2] += 1;
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||||
} 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<size_t>(d - 1, 0);
|
||||
index_head_sum = 0;
|
||||
is_done = false;
|
||||
}
|
||||
|
||||
size_t dim() { return d; }
|
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|
||||
std::vector<size_t> indexBounds() { return std::vector<size_t>(d, bound + 1); }
|
||||
};
|
||||
|
||||
class StandardBoundedSumIterator {
|
||||
size_t d;
|
||||
size_t bound;
|
||||
std::vector<size_t> 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<size_t>(d - 1, 0);
|
||||
index_sum = 0;
|
||||
is_done = false;
|
||||
}
|
||||
};
|
||||
|
||||
// class FastSparseInterpolation {
|
||||
// public:
|
||||
// FastSparseInterpolation(std::function<double(std::vector<double>)> const &f,
|
||||
// BoundedSumIterator it, std::vector<std::function<double(size_t)>> phi);
|
||||
//};
|
||||
|
||||
class MultiDimVector {
|
||||
public:
|
||||
// put the first dimension into an outer vector for processing reasons
|
||||
std::vector<std::vector<double>> 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<double> 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 <class T>
|
||||
inline std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
|
||||
os << "[";
|
||||
for (auto ii = v.begin(); ii != v.end(); ++ii) {
|
||||
os << " " << *ii;
|
||||
}
|
||||
os << " ]";
|
||||
return os;
|
||||
}
|
||||
|
||||
template <typename Func, typename It, typename Phi, typename X>
|
||||
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<double> Matrix;
|
||||
|
||||
std::vector<Matrix> 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<double>(n[k]);
|
||||
Matrix Ukinv = ublas::identity_matrix<double>(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<double> 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 */
|
||||
|
|
@ -0,0 +1,71 @@
|
|||
|
||||
#include <Interpolation.hpp>
|
||||
#include <chrono>
|
||||
#include <cmath>
|
||||
#include <iostream>
|
||||
|
||||
double f(std::vector<double> 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<double(double)> operator()(size_t idx) {
|
||||
return [=](double x) { return pow(x, idx); };
|
||||
}
|
||||
};
|
||||
|
||||
template <class T>
|
||||
inline std::ostream &operator<<(std::ostream &os, const std::vector<T> &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<MonomialFunctions> phi(d);
|
||||
std::vector<GoldenPointDistribution> 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<double> 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";
|
||||
// }
|
||||
}
|
||||
Loading…
Reference in New Issue