Added numerical analysis class. Added method for poly/sinusodial/etc. function defs, added numerical diff method for both multivar & univar functions, added a jacobian vector calculator, added newton raphson method

MLPP/NumericalAnalysis/NumericalAnalysis.cpp

@@ -0,0 +1,44 @@
+//
+//  NumericalAnalysis.cpp
+//
+//  Created by Marc Melikyan on 11/13/20.
+//
+
+#include "NumericalAnalysis.hpp"
+#include <iostream>
+
+namespace MLPP{
+
+    double NumericalAnalysis::numDiff(double(*function)(double), double x){ 
+        double eps = 1e-10;
+        return (function(x + eps) - function(x)) / eps; // This is just the formal def. of the derivative.
+    }
+
+    double NumericalAnalysis::numDiff(double(*function)(std::vector<double>), std::vector<double> x, int axis){
+        // For multivariable function analysis. 
+        // This will be used for calculating Jacobian vectors. 
+        // Diffrentiate with respect to indicated axis. (0, 1, 2 ...)
+        double eps = 1e-10;
+        std::vector<double> x_eps = x;
+        x_eps[axis] += eps;
+
+        return (function(x_eps) - function(x)) / eps; 
+    }
+
+    double NumericalAnalysis::newtonRaphsonMethod(double(*function)(double), double x_0, double epoch){
+        double x = x_0;
+        for(int i = 0; i < epoch; i++){
+            x = x - function(x)/numDiff(function, x);
+        }
+        return x;
+    }
+    
+    std::vector<double> NumericalAnalysis::jacobian(double(*function)(std::vector<double>), std::vector<double> x){
+        std::vector<double> jacobian; 
+        jacobian.resize(x.size());
+        for(int i = 0; i < jacobian.size(); i++){
+            jacobian[i] = numDiff(function, x, i); // Derivative w.r.t axis i evaluated at x. For all x_i.
+        }
+        return jacobian;
+    }
+}

MLPP/NumericalAnalysis/NumericalAnalysis.hpp

@@ -0,0 +1,27 @@
+//
+//  NumericalAnalysis.hpp
+//
+//
+
+#ifndef NumericalAnalysis_hpp
+#define NumericalAnalysis_hpp
+
+#include <vector>
+
+namespace MLPP{
+    class NumericalAnalysis{
+        public:
+            /* A numerical method for derivatives is used. This may be subject to change,
+            as an analytical method for calculating derivatives will most likely be used in
+            the future.
+            */
+            double numDiff(double(*function)(double), double x);
+            double numDiff(double(*function)(std::vector<double>), std::vector<double> x, int axis);
+            double newtonRaphsonMethod(double(*function)(double), double x_0, double epoch);
+
+            std::vector<double> jacobian(double(*function)(std::vector<double>), std::vector<double>);
+        
+    };
+}
+
+#endif /* NumericalAnalysis_hpp */

main.cpp

@@ -43,19 +43,31 @@
 #include "MLPP/Data/Data.hpp"
 #include "MLPP/Convolutions/Convolutions.hpp"
 #include "MLPP/SVC/SVC.hpp"
+#include "MLPP/NumericalAnalysis/NumericalAnalysis.hpp"
 
 
 using namespace MLPP;
 
+
+double f(double x){
+    return x*x*x + 2*x - 2;
+}
+
+double f_mv(std::vector<double> x){
+    return x[0] * x[0] + x[1] * x[1] + x[1] + 5; 
+    // Where x,y=x[0],x[1], this function is defined as:
+    // f(x,y) = x^2 + y^2 + y + 5
+}
+
 int main() {
 
-    // OBJECTS
+    // // OBJECTS
     Stat stat;
     LinAlg alg;
-    Activation avn;
-    Cost cost;
-    Data data; 
-    Convolutions conv; 
+    // Activation avn;
+    // Cost cost;
+    // Data data; 
+    // Convolutions conv; 
 
     // DATA SETS
     // std::vector<std::vector<double>> inputSet = {{1,2,3,4,5,6,7,8,9,10}, {3,5,9,12,15,18,21,24,27,30}};
@@ -460,5 +472,16 @@ int main() {
     // alg.printMatrix(L);
     // alg.printMatrix(Lt);
 
+    // Checks for numerical analysis class.
+    NumericalAnalysis numAn;
+
+    std::cout << numAn.numDiff(&f, 1) << std::endl;
+    std::cout << numAn.newtonRaphsonMethod(&f, 1, 1000) << std::endl;
+
+    std::cout << numAn.numDiff(&f_mv, {1, 1}, 1) << std::endl; // Derivative w.r.t. x.
+
+    alg.printVector(numAn.jacobian(&f_mv, {1, 1}));
+
     return 0;
 }
+