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Added third derivative (though mv not good for sinusodials) and third order housing tensor

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This commit is contained in:
novak_99 2021-11-26 00:01:39 -08:00
parent 985a8f7f78
commit dd0e9cbada
2 changed files with 67 additions and 1 deletions
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65
MLPP/NumericalAnalysis/NumericalAnalysis.cpp
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@ -18,7 +18,14 @@ namespace MLPP{
double NumericalAnalysis::numDiff_2(double(*function)(double), double x){
double eps = 1e-5;
return (function(x + eps) - 2 * function(x) + function(x - eps)) / (eps * eps);
return (function(x + 2 * eps) - 2 * function(x + eps) + function(x)) / (eps * eps);
}
double NumericalAnalysis::numDiff_3(double(*function)(double), double x){
double eps = 1e-5;
double t1 = function(x + 3 * eps) - 2 * function(x + 2 * eps) + function(x + eps);
double t2 = function(x + 2 * eps) - 2 * function(x + eps) + function(x);
return (t1 - t2)/(eps * eps * eps);
}
double NumericalAnalysis::constantApproximation(double(*function)(double), double c){
@ -61,6 +68,44 @@ namespace MLPP{
return (function(x_pp) - function(x_np) - function(x_pn) + function(x))/(eps * eps);
}
double NumericalAnalysis::numDiff_3(double(*function)(std::vector<double>), std::vector<double> x, int axis1, int axis2, int axis3){
// For third order derivative tensors.
// NOTE: Approximations do not appear to be accurate for sinusodial functions...
// Should revisit this later.
double eps = INT_MAX;
std::vector<double> x_ppp = x;
x_ppp[axis1] += eps;
x_ppp[axis2] += eps;
x_ppp[axis3] += eps;
std::vector<double> x_npp = x;
x_npp[axis2] += eps;
x_npp[axis3] += eps;
std::vector<double> x_pnp = x;
x_pnp[axis1] += eps;
x_pnp[axis3] += eps;
std::vector<double> x_nnp = x;
x_nnp[axis3] += eps;
std::vector<double> x_ppn = x;
x_ppn[axis1] += eps;
x_ppn[axis2] += eps;
std::vector<double> x_npn = x;
x_npn[axis2] += eps;
std::vector<double> x_pnn = x;
x_pnn[axis1] += eps;
double thirdAxis = function(x_ppp) - function(x_npp) - function(x_pnp) + function(x_nnp);
double noThirdAxis = function(x_ppn) - function(x_npn) - function(x_pnn) + function(x);
return (thirdAxis - noThirdAxis)/(eps * eps * eps);
}
double NumericalAnalysis::newtonRaphsonMethod(double(*function)(double), double x_0, double epoch_num){
double x = x_0;
for(int i = 0; i < epoch_num; i++){
@ -115,6 +160,24 @@ namespace MLPP{
return hessian;
}
std::vector<std::vector<std::vector<double>>> NumericalAnalysis::thirdOrderTensor(double(*function)(std::vector<double>), std::vector<double> x){
std::vector<std::vector<std::vector<double>>> tensor;
tensor.resize(x.size());
for(int i = 0; i < tensor.size(); i++){
tensor[i].resize(x.size());
for(int j = 0; j < tensor[i].size(); j++){
tensor[i][j].resize(x.size());
}
}
for(int i = 0; i < tensor.size(); i++){ // O(n^3) time complexity :(
for(int j = 0; j < tensor[i].size(); j++){
for(int k = 0; k < tensor[i][j].size(); k++)
tensor[i][j][k] = numDiff_3(function, x, i, j, k);
}
}
return tensor;
}
double NumericalAnalysis::constantApproximation(double(*function)(std::vector<double>), std::vector<double> c){
return function(c);
}

3
MLPP/NumericalAnalysis/NumericalAnalysis.hpp
View File

@ -17,6 +17,7 @@ namespace MLPP{
*/
double numDiff(double(*function)(double), double x);
double numDiff_2(double(*function)(double), double x);
double numDiff_3(double(*function)(double), double x);
double constantApproximation(double(*function)(double), double c);
double linearApproximation(double(*function)(double), double c, double x);
@ -24,6 +25,7 @@ namespace MLPP{
double numDiff(double(*function)(std::vector<double>), std::vector<double> x, int axis);
double numDiff_2(double(*function)(std::vector<double>), std::vector<double> x, int axis1, int axis2);
double numDiff_3(double(*function)(std::vector<double>), std::vector<double> x, int axis1, int axis2, int axis3);
double newtonRaphsonMethod(double(*function)(double), double x_0, double epoch_num);
double halleyMethod(double(*function)(double), double x_0, double epoch_num);
@ -31,6 +33,7 @@ namespace MLPP{
std::vector<double> jacobian(double(*function)(std::vector<double>), std::vector<double> x); // Indeed, for functions with scalar outputs the Jacobians will be vectors.
std::vector<std::vector<double>> hessian(double(*function)(std::vector<double>), std::vector<double> x);
std::vector<std::vector<std::vector<double>>> thirdOrderTensor(double(*function)(std::vector<double>), std::vector<double> x);
double constantApproximation(double(*function)(std::vector<double>), std::vector<double> c);
double linearApproximation(double(*function)(std::vector<double>), std::vector<double> c, std::vector<double> x);