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LA_library/reg.cc

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/*
LA: linear algebra C++ interface library
Kernel ridge regression module Copyright (C) 2024
Pavel Florian <florian43@seznam.cz> and Jiri Pittner <jiri.pittner@jh-inst.cas.cz> or <jiri@pittnerovi.com>
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#include "reg.h"
namespace LA {
template <typename T>
T Gaussian_kernel(const T* x, const unsigned int dimensions, const T sigma)
{
unsigned int i;
T result = 0;
for (i = 0; i < dimensions; i++)
result = result + (x[i] * x[i]);
result = std::exp(-result/(2 * sigma * sigma));
return(result);
}
template <typename T>
T Laplacian_kernel(const T* x, const unsigned int dimensions, const T sigma)
{
unsigned int i;
T result = 0;
for (i = 0; i < dimensions; i++)
result = result + abs(x[i]);
result = std::exp(-abs(result)/(sigma));
return(result);
}
template <typename T>
T Exponential_kernel(const T* x, const unsigned int dimensions, const T sigma)
{
unsigned int i;
T result = 0;
for (i = 0; i < dimensions; i++)
result = result + (x[i] * x[i]);
result = std::exp(-std::pow(result, 0.5)/sigma);
return(result);
}
template <typename T>
T Matern_kernel(const T* x, const unsigned int dimensions, const T sigma, const unsigned int n,
const T* Matern_comb_number)
{
unsigned int i;
unsigned int k;
T part_1 = 0; // sum(x^2)^1/2
T exponential_part;
T Matern_part = 0;
T result;
for (i = 0; i < dimensions; i++)
part_1 = part_1 + (x[i] * x[i]);
part_1 = std::pow(part_1, 0.5);
exponential_part = std::exp(-part_1/(sigma));
for (k = 0; k < n; k++)
Matern_part += Matern_comb_number[i] * std::pow(2 * part_1/sigma, n - k);
result = exponential_part * Matern_part;
return(result);
}
template <typename T>
unsigned int Matern_coefficient(const unsigned int n, T* comb_number) // values of (n + k)!/(2 n)! * n!/(k!(n-k)!)
{
unsigned int i , j;
unsigned int k;
unsigned int part_1; // reverse value of (n + k)!/(2 n)!
unsigned int part_2; // n!/(n-k)!
unsigned int part_3; // k!
for (k = 0; k < n; k++)
{
part_1 = 1;
part_2 = 1;
part_3 = 1;
for (i = n + k + 1; i <= 2 * n; i++)
part_1 = part_1 * i;
for (i = n - k + 1; i <= n; i++)
part_2 = part_2 * i;
for (i = 1; i < k; i++)
part_3 = part_3 * i;
comb_number[k] = T(part_2)/T(part_1 * part_3);
}
return(0);
}
template <typename T>
REG<T>::REG(const T* x, const T* y, const T* params, const unsigned int data_size, const unsigned int x_dimensions, const string kernel)
{
Init(x, y , params, data_size, x_dimensions, kernel);
}
template <typename T>
REG<T>::REG(const string x_file, const string y_file, const string param_file)
{
unsigned int i;
ifstream xfile(x_file);
ifstream yfile(y_file);
ifstream paramfile(param_file);
string line;
T line_value;
// parameters of model
unsigned int data_size;
unsigned int x_dimensions;
string kernel;
REG_param_file = new T[4];
if(!REG_param_file) laerror("allocation failure in REG constructor");
// loading parameters for regression model from param_file
if (paramfile.is_open())
{
if (getline(paramfile, line))
data_size = stoi(line);
else
return;
if (getline(paramfile, line))
x_dimensions = stoi(line);
else
return;
if (getline(paramfile, line))
kernel = line;
else
return;
if (getline(paramfile, line))
REG_param_file[0] = stod(line);
else
return;
if (getline(paramfile, line))
REG_param_file[1] = stod(line);
else
return;
if (getline(paramfile, line))
REG_param_file[2] = stod(line);
else
return;
if (kernel == "Matern")
{
if (getline(paramfile, line))
REG_param_file[3] = static_cast<unsigned int>(stod(line) + 0.5);
else
return;
}
}
REG_x_file = new T[data_size * x_dimensions];
REG_y_file = new T[data_size];
if(!REG_x_file || !REG_y_file) laerror("allocation failure 2 in REG constructor");
// loading x and y data for regression model from files
if (xfile.is_open() and yfile.is_open())
{
for (i = 0; i < data_size * x_dimensions; i++)
{
if (getline(xfile, line))
{
line_value = stod(line);
REG_x_file[i] = line_value;
}
else
return;
}
for (i = 0; i < data_size; i++)
{
if (getline(yfile, line))
{
line_value = stod(line);
REG_y_file[i] = line_value;
}
else
return;
}
xfile.close();
yfile.close();
paramfile.close();
}
else
return;
Init(REG_x_file, REG_y_file, REG_param_file, data_size, x_dimensions, kernel);
return;
}
template <typename T>
void REG<T>::Init(const T* x, const T* y, const T* params, const unsigned int data_size, const unsigned int x_dimensions,
const string kernel)
{
unsigned int i;
// Setting type of kernel
REG_kernel_type = kernel;
if (kernel != "Gaussian" and kernel != "Laplacian" and kernel != "Exponential" and kernel != "Matern")
return;
if (kernel == "Gaussian")
REG_kernel_id = 0;
if (kernel == "Laplacian")
REG_kernel_id = 1;
if (kernel == "Exponential")
REG_kernel_id = 2;
if (kernel == "Matern")
REG_kernel_id = 3;
// copy parameters and data
REG_lambda= params[0];
REG_alpha = params[1];
if (REG_alpha > 1)
REG_alpha = 1;
if (REG_alpha < 0)
REG_alpha = 0;
REG_sigma = params[2];
if (kernel == "Matern")
REG_n = static_cast<unsigned int>(params[3] + 0.5);
REG_count_kernels = data_size;
REG_count_dimensions = x_dimensions;
REG_aloc_init = false;
{
REG_params = new T[4];
if(!REG_params) laerror("allocation failure in REG::Init");
if (REG_kernel_id == 3)
{
for (i = 0; i < 4; i++)
REG_params[i] = params[i];
REG_Matern_comb_number_vec = NRVec<T>(REG_n);
REG_Matern_comb_number = REG_Matern_comb_number_vec.operator T*();
}
else
{
for (i = 0; i < 3; i++)
REG_params[i] = params[i];
REG_Matern_comb_number_vec = NRVec<T>(1);
REG_Matern_comb_number = REG_Matern_comb_number_vec.operator T*();
}
}
// copy data
REG_coordinates_vec = NRVec<T>(x, data_size * REG_count_dimensions);
REG_coordinates = REG_coordinates_vec.operator T*();
REG_y_vec = NRVec<T>(y , data_size);
REG_Y = REG_y_vec.operator T*();
// for fitting model
REG_distances_mat = NRMat<T>(data_size, data_size);
REG_distances = REG_distances_mat.operator T*();
REG_kernels_mat = NRMat<T>(data_size, data_size);
REG_kernels = REG_kernels_mat.operator T*();
REG_kernels_sums_vec = NRVec<T>(data_size);
REG_kernels_sums = REG_kernels_sums_vec.operator T*();
REG_weights_vec = NRVec<T>(data_size);
REG_weights = REG_weights_vec.operator T*();
// for predictions
REG_coordinates_diff_vec = NRVec<T>(data_size);
REG_coordinates_diff = REG_coordinates_diff_vec.operator T*();
REG_kernels_diff_vec = NRVec<T>(data_size);
REG_kernels_diff = REG_kernels_diff_vec.operator T*();
REG_y_preds_vec = NRVec<T>(data_size);
REG_y_preds = REG_y_preds_vec.operator T*();
REG_y_delta_vec = NRVec<T>(data_size);
REG_y_delta = REG_y_delta_vec.operator T*();
REG_y_temp_vec = NRVec<T>(data_size);
REG_y_temp = REG_y_temp_vec.operator T*();
REG_aloc_init = true;
// calculating Matern coefficients, if Matern kernel is selected
if (REG_kernel_id == 3)
Matern_coefficient(REG_n, REG_Matern_comb_number);
REG_base_init = true;
return;
}
template <typename T>
T REG<T>::Kernel(const T* x, const unsigned int dimensions, const unsigned int kernel_id)
{
T result;
switch (kernel_id) {
case 0:
result = Gaussian_kernel(x, dimensions, REG_sigma);
break;
case 1:
result = Laplacian_kernel(x, dimensions, REG_sigma);
break;
case 2:
result = Laplacian_kernel(x, dimensions, REG_sigma);
break;
case 3:
result = Matern_kernel(x, dimensions, REG_sigma, REG_n, REG_Matern_comb_number);
break;
}
return(result);
}
template <typename T>
unsigned int REG<T>::Build_REG_distances_mat()
{
unsigned int i, j, k;
unsigned int mat_dimension, vec_dimension;
// check the initialization
if (REG_base_init == false)
{
laerror("regression model not inicialized");
return(1);
}
mat_dimension = REG_count_kernels;
vec_dimension = REG_count_dimensions;
// building the matrix of vectors coordinates differences between kernels
for (i = 0; i < mat_dimension; i++)
{
for (j = i + 1; j < mat_dimension; j++)
for (k = 0; k < vec_dimension; k++)
{
REG_distances[(i * (mat_dimension) + j) * vec_dimension + k] = REG_coordinates[i * vec_dimension + k] -
REG_coordinates[j * vec_dimension + k];
}
}
// copy calculated values under diagonal
for (i = 0; i < mat_dimension; i++)
{
for (j = i + 1; j < mat_dimension; j++)
for (k = 0; k < vec_dimension; k++)
{
REG_distances[(j * (mat_dimension) + i) * vec_dimension + k] =
REG_distances[(i * (mat_dimension) + j) * vec_dimension + k];
}
}
// copy 0 to diagonal
for (i = 0; i < mat_dimension; i++)
for (k = 0; k < vec_dimension; k++)
REG_distances[(i * (mat_dimension + 1) * vec_dimension) + k] = 0;
return(0);
}
template <typename T>
unsigned int REG<T>::Build_REG_kernels_mat()
{
unsigned int i, j, k;
unsigned int mat_dimension, vec_dimension;
// check the initialization
if (REG_base_init == false)
{
laerror("regression model not inicialized");
return(1);
}
// copy class parameters
mat_dimension = REG_count_kernels;
vec_dimension = REG_count_dimensions;
// crete kernel coefficients matrix for gaussian kernels
for (i = 0; i < mat_dimension; i++)
for (j = i + 1; j < mat_dimension; j++)
{
REG_kernels[i * mat_dimension + j] = Kernel(&REG_distances[(i * (mat_dimension) + j) * vec_dimension],
vec_dimension, REG_kernel_id);
}
// copy calculated values under diagonal
for (i = 0; i < mat_dimension; i++)
for (j = i + 1; j < mat_dimension; j++)
REG_kernels[(j * (mat_dimension) + i)] = REG_kernels[(i * (mat_dimension) + j)];
// copy 1 to diagonal
for (i = 0; i < mat_dimension; i++)
REG_kernels[i * (mat_dimension + 1)] = 1;
return(0);
}
template <typename T>
unsigned int REG<T>::Build_REG_kernels_mat_sums()
{
unsigned int i, j;
unsigned int count_kernels;
T sum;
count_kernels = REG_count_kernels;
for (i = 0; i < count_kernels; i++)
{
sum = 0;
for (j = 0; j < count_kernels; j++)
sum += REG_kernels[(i * count_kernels) + j];
REG_kernels_sums[i] = sum;
}
return(0);
}
template <typename T>
T REG<T>::REG_RMSE()
{
T delta_square;
// check the initialization
if (REG_base_init == false)
{
laerror("regression model not inicialized");
return(1);
}
T y_max = REG_y_vec.amax();
T y_min = REG_y_vec.amin();
REG_y_delta_vec |= REG_y_preds_vec;
REG_y_delta_vec -= REG_y_vec;
REG_y_delta_vec *= REG_y_delta_vec;
delta_square = REG_y_delta_vec.sum();
delta_square = delta_square/REG_count_kernels;
delta_square = std::sqrt(delta_square);
return(delta_square);
}
template <typename T>
T REG<T>::Loss_Function()
{
unsigned int count_x;
T RMSE;
// check the initialization
if (REG_base_init == false)
{
laerror("regression model not inicialized");
return(1);
}
// calculating the root mean square error - RMSE
RMSE = REG_RMSE();
return (RMSE);
}
template <typename T>
unsigned int REG<T>::REG_Fit(const T max_Loss, const unsigned int max_learning_cycles)
{ // the kernel ridge learning algorithm
unsigned int i, j;
T Loss;
T Lasso_part;
T kernel_ridge_part;
unsigned int count_kernels;
// check the initialization
if (REG_base_init == false)
{
laerror("regression model not inicialized");
return(1);
}
// checking the input parameters
if (max_learning_cycles == 0)
{
laerror("zero learning cycles");
return(1);
}
if (max_Loss < 0)
{
laerror("negative value of maximum Loss function");
return(1);
}
Lasso_part = REG_lambda * REG_alpha;
kernel_ridge_part = REG_lambda * (1 - REG_alpha) * 0.5;
count_kernels = REG_count_kernels;
// initialization of REG_distances_mat and REG_kernels_mat if necessary
if (REG_mat_init == false)
{
Build_REG_distances_mat();
Build_REG_kernels_mat();
Build_REG_kernels_mat_sums();
REG_mat_init = true;
}
// initialitation of weight coefficients vector
REG_weights_vec |= REG_y_vec;
// Linear learning cycle of weight coefficient for learning
for (i = 0; i < max_learning_cycles; i++)
{
// calculating preds_vec vector of predicted y values
REG_y_preds_vec.gemv(0, REG_kernels_mat, 'n', 1, REG_weights_vec);
if (kernel_ridge_part != 0)
for (j = 0; j < REG_count_kernels; j++)
REG_y_preds[j] *= (REG_kernels_sums[j] + kernel_ridge_part)/REG_kernels_sums[j];
if (Lasso_part != 0)
REG_y_preds_vec += Lasso_part;
// calculating new weights
REG_y_temp_vec |= REG_y_vec;
REG_y_temp_vec /= REG_y_preds_vec;
REG_weights_vec *= REG_y_temp_vec;
// checking the Loss_Function value
if (max_Loss > 0)
{
Loss = Loss_Function();
if (Loss < max_Loss)
break;
}
}
return(0);
}
template <typename T>
unsigned int REG<T>::REG_Fit_grad(const T max_Loss, const unsigned int max_learning_cycles, const T learning_rate)
{
unsigned int i, j, k;
unsigned int count_x;
T Loss;
T delta_RMSE;
// for optimizing calculation of Kernel ridge part of Loss function difference
T kernel_ridge_part;
T delta_KRR_part;
// for optimizing calculation of Lasso part of Loss function difference
T Lasso_part;
T delta_Lasso_part;
T sqrt_count_x;
count_x = REG_count_kernels;
// check the initialization
if (REG_base_init == false)
{
laerror("regression model not inicialized");
return(1);
}
// Checking the input parameters
if (max_learning_cycles == 0)
{
laerror("zero learning cycles");
return(1);
}
if (max_Loss < 0)
{
laerror("negative value of maximum Loss function");
return(1);
}
// initialization of REG_distances_mat and REG_kernels_mat if necessary
if (REG_mat_init == false)
{
Build_REG_distances_mat();
Build_REG_kernels_mat();
Build_REG_kernels_mat_sums();
REG_mat_init = true;
}
// initialitation of weight coefficients vector
REG_weights_vec |= REG_y_vec;
kernel_ridge_part = REG_lambda * (1.00 - REG_alpha);
Lasso_part = REG_lambda * REG_alpha;
sqrt_count_x = std::sqrt(count_x);
// gradient descent Learning cycle of weight coefficient for learning
for (i = 0; i < max_learning_cycles; i++)
{
// calculating preds_vec vector of predicted y values
REG_y_preds_vec.gemv(0, REG_kernels_mat, 'n', 1, REG_weights_vec);
if (kernel_ridge_part != 0)
for (j = 0; j < count_x; j++)
REG_y_preds[j] *= (REG_kernels_sums[j] + kernel_ridge_part)/REG_kernels_sums[j];
if (Lasso_part != 0)
REG_y_preds_vec += Lasso_part;
// calculating difference of root mean square error - RMSE
for (j = 0; j < count_x; j++)
{
delta_RMSE = 0;
for (k = 0; k < count_x; k++)
delta_RMSE += (REG_y_preds[k] - REG_Y[k]) * REG_kernels[j * count_x + k];
delta_RMSE /=sqrt_count_x;
// calculating new weights
REG_weights[j] /= (1 - learning_rate * delta_RMSE);
}
// convergence criteria check
if (max_Loss > 0)
{
Loss = Loss_Function();
if (Loss < max_Loss)
break;
}
}
return(0);
}
template <typename T>
unsigned int REG<T>::REG_Save_fitted(const string model_file)
{
unsigned int i;
ofstream modelfile(model_file);
string line;
// checking the initialization
if (REG_base_init == false)
{
laerror("regression model not inicialized");
return(1);
}
// save model to file
if (modelfile.is_open())
for (i = 0; i < REG_count_kernels; i++)
{
line = to_string(REG_weights[i]);
modelfile << line << '\n';
}
modelfile.close();
return(0);
}
template <typename T>
unsigned int REG<T>::REG_Load_fitted(const string model_file)
{
unsigned int i;
ifstream modelfile(model_file);
string line;
T line_value;
// check the initialization
if (REG_base_init == false)
{
laerror("regression model not inicialized");
return(1);
}
// initialization of REG_distances_mat and REG_kernels_mat if necessary
if (REG_mat_init == false)
{
Build_REG_distances_mat();
Build_REG_kernels_mat();
REG_mat_init = true;
}
// load stored weights
if (modelfile.is_open())
{
for (i = 0; i < REG_count_kernels; i++)
if (getline(modelfile, line))
{
line_value = stod(line);
REG_weights[i] = line_value;
}
REG_y_preds_vec.gemv(0, REG_kernels_mat, 'n', 1, REG_weights_vec);
}
return(0);
}
template <typename T>
unsigned int REG<T>::REG_Get_predictions(const T* x, T* y_preds, const unsigned int data_size)
{
unsigned int i, j, k;
T pred_value;
T Lasso_part;
T kernel_ridge_part;
T sum_kernels_diff;
T weights_sum;
// check the initialization
if (REG_base_init == false)
{
laerror("regression model not inicialized");
return(1);
}
Lasso_part = REG_lambda * REG_alpha;
kernel_ridge_part = REG_lambda * (1 - REG_alpha) * 0.5;
// loop for predicting new values for each x
for (i = 0; i < data_size; i++) // For every x value
{
pred_value = 0;
// calculating the REG_coordinates_vec
for (j = 0; j < REG_count_kernels; j++) // For every kernel
{
for (k = 0; k < REG_count_dimensions; k++) // For every x coordinate
{
REG_coordinates_diff[(j * REG_count_dimensions) + k] = x[(i * REG_count_dimensions) + k] -
REG_coordinates[(j * REG_count_dimensions) + k];
}
}
// calculating the REG_kernels_vec
if (kernel_ridge_part != 0)
{
sum_kernels_diff = 0;
for (j = 0; j < REG_count_kernels; j++) // For every kernel
{
REG_kernels_diff[j] = Kernel(&REG_coordinates_diff[(j * REG_count_dimensions)], REG_count_dimensions, REG_kernel_id);
pred_value += REG_kernels_diff[j] * REG_weights[j];
sum_kernels_diff += REG_kernels_diff[j];
}
if (sum_kernels_diff != 0)
pred_value *= (sum_kernels_diff + kernel_ridge_part)/sum_kernels_diff;
}
else
for (j = 0; j < REG_count_kernels; j++) // For every kernel
{
REG_kernels_diff[j] = Kernel(&REG_coordinates_diff[(j * REG_count_dimensions)], REG_count_dimensions, REG_kernel_id);
pred_value += REG_kernels_diff[j] * REG_weights[j];
}
pred_value += Lasso_part;
// storing y prediction into memory
y_preds[i] = pred_value;
}
return(0);
}
template <typename T>
unsigned int REG<T>::REG_Get_Score(const T* x, T* y_preds, const unsigned int data_size, const T* y, T* score)
{
unsigned int i;
T prediction;
// check the initialization
if (REG_base_init == false)
{
laerror("regression model not inicialized");
return(1);
}
REG_Get_predictions(x, y_preds, data_size);
prediction = 0;
for (i = 0; i < data_size; i++)
prediction += (y[i] - y_preds[i]) * (y[i] - y_preds[i]);
score[0] = prediction;
return(0);
}
template <typename T>
unsigned int REG<T>::REG_Set_params(const T* params, const string kernel)
{
// setting type of kernel
REG_kernel_type = kernel;
if (kernel == "Gaussian")
REG_kernel_id = 0;
if (kernel == "Laplacian")
REG_kernel_id = 1;
if (kernel == "Exponential")
REG_kernel_id = 2;
if (kernel == "Matern")
REG_kernel_id = 3;
// copy parameters and data
REG_lambda = params[0];
REG_alpha = params[1];
if (REG_alpha > 1)
REG_alpha = 1;
if (REG_alpha < 0)
REG_alpha = 0;
REG_sigma = params[2];
if (kernel == "Matern")
REG_n = static_cast<unsigned int>(params[3] + 0.5);
// calculating Matern coefficients, if Matern kernel is selected
if (REG_kernel_id == 3)
{
REG_Matern_comb_number_vec.resize(REG_n);
REG_Matern_comb_number = REG_Matern_comb_number_vec.operator T*();
Matern_coefficient(REG_n, REG_Matern_comb_number);
}
return(0);
}
template <typename T>
unsigned int REG<T>::REG_Get_params(T* params, string* kernel)
{
kernel[0] = REG_kernel_type;
params[0] = REG_lambda;
params[1] = REG_alpha;
params[2] = REG_sigma;
if (REG_kernel_type == "Mattern")
params[3] = REG_n;
return(0);
}
template <typename T>
unsigned int REG<T>::REG_Get_weight_coeff(T* weight)
{
unsigned int i;
for (i = 0; i < REG_count_kernels; i++)
weight[i] = REG_weights[i];
return(0);
}
template <typename T>
REG<T>::~REG()
{
// dealocating memory to avoid memory leaks
if (REG_params != nullptr)
delete[] REG_params;
if (REG_x_file != nullptr)
delete[] REG_x_file;
if (REG_y_file != nullptr)
delete[] REG_y_file;
if (REG_param_file != nullptr)
delete[] REG_param_file;
if (REG_fit_file != nullptr)
delete[] REG_fit_file;
}
//enforce instantiation
#define INSTANTIZE(T) \
template T Gaussian_kernel(const T* x, const unsigned int dimensions, const T sigma); \
template T Laplacian_kernel(const T* x, const unsigned int dimensions, const T sigma); \
template T Exponential_kernel(const T* x, const unsigned int dimensions, const T sigma); \
template T Matern_kernel(const T* x, const unsigned int dimensions, const T sigma, const unsigned int n, const T* Matern_comb_number); \
template unsigned int Matern_coefficient(const unsigned int n, T* comb_number); \
INSTANTIZE(double)
} // end of namespace
template class REG<double>;
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