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MLPP/main.cpp
novak_99 2e935a4d87 added rgb2gray
2021-11-30 15:00:29 -08:00

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//
// 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"
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(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
// std::vector<double> inputSet;
// std::vector<double> outputSet;
// // Analytical solution used for calculating the parameters.
// data.setData("/Users/marcmelikyan/Desktop/Data/FiresAndCrime.csv", inputSet, outputSet);
// UniLinReg model(inputSet, outputSet);
// alg.printVector(model.modelSetTest(inputSet));
// // MULIVARIATE LINEAR REGRESSION
// 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};
// LinReg model(alg.transpose(inputSet), outputSet); // Can use Lasso, Ridge, ElasticNet Reg
// model.gradientDescent(0.001, 30000, 1);
// model.SGD(0.001, 30000, 1);
// model.MBGD(0.001, 10000, 2, 1);
// model.normalEquation();
// alg.printVector(model.modelSetTest((alg.transpose(inputSet))));
// std::cout << "ACCURACY: " << 100 * model.score() << "%" << 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
// std::vector<std::vector<double>> inputSet;
// std::vector<double> outputSet;
// data.setData(30, "/Users/marcmelikyan/Desktop/Data/BreastCancer.csv", inputSet, outputSet);
// LogReg model(inputSet, outputSet);
// model.SGD(0.001, 100000, 0);
// model.MLE(0.1, 10000, 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
// 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);
// // SUPPORT VECTOR CLASSIFICATION
// std::vector<std::vector<double>> inputSet;
// std::vector<double> outputSet;
// data.setData(30, "/Users/marcmelikyan/Desktop/Data/BreastCancerSVM.csv", inputSet, outputSet);
// 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
// std::vector<std::vector<double>> inputSet;
// std::vector<double> tempOutputSet;
// data.setData(13, "/Users/marcmelikyan/Desktop/Data/Wine.csv", inputSet, tempOutputSet);
// std::vector<std::vector<double>> outputSet = data.oneHotRep(tempOutputSet, 3);
// SoftmaxNet model(inputSet, outputSet, 5);
// model.SGD(0.1, 500000, 0);
// 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(10, "RELU", "Default", "Ridge", 0.0001);
// ann.addLayer(10, "Sigmoid", "Default");
// ann.addOutputLayer("Sigmoid", "LogLoss", "XavierNormal");
// ann.gradientDescent(0.1, 80000, 0);
// alg.printVector(ann.modelSetTest(alg.transpose(inputSet)));
// std::cout << "ACCURACY: " << 100 * ann.score() << "%" << std::endl;
// 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(10, "Sigmoid");
// ann.addLayer(10, "Sigmoid"); // Add more layers as needed.
// ann.addOutputLayer("Sigmoid", "LogLoss");
// ann.gradientDescent(0.1, 20000, 0);
// 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);
// std::vector<std::vector<double>> inputSet;
// std::vector<double> tempOutputSet;
// data.setData(784, "mini_mnist.csv", inputSet, tempOutputSet);
// std::vector<std::vector<double>> outputSet = data.oneHotRep(tempOutputSet, 10);
// MANN mann(inputSet, outputSet);
// mann.addLayer(2, "RELU");
// mann.addLayer(2, "RELU");
// mann.addOutputLayer("Softmax", "CrossEntropy");
// mann.gradientDescent(0.001, 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 = {
// {1,1,1,1,0,0,0,0},
// {1,1,1,1,0,0,0,0},
// {1,1,1,1,0,0,0,0},
// {1,1,1,1,0,0,0,0},
// {1,1,1,1,0,0,0,0},
// {1,1,1,1,0,0,0,0},
// {1,1,1,1,0,0,0,0},
// {1,1,1,1,0,0,0,0}
// };
// 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::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));
return 0;
}
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