Первая лаба

Author: Mis-prog

lab1/CMakeLists.txt

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+cmake_minimum_required(VERSION 3.25)
+project(Lab1)
+
+set(CMAKE_CXX_STANDARD 17)
+
+set(optimizations "-Ofast")
+
+set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${optimizations}")
+
+add_executable(Lab1
+        src/main.cpp
+        src/task1.h
+        src/task2.h
+        src/task3.h
+        src/task4.h
+        src/task5.h
+        src/task6.h
+)

lab1/data/Maple разложение в ряд.mw

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+#include "task1.h"
+#include "task2.h"
+#include "task3.h"
+#include "task4.h"
+#include "task5.h"
+#include "task6.h"
+
+
+int main() {
+    SetConsoleOutputCP(CP_UTF8);
+/*    int n=1;
+    while (n!=0){
+        switch (n) {
+            case 1:
+                task1_main(10);
+                cin >> n;
+                break;
+            case 2:
+                task2_main(10);
+                cin >> n;
+                break;
+            case 3:
+                task3_main(10);
+                cin >> n;
+                break;
+            case 6:
+                task6_main(5808);
+                cin >> n;
+                break;
+        }
+    }*/
+//    int n0 = task1_main(20);
+//    task2_main(n0);
+//    task3_main(n0);
+//task4_main();
+    task5_main();
+//    task6_main();
+    return 0;
+}

lab1/data/Презентация к ЛР-1.pdf

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+import matplotlib.pyplot as pl
+import pandas as pd
+
+
+def plot1():
+    data = pd.read_csv("D:/5sem/numerical/Lab1/cmake-build-debug/task1.txt", sep=" ", names=[1, 2])
+    pl1 = pl
+    pl1.plot(data[1], data[2])
+    pl1.axhline(y=0.0002, color='red', linestyle='--')
+    pl1.xlabel("Количесто узлов, n")
+    pl1.ylabel("Tочность")
+    pl1.title("Зависимость Δn")
+    pl1.grid(True)
+    pl1.show()
+
+
+def plot1_2():
+    data2 = pd.read_csv("D:/5sem/numerical/Lab1/cmake-build-debug/task1_2.txt", sep=" ", names=[1, 2])
+    pl2 = pl
+    pl2.figure(figsize=(10, 5))
+    pl2.plot(data2[1], data2[2])
+    pl2.xlabel("x")
+    pl2.ylabel("Tочность")
+    pl2.title("Ошибка приближения")
+    pl2.grid(True)
+    pl2.show()
+
+
+def plot2():
+    data3 = pd.read_csv("D:/5sem/numerical/Lab1/cmake-build-debug/task2.txt", sep=" ", names=[1, 2])
+    pl3 = pl
+    pl3.figure(figsize=(10, 5))
+    pl3.plot(data3[1], data3[2])
+    pl3.xlabel("x")
+    pl3.ylabel("Tочность")
+    pl3.title("Ошибка приближения")
+    pl3.grid(True)
+    pl3.show()
+
+
+def check_accur():
+    data2 = pd.read_csv("D:/5sem/numerical/Lab1/cmake-build-debug/task1_2.txt", sep=" ", names=[1, 2])
+    data3 = pd.read_csv("D:/5sem/numerical/Lab1/cmake-build-debug/task2.txt", sep=" ", names=[1, 2])
+    pl.figure(figsize=(10, 5))
+    pl.subplot(121)
+    pl.plot(data2[1], data2[2])
+    pl.subplot(122)
+    pl.plot(data3[1], data3[2])
+    pl.show()
+
+def plot3():
+    data1 = pd.read_csv("D:/5sem/numerical/Lab1/cmake-build-debug/task1_2.txt", sep=" ", names=[1, 2])
+    data2 = pd.read_csv("D:/5sem/numerical/Lab1/cmake-build-debug/task3.txt", sep=" ", names=[1, 2])
+    pl.figure(figsize=(11, 5))
+    pl.subplot(121)
+    pl.plot(data1[1], data1[2])
+    pl.subplot(122)
+    pl.plot(data2[1], data2[2])
+    pl.show()
+
+
+def plot6():
+    data = pd.read_csv("D:/5sem/numerical/Lab1/cmake-build-debug/task6.txt", sep=" ", names=[1, 2])
+    pl6 = pl
+    pl6.plot(data[1], data[2])
+    pl6.xlabel("x")
+    pl6.ylabel("Tочность")
+    pl6.title("Ошибка приближения")
+    pl6.grid(True)
+    pl6.show()
+
+plot3()

lab1/data/ЧМ_ЛР-1 (задания).pdf

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+import matplotlib.pyplot as pl
+import pandas as pd
+
+
+def plot1():
+    data = pd.read_csv("D:/5sem/numerical/practice/labs/Lab1/cmake-build-debug/task1_1.txt", sep=" ", names=[1, 2])
+    pl1 = pl
+    pl1.plot(data[1], data[2],color='red')
+#    pl1.axhline(y=0.0002, color='red', linestyle='--')
+    pl1.xlabel("Количесто узлов, n")
+    pl1.ylabel("Tочность")
+    pl1.title("Зависимость точности от количества узлов")
+    pl1.grid(True)
+    pl1.show()
+
+
+def plot1_2():
+    data2 = pd.read_csv("D:/5sem/numerical/practice/labs/Lab1/cmake-build-debug/task1_2.txt", sep=" ", names=[1, 2])
+    pl2 = pl
+    pl2.figure(figsize=(10, 5))
+    pl2.plot(data2[1], data2[2])
+    pl2.xlabel("x")
+    pl2.ylabel("Tочность")
+    pl2.title("Ошибка приближения")
+    pl2.grid(True)
+    pl2.show()
+
+plot1();plot1_2();

lab1/data/логарифмические координаты.pdf

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+import matplotlib.pyplot as pl
+import pandas as pd
+
+data_equals = pd.read_csv("D:/5sem/numerical/practice/labs/Lab1/cmake-build-debug/task1_plot.txt", sep=" ", names=[1, 2])
+data_notequals = pd.read_csv("D:/5sem/numerical/practice/labs/Lab1/cmake-build-debug/task2_plot.txt", sep=" ", names=[1, 2])
+data_notequalsnode=pd.read_csv("D:/5sem/numerical/practice/labs/Lab1/cmake-build-debug/notequalsnode.txt", sep=" ", names=[1, 2])
+
+pl.plot(data_equals[1],data_equals[2],linewidth=4,color='green',label="Равномерная сетка")
+pl.plot(data_notequals[1],data_notequals[2],linewidth=1,color='black',label="Неравномерная сетка")
+pl.scatter(data_notequalsnode[1],data_notequalsnode[2],color='red',label="Узлы")
+pl.title("График интерполяции")
+pl.xlabel("X")
+pl.ylabel("Y")
+pl.legend(loc='upper left')
+pl.show()

lab1/data/отчет.docx

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+import matplotlib.pyplot as pl
+import pandas as pd
+
+
+def plot1():
+    data = pd.read_csv("D:/5sem/numerical/practice/labs/Lab1/cmake-build-debug/task3.txt", sep=" ", names=[1, 2])
+    pl1 = pl
+    pl1.plot(data[1], data[2],color='red')
+    #    pl1.axhline(y=0.0002, color='red', linestyle='--')
+    pl1.xlabel("x")
+    pl1.ylabel("Tочность")
+    pl1.title("Точность на n=10")
+    pl1.grid(True)
+    pl1.show()
+
+plot1();

lab1/data/пояснения к ЛР1.docx

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+import matplotlib.pyplot as pl
+import pandas as pd
+
+
+def plot1():
+    data = pd.read_csv("D:/5sem/numerical/practice/labs/Lab1/cmake-build-debug/buap_n_vs_err.txt", sep=" ", names=[1, 2])
+    pl1 = pl
+    pl1.plot(data[1], data[2],color='red')
+    #    pl1.axhline(y=0.0002, color='red', linestyle='--')
+    pl1.xlabel("n")
+    pl1.ylabel("Tочность")
+    pl1.title("Зависимость количества узлов от точности")
+    pl1.grid(True)
+    pl1.show()
+
+def plot2():
+    data = pd.read_csv("D:/5sem/numerical/practice/labs/Lab1/cmake-build-debug/node_task5.txt", sep=" ", names=[1, 2])
+    data_line = pd.read_csv("D:/5sem/numerical/practice/labs/Lab1/cmake-build-debug/task1_plot.txt", sep=" ", names=[1, 2])
+    pl1 = pl
+    pl1.plot(data_line[1],data_line[2])
+    pl1.scatter(data[1], data[2],color='red')
+    #    pl1.axhline(y=0.0002, color='red', linestyle='--')
+    pl1.xlabel("n")
+    pl1.ylabel("Tочность")
+    pl1.title("Зависимость количества узлов от точности")
+    pl1.grid(True)
+    pl1.show()
+plot2()

lab1/src/main.cpp

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+import matplotlib.pyplot as pl
+import pandas as pd
+
+
+def plot6_1():
+    data = pd.read_csv("D:/5sem/numerical/practice/labs/Lab1/cmake-build-debug/test6.txt", sep=" ", names=[1, 2],nrows=100)
+    pl6 = pl
+    pl6.plot(data[1], data[2])
+    pl6.xlabel("Количество сплайнов")
+    pl6.ylabel("Tочность")
+    pl6.title("Минимальное количество сплайнов")
+    pl6.grid(True)
+    pl6.show()
+def plot6_2():
+    data = pd.read_csv("D:/5sem/numerical/practice/labs/Lab1/cmake-build-debug/task6.txt", sep=" ", names=[1, 2])
+    pl6 = pl
+    pl6.plot(data[1], data[2])
+    pl6.xlabel("x")
+    pl6.ylabel("Tочность")
+    pl6.title("Ошибка приближения")
+    pl6.grid(True)
+    pl6.show()
+
+plot6_1();plot6_2();

lab1/src/plot/plotTask1.py

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+#include <iostream>
+#include <cmath>
+#include <vector>
+#include <windows.h>
+#include <fstream>
+#include <cstdlib>
+#include <string>
+
+using namespace std;
+
+const double a = 0, b = 1;
+const double pi = acos(-1.0);
+const double epsilon = 2 * 1e-4;
+
+double acos_foo(double x) {
+    return x*x*acos(0.9*x);
+}
+
+double lagrange(vector<double> &x, vector<double> &y, double _x, int n) {
+    double result = 0.0;
+
+    for (int i = 0; i <= n; i++) {
+        double P = 1.0;
+
+        for (int j = 0; j <= n; j++)
+            if (j != i)
+                P *= (_x - x[j]) / (x[i] - x[j]);
+
+        result += P * y[i];
+    }
+    return result;
+}
+
+void nodeFillEquals(vector<double> &x, vector<double> &y, int n) {
+    double a = 0, b = 1;
+    double h = (b - a) / n;
+    x[0] = a;
+    y[0] = acos_foo(x[0]);
+    for (int i = 1; i <= n; i++) {
+        x[i] = x[i - 1] + h;
+        y[i] = acos_foo(x[i]);
+    }
+}
+
+double checkAccuracy(vector<double> &x, vector<double> &y, int n) {
+    double a = 0, b = 1;
+    double h_accurace = (b - a) / (double) 10e5;
+    double sup = -1000, diff, current = 0;
+    while (current <= b) {
+        diff = abs(acos_foo(current) - lagrange(x, y, current, n));
+        if (diff > sup) {
+            sup = diff;
+        }
+        current += h_accurace;
+    }
+    return sup;
+}
+
+int task1_1(int n) {
+    int bestNode = 0;
+    double current_rasn = 0;
+    bool node_opt = 0;
+    vector<double> x(n + 1, 0), y(n + 1, 0);
+    ofstream out1_1;
+    out1_1.open("task1_1.txt");
+    for (int i = 1; i <= n; i++) {
+        nodeFillEquals(x, y, i);
+        current_rasn = checkAccuracy(x, y, i);
+        out1_1 << i << " " << current_rasn << endl;
+        if (current_rasn < epsilon and !node_opt) {
+            bestNode = i;
+            node_opt = 1;
+        }
+    }
+    out1_1.close();
+    return bestNode;
+}
+
+double task1_2(int n) {
+    ofstream out1_2, out1_2_3;
+    out1_2.open("task1_2.txt");
+    out1_2_3.open("task1_plot.txt");
+    double a = 0, b = 1;
+    vector<double> x(n + 1, 0), y(n + 1, 0);
+    nodeFillEquals(x, y, n);
+    double h_accurace = (b - a) / (double) 1e5;
+    double x_current = 0, diff, sup = -1000;
+    double y_cur = 0;
+    while (x_current < b) {
+        y_cur = lagrange(x, y, x_current, n);
+        diff = abs(acos_foo(x_current) - y_cur);
+        out1_2 << x_current << " " << diff << endl;
+        out1_2_3 << x_current << " " << y_cur << endl;
+        if (diff > sup) {
+            sup = diff;
+        }
+        x_current += h_accurace;
+    }
+    out1_2.close();
+    out1_2_3.close();
+    return sup;
+}
+
+
+int task1_main(int n) {
+    int n0 = task1_1(n);
+    cout << "n0=" << n0 << endl;
+    cout << "Интерполяция Лагранжем(равномерная сетка): " << task1_2(n0) << endl;
+    system("python D:/5sem/numerical/practice/labs/Lab1/src/plot/plot_1.py");
+    return n0;
+}