Merge branch 'master' into leastsquares

.github/workflows/test-linux.yml

@@ -2,10 +2,8 @@ name: Test on Linux
 
 on:
   push:
-    branches: [ master ]
   pull_request:
-    branches: [ master ]
-
+
 jobs:
   build:
 

.github/workflows/test-macos.yml

@@ -2,9 +2,7 @@ name: Test on MacOS
 
 on:
   push:
-    branches: [ master ]
   pull_request:
-    branches: [ master ]
 
 jobs:
   build:

.github/workflows/test-windows.yml

@@ -13,10 +13,7 @@ name: "Test on Windows"
 
 on:
   push:
-    branches: [ master ]
   pull_request:
-    # The branches below must be a subset of the branches above
-    branches: [ master ]
   schedule:
     - cron: '26 10 * * 3'
 

Makefile

@@ -1,7 +1,8 @@
 default_target: all
-.PHONY: all example test_core test_algebra test_polynomial test_optimization test_autodiff test_calculus automatic_differentiation hamiltonian \
-		error_propagation statistics sampling_distributions multivariate_minimization benchmark \
-		clean attractor montecarlo_comparison histogram
+.PHONY: all example test_core test_algebra test_polynomial test_optimization test_autodiff \
+		test_calculus test_statistics autodiff hamiltonian error_propagation \
+		statistics sampling gradient_descent benchmark \
+		clean attractor montecarlo_integral histogram random_walk
 
 all: examples test
 
@@ -63,14 +64,21 @@ ifndef windows_build
 	@./test/test_pseudorandom
 endif
 
-test: test_core test_algebra test_autodiff test_calculus test_polynomial test_optimization test_pseudorandom
+test_statistics:
+ifndef windows_build
+	@echo Compiling statistics test cases...
+	@g++ test/test_statistics.cpp ${CXXFLAGS} -I./test/ -o test/test_statistics
+	@./test/test_statistics
+endif
+
+test: test_core test_algebra test_autodiff test_calculus test_polynomial test_optimization test_pseudorandom test_statistics
 
 
 # Example programs
 
-automatic_differentiation:
+autodiff:
 	@echo Compiling \"Automatic differentiation\" example...
-	@g++ examples/automatic_differentiation.cpp ${CXXFLAGS} -o ./examples/automatic_differentiation
+	@g++ examples/autodiff.cpp ${CXXFLAGS} -o ./examples/autodiff
 
 hamiltonian:
 	@echo Compiling \"Hamiltonian\" example...
@@ -84,17 +92,17 @@ statistics:
 	@echo Compiling \"Statistics\" example...
 	@g++ examples/statistics.cpp ${CXXFLAGS} -o ./examples/statistics
 
-sampling_distributions:
+sampling:
 	@echo Compiling \"Sampling distributions\" example...
-	@g++ examples/sampling_distributions.cpp ${CXXFLAGS} -o ./examples/sampling_distributions
+	@g++ examples/sampling.cpp ${CXXFLAGS} -o ./examples/sampling
 
-montecarlo_comparison:
+montecarlo_integral:
 	@echo Compiling \"Montecarlo comparison\" example...
-	@g++ examples/montecarlo_comparison.cpp ${CXXFLAGS} -o ./examples/montecarlo_comparison
+	@g++ examples/montecarlo_integral.cpp ${CXXFLAGS} -o ./examples/montecarlo_integral
 
-multivariate_minimization:
+gradient_descent:
 	@echo Compiling \"Multivariate minimization\" example...
-	@g++ examples/multivariate_minimization.cpp ${CXXFLAGS} -o ./examples/multivariate_minimization
+	@g++ examples/gradient_descent.cpp ${CXXFLAGS} -o ./examples/gradient_descent
 
 logfit:
 	@echo Compiling \"Log fit\" example...
@@ -108,9 +116,13 @@ histogram:
 	@echo Compiling \"Histogram\" example...
 	@g++ examples/histogram.cpp ${CXXFLAGS} -o ./examples/histogram
 
-examples: example automatic_differentiation hamiltonian error_propagation \
-		  statistics sampling_distributions montecarlo_comparison multivariate_minimization \
-		  logfit attractor histogram
+random_walk:
+	@echo Compiling \"Random walk\" example...
+	@g++ examples/random_walk.cpp ${CXXFLAGS} -o ./examples/random_walk
+
+examples: example autodiff hamiltonian error_propagation \
+		  statistics sampling montecarlo_integral gradient_descent \
+		  logfit attractor histogram random_walk
 
 
 # Benchmarks

README.md

@@ -3,7 +3,7 @@
 <!-- Home -->
 <!-- ======== -->
 
-![GitHub last commit](https://img.shields.io/github/last-commit/chaotic-society/theoretica) ![GitHub Workflow Status](https://img.shields.io/github/actions/workflow/status/chaotic-society/theoretica/test-windows.yml) [![Codacy Badge](https://app.codacy.com/project/badge/Grade/0f4ae5dc6e1140ad855a3d6325d44b35)](https://www.codacy.com/gh/chaotic-society/theoretica/dashboard?utm_source=github.com&amp;utm_medium=referral&amp;utm_content=chaotic-society/theoretica&amp;utm_campaign=Badge_Grade)  ![License](https://img.shields.io/github/license/chaotic-society/theoretica)
+![GitHub last commit](https://img.shields.io/github/last-commit/chaotic-society/theoretica) ![GitHub Workflow Status](https://img.shields.io/github/actions/workflow/status/chaotic-society/theoretica/test-windows.yml) [![Codacy Badge](https://app.codacy.com/project/badge/Grade/0f4ae5dc6e1140ad855a3d6325d44b35)](https://app.codacy.com/gh/chaotic-society/theoretica/dashboard?utm_source=github.com&amp;utm_medium=referral&amp;utm_content=chaotic-society/theoretica&amp;utm_campaign=Badge_Grade)  ![License](https://img.shields.io/github/license/chaotic-society/theoretica)
 
 > A numerical and automatic math library for scientific research and graphical applications
 
@@ -18,7 +18,7 @@ mat<N, N> J = mat<N, N>::symplectic();
 real df_dt = gradient(f, eta) * J * gradient(H, eta);
 ```
 
-The library includes basic functionalities like real and complex analysis functions enhanced for x86 architectures, vector and matrix operations (both row-major and column-major), quaternions and function roots and extrema search, as well as more advanced features like dual numbers for automatic differentiation, statistical functions including distribution sampling, pseudorandom and quasirandom number generation for Monte Carlo methods and simulations.
+The library includes real and complex analysis functions optimized for the x86 architecture, linear algebra, quaternions, roots and extrema search, numerical approximation of derivatives, integrals and differential equations, as well as more advanced features like dual numbers for automatic differentiation, statistical functions including distribution sampling, pseudorandom and quasirandom number generation for Monte Carlo methods and simulations.
 
 ## Table of Contents
 - [Key Features](#key-features)
@@ -40,7 +40,7 @@ This is an overview of the library's functionalities. For a more detailed list s
 - Dual numbers, **Multivariable Automatic Differentiation** and Differential Operators
 - Pseudorandom and Quasirandom number generation (LCG, Xoshiro256++, Splitmix64, Wyrand, Weyl)
 - Statistical functions, including **Least Squares Linearization**
-- Random distribution sampling
+- Random distribution sampling and Monte Carlo
 - Approximation of roots, extrema, derivatives and integrals of real functions
 - Numerical integration of **Ordinary Differential Equations** (Euler, Heun, RK4, K38, multistep)
 - Polynomial interpolation with Chebyshev nodes, Bezier curves and spline interpolation
@@ -51,11 +51,12 @@ The library has no dependencies. Only the C++ Standard Library with C++11 capabi
 ## Setup
 You don't need anything other than your compiler to use the library. You can run `make all` in the root directory of the library to make sure it works.
 Define **THEORETICA_INCLUDE_BASE** if you intend to use only basic functionalities (linear algebra, real functions, complex numbers), as by default `theoretica.h` includes all headers.
-All library functions are implemented in the `theoretica` namespace (`th` is a shorter namespace alias).
+All library functions and objects are implemented in the `theoretica` namespace (`th` is a shorter namespace alias).
 
 ## Documentation
 The documentation for the library is available [here](https://chaotic-society.github.io/theoretica/).
 Introductory examples can be found in [EXAMPLES.md](https://github.com/chaotic-society/theoretica/blob/master/docs/txt/EXAMPLES.md) and more advanced examples can be found inside the `examples/` folder.
+The bibliography used for researching the algorithms used in the library is available [here](https://github.com/chaotic-society/theoretica/blob/master/docs/txt/BIBLIOGRAPHY.md).
 
 ### Quickstart
 You can try to compile this simple code to check if you set up the library correctly:
@@ -74,11 +75,11 @@ int main() {
 ```
 
 ### Other examples
-- [Chaotic Attractors](https://github.com/chaotic-society/theoretica/blob/master/examples/attractor.cpp)
 - [Statistics](https://github.com/chaotic-society/theoretica/blob/master/examples/statistics.cpp)
-- [Automatic differentiation](https://github.com/chaotic-society/theoretica/blob/master/examples/automatic_differentiation.cpp)
-- [Sampling distributions](https://github.com/chaotic-society/theoretica/blob/master/examples/sampling_distributions.cpp)
-- [Monte Carlo methods](https://github.com/chaotic-society/theoretica/blob/master/examples/montecarlo_comparison.cpp)
+- [Chaotic Attractors](https://github.com/chaotic-society/theoretica/blob/master/examples/attractor.cpp)
+- [Automatic differentiation](https://github.com/chaotic-society/theoretica/blob/master/examples/autodiff.cpp)
+- [Sampling distributions](https://github.com/chaotic-society/theoretica/blob/master/examples/sampling.cpp)
+- [Monte Carlo integration](https://github.com/chaotic-society/theoretica/blob/master/examples/montecarlo_integral.cpp)
 - [Fitting data](https://github.com/chaotic-society/theoretica/blob/master/examples/logfit.cpp)
 - [Automatic error propagation](https://github.com/chaotic-society/theoretica/blob/master/examples/error_propagation.cpp)
 - [Histogram usage](https://github.com/chaotic-society/theoretica/blob/master/examples/histogram.cpp)
@@ -91,7 +92,7 @@ Contributions are welcome and very appreciated! Make sure to read the [Contribut
 
 The library uses the custom built [Chebyshev testing framework](https://github.com/chaotic-society/chebyshev) to **estimate the precision** of functions and test their **performance**. Tests are automatically run on Windows, Linux and MacOS on every commit to ensure stability. Test units are placed inside the `test` folder while benchmarks are placed inside the `benchmark` folder.
 
-## Other informations
+## Other information
 
 ### License
 This project is currently under the [GNU Lesser General Public License 3.0](https://github.com/chaotic-society/theoretica/blob/master/LICENSE).

benchmark/benchmark_algebra.cpp

@@ -9,13 +9,13 @@ using benchmark::benchmark_result;
 
 
 template<unsigned int N, unsigned int M = N>
-mat<N, M> rand_mat(real min, real max, PRNG& g) {
+mat<real, N, M> rand_mat(real min, real max, PRNG& g) {
 
-	mat<N, M> A;
+	mat<real, N, M> A;
 
 	for (unsigned int i = 0; i < N; ++i)
 		for (unsigned int j = 0; j < M; ++j)
-			A.iat(i, j) = rand_uniform(min, max, g);
+			A.at(i, j) = rand_uniform(min, max, g);
 
 	return A;
 }
@@ -24,7 +24,7 @@ mat<N, M> rand_mat(real min, real max, PRNG& g) {
 template<unsigned int N>
 benchmark_result benchmark_mat_det(unsigned int iter, unsigned int runs) {
 
-	std::vector<mat<N, N>> A(iter);
+	std::vector<mat<real, N, N>> A(iter);
 	volatile real c = 0;
 
 	const int MAX = 100000;
@@ -53,7 +53,7 @@ benchmark_result benchmark_mat_det(unsigned int iter, unsigned int runs) {
 template<unsigned int N>
 benchmark_result benchmark_mat_inverse(unsigned int iter, unsigned int runs) {
 
-	std::vector<mat<N, N>> A(iter);
+	std::vector<mat<real, N, N>> A(iter);
 	volatile real c = 0;
 
 	const int MAX = 100000;

benchmark/benchmark_real_analysis.cpp

@@ -86,5 +86,7 @@ int main(int argc, char const *argv[]) {
 		benchmark::request("th::binomial_coeff",
 			[](real x) { return binomial_coeff<uint32_t>(10, x); }, uniform_generator(0, 9));
 
+		BENCHMARK(th::special::gamma, 0.1, 20);
+
 	benchmark::terminate();
 }

docs/annotated.html

@@ -119,7 +119,7 @@
 <!-- start footer part -->
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
-    <li class="footer">Generated on Tue Jun 27 2023 15:20:19 for Theoretica by <a href="https://www.doxygen.org/index.html"><img class="footer" src="doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
+    <li class="footer">Generated on Wed Sep 13 2023 16:25:44 for Theoretica by <a href="https://www.doxygen.org/index.html"><img class="footer" src="doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
   </ul>
 </div>
 </body>

docs/attractor_8cpp.html

@@ -135,15 +135,6 @@
 <tr class="memitem:a9beca8606cc317769958c4658d98554c"><td class="memItemLeft" align="right" valign="top"><a id="a9beca8606cc317769958c4658d98554c" name="a9beca8606cc317769958c4658d98554c"></a>
 const <a class="el" href="namespacetheoretica.html#a049966946220f1f7e5eae57293703066">real</a>&#160;</td><td class="memItemRight" valign="bottom"><b>c</b> = 8 / 3.0</td></tr>
 <tr class="separator:a9beca8606cc317769958c4658d98554c"><td class="memSeparator" colspan="2">&#160;</td></tr>
-<tr class="memitem:ae0af7a6e62928a88cc7aacd7fa840c6a"><td class="memItemLeft" align="right" valign="top"><a id="ae0af7a6e62928a88cc7aacd7fa840c6a" name="ae0af7a6e62928a88cc7aacd7fa840c6a"></a>
-const <a class="el" href="namespacetheoretica.html#a049966946220f1f7e5eae57293703066">real</a>&#160;</td><td class="memItemRight" valign="bottom"><b>d</b> = 0</td></tr>
-<tr class="separator:ae0af7a6e62928a88cc7aacd7fa840c6a"><td class="memSeparator" colspan="2">&#160;</td></tr>
-<tr class="memitem:a239fc54a76293a87f4e239ce20cfe69e"><td class="memItemLeft" align="right" valign="top"><a id="a239fc54a76293a87f4e239ce20cfe69e" name="a239fc54a76293a87f4e239ce20cfe69e"></a>
-const <a class="el" href="namespacetheoretica.html#a049966946220f1f7e5eae57293703066">real</a>&#160;</td><td class="memItemRight" valign="bottom"><b>e</b> = 0</td></tr>
-<tr class="separator:a239fc54a76293a87f4e239ce20cfe69e"><td class="memSeparator" colspan="2">&#160;</td></tr>
-<tr class="memitem:a99c80d79be5c2549f93a911da7724e69"><td class="memItemLeft" align="right" valign="top"><a id="a99c80d79be5c2549f93a911da7724e69" name="a99c80d79be5c2549f93a911da7724e69"></a>
-const <a class="el" href="namespacetheoretica.html#a049966946220f1f7e5eae57293703066">real</a>&#160;</td><td class="memItemRight" valign="bottom"><b>g</b> = 0</td></tr>
-<tr class="separator:a99c80d79be5c2549f93a911da7724e69"><td class="memSeparator" colspan="2">&#160;</td></tr>
 </table>
 <a name="details" id="details"></a><h2 class="groupheader">Detailed Description</h2>
 <div class="textblock"><p >Compute the orbit of a chaotic attractor. </p>
@@ -153,7 +144,7 @@
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="dir_d28a4824dc47e487b107a5db32ef43c4.html">examples</a></li><li class="navelem"><a class="el" href="attractor_8cpp.html">attractor.cpp</a></li>
-    <li class="footer">Generated on Tue Jun 27 2023 15:20:17 for Theoretica by <a href="https://www.doxygen.org/index.html"><img class="footer" src="doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
+    <li class="footer">Generated on Wed Sep 13 2023 16:25:42 for Theoretica by <a href="https://www.doxygen.org/index.html"><img class="footer" src="doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
   </ul>
 </div>
 </body>

docs/autodiff_8h.html

@@ -194,7 +194,7 @@
 <div id="nav-path" class="navpath"><!-- id is needed for treeview function! -->
   <ul>
     <li class="navelem"><a class="el" href="dir_42425a70e384b694fde5273f8252c9aa.html">autodiff</a></li><li class="navelem"><a class="el" href="autodiff_8h.html">autodiff.h</a></li>
-    <li class="footer">Generated on Tue Jun 27 2023 15:20:17 for Theoretica by <a href="https://www.doxygen.org/index.html"><img class="footer" src="doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
+    <li class="footer">Generated on Wed Sep 13 2023 16:25:42 for Theoretica by <a href="https://www.doxygen.org/index.html"><img class="footer" src="doxygen.svg" width="104" height="31" alt="doxygen"/></a> 1.9.3 </li>
   </ul>
 </div>
 </body>