From cd0de3bf7c974cb299a3685d2ed1056c1a225e0d Mon Sep 17 00:00:00 2001
From: novak_99 <cooljohn312@gmail.com>
Date: Sun, 21 Nov 2021 16:02:21 -0800
Subject: [PATCH] added laplacians

---
 MLPP/NumericalAnalysis/NumericalAnalysis.cpp | 10 ++++++++++
 MLPP/NumericalAnalysis/NumericalAnalysis.hpp |  2 +-
 main.cpp                                     |  6 ++++--
 3 files changed, 15 insertions(+), 3 deletions(-)

diff --git a/MLPP/NumericalAnalysis/NumericalAnalysis.cpp b/MLPP/NumericalAnalysis/NumericalAnalysis.cpp
index 3c348a0..d66f648 100644
--- a/MLPP/NumericalAnalysis/NumericalAnalysis.cpp
+++ b/MLPP/NumericalAnalysis/NumericalAnalysis.cpp
@@ -104,4 +104,14 @@ namespace MLPP{
         LinAlg alg;
         return linearApproximation(function, c, x) + 0.5 * alg.matmult({(alg.subtraction(x, c))}, alg.matmult(hessian(function, c), alg.transpose({alg.subtraction(x, c)})))[0][0];
     }
+
+    double NumericalAnalysis::laplacian(double(*function)(std::vector<double>), std::vector<double> x){
+        LinAlg alg;
+        std::vector<std::vector<double>> hessian_matrix = hessian(function, x);
+        double laplacian = 0;
+        for(int i = 0; i < hessian_matrix.size(); i++){
+            laplacian += hessian_matrix[i][i]; // homogenous 2nd derivs w.r.t i, then i
+        }
+        return laplacian;
+    }
 }
\ No newline at end of file
diff --git a/MLPP/NumericalAnalysis/NumericalAnalysis.hpp b/MLPP/NumericalAnalysis/NumericalAnalysis.hpp
index d0f5c2b..0c9b57f 100644
--- a/MLPP/NumericalAnalysis/NumericalAnalysis.hpp
+++ b/MLPP/NumericalAnalysis/NumericalAnalysis.hpp
@@ -34,7 +34,7 @@ namespace MLPP{
             double linearApproximation(double(*function)(std::vector<double>), std::vector<double> c, std::vector<double> x);
             double quadraticApproximation(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 6bb65f5..1ea4d09 100644
--- a/main.cpp
+++ b/main.cpp
@@ -79,7 +79,7 @@ double f_mv(std::vector<double> x){
 }
 /*
     Where x, y = x[0], x[1], this function is defined as:
-    f(x, y) = x^4 + xy^3 + yz^2
+    f(x, y) = x^3 + x + xy^3 + yz^2
 
     ∂f/∂x = 4x^3 + 3y^2 
     ∂^2f/∂x^2 = 6x 
@@ -528,7 +528,7 @@ int main() {
 
     //std::cout << numAn.quadraticApproximation(f, 0, 1) << std::endl;
 
-    std::cout << numAn.quadraticApproximation(f_mv, {0, 0, 0}, {1, 1, 1}) << std::endl;
+    // std::cout << numAn.quadraticApproximation(f_mv, {0, 0, 0}, {1, 1, 1}) << std::endl;
 
     // std::cout << numAn.numDiff(&f, 1) << std::endl;
     // std::cout << numAn.newtonRaphsonMethod(&f, 1, 1000) << std::endl;
@@ -543,6 +543,8 @@ int main() {
     // std::cout << "Our Hessian." << std::endl;
     // alg.printMatrix(numAn.hessian(&f_mv, {2, 2, 500}));
 
+    std::cout << numAn.laplacian(f_mv, {1,1,1}) << std::endl;
+
     return 0;
 }