Reformat ipynb + new rules for gitignore

Убрал в линейной солвере переменную C + поправил внешний вид кубического солвера
2025-09-25 01:38:30 +03:00 · 2025-09-25 01:36:55 +03:00
4 changed files with 132 additions and 81 deletions
--- a/.gitignore
+++ b/.gitignore
@@ -636,4 +636,7 @@ FodyWeavers.xsd
 *.msix
 *.msm
 *.msp
+
 *.txt
+!CMakeLists.txt
+*.png
--- a/Solver.cpp
+++ b/Solver.cpp
@@ -1,4 +1,4 @@
-#include "Header.h"
+#include "Header.h"
 #include <Eigen/Dense>
 using namespace Eigen;

@@ -16,10 +16,10 @@ void Solver::Execute_Linear(double val1, double val2) {
    // Локальный вектор нагрузки
    VectorXd local_load(2);

-    local(0, 0) = -A / L - B / 2. + C * L / 3.;
-    local(0, 1) = A / L + B / 2. + C * L / 6.;
-    local(1, 0) = A / L - B / 2. + C * L / 6.;
-    local(1, 1) = -A / L + B / 2. + C * L / 3.;
+    local(0, 0) = -A / L - B / 2.;// +C * L / 3.;
+    local(0, 1) = A / L + B / 2.; // +C * L / 6.;
+    local(1, 0) = A / L - B / 2.; // +C * L / 6.;
+    local(1, 1) = -A / L + B / 2.;// +C * L / 3.;

    local_load(0) = -D * L / 2.;
    local_load(1) = -D * L / 2.;
@@ -80,81 +80,93 @@ void Solver::Execute_Linear(double val1, double val2) {
    file << std::endl;
 }

-// TODO: переделать под себя
 void Solver::Execute_Cubic(double val1, double val2) {

    int mat_dim = 1 + N * 3;

+    // 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;
+    local(0, 1) = -A * (-189.0) / 40.0 / L + B * 57.0 / 80.0;
+    local(0, 2) = -A * 27.0 / 20.0 / L + B * (-3.0) / 10.0;
+    local(0, 3) = -A * (-13.0) / 40.0 / L + B * 7.0 / 80.0;
+
+    local(1, 0) = -A * (-189.0) / 40.0 / L + B * (-57.0) / 80.0;
+    local(1, 1) = -A * 54.0 / 5.0 / L;
+    local(1, 2) = -A * (-297.0) / 40.0 / L + B * 81.0 / 80.0;
+    local(1, 3) = -A * 27.0 / 20.0 / L + B * (-3.0) / 10.0;
+
+    local(2, 0) = -A * 27.0 / 20.0 / L + B * 3.0 / 10.0;
+    local(2, 1) = -A * (-297.0) / 40.0 / L + B * (-81.0) / 80.0;
+    local(2, 2) = -A * 54.0 / 5.0 / L;
+    local(2, 3) = -A * (-189.0) / 40.0 / L + B * 57.0 / 80.0;
+
+    local(3, 0) = -A * (-13.0) / 40.0 / L + B * (-7.0) / 80.0;
+    local(3, 1) = -A * 27.0 / 20.0 / L + B * 3.0 / 10.0;
+    local(3, 2) = -A * (-189.0) / 40.0 / L + B * (-57.0) / 80.0;
+    local(3, 3) = -A * 37.0 / 10.0 / L + B * 1.0 / 2.0;
+
+    // Формирование локального вектора 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;
+
    // Глобальная матрица жёсткости
-    Eigen::MatrixXd Amat(mat_dim, mat_dim);
+    MatrixXd ansamb = MatrixXd::Zero(mat_dim, mat_dim);

    // Глобальный вектор нагрузок
-    Eigen::VectorXd b(mat_dim);
-    Amat.setZero();
-    b.setZero();
+    VectorXd global_load = VectorXd::Zero(mat_dim);

-    // Assemble matrix
-    for (int i = 0; i < mat_dim - 3; i += 3) {
-        Amat(i, i + 0) -= A * 37.0 / 10.0 / L;
-        Amat(i, i + 1) -= A * (-189.0) / 40.0 / L;
-        Amat(i, i + 2) -= A * 27.0 / 20.0 / L;
-        Amat(i, i + 3) -= A * (-13.0) / 40.0 / L;
-        Amat(i + 1, i + 0) -= A * (-189.0) / 40.0 / L;
-        Amat(i + 1, i + 1) -= A * 54.0 / 5.0 / L;
-        Amat(i + 1, i + 2) -= A * (-297.0) / 40.0 / L;
-        Amat(i + 1, i + 3) -= A * 27.0 / 20.0 / L;
-        Amat(i + 2, i + 0) -= A * 27.0 / 20.0 / L;
-        Amat(i + 2, i + 1) -= A * (-297.0) / 40.0 / L;
-        Amat(i + 2, i + 2) -= A * 54.0 / 5.0 / L;
-        Amat(i + 2, i + 3) -= A * (-189.0) / 40.0 / L;
-        Amat(i + 3, i + 0) -= A * (-13.0) / 40.0 / L;
-        Amat(i + 3, i + 1) -= A * 27.0 / 20.0 / L;
-        Amat(i + 3, i + 2) -= A * (-189.0) / 40.0 / L;
-        Amat(i + 3, i + 3) -= A * 37.0 / 10.0 / L;
+    // Ансамблирование
+    for (int elem = 0; elem < N; ++elem) {
+        int node_i = elem * 3;

-        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;
+        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);
+        }
    }

-    // AssembLe vector
-    for (int i = 0; i < mat_dim - 3; i += 3) {
-        b(i) -= D * L / 8.0;
-        b(i + 1) -= D * 3.0 * L / 8.0;
-        b(i + 2) -= D * 3.0 * L / 8.0;
-        b(i + 3) -= D * L / 8.0;
-    }
+#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

-    Amat.row(0).setZero();
-    Amat(0, 0) = L / 3.0 + 1;
-    Amat(0, 1) = -1;
-    b(0) = 0;
+    // Граничные условия
+    double u_right = val2;

-    Amat.row(mat_dim - 1).setZero();
-    Amat(mat_dim - 1, mat_dim - 1) = 1;
-    b(mat_dim - 1) = val2;
+    ansamb.row(0).setZero();
+    ansamb(0, 0) = L / 3.0 + 1;
+    ansamb(0, 1) = -1;
+    global_load(0) = 0;
+
+    ansamb.row(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 = Amat.fullPivLu().solve(b);
+    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 = 0; i < solution.size(); i++) {
        file << solution(i) << ' ';
    }
    file << std::endl;
-}
+}
--- a/Solver.h
+++ b/Solver.h
@@ -2,13 +2,13 @@

 class Solver {
 private:
-	// <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20> <20><>
+	// Коэффициенты в ДУ
 	double A, B, C, D;
-	// <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
+	// Длина конечного элемента
 	double L;
-	// <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
+	// Количество конечных элементов
 	int N;
-	// <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> <20><>
+	// Границы частного решения ДУ
 	int upper, lower;
 public:
 	Solver(double _A, double _B, double _C, double _D, int _N, int _l, int _u);
--- a/graphics.ipynb
+++ b/graphics.ipynb
@@ -8,6 +8,34 @@
    "# 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,
@@ -37,7 +65,7 @@
   "id": "8af07a56",
   "metadata": {},
   "source": [
-    "## Solution of $5u'' + 4u' + 1 = 0, u'(0) = u(0), u(10) = 5$"
+    "### Solution of $5u'' + 4u' + 1 = 0, u'(0) = u(0), u(10) = 5$"
   ]
  },
  {
@@ -56,7 +84,7 @@
   "id": "efac514a",
   "metadata": {},
   "source": [
-    "## Linear element"
+    "### Linear element"
   ]
  },
  {
@@ -78,8 +106,8 @@
    "    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(\"Y\")\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",
@@ -92,7 +120,7 @@
   "id": "d9a38740",
   "metadata": {},
   "source": [
-    "## Cubic element"
+    "### Cubic element"
   ]
  },
  {
@@ -110,11 +138,11 @@
    "    y = np.fromstring(data_str, sep=' ')\n",
    "    y_real = u(x)\n",
    "\n",
-    "    plt.plot(x, y, label=\"Cubic element solution\", color=\"green\")\n",
+    "    plt.plot(x, y, label=\"Cubic element solution\", color=\"orange\")\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(\"Y\")\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",
@@ -138,9 +166,8 @@
   "metadata": {},
   "outputs": [],
   "source": [
-    "N = 20\n",
-    "show_plot_linear(\"matrix_linear.txt\", N)\n",
-    "show_plot_cubic(\"matrix_cubic.txt\", N)"
+    "show_plot_linear(linear_file, N)\n",
+    "show_plot_cubic(cubic_file, N)"
   ]
  },
  {
@@ -154,7 +181,7 @@
  {
   "cell_type": "code",
   "execution_count": null,
-   "id": "e0e9266d",
+   "id": "31de1104",
   "metadata": {},
   "outputs": [],
   "source": [
@@ -162,8 +189,16 @@
    "    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\n",
-    "\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",
@@ -192,13 +227,14 @@
   "metadata": {},
   "outputs": [],
   "source": [
-    "show_error(\"matrix_linear.txt\", \"linear_real_y_20.txt\")"
+    "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": ".venv",
+   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
Author	SHA1	Message	Date
ParkSuMin	cac280deb1	Reformat ipynb + new rules for gitignore	2025-09-25 01:38:30 +03:00
ParkSuMin	b8bc3f705a	Убрал в линейной солвере переменную C + поправил внешний вид кубического солвера	2025-09-25 01:36:55 +03:00