Merge branch 'main' into fix

Reviewed-on: https://git.tjoyspotifylastfm.tech/ParkSuMin/MemMAPR-MKE/pulls/1

.gitignore

@@ -636,4 +636,7 @@ FodyWeavers.xsd
 *.msix
 *.msm
 *.msp
+
 *.txt
+!CMakeLists.txt
+*.png

MemMAPR-MKE.cpp

@@ -1,12 +0,0 @@
-#include "Header.h"
-#include "Solver.h"
-#include <Eigen/Dense>
-using namespace Eigen;
-int main() {
-    Solver slv(5., 4., 0., 1., 30, 0, 10);
-    std::cout << "Linear element:";
-    slv.Execute_Linear(0, 5);
-    //std::cout << "\nCubic  element:" << std::endl;
-    //slv.Execute_Cubic(0, 5);
-    return 0;
-}

MemMAPR-MKE.vcxproj

@@ -142,6 +142,7 @@
       <ConformanceMode>true</ConformanceMode>
       <LanguageStandard>Default</LanguageStandard>
       <LanguageStandard_C>Default</LanguageStandard_C>
+      <AdditionalIncludeDirectories>include/</AdditionalIncludeDirectories>
     </ClCompile>
     <Link>
       <SubSystem>Console</SubSystem>
@@ -156,6 +157,7 @@
       <ConformanceMode>true</ConformanceMode>
       <LanguageStandard>Default</LanguageStandard>
       <LanguageStandard_C>Default</LanguageStandard_C>
+      <AdditionalIncludeDirectories>include/</AdditionalIncludeDirectories>
     </ClCompile>
     <Link>
       <SubSystem>Console</SubSystem>
@@ -172,6 +174,7 @@
       <ConformanceMode>true</ConformanceMode>
       <LanguageStandard>Default</LanguageStandard>
       <LanguageStandard_C>Default</LanguageStandard_C>
+      <AdditionalIncludeDirectories>include/</AdditionalIncludeDirectories>
     </ClCompile>
     <Link>
       <SubSystem>Console</SubSystem>
@@ -179,15 +182,15 @@
     </Link>
   </ItemDefinitionGroup>
   <ItemGroup>
-    <ClCompile Include="MemMAPR-MKE.cpp" />
-    <ClCompile Include="Solver.cpp" />
+    <ClCompile Include="src\MemMAPR-MKE.cpp" />
+    <ClCompile Include="src\Solver.cpp" />
   </ItemGroup>
   <ItemGroup>
     <None Include="packages.config" />
   </ItemGroup>
   <ItemGroup>
-    <ClInclude Include="Header.h" />
-    <ClInclude Include="Solver.h" />
+    <ClInclude Include="include\Header.h" />
+    <ClInclude Include="include\Solver.h" />
   </ItemGroup>
   <Import Project="$(VCTargetsPath)\Microsoft.Cpp.targets" />
   <ImportGroup Label="ExtensionTargets">

MemMAPR-MKE.vcxproj.filters

@@ -18,22 +18,22 @@
     </Filter>
   </ItemGroup>
   <ItemGroup>
-    <ClCompile Include="MemMAPR-MKE.cpp">
-      <Filter>Исходные файлы</Filter>
-    </ClCompile>
-    <ClCompile Include="Solver.cpp">
+    <ClCompile Include="src\Solver.cpp">
       <Filter>Solver</Filter>
     </ClCompile>
+    <ClCompile Include="src\MemMAPR-MKE.cpp">
+      <Filter>Исходные файлы</Filter>
+    </ClCompile>
   </ItemGroup>
   <ItemGroup>
     <None Include="packages.config" />
   </ItemGroup>
   <ItemGroup>
-    <ClInclude Include="Header.h">
-      <Filter>Исходные файлы</Filter>
-    </ClInclude>
-    <ClInclude Include="Solver.h">
+    <ClInclude Include="include\Solver.h">
       <Filter>Solver</Filter>
     </ClInclude>
+    <ClInclude Include="include\Header.h">
+      <Filter>Исходные файлы</Filter>
+    </ClInclude>
   </ItemGroup>
 </Project>

Solver.cpp

@@ -1,153 +0,0 @@
-#include "Header.h"
-#include <Eigen/Dense>
-using namespace Eigen;
-
-Solver::Solver(double _A, double _B, double _C, double _D, int _N, int _l, int _u) {
-    A = _A, B = _B, C = _C, D = _D, N = _N;
-    upper = _u, lower = _l;
-	L = upper - lower;
-	dx = L / N;
-}
-
-void Solver::Execute_Linear(double val1, double val2) {
-
-    MatrixXd local = MatrixXd::Zero(2, 2);
-    VectorXd local_load(2);
-
-    local(0, 0) = -A / dx - B / 2. + C * dx / 3.;
-    local(0, 1) = A / dx + B / 2. + C * dx / 6.;
-    local(1, 0) = A / dx - B / 2. + C * dx / 6.;
-    local(1, 1) = -A / dx + B / 2. + C * dx / 3.;
-
-    local_load(0) = -D * dx / 2.;
-    local_load(1) = -D * dx / 2.;
-
-    MatrixXd ansamb = MatrixXd::Zero(N + 1, N + 1);
-    VectorXd global_load = VectorXd::Zero(N + 1);
-
-    // Ансамблирование
-    for (int elem = 0; elem < N; ++elem) {
-        int node_i = elem;
-        int node_j = elem + 1;
-
-        ansamb(node_i, node_i) += local(0, 0);
-        ansamb(node_i, node_j) += local(0, 1);
-        ansamb(node_j, node_i) += local(1, 0);
-        ansamb(node_j, node_j) += local(1, 1);
-
-        global_load(node_i) += local_load(0);
-        global_load(node_j) += local_load(1);
-    }
-
-#if DEBUG
-    std::cout << std::endl << "Before:" << std::endl;
-    std::cout << "Ansamb matrix:\n" << ansamb << std::endl;
-    std::cout << "Ansamb load vector:\n" << global_load << std::endl;
-#endif
-
-    double u_right = val2;
-
-    // Clear first and last rows
-    ansamb.row(0).setZero();
-    ansamb.row(N).setZero();
-
-    // u'(0) = u(0)
-    ansamb(0, 0) = dx + 1;
-    ansamb(0, 1) = -1;
-    global_load(0) = 0;
-
-    // u(10) = u_right = 5
-    ansamb(N, N) = 1;
-    global_load(N) = u_right;
-
-#if DEBUG
-    std::cout << "\nAfter:" << std::endl;
-    std::cout << "Modified matrix:\n" << ansamb << std::endl;
-    std::cout << "Modified load vector:\n" << global_load << std::endl;
-#endif
-
-    VectorXd solution = ansamb.fullPivLu().solve(global_load);
-    std::cout << "\nSolution:" << std::endl;
-    std::cout << solution << std::endl;
-
-    std::ofstream file("matrix_linear.txt");
-    for (int i = 0; i < N; i++) {
-        file << solution(i) << ' ';
-    }
-    file << std::endl;
-}
-
-void Solver::Execute_Cubic(double val1, double val2) {
-
-    int mat_dim = 1 + N * 3;
-    Eigen::MatrixXd Amat(mat_dim, mat_dim);
-    Eigen::VectorXd b(mat_dim);
-    Amat.setZero();
-    b.setZero();
-
-    // Assemble matrix
-    for (int i = 0; i < mat_dim - 3; i += 3) {
-        Amat(i, i + 0) -= A * 37.0 / 10.0 / dx;
-        Amat(i, i + 1) -= A * (-189.0) / 40.0 / dx;
-        Amat(i, i + 2) -= A * 27.0 / 20.0 / dx;
-        Amat(i, i + 3) -= A * (-13.0) / 40.0 / dx;
-        Amat(i + 1, i + 0) -= A * (-189.0) / 40.0 / dx;
-        Amat(i + 1, i + 1) -= A * 54.0 / 5.0 / dx;
-        Amat(i + 1, i + 2) -= A * (-297.0) / 40.0 / dx;
-        Amat(i + 1, i + 3) -= A * 27.0 / 20.0 / dx;
-        Amat(i + 2, i + 0) -= A * 27.0 / 20.0 / dx;
-        Amat(i + 2, i + 1) -= A * (-297.0) / 40.0 / dx;
-        Amat(i + 2, i + 2) -= A * 54.0 / 5.0 / dx;
-        Amat(i + 2, i + 3) -= A * (-189.0) / 40.0 / dx;
-        Amat(i + 3, i + 0) -= A * (-13.0) / 40.0 / dx;
-        Amat(i + 3, i + 1) -= A * 27.0 / 20.0 / dx;
-        Amat(i + 3, i + 2) -= A * (-189.0) / 40.0 / dx;
-        Amat(i + 3, i + 3) -= A * 37.0 / 10.0 / dx;
-
-        Amat(i + 0, i + 0) += B * (-1.0) / 2.0;
-        Amat(i + 0, i + 1) += B * 57.0 / 80.0;
-        Amat(i + 0, i + 2) += B * (-3.0) / 10.0;
-        Amat(i + 0, i + 3) += B * 7.0 / 80.0;
-        Amat(i + 1, i + 0) += B * (-57.0) / 80.0;
-
-        Amat(i + 1, i + 2) += B * 81.0 / 80.0;
-        Amat(i + 1, i + 3) += B * (-3.0) / 10;
-        Amat(i + 2, i + 0) += B * 3.0 / 10.0;
-        Amat(i + 2, i + 1) += B * (-81.0) / 80.0;
-
-        Amat(i + 2, i + 3) += B * 57.0 / 80.0;
-        Amat(i + 3, i + 0) += B * (-7.0) / 80.0;
-        Amat(i + 3, i + 1) += B * 3.0 / 10.0;
-        Amat(i + 3, i + 2) += B * (-57.0) / 80.0;
-        Amat(i + 3, i + 3) += B * 1.0 / 2.0;
-    }
-
-    // Assembdxe vector
-    for (int i = 0; i < mat_dim - 3; i += 3) {
-        b(i) -= D * dx / 8.0;
-        b(i + 1) -= D * 3.0 * dx / 8.0;
-        b(i + 2) -= D * 3.0 * dx / 8.0;
-        b(i + 3) -= D * dx / 8.0;
-    }
-
-
-    Amat.row(0).setZero();
-    Amat(0, 0) = dx / 3.0 + 1;
-    Amat(0, 1) = -1;
-    b(0) = 0;
-
-    Amat.row(mat_dim - 1).setZero();
-    Amat(mat_dim - 1, mat_dim - 1) = 1;
-    b(mat_dim - 1) = val2;
-
-    // Решение системы
-    VectorXd solution = Amat.colPivHouseholderQr().solve(b);
-    std::cout << "\nSolution:" << std::endl;
-    std::cout << solution << std::endl;
-    
-    std::ofstream file("matrix_cubic.txt");
-    for (int i = 0; i < solution.size(); i++) {
-        file << solution(i) << ' ';
-    }
-    file << std::endl;
-}

Solver.h

@@ -1,11 +0,0 @@
-#pragma once
-
-class Solver {
-private:
-	double A, B, C, D, L, dx;
-	int N, upper, lower;
-public:
-	Solver(double _A, double _B, double _C, double _D, int _N, int _l, int _u);
-	void Execute_Linear(double value_1, double value_2);
-	void Execute_Cubic(double value_1, double value_2);
-};

graphics.ipynb

@@ -0,0 +1,256 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "fda98006",
+   "metadata": {},
+   "source": [
+    "# Solution of second-order linear ordinary differential equation"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a4b21c72",
+   "metadata": {},
+   "source": [
+    "## Input vars"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "6653253d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "N = 20\n",
+    "linear_file = f\"matrix_linear_{N}.txt\"\n",
+    "cubic_file = f\"matrix_cubic_{N}.txt\""
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "781047cc",
+   "metadata": {},
+   "source": [
+    "## System cells"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7fced95c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def write_to_file(name: str, array):\n",
+    "    with open(f\"{name}\", 'w') as file:\n",
+    "        for element in array:\n",
+    "            file.write(f\"{element} \")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d20bde93",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8af07a56",
+   "metadata": {},
+   "source": [
+    "### Solution of $5u'' + 4u' + 1 = 0, u'(0) = u(0), u(10) = 5$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d0fe0703",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def u(x):\n",
+    "    return (9 * np.exp(8) * (x - 30) + 155 * np.exp(8 - 4 * x / 5) - 5 * (x + 1)) / (20 - 36 * np.exp(8))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "efac514a",
+   "metadata": {},
+   "source": [
+    "### Linear element"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "18bd929b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def show_plot_linear(filename: str, elements: int):\n",
+    "    with open(filename, 'r') as file:\n",
+    "        data_str = file.read()\n",
+    "\n",
+    "    x = np.linspace(0, 10, elements + 1)\n",
+    "    y = np.fromstring(data_str, sep=' ')\n",
+    "    y_real = u(x)\n",
+    "\n",
+    "    plt.plot(x, y, label=\"Linear element solution\", color='blue')\n",
+    "    plt.plot(x, y_real, label=\"Numeral solution\", color='black')\n",
+    "    plt.title(f\"Linear element, elements = {elements}\")\n",
+    "    plt.grid(True)\n",
+    "    plt.xlabel(\"x\")\n",
+    "    plt.ylabel(\"u(x)\")\n",
+    "    plt.legend()\n",
+    "    plt.savefig(f\"linear_{elements}.png\", dpi=300)\n",
+    "    plt.show()\n",
+    "\n",
+    "    write_to_file(f\"linear_real_y_{elements}.txt\", y_real)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d9a38740",
+   "metadata": {},
+   "source": [
+    "### Cubic element"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "73525bc7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def show_plot_cubic(filename: str, elements: int):\n",
+    "    with open(filename, 'r') as file:\n",
+    "        data_str = file.read()\n",
+    "\n",
+    "    x = np.linspace(0, 10, 3 * elements + 1)\n",
+    "    y = np.fromstring(data_str, sep=' ')\n",
+    "    y_real = u(x)\n",
+    "\n",
+    "    plt.plot(x, y, label=\"Cubic element solution\", color=\"red\")\n",
+    "    plt.plot(x, y_real, label=\"Numeral solution\", color='black')\n",
+    "    plt.title(f\"Cubic element, elements = {elements} \")\n",
+    "    plt.xlabel(\"x\")\n",
+    "    plt.ylabel(\"u(x)\")\n",
+    "    plt.grid(True)\n",
+    "    plt.legend()\n",
+    "    plt.savefig(f\"cubic_{elements}.png\", dpi=300)\n",
+    "    plt.show()\n",
+    "\n",
+    "    write_to_file(f\"cubic_real_y_{elements}.txt\", y_real)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3584baa4",
+   "metadata": {},
+   "source": [
+    "## Main part"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b8a772e3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "show_plot_linear(linear_file, N)\n",
+    "show_plot_cubic(cubic_file, N)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "22fe3de6",
+   "metadata": {},
+   "source": [
+    "## Errors"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "31de1104",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def read_data_from_file(filename):\n",
+    "    with open(filename, 'r') as file:\n",
+    "        content = file.read().strip()\n",
+    "        data = np.array([float(x) for x in content.split()])\n",
+    "    return data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e0e9266d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def show_error(program_file: str, analytical_file: str):\n",
+    "    # Считывание данных из файлов\n",
+    "    real = read_data_from_file(analytical_file)\n",
+    "    matrix = read_data_from_file(program_file)\n",
+    "    \n",
+    "    absolute_errors = np.abs(real - matrix)\n",
+    "    relative_errors = absolute_errors / (np.abs(real))\n",
+    "    relative_errors_percent = relative_errors * 100\n",
+    "\n",
+    "    max_relative_error = np.max(relative_errors)\n",
+    "    max_relative_error_percent = np.max(relative_errors_percent)\n",
+    "    max_error_index = np.argmax(relative_errors)\n",
+    "\n",
+    "    print(f\"\\nМаксимальная относительная погрешность: {max_relative_error:.6f} ({max_relative_error_percent:.2f}%)\")\n",
+    "    print(f\"Индекс точки с максимальной погрешностью: {max_error_index}\")\n",
+    "    print(f\"Значения в точке с максимальной погрешностью:\")\n",
+    "    print(f\"  cubic_real: {real[max_error_index]}\")\n",
+    "    print(f\"  matrix_cubic: {matrix[max_error_index]}\")\n",
+    "    print(f\"  Абсолютная разность: {absolute_errors[max_error_index]:.6f}\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "89918171",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "show_error(linear_file, f\"linear_real_y_{N}.txt\")\n",
+    "show_error(cubic_file, f\"cubic_real_y_{N}.txt\")"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

include/Solver.h

@@ -0,0 +1,31 @@
+// Особенности MSVC
+#define _SILENCE_EXPERIMENTAL_FILESYSTEM_DEPRECATION_WARNING
+
+#pragma once
+#include <experimental/filesystem>
+using namespace std;
+using namespace std::experimental::filesystem;
+
+class Solver {
+private:
+	// Коэффициенты в ДУ
+	double A, B, C, D;
+	// Длина конечного элемента
+	double L;
+	// Количество конечных элементов
+	int N;
+	// Границы частного решения ДУ
+	int upper, lower;
+public:
+	Solver(double _A, double _B, double _C, double _D, int _N, int _l, int _u);
+	void Execute_Linear(double value_1, double value_2);
+	void Execute_Cubic(double value_1, double value_2);
+
+	bool check_path(string path) {
+		return exists(path);
+	}
+
+	void make_path(string path) {
+		create_directory(path);
+	}
+};

src/MemMAPR-MKE.cpp

@@ -0,0 +1,18 @@
+#include "Solver.h"
+#include "Header.h"
+#include <Eigen/Dense>
+#define A 5.
+#define B 4.
+#define C 0.
+#define D 1.
+
+using namespace Eigen;
+int main() {
+    std::cout << A << "u''" << " + " << B << "u'" << "+ " << C << "u + " << D << " = 0" << std::endl;
+    Solver slv(A, B, C, D, 20, 0, 10);
+    std::cout << "Linear element:";
+    slv.Execute_Linear(0, 5);
+    std::cout << "\nCubic element:";
+    slv.Execute_Cubic(0, 5);
+    return 0;
+}

src/Solver.cpp

@@ -0,0 +1,186 @@
+#include "Header.h"
+#include <Eigen/Dense>
+using namespace Eigen;
+
+Solver::Solver(double _A, double _B, double _C, double _D, int _N, int _l, int _u) {
+    if (_N < 1)
+        throw std::runtime_error("N CAN BE OVER THAN 1!");
+
+    A = _A, B = _B, C = _C, D = _D, N = _N;
+    upper = _u, lower = _l;
+	L = (double)(upper - lower) / N;
+}
+
+void Solver::Execute_Linear(double val1, double val2) {
+
+    // Локальная матрица жёсткости
+    MatrixXd local = MatrixXd::Zero(2, 2);
+    
+    // Локальный вектор нагрузки
+    VectorXd local_load(2);
+
+    local(0, 0) = -A / L - B / 2. + C * L / 2.;
+    local(0, 1) = A / L + B / 2. + C * L / 2.;
+    local(1, 0) = A / L - B / 2. + C * L / 2.;
+    local(1, 1) = -A / L + B / 2. + C * L / 2.;
+
+    local_load(0) = -D * L / 2.;
+    local_load(1) = -D * L / 2.;
+    
+    // Глобальная матрица жёсткости
+    MatrixXd ansamb = MatrixXd::Zero(N + 2, N + 2);
+
+    // Глобальный вектор нагрузок
+    VectorXd global_load = VectorXd::Zero(N + 2);
+
+    // Ансамблирование (с учётом смещения на 1)
+    for (int elem = 0; elem < N; ++elem) {
+        int node_i = elem + 1;
+        int node_j = elem + 2;
+
+        ansamb(node_i, node_i) += local(0, 0);
+        ansamb(node_i, node_j) += local(0, 1);
+        ansamb(node_j, node_i) += local(1, 0);
+        ansamb(node_j, node_j) += local(1, 1);
+
+        global_load(node_i) += local_load(0);
+        global_load(node_j) += local_load(1);
+    }
+
+#if DEBUG
+    std::cout << std::endl << "Before:" << std::endl;
+    std::cout << "Ansamb matrix:\n" << ansamb << std::endl;
+    std::cout << "Ansamb load vector:\n" << global_load << std::endl;
+#endif
+
+    // Boundary conditions
+    double u_right = val2;
+
+    // 3rd type of boundary condition
+    ansamb.row(0).setZero();
+    ansamb(0, 0) = 1;
+    ansamb(0, 1) = -1;
+    global_load(0) = 0;
+    ansamb(1, 1) -= A;
+
+    // 1st type of boundary condition
+    for (int i = 0; i < global_load.size(); ++i) {
+        global_load(i) = global_load(i) - u_right * ansamb(i, N + 1);
+    }
+    ansamb.row(N + 1).setZero();
+    ansamb.col(N + 1).setZero();
+    ansamb(N + 1, N + 1) = 1;
+    global_load(N + 1) = u_right;
+
+#if DEBUG
+    std::cout << "\nAfter:" << std::endl;
+    std::cout << "Modified matrix:\n" << ansamb << std::endl;
+    std::cout << "Modified load vector:\n" << global_load << std::endl;
+#endif
+
+    // Решение системы 
+    VectorXd solution = ansamb.fullPivLu().solve(global_load);
+    std::cout << "\nSolution:" << std::endl;
+    std::cout << solution << std::endl;
+
+    std::ofstream file("matrix_linear_" + std::to_string(N) + ".txt");
+    for (int i = 1; i < solution.size(); i++) {
+        file << solution(i) << ' ';
+    }
+    file << std::endl;
+}
+
+void Solver::Execute_Cubic(double val1, double val2) {
+
+    int mat_dim = N * 3 + 2;  // +2 для граничных узлов, как в линейном случае
+
+    // Локальная матрица жёсткости
+    MatrixXd local = MatrixXd::Zero(4, 4);
+
+    // Локальный вектор нагрузки
+    VectorXd local_load(4);
+
+    // Формирование локальной матрицы жёсткости
+    local(0, 0) = -A * 37.0 / 10.0 / L + B * (-1.0) / 2.0 + C * 8. * L / 105.;
+    local(0, 1) = -A * (-189.0) / 40.0 / L + B * 57.0 / 80.0 + C * 33. * L / 560.;
+    local(0, 2) = -A * 27.0 / 20.0 / L + B * (-3.0) / 10.0 - C * 3. * L / 140.;
+    local(0, 3) = -A * (-13.0) / 40.0 / L + B * 7.0 / 80.0 + C * 19. * L / 1680.;
+
+    local(1, 0) = -A * (-189.0) / 40.0 / L + B * (-57.0) / 80.0 + C * 33. * L / 560.;
+    local(1, 1) = -A * 54.0 / 5.0 / L + C * 27. * L / 70.;
+    local(1, 2) = -A * (-297.0) / 40.0 / L + B * 81.0 / 80.0 - C * 27. * L / 560.;
+    local(1, 3) = -A * 27.0 / 20.0 / L + B * (-3.0) / 10.0 - C * 3. * L / 140.;
+
+    local(2, 0) = -A * 27.0 / 20.0 / L + B * 3.0 / 10.0 - C * 3. * L / 140.;
+    local(2, 1) = -A * (-297.0) / 40.0 / L + B * (-81.0) / 80.0 - C * 27. * L / 560.;
+    local(2, 2) = -A * 54.0 / 5.0 / L + C * 27. * L / 70.;
+    local(2, 3) = -A * (-189.0) / 40.0 / L + B * 57.0 / 80.0 + C * 33. * L / 560.;
+
+    local(3, 0) = -A * (-13.0) / 40.0 / L + B * (-7.0) / 80.0 + C * 19. * L / 1680.;
+    local(3, 1) = -A * 27.0 / 20.0 / L + B * 3.0 / 10.0 - C * 3. * L / 140.;
+    local(3, 2) = -A * (-189.0) / 40.0 / L + B * (-57.0) / 80.0 + C * 33. * L / 560.;
+    local(3, 3) = -A * 37.0 / 10.0 / L + B * 1.0 / 2.0 + C * 8. * L / 105.;
+
+    // Локальный вектор нагрузки
+    local_load(0) = -D * L / 8.0;
+    local_load(1) = -D * 3.0 * L / 8.0;
+    local_load(2) = -D * 3.0 * L / 8.0;
+    local_load(3) = -D * L / 8.0;
+
+    // Глобальные матрицы
+    MatrixXd ansamb = MatrixXd::Zero(mat_dim, mat_dim);
+    VectorXd global_load = VectorXd::Zero(mat_dim);
+
+    // Ансамблирование (со смещением на 1, как в линейной версии)
+    for (int elem = 0; elem < N; ++elem) {
+        int node_i = 1 + elem * 3; // смещение на 1
+        for (int i = 0; i < 4; ++i) {
+            for (int j = 0; j < 4; ++j) {
+                ansamb(node_i + i, node_i + j) += local(i, j);
+            }
+            global_load(node_i + i) += local_load(i);
+        }
+    }
+
+#if DEBUG
+    std::cout << std::endl << "Before:" << std::endl;
+    std::cout << "Ansamb matrix:\n" << ansamb << std::endl;
+    std::cout << "Ansamb load vector:\n" << global_load << std::endl;
+#endif
+
+    // Граничные условия
+    double u_right = val2;
+
+    // 3rd type of boundary condition
+    ansamb.row(0).setZero();
+    ansamb(0, 0) = 1;
+    ansamb(0, 1) = -1;
+    global_load(0) = 0;
+    ansamb(1, 1) -= A;
+
+    // 1st type of boundary condition
+    for (int i = 0; i < global_load.size(); ++i) {
+        global_load(i) = global_load(i) - u_right * ansamb(i, mat_dim - 1);
+    }
+    ansamb.row(mat_dim - 1).setZero();
+    ansamb.col(mat_dim - 1).setZero();
+    ansamb(mat_dim - 1, mat_dim - 1) = 1;
+    global_load(mat_dim - 1) = u_right;
+
+#if DEBUG
+    std::cout << "\nAfter:" << std::endl;
+    std::cout << "Modified matrix:\n" << ansamb << std::endl;
+    std::cout << "Modified load vector:\n" << global_load << std::endl;
+#endif
+
+    // Решение системы
+    VectorXd solution = ansamb.fullPivLu().solve(global_load);
+    std::cout << "\nSolution:" << std::endl;
+    std::cout << solution << std::endl;
+
+    std::ofstream file("matrix_cubic_" + std::to_string(N) + ".txt");
+    for (int i = 1; i < solution.size(); i++) {
+        file << solution(i) << ' ';
+    }
+    file << std::endl;
+}