From 074de5b24b7fc7f5fd62264afb82fde924977ac4 Mon Sep 17 00:00:00 2001
From: novak_99 <cooljohn312@gmail.com>
Date: Sat, 27 Nov 2021 22:55:44 -0800
Subject: [PATCH] Added euler's method for solving diffrential equations.
 Single and double variable functions.

---
 MLPP/NumericalAnalysis/NumericalAnalysis.cpp | 22 ++++++++++++++++++++
 MLPP/NumericalAnalysis/NumericalAnalysis.hpp |  4 ++++
 main.cpp                                     | 14 ++++++++++++-
 3 files changed, 39 insertions(+), 1 deletion(-)

diff --git a/MLPP/NumericalAnalysis/NumericalAnalysis.cpp b/MLPP/NumericalAnalysis/NumericalAnalysis.cpp
index c84ee84..1ff3261 100644
--- a/MLPP/NumericalAnalysis/NumericalAnalysis.cpp
+++ b/MLPP/NumericalAnalysis/NumericalAnalysis.cpp
@@ -141,6 +141,28 @@ namespace MLPP{
         }
         return x; 
     }
+
+    double NumericalAnalysis::eulerianMethod(double(*derivative)(double), std::vector<double> q_0, double p, double h){
+        double max_epoch = (p - q_0[0])/h; 
+        double x = q_0[0];
+        double y = q_0[1];
+        for(int i = 0; i < max_epoch; i++){
+            y = y + h * derivative(x);
+            x += h;
+        }
+        return y;
+    }
+
+    double NumericalAnalysis::eulerianMethod(double(*derivative)(std::vector<double>), std::vector<double> q_0, double p, double h){
+        double max_epoch = (p - q_0[0])/h; 
+        double x = q_0[0];
+        double y = q_0[1];
+        for(int i = 0; i < max_epoch; i++){
+            y = y + h * derivative({x, y});
+            x += h;
+        }
+        return y;
+    }
     
     std::vector<double> NumericalAnalysis::jacobian(double(*function)(std::vector<double>), std::vector<double> x){
         std::vector<double> jacobian; 
diff --git a/MLPP/NumericalAnalysis/NumericalAnalysis.hpp b/MLPP/NumericalAnalysis/NumericalAnalysis.hpp
index cc49094..cde9122 100644
--- a/MLPP/NumericalAnalysis/NumericalAnalysis.hpp
+++ b/MLPP/NumericalAnalysis/NumericalAnalysis.hpp
@@ -32,6 +32,9 @@ namespace MLPP{
             double halleyMethod(double(*function)(double), double x_0, double epoch_num);
             double invQuadraticInterpolation(double (*function)(double), std::vector<double> x_0, double epoch_num);
 
+            double eulerianMethod(double(*derivative)(double), std::vector<double> q_0, double p, double h); // Euler's method for solving diffrential equations. 
+            double eulerianMethod(double(*derivative)(std::vector<double>), std::vector<double> q_0, double p, double h); // Euler's method for solving diffrential equations. 
+
             std::vector<double> jacobian(double(*function)(std::vector<double>), std::vector<double> x); // Indeed, for functions with scalar outputs the Jacobians will be vectors.
             std::vector<std::vector<double>> hessian(double(*function)(std::vector<double>), std::vector<double> x);
             std::vector<std::vector<std::vector<double>>> thirdOrderTensor(double(*function)(std::vector<double>), std::vector<double> x);
@@ -42,6 +45,7 @@ namespace MLPP{
             double cubicApproximation(double(*function)(std::vector<double>), std::vector<double> c, std::vector<double> x);
 
             double laplacian(double(*function)(std::vector<double>), std::vector<double> x); // laplacian
+
     };
 }
 
diff --git a/main.cpp b/main.cpp
index eb2dbb6..c3b1bfe 100644
--- a/main.cpp
+++ b/main.cpp
@@ -58,6 +58,14 @@ using namespace MLPP;
 double f(double x){
     return sin(x);
 }
+
+double f_prime(double x){
+    return 2 * x;
+}
+
+double f_prime_2var(std::vector<double> x){
+    return 2 * x[0] + x[1];
+}
 /*
     y = x^3 + 2x - 2
     y' = 3x^2 + 2
@@ -587,7 +595,11 @@ int main() {
 
     // alg.printMatrix(alg.tensor_vec_mult(tensor, {1,2}));
 
-    std::cout << numAn.cubicApproximation(f_mv, {0, 0, 0}, {1, 1, 1}) << std::endl;
+    // std::cout << numAn.cubicApproximation(f_mv, {0, 0, 0}, {1, 1, 1}) << std::endl;
+
+    //std::cout << numAn.eulerianMethod(f_prime, {1, 1}, 1.5, 0.000001) << std::endl;
+
+    std::cout << numAn.eulerianMethod(f_prime_2var, {2, 3}, 2.5, 0.00000001) << std::endl;
 
     return 0;
 }