main.cpp

//
//  main.cpp
//  TEST_APP
//
//  Created by Marc on 1/20/21.
//

// THINGS CURRENTLY TO DO: 
// POLYMORPHIC IMPLEMENTATION OF REGRESSION CLASSES
// EXTEND SGD/MBGD SUPPORT FOR DYN. SIZED ANN 
// ADD LEAKYRELU, ELU, SELU TO ANN
// FIX VECTOR/MATRIX/TENSOR RESIZE ROUTINE

// HYPOTHESIS TESTING CLASS 
// GAUSS MARKOV CHECKER CLASS

#include <iostream>
#include <ctime>
#include <cmath>
#include <vector>
#include "MLPP/UniLinReg/UniLinReg.hpp"
#include "MLPP/LinReg/LinReg.hpp"
#include "MLPP/LogReg/LogReg.hpp"
#include "MLPP/CLogLogReg/CLogLogReg.hpp"
#include "MLPP/ExpReg/ExpReg.hpp"
#include "MLPP/ProbitReg/ProbitReg.hpp"
#include "MLPP/SoftmaxReg/SoftmaxReg.hpp"
#include "MLPP/TanhReg/TanhReg.hpp"
#include "MLPP/MLP/MLP.hpp"
#include "MLPP/SoftmaxNet/SoftmaxNet.hpp"
#include "MLPP/AutoEncoder/AutoEncoder.hpp"
#include "MLPP/ANN/ANN.hpp"
#include "MLPP/MANN/MANN.hpp"
#include "MLPP/MultinomialNB/MultinomialNB.hpp"
#include "MLPP/BernoulliNB/BernoulliNB.hpp"
#include "MLPP/GaussianNB/GaussianNB.hpp"
#include "MLPP/KMeans/KMeans.hpp"
#include "MLPP/kNN/kNN.hpp"
#include "MLPP/PCA/PCA.hpp"
#include "MLPP/OutlierFinder/OutlierFinder.hpp"
#include "MLPP/Stat/Stat.hpp"
#include "MLPP/LinAlg/LinAlg.hpp"
#include "MLPP/Activation/Activation.hpp"
#include "MLPP/Cost/Cost.hpp"
#include "MLPP/Data/Data.hpp"
#include "MLPP/Convolutions/Convolutions.hpp"
#include "MLPP/SVC/SVC.hpp"
#include "MLPP/NumericalAnalysis/NumericalAnalysis.hpp"
#include "MLPP/DualSVC/DualSVC.hpp"
#include "MLPP/GAN/GAN.hpp"
#include "MLPP/WGAN/WGAN.hpp"
#include "MLPP/Transforms/Transforms.hpp"

using namespace MLPP;


// double f(double x){
//     return x*x*x + 2*x - 2; 
// }

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
    y'' = 6x
    y''(2) = 12
*/

// double f_mv(std::vector<double> x){
//     return x[0] * 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 + xy^2 + y + 5
    ∂f/∂x = 2x + 2y
    ∂^2f/∂x∂y = 2
*/

double f_mv(std::vector<double> x){
    return x[0] * x[0] * x[0] + x[0] + x[1] * x[1] * x[1] * x[0] + x[2] * x[2] * x[1];
}

/*
    Where x, y = x[0], x[1], this function is defined as:
    f(x, y) = x^3 + x + xy^3 + yz^2

    fy = 3xy^2 + 2yz
    fyy = 6xy + 2z
    fyyz = 2

    ∂^2f/∂y^2 = 6xy + 2z
    ∂^3f/∂y^3 = 6x

    ∂f/∂z = 2zy
    ∂^2f/∂z^2 = 2y
    ∂^3f/∂z^3 = 0
    
    ∂f/∂x = 3x^2 + 1 + y^3
    ∂^2f/∂x^2 = 6x
    ∂^3f/∂x^3 = 6

    ∂f/∂z = 2zy
    ∂^2f/∂z^2 = 2z

    ∂f/∂y = 3xy^2
    ∂^2f/∂y∂x = 3y^2

*/


int main() {

    // // OBJECTS
    Stat stat;
    LinAlg alg;
    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}};
    // std::vector<double> outputSet = {2,4,6,8,10,12,14,16,18,20};

    // std::vector<std::vector<double>> inputSet = {{1,2,3,4,5,6,7,8}, {0,0,0,0,1,1,1,1}};
    // std::vector<double> outputSet = {0,0,0,0,1,1,1,1};

    // std::vector<std::vector<double>> inputSet = {{4,3,0,-3,-4}, {0,0,0,1,1}};
    // std::vector<double> outputSet = {1,1,0,-1,-1};

    // std::vector<std::vector<double>> inputSet = {{0,1,2,3,4}};
    // std::vector<double> outputSet = {1,2,4,8,16};

    //std::vector<std::vector<double>> inputSet = {{32, 0, 7}, {2, 28, 17}, {0, 9, 23}}; 

    // std::vector<std::vector<double>> inputSet = {{1,1,0,0,1}, {0,0,1,1,1}, {0,1,1,0,1}};
    // std::vector<double> outputSet = {0,1,0,1,1};

    // std::vector<std::vector<double>> inputSet = {{0,0,1,1}, {0,1,0,1}};
    // std::vector<double> outputSet = {0,1,1,0};

    // // STATISTICS
    // std::vector<double> x = {1,2,3,4,5,6,7,8,9,10};
    // std::vector<double> y = {10,9,8,7,6,5,4,3,2,1};
    // std::vector<double> w = {0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1};

    // std::cout << "Arithmetic Mean: " << stat.mean(x) << std::endl;
    // std::cout << "Median: " << stat.median(x) << std::endl;
    // alg.printVector(x);
    // alg.printVector(stat.mode(x));
    // std::cout << "Range: " << stat.range(x) << std::endl;
    // std::cout << "Midrange: " << stat.midrange(x) << std::endl;
    // std::cout << "Absolute Average Deviation: " << stat.absAvgDeviation(x) << std::endl;
    // std::cout << "Standard Deviation: " << stat.standardDeviation(x) << std::endl;
    // std::cout << "Variance: " << stat.variance(x) << std::endl;
    // std::cout << "Covariance: " << stat.covariance(x, y) << std::endl;
    // std::cout << "Correlation: " << stat.correlation(x, y) << std::endl;
    // std::cout << "R^2: " << stat.R2(x, y) << std::endl;
    // // Returns 1 - (1/k^2)
    // std::cout << "Chebyshev Inequality: " << stat.chebyshevIneq(2) << std::endl;
    // std::cout << "Weighted Mean: " << stat.weightedMean(x, w) << std::endl;
    // std::cout << "Geometric Mean: " << stat.geometricMean(x) << std::endl;
    // std::cout << "Harmonic Mean: " << stat.harmonicMean(x) << std::endl;
    // std::cout << "Root Mean Square (Quadratic mean): " << stat.RMS(x) << std::endl;
    // std::cout << "Power Mean (p = 5): " << stat.powerMean(x, 5) << std::endl;
    // std::cout << "Lehmer Mean (p = 5): " << stat.lehmerMean(x, 5) << std::endl;
    // std::cout << "Weighted Lehmer Mean (p = 5): " << stat.weightedLehmerMean(x, w, 5) << std::endl;
    // std::cout << "Contraharmonic Mean: " << stat.contraHarmonicMean(x) << std::endl;
    // std::cout << "Hernonian Mean: " << stat.heronianMean(1, 10) << std::endl;
    // std::cout << "Heinz Mean (x = 1): " << stat.heinzMean(1, 10, 1) << std::endl;
    // std::cout << "Neuman-Sandor Mean: " << stat.neumanSandorMean(1, 10) << std::endl;
    // std::cout << "Stolarsky Mean (p = 5): " << stat.stolarskyMean(1, 10, 5) << std::endl;
    // std::cout << "Identric Mean: " << stat.identricMean(1, 10) << std::endl;
    // std::cout << "Logarithmic Mean: " << stat.logMean(1, 10) << std::endl;
    // std::cout << "Absolute Average Deviation: " << stat.absAvgDeviation(x) << std::endl;

    // LINEAR ALGEBRA
    // std::vector<std::vector<double>> square = {{1, 1}, {-1, 1}, {1, -1}, {-1, -1}};

    // alg.printMatrix(alg.rotate(square, M_PI/4));

    // std::vector<std::vector<double>> A = {
    //     {1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
    //     {1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
    // };
    // std::vector<double> a = {4, 3, 1, 3}; 
    // std::vector<double> b = {3, 5, 6, 1};

    // alg.printMatrix(alg.matmult(alg.transpose(A), A)); 
    // std::cout << std::endl;
    // std::cout << alg.dot(a, b) << std::endl;
    // std::cout << std::endl;
    // alg.printMatrix(alg.hadamard_product(A, A));
    // std::cout << std::endl;
    // alg.printMatrix(alg.identity(10));

    // UNIVARIATE LINEAR REGRESSION 
    // Univariate, simple linear regression, case where k = 1
    // auto [inputSet, outputSet] = data.loadFiresAndCrime();
    // UniLinReg model(inputSet, outputSet);
    // alg.printVector(model.modelSetTest(inputSet));

    // // MULIVARIATE LINEAR REGRESSION
    // auto [inputSet, outputSet] = data.loadCaliforniaHousing();

    // LinReg model(inputSet, outputSet); // Can use Lasso, Ridge, ElasticNet Reg

    //model.gradientDescent(0.001, 30, 0);
    //model.SGD(0.00000001, 300000, 1);
    //model.MBGD(0.001, 10000, 2, 1);
    //model.normalEquation(); 

    // LinReg adamModel(alg.transpose(inputSet), outputSet);
    // alg.printVector(model.modelSetTest(inputSet));
    // std::cout << "ACCURACY: " << 100 * model.score() << "%" << std::endl;


    // const int TRIAL_NUM = 1000; 

    // double scoreSGD = 0; 
    // double scoreADAM = 0; 
    // for(int i = 0; i < TRIAL_NUM; i++){
    //     LinReg model(alg.transpose(inputSet), outputSet);
    //     model.MBGD(0.001, 5, 1, 0);
    //     scoreSGD += model.score();

    //     LinReg adamModel(alg.transpose(inputSet), outputSet);
    //     adamModel.Adam(0.1, 5, 1, 0.9, 0.999, 1e-8, 0); // Change batch size = sgd, bgd
    //     scoreADAM += adamModel.score();
    // }

    // std::cout << "ACCURACY, AVG, SGD: " << 100 * scoreSGD/TRIAL_NUM << "%" << std::endl;

    // std::cout << std::endl;

    // std::cout << "ACCURACY, AVG, ADAM: " << 100 * scoreADAM/TRIAL_NUM << "%" << std::endl;


    // std::cout << "Total epoch num: 300" << std::endl;
    // std::cout << "Method: 1st Order w/ Jacobians" << std::endl;

    // LinReg model(alg.transpose(inputSet), outputSet); // Can use Lasso, Ridge, ElasticNet Reg

    // model.gradientDescent(0.001, 300, 0);


    // std::cout << "--------------------------------------------" << std::endl;
    // std::cout << "Total epoch num: 300" << std::endl;
    // std::cout << "Method: Newtonian 2nd Order w/ Hessians" << std::endl;
    // LinReg model2(alg.transpose(inputSet), outputSet); 

    // model2.NewtonRaphson(1.5, 300, 0);


    // // LOGISTIC REGRESSION
    // auto [inputSet, outputSet] = data.load rastCancer();
    // LogReg model(inputSet, outputSet); 
    // model.SGD(0.001, 100000, 0);
    // alg.printVector(model.modelSetTest(inputSet));
    // std::cout << "ACCURACY: " << 100 * model.score() << "%" << std::endl;

    // // PROBIT REGRESSION
    // std::vector<std::vector<double>> inputSet;
    // std::vector<double> outputSet;
    // data.setData(30, "/Users/marcmelikyan/Desktop/Data/BreastCancer.csv", inputSet, outputSet);
    // ProbitReg model(inputSet, outputSet); 
    // model.SGD(0.001, 10000, 1);
    // alg.printVector(model.modelSetTest(inputSet));
    // std::cout << "ACCURACY: " << 100 * model.score() << "%" << std::endl;

    // // CLOGLOG REGRESSION
    // std::vector<std::vector<double>> inputSet = {{1,2,3,4,5,6,7,8}, {0,0,0,0,1,1,1,1}};
    // std::vector<double> outputSet = {0,0,0,0,1,1,1,1};
    // CLogLogReg model(alg.transpose(inputSet), outputSet); 
    // model.SGD(0.1, 10000, 0);
    // alg.printVector(model.modelSetTest(alg.transpose(inputSet)));
    // std::cout << "ACCURACY: " << 100 * model.score() << "%" << std::endl;

    // // EXPREG REGRESSION
    // std::vector<std::vector<double>> inputSet = {{0,1,2,3,4}};
    // std::vector<double> outputSet = {1,2,4,8,16};
    // ExpReg model(alg.transpose(inputSet), outputSet); 
    // model.SGD(0.001, 10000, 0);
    // alg.printVector(model.modelSetTest(alg.transpose(inputSet)));
    // std::cout << "ACCURACY: " << 100 * model.score() << "%" << std::endl;

    // // TANH REGRESSION
    // std::vector<std::vector<double>> inputSet = {{4,3,0,-3,-4}, {0,0,0,1,1}};
    // std::vector<double> outputSet = {1,1,0,-1,-1};
    // TanhReg model(alg.transpose(inputSet), outputSet); 
    // model.SGD(0.1, 10000, 0);
    // alg.printVector(model.modelSetTest(alg.transpose(inputSet)));
    // std::cout << "ACCURACY: " << 100 * model.score() << "%" << std::endl;

    // // SOFTMAX REGRESSION
    // auto [inputSet, outputSet] = data.loadIris();
    // SoftmaxReg model(inputSet, outputSet);
    // model.SGD(0.1, 10000, 1);
    // alg.printMatrix(model.modelSetTest(inputSet));
    // std::cout << "ACCURACY: " << 100 * model.score() << "%" << std::endl;

    // // SUPPORT VECTOR CLASSIFICATION
    // auto [inputSet, outputSet] = data.loadBreastCancerSVC();
    // SVC model(inputSet, outputSet, 1); 
    // model.SGD(0.00001, 100000, 1);
    // alg.printVector(model.modelSetTest(inputSet));
    // std::cout << "ACCURACY: " << 100 * model.score() << "%" << std::endl;

    // SoftmaxReg model(inputSet, outputSet); 
    // model.SGD(0.001, 20000, 0);
    // alg.printMatrix(model.modelSetTest(inputSet));

    // // MLP
    // std::vector<std::vector<double>> inputSet = {{0,0,1,1}, {0,1,0,1}};
    // inputSet = alg.transpose(inputSet);
    // std::vector<double> outputSet = {0,1,1,0};

    // MLP model(inputSet, outputSet, 2); 
    // model.gradientDescent(0.1, 10000, 0);
    // alg.printVector(model.modelSetTest(inputSet));
    // std::cout << "ACCURACY: " << 100 * model.score() << "%" << std::endl;

    // // SOFTMAX NETWORK
    // auto [inputSet, outputSet] = data.loadWine();
    // SoftmaxNet model(inputSet, outputSet, 1); 
    // model.gradientDescent(0.01, 100000, 1);
    // alg.printMatrix(model.modelSetTest(inputSet));
    // std::cout << "ACCURACY: " << 100 * model.score() << "%" << std::endl;

    // // AUTOENCODER
    // 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}};
    // AutoEncoder model(alg.transpose(inputSet), 5); 
    // model.SGD(0.001, 300000, 0);
    // alg.printMatrix(model.modelSetTest(alg.transpose(inputSet)));
    // std::cout << "ACCURACY: " << 100 * model.score() << "%" << std::endl;

    // DYNAMICALLY SIZED ANN
    // Possible Weight Init Methods: Default, Uniform, HeNormal, HeUniform, XavierNormal, XavierUniform
    // Possible Activations: Linear, Sigmoid, Swish, Softplus, Softsign, CLogLog, Ar{Sinh, Cosh, Tanh, Csch, Sech, Coth},  GaussianCDF, GELU, UnitStep
    // Possible Loss Functions: MSE, RMSE, MBE, LogLoss, CrossEntropy, HingeLoss
    // std::vector<std::vector<double>> inputSet = {{0,0,1,1}, {0,1,0,1}};
    // std::vector<double> outputSet = {0,1,1,0};
    // ANN ann(alg.transpose(inputSet), outputSet);
    // ann.addLayer(2, "Cosh");
    // ann.addOutputLayer("Sigmoid", "LogLoss");


    // ann.AMSGrad(0.1, 10000, 1, 0.9, 0.999, 0.000001, 1);
    // ann.Adadelta(1, 1000, 2, 0.9, 0.000001, 1);
    // ann.Momentum(0.1, 8000, 2, 0.9, true, 1);

    //ann.setLearningRateScheduler("Step", 0.5, 1000);
    // ann.gradientDescent(0.01, 30000);
    // alg.printVector(ann.modelSetTest(alg.transpose(inputSet)));
    // std::cout << "ACCURACY: " << 100 * ann.score() << "%" << std::endl;

    std::vector<std::vector<double>> outputSet = {{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20}, 
                                               {2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40}};

    WGAN gan(2, alg.transpose(outputSet)); // our gan is a wasserstein gan (wgan)
    gan.addLayer(5, "Sigmoid");
    gan.addLayer(2, "RELU");
    gan.addLayer(5, "Sigmoid");
    gan.addOutputLayer(); // User can specify weight init- if necessary.
    gan.gradientDescent(0.1, 55000, 0);
    std::cout << "GENERATED INPUT: (Gaussian-sampled noise):" << std::endl;
    alg.printMatrix(gan.generateExample(100));


    // typedef std::vector<std::vector<double>> Matrix;
    // typedef std::vector<double> Vector;

    // Matrix inputSet = {{0,0}, {0,1}, {1,0}, {1,1}}; // XOR 
    // Vector outputSet = {0,1,1,0};

    // ANN ann(inputSet, outputSet);
    // ann.addLayer(5, "Sigmoid");
    // ann.addLayer(8, "Sigmoid"); // Add more layers as needed. 
    // ann.addOutputLayer("Sigmoid", "LogLoss");
    // ann.gradientDescent(1, 20000, 1);

    // Vector predictions = ann.modelSetTest(inputSet);
    // alg.printVector(predictions); // Testing out the model's preds for train set.
    // std::cout << "ACCURACY: " << 100 * ann.score() << "%" << std::endl; // Accuracy.

    // // DYNAMICALLY SIZED MANN (Multidimensional Output ANN)
    // std::vector<std::vector<double>> inputSet = {{1,2,3},{2,4,6},{3,6,9},{4,8,12}};
    // std::vector<std::vector<double>> outputSet = {{1,5}, {2,10}, {3,15}, {4,20}};

    // MANN mann(inputSet, outputSet);
    // mann.addOutputLayer("Linear", "MSE");
    // mann.gradientDescent(0.001, 80000, 0);
    // alg.printMatrix(mann.modelSetTest(inputSet));
    // std::cout << "ACCURACY: " << 100 * mann.score() << "%" << std::endl;

    // std::vector<std::vector<double>> inputSet;
    // std::vector<double> tempOutputSet;
    // data.setData(4, "/Users/marcmelikyan/Desktop/Data/Iris.csv", inputSet, tempOutputSet);
    // std::vector<std::vector<double>> outputSet = data.oneHotRep(tempOutputSet, 3);

    // TRAIN TEST SPLIT CHECK
    // std::vector<std::vector<double>> inputSet1 = {{1,2,3,4,5,6,7,8,9,10}, {3,5,9,12,15,18,21,24,27,30}};
    // std::vector<std::vector<double>> outputSet1 = {{2,4,6,8,10,12,14,16,18,20}};
    // auto [inputSet, outputSet, inputTestSet, outputTestSet] = data.trainTestSplit(alg.transpose(inputSet1), alg.transpose(outputSet1), 0.2);
    // alg.printMatrix(inputSet);
    // alg.printMatrix(outputSet);
    // alg.printMatrix(inputTestSet);
    // alg.printMatrix(outputTestSet);


    // alg.printMatrix(inputSet);
    // alg.printMatrix(outputSet);

    // MANN mann(inputSet, outputSet);
    // mann.addLayer(100, "RELU", "XavierNormal");
    // mann.addOutputLayer("Softmax", "CrossEntropy", "XavierNormal");
    // mann.gradientDescent(0.1, 80000, 1);
    // alg.printMatrix(mann.modelSetTest(inputSet));
    // std::cout << "ACCURACY: " << 100 * mann.score() << "%" << std::endl;

    // // NAIVE BAYES
    // std::vector<std::vector<double>> inputSet = {{1,1,1,1,1}, {0,0,1,1,1}, {0,0,1,0,1}};
    // std::vector<double> outputSet = {0,1,0,1,1};

    // MultinomialNB MNB(alg.transpose(inputSet), outputSet, 2);
    // alg.printVector(MNB.modelSetTest(alg.transpose(inputSet)));

    // BernoulliNB BNB(alg.transpose(inputSet), outputSet);
    // alg.printVector(BNB.modelSetTest(alg.transpose(inputSet)));

    // GaussianNB GNB(alg.transpose(inputSet), outputSet, 2);
    // alg.printVector(GNB.modelSetTest(alg.transpose(inputSet)));

    // // KMeans
    // std::vector<std::vector<double>> inputSet = {{32, 0, 7}, {2, 28, 17}, {0, 9, 23}}; 
    // KMeans kmeans(inputSet, 3, "KMeans++");
    // kmeans.train(3, 1);
    // std::cout << std::endl;
    // alg.printMatrix(kmeans.modelSetTest(inputSet)); // Returns the assigned centroids to each of the respective training examples
    // std::cout << std::endl;
    // alg.printVector(kmeans.silhouette_scores());

    // // kNN 
    // std::vector<std::vector<double>> inputSet = {{1,2,3,4,5,6,7,8}, {0,0,0,0,1,1,1,1}};
    // std::vector<double> outputSet = {0,0,0,0,1,1,1,1};
    // kNN knn(alg.transpose(inputSet), outputSet, 8);
    // alg.printVector(knn.modelSetTest(alg.transpose(inputSet)));
    // std::cout << "ACCURACY: " << 100 * knn.score() << "%" << std::endl;


    // // CONVOLUTION, POOLING, ETC.. 
    // std::vector<std::vector<double>> input = {
    //     {1},
    // };

    // std::vector<std::vector<std::vector<double>>> tensorSet; 
    // tensorSet.push_back(input);
    // tensorSet.push_back(input);
    // tensorSet.push_back(input);

    // alg.printTensor(data.rgb2xyz(tensorSet));

    // std::vector<std::vector<double>> input = {
    //     {62,55,55,54,49,48,47,55},
    //     {62,57,54,52,48,47,48,53},
    //     {61,60,52,49,48,47,49,54},
    //     {63,61,60,60,63,65,68,65},
    //     {67,67,70,74,79,85,91,92},
    //     {82,95,101,106,114,115,112,117},
    //     {96,111,115,119,128,128,130,127},
    //     {109,121,127,133,139,141,140,133},
    // };

    // Transforms trans; 

    // alg.printMatrix(trans.discreteCosineTransform(input));

    // alg.printMatrix(conv.convolve(input, conv.getPrewittVertical(), 1)); // Can use padding
    // alg.printMatrix(conv.pool(input, 4, 4, "Max")); // Can use Max, Min, or Average pooling. 

    // std::vector<std::vector<std::vector<double>>> tensorSet; 
    // tensorSet.push_back(input);
    // tensorSet.push_back(input);
    // alg.printVector(conv.globalPool(tensorSet, "Average")); // Can use Max, Min, or Average global pooling. 

    // std::vector<std::vector<double>> laplacian = {{1, 1, 1}, {1, -4, 1}, {1, 1, 1}};
    // alg.printMatrix(conv.convolve(conv.gaussianFilter2D(5, 1), laplacian, 1));


    // // PCA, SVD, eigenvalues & eigenvectors
    // std::vector<std::vector<double>> inputSet = {{1,1}, {1,1}};
    // auto [Eigenvectors, Eigenvalues] = alg.eig(inputSet); 
    // std::cout << "Eigenvectors:" << std::endl; 
    // alg.printMatrix(Eigenvectors);
    // std::cout << std::endl;
    // std::cout << "Eigenvalues:" << std::endl; 
    // alg.printMatrix(Eigenvalues);

    // auto [U, S, Vt] = alg.SVD(inputSet);

    // // PCA done using Jacobi's method to approximate eigenvalues and eigenvectors.
    // PCA dr(inputSet, 1); // 1 dimensional representation. 
    // std::cout << std::endl;
    // std::cout << "Dimensionally reduced representation:" << std::endl;
    // alg.printMatrix(dr.principalComponents());
    // std::cout << "SCORE: " << dr.score() << std::endl; 


    // // NLP/DATA
    // std::string verbText = "I am appearing and thinking, as well as conducting.";
    // std::cout << "Stemming Example:" << std::endl;
    // std::cout << data.stemming(verbText) << std::endl;
    // std::cout << std::endl;

    // std::vector<std::string> sentences = {"He is a good boy", "She is a good girl", "The boy and girl are good"};
    // std::cout << "Bag of Words Example:" << std::endl;
    // alg.printMatrix(data.BOW(sentences, "Default"));
    // std::cout << std::endl;
    // std::cout << "TFIDF Example:" << std::endl;
    // alg.printMatrix(data.TFIDF(sentences));
    // std::cout << std::endl;

    // std::cout << "Tokenization:" << std::endl;
    // alg.printVector(data.tokenize(verbText));
    // std::cout << std::endl;

    // std::cout << "Word2Vec:" << std::endl;
    // std::string textArchive = {"He is a good boy. She is a good girl. The boy and girl are good."};
    // std::vector<std::string> corpus = data.splitSentences(textArchive);
    // auto [wordEmbeddings, wordList] = data.word2Vec(corpus, "CBOW", 2, 2, 0.1, 10000); // Can use either CBOW or Skip-n-gram.
    // alg.printMatrix(wordEmbeddings);
    // std::cout << std::endl;

    // std::vector<std::string> textArchive = {"pizza", "pizza hamburger cookie", "hamburger", "ramen", "sushi", "ramen sushi"};

    // alg.printMatrix(data.LSA(textArchive, 2));
    // //alg.printMatrix(data.BOW(textArchive, "Default"));
    // std::cout << std::endl;
    

    // std::vector<std::vector<double>> inputSet = {{1,2},{2,3},{3,4},{4,5},{5,6}};
    // std::cout << "Feature Scaling Example:" << std::endl;
    // alg.printMatrix(data.featureScaling(inputSet));
    // std::cout << std::endl;

    // std::cout << "Mean Centering Example:" << std::endl;
    // alg.printMatrix(data.meanCentering(inputSet));
    // std::cout << std::endl;

    // std::cout << "Mean Normalization Example:" << std::endl;
    // alg.printMatrix(data.meanNormalization(inputSet));
    // std::cout << std::endl;

    // // Outlier Finder
    // std::vector<double> inputSet = {1,2,3,4,5,6,7,8,9,23554332523523};
    // OutlierFinder outlierFinder(2); // Any datapoint outside of 2 stds from the mean is marked as an outlier. 
    // alg.printVector(outlierFinder.modelTest(inputSet));

    // // Testing new Functions
    // double z_s = 0.001;
    // std::cout << avn.logit(z_s) << std::endl;
    // std::cout << avn.logit(z_s, 1) << std::endl;

    // std::vector<double> z_v = {0.001};
    // alg.printVector(avn.logit(z_v));
    // alg.printVector(avn.logit(z_v, 1));

    // std::vector<std::vector<double>> Z_m = {{0.001}};
    // alg.printMatrix(avn.logit(Z_m));
    // alg.printMatrix(avn.logit(Z_m, 1));

    // std::cout << alg.trace({{1,2}, {3,4}}) << std::endl;
    // alg.printMatrix(alg.pinverse({{1,2}, {3,4}}));
    // alg.printMatrix(alg.diag({1,2,3,4,5}));
    // alg.printMatrix(alg.kronecker_product({{1,2,3,4,5}}, {{6,7,8,9,10}}));
    // alg.printMatrix(alg.matrixPower({{5,5},{5,5}}, 2));
    // alg.printVector(alg.solve({{1,1}, {1.5, 4.0}}, {2200, 5050}));

    // std::vector<std::vector<double>> matrixOfCubes = {{1,2,64,27}};
    // std::vector<double> vectorOfCubes = {1,2,64,27};
    // alg.printMatrix(alg.cbrt(matrixOfCubes));
    // alg.printVector(alg.cbrt(vectorOfCubes));
    // std::cout << alg.max({{1,2,3,4,5}, {6,5,3,4,1}, {9,9,9,9,9}}) << std::endl;
    // std::cout << alg.min({{1,2,3,4,5}, {6,5,3,4,1}, {9,9,9,9,9}}) << std::endl;

    // std::vector<double> chicken; 
    // data.getImage("../../Data/apple.jpeg", chicken);
    // alg.printVector(chicken);

    // std::vector<std::vector<double>> P = {{12, -51, 4}, {6, 167, -68}, {-4, 24, -41}};
    // alg.printMatrix(P);

    // alg.printMatrix(alg.gramSchmidtProcess(P));

    // auto [Q, R] = alg.QRD(P); // It works! 
    
    //  alg.printMatrix(Q);

    //  alg.printMatrix(R); 

    // // Checking positive-definiteness checker. For Cholesky Decomp. 
    // std::vector<std::vector<double>> A = 
    // {
    //     {1,-1,-1,-1},                        
    //     {-1,2,2,2},
    //     {-1,2,3,1},
    //     {-1,2,1,4}
    // };

    // std::cout << std::boolalpha << alg.positiveDefiniteChecker(A) << std::endl;
    // auto [L, Lt] = alg.chol(A); // works.
    // alg.printMatrix(L);
    // alg.printMatrix(Lt);

    // Checks for numerical analysis class.
    NumericalAnalysis numAn;

    //std::cout << numAn.quadraticApproximation(f, 0, 1) << std::endl;

    // std::cout << numAn.cubicApproximation(f, 0, 1.001) << std::endl;

    // std::cout << f(1.001) << 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;
    //std::cout << numAn.invQuadraticInterpolation(&f, {100, 2,1.5}, 10) << 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}));

    //std::cout << numAn.numDiff_2(&f, 2) << std::endl; 

    //std::cout << numAn.numDiff_3(&f, 2) << std::endl; 

    // std::cout << numAn.numDiff_2(&f_mv, {2, 2, 500}, 2, 2) << std::endl;
    //std::cout << numAn.numDiff_3(&f_mv, {2, 1000, 130}, 0, 0, 0) << std::endl;

    // alg.printTensor(numAn.thirdOrderTensor(&f_mv, {1, 1, 1}));
    // 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;

    // std::vector<std::vector<std::vector<double>>> tensor;
    // tensor.push_back({{1,2}, {1,2}, {1,2}});
    // tensor.push_back({{1,2}, {1,2}, {1,2}});

    // alg.printTensor(tensor);

    // 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.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;

    // alg.printMatrix(conv.dx(A));
    // alg.printMatrix(conv.dy(A));

    // alg.printMatrix(conv.gradOrientation(A));

    // std::vector<std::vector<double>> A = 
    // {
    //     {1,0,0,0},                        
    //     {0,0,0,0},
    //     {0,0,0,0},
    //     {0,0,0,1}
    // };

    // std::vector<std::vector<std::string>> h = conv.harrisCornerDetection(A); 

    // for(int i = 0; i < h.size(); i++){
    //     for(int j = 0; j < h[i].size(); j++){
    //         std::cout << h[i][j] << " ";
    //     }
    //     std::cout << std::endl;
    // } // Harris detector works. Life is good!

    // std::vector<double> a = {3,4,4};
    // std::vector<double> b = {4,4,4};
    // alg.printVector(alg.cross(a,b));

    //SUPPORT VECTOR CLASSIFICATION (kernel method)
    // std::vector<std::vector<double>> inputSet; 
    // std::vector<double> outputSet; 
    // data.setData(30, "/Users/marcmelikyan/Desktop/Data/BreastCancerSVM.csv", inputSet, outputSet);

    // std::vector<std::vector<double>> inputSet; 
    // std::vector<double> outputSet; 
    // data.setData(4, "/Users/marcmelikyan/Desktop/Data/IrisSVM.csv", inputSet, outputSet);

    // DualSVC kernelSVM(inputSet, outputSet, 1000);
    // kernelSVM.gradientDescent(0.0001, 20, 1);

    // std::vector<std::vector<double>> linearlyIndependentMat = 
    
    // {
    //     {1,2,3,4},
    //     {234538495,4444,6111,55}
    // };

    // std::cout << "True of false: linearly independent?: " << std::boolalpha << alg.linearIndependenceChecker(linearlyIndependentMat) << std::endl;
    

    return 0;
}