Merge pull request #3 from Alpaca-zip/fix/outputs_and_default_values

Fix/outputs and default values

README.md

@@ -9,13 +9,13 @@ $ git clone https://github.com/Alpaca-zip/gradient_descent_algorithm.git
 ```
 ### 2. Install dependencies and compile the program.
 ```
-$ python3 -m pip install matplotlib numpy
+$ sudo apt-get install -y python3-matplotlib python3-numpy python3-dev
 $ bash build.sh
 ```
 ### 3. Run the program. 
-1. Upon running the program, you need to input the objective function as vectors for two variables (x1, x2), each defined by their degree and coefficient. You're asked to enter the order matrices for x1, x2, and the coefficient respectively.
+1. Upon running the program, you need to input the objective function as vectors for two variables $(x_{1}, x_{2})$, each defined by their degree and coefficient. You're asked to enter the order matrices for $x_{1}$, $x_{2}$, and the coefficient respectively.
 2. Then, you define the gradient vector similar to the objective function, with two components, each being a function of x1 and x2.
-3. Next, you provide an initial pair of numbers (x1, x2) as the starting point for gradient descent.
+3. Next, you provide an initial pair of numbers $(x_{1}, x_{2})$ as the starting point for gradient descent.
 
 **Example**
 
@@ -27,7 +27,7 @@ $$
 \nabla f(x_{1}, x_{2}) = [4x_{1}+x_{2}, x_{1}+2x_{2}]^T
 $$
 ```
-$ run.sh
+$ bash run.sh
 Objective function
  Enter the order matrix of x1: 2 0 1
  Enter the order matrix of x2: 0 2 1
@@ -48,24 +48,30 @@ x2-component of the gradient
 Enter the starting point (x1, x2): 1.5 1.5
 
 Default values:
- max_iter = 10000
+ max_iter = 100000
  precision = 0.0001
- xi = 0.3
- tau = 0.9
+ xi = 0.0001
+ tau = 0.5
 If these values are not suitable, please modify them in the code.
 
 ====================
 Iteration: 1
- x_curr = [1.5, 1.5]
- grad_curr = [7.5, 4.5]
+ Current x1 and x2 values = [1.5, 1.5]
+ Objective Function Value = 9
+ Gradient = [7.5, 4.5]
+ Gradient Norm = 8.74643
+ Elapsed Time = 277 microseconds
 ====================
 Iteration: 2
- x_curr = [-0.853579, 0.0878523]
- grad_curr = [-3.32647, -0.677875]
+ Current x1 and x2 values = [-0.375, 0.375]
+ Objective Function Value = 0.28125
+ Gradient = [-1.125, 0.375]
+ Gradient Norm = 1.18585
+ Elapsed Time = 587 microseconds
 ====================
 ...
 ```
 ### 4. The results will be displayed as figure.
 Finally, the program outputs the contour and the path of the gradient descent as plots. You can modify parameters like max iterations, precision, step size in the code itself.
 
-<img src="https://github.com/Alpaca-zip/dijkstra_algorithm/assets/84959376/e33b595b-f3d9-4204-aa60-29cc5580e4a5" width="600px">
+<img src="https://github.com/Alpaca-zip/gradient_descent_algorithm/assets/84959376/1bde4e46-b624-4155-a275-eefdd537be40" width="600px">

include/gradient_descent_node.hpp

@@ -16,6 +16,7 @@
 
 #pragma once
 
+#include <chrono>
 #include <cmath>
 #include <iostream>
 #include <sstream>

src/gradient_descent_node.cpp

@@ -112,10 +112,11 @@ void GradientDescentNode::displayFunction(
 
 void GradientDescentNode::solveGradientDescent()
 {
-  const int max_iter = 10000;
+  auto start_time = std::chrono::high_resolution_clock::now();
+  const int max_iter = 100000;
   const double precision = 1e-4;
-  const double xi = 0.3;
-  const double tau = 0.9;
+  const double xi = 1e-4;
+  const double tau = 0.5;
   std::cout << "\n";
   std::cout << "Default values:" << std::endl;
   std::cout << " max_iter = " << max_iter << std::endl;
@@ -131,13 +132,20 @@ void GradientDescentNode::solveGradientDescent()
   x_curr = {_x_start, _y_start};
 
   for (int i = 0; i < max_iter; i++) {
+    auto elapsed_time = std::chrono::duration_cast<std::chrono::microseconds>(
+                          std::chrono::high_resolution_clock::now() - start_time)
+                          .count();
     alpha = 1.0;
     grad_curr = calcGradient(x_curr[0], x_curr[1]);
     _path.push_back({x_curr[0], x_curr[1]});
     std::cout << "====================" << std::endl;
     std::cout << "Iteration: " << i + 1 << std::endl;
-    std::cout << " x_curr = [" << x_curr[0] << ", " << x_curr[1] << "]" << std::endl;
-    std::cout << " grad_curr = [" << grad_curr[0] << ", " << grad_curr[1] << "]" << std::endl;
+    std::cout << " Current x1 and x2 values = [" << x_curr[0] << ", " << x_curr[1] << "]"
+              << std::endl;
+    std::cout << " Objective Function Value = " << calcObjective(x_curr[0], x_curr[1]) << std::endl;
+    std::cout << " Gradient = [" << grad_curr[0] << ", " << grad_curr[1] << "]" << std::endl;
+    std::cout << " Gradient Norm = " << norm(grad_curr[0], grad_curr[1]) << std::endl;
+    std::cout << " Elapsed Time = " << elapsed_time << " microseconds" << std::endl;
 
     if (norm(grad_curr[0], grad_curr[1]) < precision) {
       break;