mirror of
https://github.com/Relintai/pmlpp.git
synced 2024-11-08 13:12:09 +01:00
Reworked MLPPNumericalAnalysis.
This commit is contained in:
parent
6f691f9f26
commit
ab24693f37
@ -7,145 +7,145 @@
|
||||
#include "numerical_analysis.h"
|
||||
#include "../lin_alg/lin_alg.h"
|
||||
|
||||
#include <climits>
|
||||
#include <cmath>
|
||||
#include <iostream>
|
||||
#include <string>
|
||||
#include "../lin_alg/mlpp_matrix.h"
|
||||
#include "../lin_alg/mlpp_tensor3.h"
|
||||
#include "../lin_alg/mlpp_vector.h"
|
||||
|
||||
/*
|
||||
real_t MLPPNumericalAnalysis::numDiff(real_t (*function)(real_t), real_t x) {
|
||||
real_t MLPPNumericalAnalysis::num_diffr(real_t (*function)(real_t), real_t x) {
|
||||
real_t eps = 1e-10;
|
||||
return (function(x + eps) - function(x)) / eps; // This is just the formal def. of the derivative.
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::numDiff_2(real_t (*function)(real_t), real_t x) {
|
||||
real_t MLPPNumericalAnalysis::num_diff_2r(real_t (*function)(real_t), real_t x) {
|
||||
real_t eps = 1e-5;
|
||||
return (function(x + 2 * eps) - 2 * function(x + eps) + function(x)) / (eps * eps);
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::numDiff_3(real_t (*function)(real_t), real_t x) {
|
||||
real_t MLPPNumericalAnalysis::num_diff_3r(real_t (*function)(real_t), real_t x) {
|
||||
real_t eps = 1e-5;
|
||||
real_t t1 = function(x + 3 * eps) - 2 * function(x + 2 * eps) + function(x + eps);
|
||||
real_t t2 = function(x + 2 * eps) - 2 * function(x + eps) + function(x);
|
||||
return (t1 - t2) / (eps * eps * eps);
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::constantApproximation(real_t (*function)(real_t), real_t c) {
|
||||
real_t MLPPNumericalAnalysis::constant_approximationr(real_t (*function)(real_t), real_t c) {
|
||||
return function(c);
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::linearApproximation(real_t (*function)(real_t), real_t c, real_t x) {
|
||||
return constantApproximation(function, c) + numDiff(function, c) * (x - c);
|
||||
real_t MLPPNumericalAnalysis::linear_approximationr(real_t (*function)(real_t), real_t c, real_t x) {
|
||||
return constant_approximationr(function, c) + num_diffr(function, c) * (x - c);
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::quadraticApproximation(real_t (*function)(real_t), real_t c, real_t x) {
|
||||
return linearApproximation(function, c, x) + 0.5 * numDiff_2(function, c) * (x - c) * (x - c);
|
||||
real_t MLPPNumericalAnalysis::quadratic_approximationr(real_t (*function)(real_t), real_t c, real_t x) {
|
||||
return linear_approximationr(function, c, x) + 0.5 * num_diff_2r(function, c) * (x - c) * (x - c);
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::cubicApproximation(real_t (*function)(real_t), real_t c, real_t x) {
|
||||
return quadraticApproximation(function, c, x) + (1 / 6) * numDiff_3(function, c) * (x - c) * (x - c) * (x - c);
|
||||
real_t MLPPNumericalAnalysis::cubic_approximationr(real_t (*function)(real_t), real_t c, real_t x) {
|
||||
return quadratic_approximationr(function, c, x) + (1 / 6) * num_diff_3r(function, c) * (x - c) * (x - c) * (x - c);
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::numDiff(real_t (*function)(std::vector<real_t>), std::vector<real_t> x, int axis) {
|
||||
real_t MLPPNumericalAnalysis::num_diffv(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x, int axis) {
|
||||
// For multivariable function analysis.
|
||||
// This will be used for calculating Jacobian vectors.
|
||||
// Diffrentiate with respect to indicated axis. (0, 1, 2 ...)
|
||||
real_t eps = 1e-10;
|
||||
std::vector<real_t> x_eps = x;
|
||||
x_eps[axis] += eps;
|
||||
Ref<MLPPVector> x_eps = x->duplicate_fast();
|
||||
x_eps->element_get_ref(axis) += eps;
|
||||
|
||||
return (function(x_eps) - function(x)) / eps;
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::numDiff_2(real_t (*function)(std::vector<real_t>), std::vector<real_t> x, int axis1, int axis2) {
|
||||
real_t MLPPNumericalAnalysis::num_diff_2v(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x, int axis1, int axis2) {
|
||||
//For Hessians.
|
||||
real_t eps = 1e-5;
|
||||
|
||||
std::vector<real_t> x_pp = x;
|
||||
x_pp[axis1] += eps;
|
||||
x_pp[axis2] += eps;
|
||||
Ref<MLPPVector> x_pp = x->duplicate_fast();
|
||||
x_pp->element_get_ref(axis1) += eps;
|
||||
x_pp->element_get_ref(axis2) += eps;
|
||||
|
||||
std::vector<real_t> x_np = x;
|
||||
x_np[axis2] += eps;
|
||||
Ref<MLPPVector> x_np = x->duplicate_fast();
|
||||
x_np->element_get_ref(axis2) += eps;
|
||||
|
||||
std::vector<real_t> x_pn = x;
|
||||
x_pn[axis1] += eps;
|
||||
Ref<MLPPVector> x_pn = x->duplicate_fast();
|
||||
x_pn->element_get_ref(axis1) += eps;
|
||||
|
||||
return (function(x_pp) - function(x_np) - function(x_pn) + function(x)) / (eps * eps);
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::numDiff_3(real_t (*function)(std::vector<real_t>), std::vector<real_t> x, int axis1, int axis2, int axis3) {
|
||||
real_t MLPPNumericalAnalysis::num_diff_3v(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &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.
|
||||
real_t eps = 1e-5;
|
||||
|
||||
std::vector<real_t> x_ppp = x;
|
||||
x_ppp[axis1] += eps;
|
||||
x_ppp[axis2] += eps;
|
||||
x_ppp[axis3] += eps;
|
||||
Ref<MLPPVector> x_ppp = x->duplicate_fast();
|
||||
x_ppp->element_get_ref(axis1) += eps;
|
||||
x_ppp->element_get_ref(axis2) += eps;
|
||||
x_ppp->element_get_ref(axis3) += eps;
|
||||
|
||||
std::vector<real_t> x_npp = x;
|
||||
x_npp[axis2] += eps;
|
||||
x_npp[axis3] += eps;
|
||||
Ref<MLPPVector> x_npp = x->duplicate_fast();
|
||||
x_npp->element_get_ref(axis2) += eps;
|
||||
x_npp->element_get_ref(axis3) += eps;
|
||||
|
||||
std::vector<real_t> x_pnp = x;
|
||||
x_pnp[axis1] += eps;
|
||||
x_pnp[axis3] += eps;
|
||||
Ref<MLPPVector> x_pnp = x->duplicate_fast();
|
||||
x_pnp->element_get_ref(axis1) += eps;
|
||||
x_pnp->element_get_ref(axis3) += eps;
|
||||
|
||||
std::vector<real_t> x_nnp = x;
|
||||
x_nnp[axis3] += eps;
|
||||
Ref<MLPPVector> x_nnp = x->duplicate_fast();
|
||||
x_nnp->element_get_ref(axis3) += eps;
|
||||
|
||||
std::vector<real_t> x_ppn = x;
|
||||
x_ppn[axis1] += eps;
|
||||
x_ppn[axis2] += eps;
|
||||
Ref<MLPPVector> x_ppn = x->duplicate_fast();
|
||||
x_ppn->element_get_ref(axis1) += eps;
|
||||
x_ppn->element_get_ref(axis2) += eps;
|
||||
|
||||
std::vector<real_t> x_npn = x;
|
||||
x_npn[axis2] += eps;
|
||||
Ref<MLPPVector> x_npn = x->duplicate_fast();
|
||||
x_npn->element_get_ref(axis2) += eps;
|
||||
|
||||
std::vector<real_t> x_pnn = x;
|
||||
x_pnn[axis1] += eps;
|
||||
Ref<MLPPVector> x_pnn = x->duplicate_fast();
|
||||
x_pnn->element_get_ref(axis1) += eps;
|
||||
|
||||
real_t thirdAxis = function(x_ppp) - function(x_npp) - function(x_pnp) + function(x_nnp);
|
||||
real_t noThirdAxis = function(x_ppn) - function(x_npn) - function(x_pnn) + function(x);
|
||||
return (thirdAxis - noThirdAxis) / (eps * eps * eps);
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::newtonRaphsonMethod(real_t (*function)(real_t), real_t x_0, real_t epoch_num) {
|
||||
real_t MLPPNumericalAnalysis::newton_raphson_method(real_t (*function)(real_t), real_t x_0, real_t epoch_num) {
|
||||
real_t x = x_0;
|
||||
for (int i = 0; i < epoch_num; i++) {
|
||||
x -= function(x) / numDiff(function, x);
|
||||
x -= function(x) / num_diffr(function, x);
|
||||
}
|
||||
return x;
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::halleyMethod(real_t (*function)(real_t), real_t x_0, real_t epoch_num) {
|
||||
real_t MLPPNumericalAnalysis::halley_method(real_t (*function)(real_t), real_t x_0, real_t epoch_num) {
|
||||
real_t x = x_0;
|
||||
for (int i = 0; i < epoch_num; i++) {
|
||||
x -= ((2 * function(x) * numDiff(function, x)) / (2 * numDiff(function, x) * numDiff(function, x) - function(x) * numDiff_2(function, x)));
|
||||
x -= ((2 * function(x) * num_diffr(function, x)) / (2 * num_diffr(function, x) * num_diffr(function, x) - function(x) * num_diff_2r(function, x)));
|
||||
}
|
||||
return x;
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::invQuadraticInterpolation(real_t (*function)(real_t), std::vector<real_t> x_0, int epoch_num) {
|
||||
real_t MLPPNumericalAnalysis::inv_quadratic_interpolation(real_t (*function)(real_t), const Ref<MLPPVector> &x_0, int epoch_num) {
|
||||
real_t x = 0;
|
||||
std::vector<real_t> currentThree = x_0;
|
||||
Ref<MLPPVector> ct = x_0->duplicate_fast();
|
||||
MLPPVector ¤t_three = *(ct.ptr());
|
||||
|
||||
for (int i = 0; i < epoch_num; i++) {
|
||||
real_t t1 = ((function(currentThree[1]) * function(currentThree[2])) / ((function(currentThree[0]) - function(currentThree[1])) * (function(currentThree[0]) - function(currentThree[2])))) * currentThree[0];
|
||||
real_t t2 = ((function(currentThree[0]) * function(currentThree[2])) / ((function(currentThree[1]) - function(currentThree[0])) * (function(currentThree[1]) - function(currentThree[2])))) * currentThree[1];
|
||||
real_t t3 = ((function(currentThree[0]) * function(currentThree[1])) / ((function(currentThree[2]) - function(currentThree[0])) * (function(currentThree[2]) - function(currentThree[1])))) * currentThree[2];
|
||||
real_t t1 = ((function(current_three[1]) * function(current_three[2])) / ((function(current_three[0]) - function(current_three[1])) * (function(current_three[0]) - function(current_three[2])))) * current_three[0];
|
||||
real_t t2 = ((function(current_three[0]) * function(current_three[2])) / ((function(current_three[1]) - function(current_three[0])) * (function(current_three[1]) - function(current_three[2])))) * current_three[1];
|
||||
real_t t3 = ((function(current_three[0]) * function(current_three[1])) / ((function(current_three[2]) - function(current_three[0])) * (function(current_three[2]) - function(current_three[1])))) * current_three[2];
|
||||
x = t1 + t2 + t3;
|
||||
|
||||
currentThree.erase(currentThree.begin());
|
||||
currentThree.push_back(x);
|
||||
current_three.remove(0);
|
||||
current_three.push_back(x);
|
||||
}
|
||||
return x;
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::eulerianMethod(real_t (*derivative)(real_t), std::vector<real_t> q_0, real_t p, real_t h) {
|
||||
int max_epoch = static_cast<int>((p - q_0[0]) / h);
|
||||
real_t x = q_0[0];
|
||||
real_t y = q_0[1];
|
||||
real_t MLPPNumericalAnalysis::eulerian_methodr(real_t (*derivative)(real_t), real_t q_0, real_t q_1, real_t p, real_t h) {
|
||||
int max_epoch = static_cast<int>((p - q_0) / h);
|
||||
real_t x = q_0;
|
||||
real_t y = q_1;
|
||||
for (int i = 0; i < max_epoch; i++) {
|
||||
y = y + h * derivative(x);
|
||||
x += h;
|
||||
@ -153,18 +153,25 @@ real_t MLPPNumericalAnalysis::eulerianMethod(real_t (*derivative)(real_t), std::
|
||||
return y;
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::eulerianMethod(real_t (*derivative)(std::vector<real_t>), std::vector<real_t> q_0, real_t p, real_t h) {
|
||||
int max_epoch = static_cast<int>((p - q_0[0]) / h);
|
||||
real_t x = q_0[0];
|
||||
real_t y = q_0[1];
|
||||
real_t MLPPNumericalAnalysis::eulerian_methodv(real_t (*derivative)(const Ref<MLPPVector> &), real_t q_0, real_t q_1, real_t p, real_t h) {
|
||||
int max_epoch = static_cast<int>((p - q_0) / h);
|
||||
|
||||
Ref<MLPPVector> v;
|
||||
v.instance();
|
||||
v->resize(2);
|
||||
|
||||
real_t x = q_0;
|
||||
real_t y = q_1;
|
||||
for (int i = 0; i < max_epoch; i++) {
|
||||
y = y + h * derivative({ x, y });
|
||||
v->element_set(0, x);
|
||||
v->element_set(1, y);
|
||||
y = y + h * derivative(v);
|
||||
x += h;
|
||||
}
|
||||
return y;
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::growthMethod(real_t C, real_t k, real_t t) {
|
||||
real_t MLPPNumericalAnalysis::growth_method(real_t C, real_t k, real_t t) {
|
||||
//dP/dt = kP
|
||||
//dP/P = kdt
|
||||
//integral(1/P)dP = integral(k) dt
|
||||
@ -173,73 +180,123 @@ real_t MLPPNumericalAnalysis::growthMethod(real_t C, real_t k, real_t t) {
|
||||
//|P| = e^(C_initial) * e^(kt)
|
||||
//P = +/- e^(C_initial) * e^(kt)
|
||||
//P = C * e^(kt)
|
||||
|
||||
|
||||
// auto growthFunction = [&C, &k](real_t t) { return C * exp(k * t); };
|
||||
return C * std::exp(k * t);
|
||||
return C * Math::exp(k * t);
|
||||
}
|
||||
|
||||
std::vector<real_t> MLPPNumericalAnalysis::jacobian(real_t (*function)(std::vector<real_t>), std::vector<real_t> x) {
|
||||
std::vector<real_t> jacobian;
|
||||
jacobian.resize(x.size());
|
||||
for (uint32_t i = 0; i < jacobian.size(); i++) {
|
||||
jacobian[i] = numDiff(function, x, i); // Derivative w.r.t axis i evaluated at x. For all x_i.
|
||||
Ref<MLPPVector> MLPPNumericalAnalysis::jacobian(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x) {
|
||||
Ref<MLPPVector> jacobian;
|
||||
jacobian.instance();
|
||||
jacobian->resize(x->size());
|
||||
|
||||
int jacobian_size = jacobian->size();
|
||||
|
||||
for (int i = 0; i < jacobian_size; ++i) {
|
||||
jacobian->element_set(i, num_diffv(function, x, i)); // Derivative w.r.t axis i evaluated at x. For all x_i.
|
||||
}
|
||||
|
||||
return jacobian;
|
||||
}
|
||||
std::vector<std::vector<real_t>> MLPPNumericalAnalysis::hessian(real_t (*function)(std::vector<real_t>), std::vector<real_t> x) {
|
||||
std::vector<std::vector<real_t>> hessian;
|
||||
hessian.resize(x.size());
|
||||
|
||||
for (uint32_t i = 0; i < hessian.size(); i++) {
|
||||
hessian[i].resize(x.size());
|
||||
}
|
||||
Ref<MLPPMatrix> MLPPNumericalAnalysis::hessian(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x) {
|
||||
Ref<MLPPMatrix> hessian;
|
||||
hessian.instance();
|
||||
hessian->resize(Size2i(x->size(), x->size()));
|
||||
|
||||
for (uint32_t i = 0; i < hessian.size(); i++) {
|
||||
for (uint32_t j = 0; j < hessian[i].size(); j++) {
|
||||
hessian[i][j] = numDiff_2(function, x, i, j);
|
||||
Size2i hessian_size = hessian->size();
|
||||
|
||||
for (int i = 0; i < hessian_size.y; i++) {
|
||||
for (int j = 0; j < hessian_size.x; j++) {
|
||||
hessian->element_set(i, j, num_diff_2v(function, x, i, j));
|
||||
}
|
||||
}
|
||||
|
||||
return hessian;
|
||||
}
|
||||
|
||||
std::vector<std::vector<std::vector<real_t>>> MLPPNumericalAnalysis::thirdOrderTensor(real_t (*function)(std::vector<real_t>), std::vector<real_t> x) {
|
||||
std::vector<std::vector<std::vector<real_t>>> tensor;
|
||||
tensor.resize(x.size());
|
||||
Ref<MLPPTensor3> MLPPNumericalAnalysis::third_order_tensor(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x) {
|
||||
Ref<MLPPTensor3> tensor;
|
||||
tensor.instance();
|
||||
tensor->resize(Size3i(x->size(), x->size(), x->size()));
|
||||
|
||||
for (uint32_t i = 0; i < tensor.size(); i++) {
|
||||
tensor[i].resize(x.size());
|
||||
for (uint32_t j = 0; j < tensor[i].size(); j++) {
|
||||
tensor[i][j].resize(x.size());
|
||||
}
|
||||
}
|
||||
Size3i tensor_size = tensor->size();
|
||||
|
||||
for (uint32_t i = 0; i < tensor.size(); i++) { // O(n^3) time complexity :(
|
||||
for (uint32_t j = 0; j < tensor[i].size(); j++) {
|
||||
for (uint32_t k = 0; k < tensor[i][j].size(); k++)
|
||||
tensor[i][j][k] = numDiff_3(function, x, i, j, k);
|
||||
for (int i = 0; i < tensor_size.z; i++) { // O(n^3) time complexity :(
|
||||
for (int j = 0; j < tensor_size.y; j++) {
|
||||
for (int k = 0; k < tensor_size.x; k++)
|
||||
tensor->element_set(i, j, k, num_diff_3v(function, x, i, j, k));
|
||||
}
|
||||
}
|
||||
|
||||
return tensor;
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::constantApproximation(real_t (*function)(std::vector<real_t>), std::vector<real_t> c) {
|
||||
Vector<Ref<MLPPMatrix>> MLPPNumericalAnalysis::third_order_tensorvt(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x) {
|
||||
int x_size = x->size();
|
||||
|
||||
Vector<Ref<MLPPMatrix>> tensor;
|
||||
tensor.resize(x_size);
|
||||
|
||||
for (int i = 0; i < tensor.size(); i++) {
|
||||
Ref<MLPPMatrix> m;
|
||||
m.instance();
|
||||
m->resize(Size2i(x_size, x_size));
|
||||
|
||||
tensor.write[i] = m;
|
||||
}
|
||||
|
||||
for (int i = 0; i < tensor.size(); i++) { // O(n^3) time complexity :(
|
||||
Ref<MLPPMatrix> m = tensor[i];
|
||||
|
||||
for (int j = 0; j < x_size; j++) {
|
||||
for (int k = 0; k < x_size; k++) {
|
||||
m->element_set(j, k, num_diff_3v(function, x, i, j, k));
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return tensor;
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::constant_approximationv(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &c) {
|
||||
return function(c);
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::linearApproximation(real_t (*function)(std::vector<real_t>), std::vector<real_t> c, std::vector<real_t> x) {
|
||||
real_t MLPPNumericalAnalysis::linear_approximationv(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &c, const Ref<MLPPVector> &x) {
|
||||
MLPPLinAlg alg;
|
||||
return constantApproximation(function, c) + alg.matmult(alg.transpose({ jacobian(function, c) }), { alg.subtraction(x, c) })[0][0];
|
||||
|
||||
Ref<MLPPVector> j = jacobian(function, c);
|
||||
Ref<MLPPMatrix> mj;
|
||||
mj.instance();
|
||||
mj->row_add_mlpp_vector(j);
|
||||
|
||||
Ref<MLPPVector> xsc = x->subn(c);
|
||||
Ref<MLPPMatrix> mxsc;
|
||||
mxsc.instance();
|
||||
mxsc->row_add_mlpp_vector(xsc);
|
||||
|
||||
Ref<MLPPMatrix> m = mj->transposen()->multn(mxsc);
|
||||
|
||||
return constant_approximationv(function, c) + m->element_get(0, 0);
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::quadraticApproximation(real_t (*function)(std::vector<real_t>), std::vector<real_t> c, std::vector<real_t> x) {
|
||||
real_t MLPPNumericalAnalysis::quadratic_approximationv(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &c, const Ref<MLPPVector> &x) {
|
||||
MLPPLinAlg 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];
|
||||
|
||||
Ref<MLPPMatrix> h = hessian(function, c);
|
||||
|
||||
Ref<MLPPVector> xsc = x->subn(c);
|
||||
Ref<MLPPMatrix> mxsc;
|
||||
mxsc.instance();
|
||||
mxsc->row_add_mlpp_vector(xsc);
|
||||
|
||||
Ref<MLPPMatrix> r = mxsc->multn(h->multn(mxsc->transposen()));
|
||||
|
||||
return linear_approximationv(function, c, x) + 0.5 * r->element_get(0, 0);
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::cubicApproximation(real_t (*function)(std::vector<real_t>), std::vector<real_t> c, std::vector<real_t> x) {
|
||||
real_t MLPPNumericalAnalysis::cubic_approximationv(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &c, const Ref<MLPPVector> &x) {
|
||||
//Not completely sure as the literature seldom discusses the third order taylor approximation,
|
||||
//in particular for multivariate cases, but ostensibly, the matrix/tensor/vector multiplies
|
||||
//should look something like this:
|
||||
@ -247,35 +304,45 @@ real_t MLPPNumericalAnalysis::cubicApproximation(real_t (*function)(std::vector<
|
||||
//(N x N x N) (N x 1) [tensor vector mult] => (N x N x 1) => (N x N)
|
||||
//Perform remaining multiplies as done for the 2nd order approximation.
|
||||
//Result is a scalar.
|
||||
|
||||
MLPPLinAlg alg;
|
||||
std::vector<std::vector<real_t>> resultMat = alg.tensor_vec_mult(thirdOrderTensor(function, c), alg.subtraction(x, c));
|
||||
real_t resultScalar = alg.matmult({ (alg.subtraction(x, c)) }, alg.matmult(resultMat, alg.transpose({ alg.subtraction(x, c) })))[0][0];
|
||||
|
||||
return quadraticApproximation(function, c, x) + (1 / 6) * resultScalar;
|
||||
MLPPLinAlg alg;
|
||||
|
||||
Ref<MLPPVector> xsc = x->subn(c);
|
||||
Ref<MLPPMatrix> mxsc;
|
||||
mxsc.instance();
|
||||
mxsc->row_add_mlpp_vector(xsc);
|
||||
|
||||
Ref<MLPPMatrix> result_mat = third_order_tensor(function, c)->tensor_vec_mult(xsc);
|
||||
real_t result_scalar = mxsc->multn(result_mat->multn(mxsc->transposen()))->element_get(0, 0);
|
||||
|
||||
return quadratic_approximationv(function, c, x) + (1 / 6) * result_scalar;
|
||||
}
|
||||
|
||||
real_t MLPPNumericalAnalysis::laplacian(real_t (*function)(std::vector<real_t>), std::vector<real_t> x) {
|
||||
std::vector<std::vector<real_t>> hessian_matrix = hessian(function, x);
|
||||
real_t MLPPNumericalAnalysis::laplacian(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x) {
|
||||
Ref<MLPPMatrix> hessian_matrix = hessian(function, x);
|
||||
real_t laplacian = 0;
|
||||
|
||||
for (uint32_t i = 0; i < hessian_matrix.size(); i++) {
|
||||
laplacian += hessian_matrix[i][i]; // homogenous 2nd derivs w.r.t i, then i
|
||||
Size2i hessian_matrix_size = hessian_matrix->size();
|
||||
|
||||
for (int i = 0; i < hessian_matrix_size.y; i++) {
|
||||
laplacian += hessian_matrix->element_get(i, i); // homogenous 2nd derivs w.r.t i, then i
|
||||
}
|
||||
|
||||
return laplacian;
|
||||
}
|
||||
|
||||
std::string MLPPNumericalAnalysis::secondPartialDerivativeTest(real_t (*function)(std::vector<real_t>), std::vector<real_t> x) {
|
||||
String MLPPNumericalAnalysis::second_partial_derivative_test(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x) {
|
||||
MLPPLinAlg alg;
|
||||
std::vector<std::vector<real_t>> hessianMatrix = hessian(function, x);
|
||||
|
||||
Ref<MLPPMatrix> hessian_matrix = hessian(function, x);
|
||||
|
||||
Size2i hessian_matrix_size = hessian_matrix->size();
|
||||
|
||||
// The reason we do this is because the 2nd partial derivative test is less conclusive for functions of variables greater than
|
||||
// 2, and the calculations specific to the bivariate case are less computationally intensive.
|
||||
|
||||
if (x.size() == 2) {
|
||||
real_t det = alg.det(hessianMatrix, hessianMatrix.size());
|
||||
real_t secondDerivative = numDiff_2(function, x, 0, 0);
|
||||
|
||||
if (hessian_matrix_size.y == 2) {
|
||||
real_t det = hessian_matrix->det();
|
||||
real_t secondDerivative = num_diff_2v(function, x, 0, 0);
|
||||
if (secondDerivative > 0 && det > 0) {
|
||||
return "min";
|
||||
} else if (secondDerivative < 0 && det > 0) {
|
||||
@ -286,18 +353,17 @@ std::string MLPPNumericalAnalysis::secondPartialDerivativeTest(real_t (*function
|
||||
return "test was inconclusive";
|
||||
}
|
||||
} else {
|
||||
if (alg.positiveDefiniteChecker(hessianMatrix)) {
|
||||
if (alg.positive_definite_checker(hessian_matrix)) {
|
||||
return "min";
|
||||
} else if (alg.negativeDefiniteChecker(hessianMatrix)) {
|
||||
} else if (alg.negative_definite_checker(hessian_matrix)) {
|
||||
return "max";
|
||||
} else if (!alg.zeroEigenvalue(hessianMatrix)) {
|
||||
} else if (!alg.zero_eigenvalue(hessian_matrix)) {
|
||||
return "saddle";
|
||||
} else {
|
||||
return "test was inconclusive";
|
||||
}
|
||||
}
|
||||
}
|
||||
*/
|
||||
|
||||
void MLPPNumericalAnalysis::_bind_methods() {
|
||||
}
|
||||
|
||||
@ -11,8 +11,12 @@
|
||||
|
||||
#include "core/object/reference.h"
|
||||
|
||||
#include <string>
|
||||
#include <vector>
|
||||
#include "core/containers/vector.h"
|
||||
#include "core/string/ustring.h"
|
||||
|
||||
class MLPPVector;
|
||||
class MLPPMatrix;
|
||||
class MLPPTensor3;
|
||||
|
||||
class MLPPNumericalAnalysis : public Reference {
|
||||
GDCLASS(MLPPNumericalAnalysis, Reference);
|
||||
@ -22,42 +26,42 @@ public:
|
||||
as an analytical method for calculating derivatives will most likely be used in
|
||||
the future.
|
||||
*/
|
||||
/*
|
||||
real_t numDiff(real_t (*function)(real_t), real_t x);
|
||||
real_t numDiff_2(real_t (*function)(real_t), real_t x);
|
||||
real_t numDiff_3(real_t (*function)(real_t), real_t x);
|
||||
|
||||
real_t constantApproximation(real_t (*function)(real_t), real_t c);
|
||||
real_t linearApproximation(real_t (*function)(real_t), real_t c, real_t x);
|
||||
real_t quadraticApproximation(real_t (*function)(real_t), real_t c, real_t x);
|
||||
real_t cubicApproximation(real_t (*function)(real_t), real_t c, real_t x);
|
||||
real_t num_diffr(real_t (*function)(real_t), real_t x);
|
||||
real_t num_diff_2r(real_t (*function)(real_t), real_t x);
|
||||
real_t num_diff_3r(real_t (*function)(real_t), real_t x);
|
||||
|
||||
real_t numDiff(real_t (*function)(std::vector<real_t>), std::vector<real_t> x, int axis);
|
||||
real_t numDiff_2(real_t (*function)(std::vector<real_t>), std::vector<real_t> x, int axis1, int axis2);
|
||||
real_t numDiff_3(real_t (*function)(std::vector<real_t>), std::vector<real_t> x, int axis1, int axis2, int axis3);
|
||||
real_t constant_approximationr(real_t (*function)(real_t), real_t c);
|
||||
real_t linear_approximationr(real_t (*function)(real_t), real_t c, real_t x);
|
||||
real_t quadratic_approximationr(real_t (*function)(real_t), real_t c, real_t x);
|
||||
real_t cubic_approximationr(real_t (*function)(real_t), real_t c, real_t x);
|
||||
|
||||
real_t newtonRaphsonMethod(real_t (*function)(real_t), real_t x_0, real_t epoch_num);
|
||||
real_t halleyMethod(real_t (*function)(real_t), real_t x_0, real_t epoch_num);
|
||||
real_t invQuadraticInterpolation(real_t (*function)(real_t), std::vector<real_t> x_0, int epoch_num);
|
||||
real_t num_diffv(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &, int axis);
|
||||
real_t num_diff_2v(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &, int axis1, int axis2);
|
||||
real_t num_diff_3v(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &, int axis1, int axis2, int axis3);
|
||||
|
||||
real_t eulerianMethod(real_t (*derivative)(real_t), std::vector<real_t> q_0, real_t p, real_t h); // Euler's method for solving diffrential equations.
|
||||
real_t eulerianMethod(real_t (*derivative)(std::vector<real_t>), std::vector<real_t> q_0, real_t p, real_t h); // Euler's method for solving diffrential equations.
|
||||
real_t newton_raphson_method(real_t (*function)(real_t), real_t x_0, real_t epoch_num);
|
||||
real_t halley_method(real_t (*function)(real_t), real_t x_0, real_t epoch_num);
|
||||
real_t inv_quadratic_interpolation(real_t (*function)(real_t), const Ref<MLPPVector> &x_0, int epoch_num);
|
||||
|
||||
real_t growthMethod(real_t C, real_t k, real_t t); // General growth-based diffrential equations can be solved by seperation of variables.
|
||||
real_t eulerian_methodr(real_t (*derivative)(real_t), real_t q_0, real_t q_1, real_t p, real_t h); // Euler's method for solving diffrential equations.
|
||||
real_t eulerian_methodv(real_t (*derivative)(const Ref<MLPPVector> &), real_t q_0, real_t q_1, real_t p, real_t h); // Euler's method for solving diffrential equations.
|
||||
|
||||
std::vector<real_t> jacobian(real_t (*function)(std::vector<real_t>), std::vector<real_t> x); // Indeed, for functions with scalar outputs the Jacobians will be vectors.
|
||||
std::vector<std::vector<real_t>> hessian(real_t (*function)(std::vector<real_t>), std::vector<real_t> x);
|
||||
std::vector<std::vector<std::vector<real_t>>> thirdOrderTensor(real_t (*function)(std::vector<real_t>), std::vector<real_t> x);
|
||||
real_t growth_method(real_t C, real_t k, real_t t); // General growth-based diffrential equations can be solved by seperation of variables.
|
||||
|
||||
real_t constantApproximation(real_t (*function)(std::vector<real_t>), std::vector<real_t> c);
|
||||
real_t linearApproximation(real_t (*function)(std::vector<real_t>), std::vector<real_t> c, std::vector<real_t> x);
|
||||
real_t quadraticApproximation(real_t (*function)(std::vector<real_t>), std::vector<real_t> c, std::vector<real_t> x);
|
||||
real_t cubicApproximation(real_t (*function)(std::vector<real_t>), std::vector<real_t> c, std::vector<real_t> x);
|
||||
Ref<MLPPVector> jacobian(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x); // Indeed, for functions with scalar outputs the Jacobians will be vectors.
|
||||
Ref<MLPPMatrix> hessian(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x);
|
||||
Ref<MLPPTensor3> third_order_tensor(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x);
|
||||
Vector<Ref<MLPPMatrix>> third_order_tensorvt(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x);
|
||||
|
||||
real_t laplacian(real_t (*function)(std::vector<real_t>), std::vector<real_t> x); // laplacian
|
||||
real_t constant_approximationv(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &c);
|
||||
real_t linear_approximationv(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &c, const Ref<MLPPVector> &x);
|
||||
real_t quadratic_approximationv(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &c, const Ref<MLPPVector> &x);
|
||||
real_t cubic_approximationv(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &c, const Ref<MLPPVector> &x);
|
||||
|
||||
std::string secondPartialDerivativeTest(real_t (*function)(std::vector<real_t>), std::vector<real_t> x);
|
||||
*/
|
||||
real_t laplacian(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x); // laplacian
|
||||
|
||||
String second_partial_derivative_test(real_t (*function)(const Ref<MLPPVector> &), const Ref<MLPPVector> &x);
|
||||
|
||||
protected:
|
||||
static void _bind_methods();
|
||||
|
||||
@ -1206,7 +1206,9 @@ real_t f_prime(real_t x) {
|
||||
return 2 * x;
|
||||
}
|
||||
|
||||
real_t f_prime_2var(std::vector<real_t> x) {
|
||||
real_t f_prime_2var(const Ref<MLPPVector> &p_x) {
|
||||
const real_t *x = p_x->ptr();
|
||||
|
||||
return 2 * x[0] + x[1];
|
||||
}
|
||||
/*
|
||||
@ -1227,7 +1229,9 @@ real_t f_prime_2var(std::vector<real_t> x) {
|
||||
∂^2f/∂x∂y = 2
|
||||
*/
|
||||
|
||||
real_t f_mv(std::vector<real_t> x) {
|
||||
real_t f_mv(const Ref<MLPPVector> &p_x) {
|
||||
const real_t *x = p_x->ptr();
|
||||
|
||||
return x[0] * x[0] * x[0] + x[0] + x[1] * x[1] * x[1] * x[0] + x[2] * x[2] * x[1];
|
||||
}
|
||||
|
||||
@ -1259,79 +1263,266 @@ real_t f_mv(std::vector<real_t> x) {
|
||||
*/
|
||||
|
||||
void MLPPTests::test_numerical_analysis() {
|
||||
/*
|
||||
MLPPLinAlg alg;
|
||||
MLPPConvolutionsOld conv;
|
||||
MLPPConvolutions conv;
|
||||
|
||||
// Checks for numerical analysis class.
|
||||
MLPPNumericalAnalysisOld numAn;
|
||||
MLPPNumericalAnalysis num_an;
|
||||
|
||||
std::cout << numAn.quadraticApproximation(f, 0, 1) << std::endl;
|
||||
/*
|
||||
//1
|
||||
PLOG_MSG("num_an.quadratic_approximationr(f, 0, 1)");
|
||||
PLOG_MSG(String::num(num_an.quadratic_approximationr(f, 0, 1)));
|
||||
|
||||
std::cout << numAn.cubicApproximation(f, 0, 1.001) << std::endl;
|
||||
//1.001
|
||||
PLOG_MSG("num_an.cubic_approximationr(f, 0, 1.001)");
|
||||
PLOG_MSG(String::num(num_an.cubic_approximationr(f, 0, 1.001)));
|
||||
|
||||
std::cout << f(1.001) << std::endl;
|
||||
//0.842011
|
||||
PLOG_MSG("f(1.001)");
|
||||
PLOG_MSG(String::num(f(1.001)));
|
||||
|
||||
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;
|
||||
Ref<MLPPVector> v30;
|
||||
v30.instance();
|
||||
v30->resize(3);
|
||||
v30->fill(0);
|
||||
|
||||
std::cout << numAn.numDiff(&f_mv, { 1, 1 }, 1) << std::endl; // Derivative w.r.t. x.
|
||||
|
||||
alg.printVector(numAn.jacobian(&f_mv, { 1, 1 }));
|
||||
Ref<MLPPVector> v31;
|
||||
v31.instance();
|
||||
v31->resize(3);
|
||||
v31->fill(1);
|
||||
|
||||
std::cout << numAn.numDiff_2(&f, 2) << std::endl;
|
||||
//1.00001
|
||||
PLOG_MSG("num_an.quadratic_approximationv(f_mv, v30, v31)");
|
||||
PLOG_MSG(String::num(num_an.quadratic_approximationv(f_mv, v30, v31)));
|
||||
|
||||
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;
|
||||
const real_t iqi_arr[] = { 100, 2, 1.5 };
|
||||
Ref<MLPPVector> iqi(memnew(MLPPVector(iqi_arr, 3)));
|
||||
|
||||
alg.printTensor(numAn.thirdOrderTensor(&f_mv, { 1, 1, 1 }));
|
||||
std::cout << "Our Hessian." << std::endl;
|
||||
alg.printMatrix(numAn.hessian(&f_mv, { 2, 2, 500 }));
|
||||
//0
|
||||
PLOG_MSG("num_an.num_diffr(&f, 1)");
|
||||
PLOG_MSG(String::num(num_an.num_diffr(&f, 1)));
|
||||
|
||||
std::cout << numAn.laplacian(f_mv, { 1, 1, 1 }) << std::endl;
|
||||
//-nan
|
||||
//nan
|
||||
PLOG_MSG("num_an.newton_raphson_method(&f, 1, 1000)");
|
||||
PLOG_MSG(String::num(num_an.newton_raphson_method(&f, 1, 1000)));
|
||||
|
||||
std::vector<std::vector<std::vector<real_t>>> tensor;
|
||||
tensor.push_back({ { 1, 2 }, { 1, 2 }, { 1, 2 } });
|
||||
tensor.push_back({ { 1, 2 }, { 1, 2 }, { 1, 2 } });
|
||||
//2.17152e+07
|
||||
//21715200
|
||||
PLOG_MSG("num_an.inv_quadratic_interpolation(&f, iqi, 10)");
|
||||
PLOG_MSG(String::num(num_an.inv_quadratic_interpolation(&f, iqi, 10)));
|
||||
|
||||
alg.printTensor(tensor);
|
||||
|
||||
alg.printMatrix(alg.tensor_vec_mult(tensor, { 1, 2 }));
|
||||
Ref<MLPPVector> v21;
|
||||
v21.instance();
|
||||
v21->resize(2);
|
||||
v21->fill(1);
|
||||
|
||||
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;
|
||||
//0
|
||||
PLOG_MSG("num_an.num_diffv(&f_mv, v21, 1)");
|
||||
PLOG_MSG(String::num(num_an.num_diffv(&f_mv, v21, 1))); // Derivative w.r.t. x.
|
||||
|
||||
std::vector<std::vector<real_t>> A = {
|
||||
//[MLPPVector: 0 0 ]
|
||||
PLOG_MSG("num_an.jacobian(&f_mv, v21)");
|
||||
PLOG_MSG(num_an.jacobian(&f_mv, v21)->to_string());
|
||||
|
||||
//596.046509
|
||||
PLOG_MSG("num_an.num_diff_2r(&f, 2)");
|
||||
PLOG_MSG(String::num(num_an.num_diff_2r(&f, 2)));
|
||||
|
||||
//-119209304
|
||||
PLOG_MSG("num_an.num_diff_3r(&f, 2)");
|
||||
PLOG_MSG(String::num(num_an.num_diff_3r(&f, 2)));
|
||||
|
||||
const real_t nd2v_arr[] = { 100, 2, 1.5 };
|
||||
Ref<MLPPVector> nd2v(memnew(MLPPVector(nd2v_arr, 3)));
|
||||
|
||||
//0
|
||||
PLOG_MSG("num_an.num_diff_2v(&f_mv, nd2v, 2, 2)");
|
||||
PLOG_MSG(String::num(num_an.num_diff_2v(&f_mv, nd2v, 2, 2)));
|
||||
|
||||
const real_t nd3v_arr[] = { 2, 1000, 130 };
|
||||
Ref<MLPPVector> nd3v(memnew(MLPPVector(nd3v_arr, 3)));
|
||||
|
||||
//128000015514730496
|
||||
PLOG_MSG("num_an.num_diff_3v(&f_mv, nd3v, 0, 0, 0)");
|
||||
PLOG_MSG(String::num(num_an.num_diff_3v(&f_mv, nd3v, 0, 0, 0)));
|
||||
*/
|
||||
|
||||
Ref<MLPPVector> v31t;
|
||||
v31t.instance();
|
||||
v31t->resize(3);
|
||||
v31t->fill(1);
|
||||
|
||||
/*
|
||||
[MLPPTensor3:
|
||||
[ [ 0 0 0 ]
|
||||
[ 0 0 0 ]
|
||||
[ 0 0 0 ]
|
||||
],
|
||||
[ [ 0 0 0 ]
|
||||
[ 0 0 0 ]
|
||||
[ 0 0 0 ]
|
||||
],
|
||||
[ [ 0 0 0 ]
|
||||
[ 0 0 0 ]
|
||||
[ 0 0 0 ]
|
||||
],
|
||||
]
|
||||
*/
|
||||
PLOG_MSG("num_an.third_order_tensor(&f_mv, v31t)");
|
||||
PLOG_MSG(num_an.third_order_tensor(&f_mv, v31t)->to_string());
|
||||
|
||||
const real_t hess_arr[] = { 2, 2, 500 };
|
||||
Ref<MLPPVector> hess(memnew(MLPPVector(hess_arr, 3)));
|
||||
|
||||
/*
|
||||
[MLPPMatrix:
|
||||
[ 0 0 0 ]
|
||||
[ 0 0 0 ]
|
||||
[ 0 0 0 ]
|
||||
]
|
||||
*/
|
||||
PLOG_MSG("Our Hessian.");
|
||||
PLOG_MSG(num_an.hessian(&f_mv, hess)->to_string());
|
||||
|
||||
Ref<MLPPVector> v31l;
|
||||
v31l.instance();
|
||||
v31l->resize(3);
|
||||
v31l->fill(1);
|
||||
|
||||
//0
|
||||
PLOG_MSG("num_an.laplacian(f_mv, v31l)");
|
||||
PLOG_MSG(String::num(num_an.laplacian(f_mv, v31l)));
|
||||
|
||||
std::vector<std::vector<std::vector<real_t>>> tensor_arr;
|
||||
tensor_arr.push_back({ { 1, 2 }, { 1, 2 }, { 1, 2 } });
|
||||
tensor_arr.push_back({ { 1, 2 }, { 1, 2 }, { 1, 2 } });
|
||||
|
||||
Ref<MLPPTensor3> tensor;
|
||||
tensor.instance();
|
||||
tensor->set_from_std_vectors(tensor_arr);
|
||||
|
||||
/*
|
||||
[MLPPTensor3:
|
||||
[ [ 1 2 ]
|
||||
[ 1 2 ]
|
||||
[ 1 2 ]
|
||||
],
|
||||
[ [ 1 2 ]
|
||||
[ 1 2 ]
|
||||
[ 1 2 ]
|
||||
],
|
||||
]
|
||||
*/
|
||||
PLOG_MSG("tensor->to_string()");
|
||||
PLOG_MSG(tensor->to_string());
|
||||
|
||||
const real_t tvm_arr[] = { 1, 2 };
|
||||
Ref<MLPPVector> tvm(memnew(MLPPVector(tvm_arr, 2)));
|
||||
|
||||
/*
|
||||
[MLPPMatrix:
|
||||
[ 5 5 5 ]
|
||||
[ 5 5 5 ]
|
||||
]
|
||||
*/
|
||||
PLOG_MSG("tensor->tensor_vec_mult(tvm)");
|
||||
PLOG_MSG(tensor->tensor_vec_mult(tvm)->to_string());
|
||||
|
||||
Ref<MLPPVector> v30;
|
||||
v30.instance();
|
||||
v30->resize(3);
|
||||
v30->fill(0);
|
||||
|
||||
Ref<MLPPVector> v31;
|
||||
v31.instance();
|
||||
v31->resize(3);
|
||||
v31->fill(1);
|
||||
|
||||
//1.00001
|
||||
PLOG_MSG("num_an.cubic_approximationv(f_mv, v30, v31)");
|
||||
PLOG_MSG(String::num(num_an.cubic_approximationv(f_mv, v30, v31)));
|
||||
|
||||
//2.236699
|
||||
PLOG_MSG("num_an.eulerian_methodv(f_prime, 1, 1, 1.5, 0.000001)");
|
||||
PLOG_MSG(String::num(num_an.eulerian_methodr(f_prime, 1, 1, 1.5, 0.000001)));
|
||||
|
||||
//3
|
||||
PLOG_MSG("num_an.eulerian_methodv(f_prime_2var, 2, 3, 2.5, 0.00000001)");
|
||||
PLOG_MSG(String::num(num_an.eulerian_methodv(f_prime_2var, 2, 3, 2.5, 0.00000001)));
|
||||
|
||||
std::vector<std::vector<real_t>> A_arr = {
|
||||
{ 1, 0, 0, 0 },
|
||||
{ 0, 0, 0, 0 },
|
||||
{ 0, 0, 0, 0 },
|
||||
{ 0, 0, 0, 1 }
|
||||
};
|
||||
|
||||
alg.printMatrix(conv.dx(A));
|
||||
alg.printMatrix(conv.dy(A));
|
||||
Ref<MLPPMatrix> A(memnew(MLPPMatrix(A_arr)));
|
||||
|
||||
alg.printMatrix(conv.grad_orientation(A));
|
||||
/*
|
||||
[MLPPMatrix:
|
||||
[ 0 -1 0 -0 ]
|
||||
[ 0 0 0 -0 ]
|
||||
[ 0 0 0 -0 ]
|
||||
[ 0 0 1 -0 ]
|
||||
]
|
||||
*/
|
||||
PLOG_MSG("conv.dx(A)");
|
||||
PLOG_MSG(conv.dx(A)->to_string());
|
||||
|
||||
std::vector<std::vector<std::string>> h = conv.harris_corner_detection(A);
|
||||
/*
|
||||
0 0 0 0
|
||||
1 0 0 0
|
||||
0 0 0 -1
|
||||
0 0 0 0
|
||||
*/
|
||||
PLOG_MSG("conv.dy(A)");
|
||||
PLOG_MSG(conv.dy(A)->to_string());
|
||||
|
||||
for (uint32_t i = 0; i < h.size(); i++) {
|
||||
for (uint32_t j = 0; j < h[i].size(); j++) {
|
||||
std::cout << h[i][j] << " ";
|
||||
/*
|
||||
0 3.14159 0 0
|
||||
1.5708 0 0 0
|
||||
0 0 0 -1.5708
|
||||
0 0 0 0
|
||||
*/
|
||||
PLOG_MSG("conv.grad_orientation(A)");
|
||||
PLOG_MSG(conv.grad_orientation(A)->to_string());
|
||||
|
||||
/*
|
||||
C C E N
|
||||
C C C E
|
||||
E C C C
|
||||
N E C C
|
||||
*/
|
||||
PLOG_MSG("conv.harris_corner_detection(A)");
|
||||
Vector<Vector<CharType>> h = conv.harris_corner_detection(A);
|
||||
|
||||
String h_res;
|
||||
|
||||
for (int i = 0; i < h.size(); i++) {
|
||||
for (int j = 0; j < h[i].size(); j++) {
|
||||
h_res += h[i][j];
|
||||
h_res += " ";
|
||||
}
|
||||
std::cout << std::endl;
|
||||
h_res += "\n";
|
||||
} // Harris detector works. Life is good!
|
||||
|
||||
std::vector<real_t> a = { 3, 4, 4 };
|
||||
std::vector<real_t> b = { 4, 4, 4 };
|
||||
alg.printVector(alg.cross(a, b));
|
||||
*/
|
||||
PLOG_MSG(h_res);
|
||||
|
||||
std::vector<real_t> a_arr = { 3, 4, 4 };
|
||||
Ref<MLPPVector> a(memnew(MLPPVector(a_arr)));
|
||||
std::vector<real_t> b_arr = { 4, 4, 4 };
|
||||
Ref<MLPPVector> b(memnew(MLPPVector(b_arr)));
|
||||
|
||||
//[MLPPVector: 0 4 -4 ]
|
||||
PLOG_MSG("a->cross(b)");
|
||||
PLOG_MSG(a->cross(b)->to_string());
|
||||
}
|
||||
void MLPPTests::test_support_vector_classification_kernel(bool ui) {
|
||||
MLPPLinAlg alg;
|
||||
|
||||
@ -541,6 +541,7 @@ void MLPPTestsOld::test_numerical_analysis() {
|
||||
// Checks for numerical analysis class.
|
||||
MLPPNumericalAnalysisOld numAn;
|
||||
|
||||
/*
|
||||
std::cout << numAn.quadraticApproximation(f_old, 0, 1) << std::endl;
|
||||
|
||||
std::cout << numAn.cubicApproximation(f_old, 0, 1.001) << std::endl;
|
||||
@ -549,10 +550,12 @@ void MLPPTestsOld::test_numerical_analysis() {
|
||||
|
||||
std::cout << numAn.quadraticApproximation(f_mv_old, { 0, 0, 0 }, { 1, 1, 1 }) << std::endl;
|
||||
|
||||
|
||||
std::cout << numAn.numDiff(&f_old, 1) << std::endl;
|
||||
std::cout << numAn.newtonRaphsonMethod(&f_old, 1, 1000) << std::endl;
|
||||
std::cout << numAn.invQuadraticInterpolation(&f_old, { 100, 2, 1.5 }, 10) << std::endl;
|
||||
|
||||
|
||||
std::cout << numAn.numDiff(&f_mv_old, { 1, 1 }, 1) << std::endl; // Derivative w.r.t. x.
|
||||
|
||||
alg.printVector(numAn.jacobian(&f_mv_old, { 1, 1 }));
|
||||
@ -564,6 +567,8 @@ void MLPPTestsOld::test_numerical_analysis() {
|
||||
std::cout << numAn.numDiff_2(&f_mv_old, { 2, 2, 500 }, 2, 2) << std::endl;
|
||||
std::cout << numAn.numDiff_3(&f_mv_old, { 2, 1000, 130 }, 0, 0, 0) << std::endl;
|
||||
|
||||
|
||||
|
||||
alg.printTensor(numAn.thirdOrderTensor(&f_mv_old, { 1, 1, 1 }));
|
||||
std::cout << "Our Hessian." << std::endl;
|
||||
alg.printMatrix(numAn.hessian(&f_mv_old, { 2, 2, 500 }));
|
||||
@ -577,11 +582,12 @@ void MLPPTestsOld::test_numerical_analysis() {
|
||||
alg.printTensor(tensor);
|
||||
|
||||
alg.printMatrix(alg.tensor_vec_mult(tensor, { 1, 2 }));
|
||||
|
||||
|
||||
std::cout << numAn.cubicApproximation(f_mv_old, { 0, 0, 0 }, { 1, 1, 1 }) << std::endl;
|
||||
std::cout << numAn.eulerianMethod(f_prime_old, { 1, 1 }, 1.5, 0.000001) << std::endl;
|
||||
std::cout << numAn.eulerianMethod(f_prime_2var_old, { 2, 3 }, 2.5, 0.00000001) << std::endl;
|
||||
|
||||
*/
|
||||
std::vector<std::vector<real_t>> A = {
|
||||
{ 1, 0, 0, 0 },
|
||||
{ 0, 0, 0, 0 },
|
||||
@ -589,8 +595,9 @@ void MLPPTestsOld::test_numerical_analysis() {
|
||||
{ 0, 0, 0, 1 }
|
||||
};
|
||||
|
||||
alg.printMatrix(conv.dx(A));
|
||||
alg.printMatrix(conv.dy(A));
|
||||
//alg.printMatrix(conv.dx(A));
|
||||
//alg.printMatrix(conv.dy(A));
|
||||
|
||||
|
||||
alg.printMatrix(conv.grad_orientation(A));
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user