├── Books ├── [HIT教材]计算方法学习指导(吴勃英).pdf ├── 数值分析原理_吴勃英.pdf └── 科学出版社 │ ├── 前言.doc │ ├── 第1章.doc │ ├── 第2章.doc │ ├── 第3章.doc │ ├── 第4章.doc │ ├── 第5章.doc │ ├── 第6章.doc │ └── 第7章.doc ├── Labs ├── 2020春-《计算方法》上机实验（一）插值.docx ├── 2020春计算方法实验指导及实验报告模板.doc ├── Lab1 │ ├── Lagrange.cpp │ ├── figure.ipynb │ ├── ~$实验报告1.docx │ ├── 实验报告1.docx │ └── 实验报告1.pdf ├── Lab2 │ ├── Romberg.cpp │ ├── 实验报告2.docx │ └── 实验报告2.pdf ├── Lab3 │ ├── Runge_Kutta.cpp │ └── 实验报告3.docx ├── Lab4 │ ├── Newton.cpp │ ├── figure.ipynb │ └── 实验报告4.docx ├── Lab5 │ ├── Gauss_1.cpp │ ├── Gauss_2.cpp │ └── 实验报告5.docx ├── 流程图 │ ├── 分段线性插值流程图.jpg │ ├── 四阶龙格-库塔流程图.jpg │ ├── 多项式最小二乘法流程图.jpg │ ├── 拉格朗日插值法流程图.jpg │ ├── 牛顿迭代法流程图.jpg │ └── 高斯列主消去法流程图.jpg └── 计算方法实验报告1183710109郭茁宁.docx ├── Notes ├── 第1章.pdf ├── 第2章.pdf ├── 第3章.pdf ├── 第4章.pdf ├── 第5章.pdf ├── 第6章.pdf └── 第7章.pdf ├── PPTs ├── 插值与逼近.ppt ├── 数值分析原理-第三章正文.pdf ├── 数值分析原理-第四章正文-2.pdf ├── 数值分析原理第六章-正文-3.pdf ├── 第三章---2（网课）.pdf ├── 第四章-1.pdf ├── 线性方程组的数值解法.ppt ├── 绪论.ppt └── 非线性方程数值解法.ppt └── 大作业 ├── 1183710109+郭茁宁_课程论文.docx ├── 1183710109+郭茁宁_课程论文 ├── 1183710109+郭茁宁_课程论文.pdf ├── Gauss_1.cpp ├── Gauss_2.cpp ├── Lagrange.cpp ├── Newton.cpp ├── Romberg.cpp ├── Runge_Kutta.cpp ├── figure_1.ipynb └── figure_2.ipynb ├── 2020春季计算方法课程期末考核方案0623(1).pdf ├── 《计算方法》课程论文封面.doc └── 《计算方法》课程论文封面.pdf /Books/[HIT教材]计算方法学习指导(吴勃英).pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gzn00417/2020Spring-Computational-Method/11c99df6e18702d6c34556556098b75ead5a6823/Books/[HIT教材]计算方法学习指导(吴勃英).pdf -------------------------------------------------------------------------------- /Books/数值分析原理_吴勃英.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gzn00417/2020Spring-Computational-Method/11c99df6e18702d6c34556556098b75ead5a6823/Books/数值分析原理_吴勃英.pdf -------------------------------------------------------------------------------- /Books/科学出版社/前言.doc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gzn00417/2020Spring-Computational-Method/11c99df6e18702d6c34556556098b75ead5a6823/Books/科学出版社/前言.doc -------------------------------------------------------------------------------- /Books/科学出版社/第1章.doc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gzn00417/2020Spring-Computational-Method/11c99df6e18702d6c34556556098b75ead5a6823/Books/科学出版社/第1章.doc -------------------------------------------------------------------------------- /Books/科学出版社/第2章.doc: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gzn00417/2020Spring-Computational-Method/11c99df6e18702d6c34556556098b75ead5a6823/Books/科学出版社/第2章.doc -------------------------------------------------------------------------------- /Books/科学出版社/第3章.doc: 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-------------------------------------------------------------------------------- https://raw.githubusercontent.com/gzn00417/2020Spring-Computational-Method/11c99df6e18702d6c34556556098b75ead5a6823/Labs/2020春计算方法实验指导及实验报告模板.doc -------------------------------------------------------------------------------- /Labs/Lab1/Lagrange.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #define N1 1 // n amount 4 | #define N2 4 // x amount 5 | #define N3 20 // n max 6 | 7 | int Ns[N1] = {3}; 8 | double x[N2] = {5, 50, 115, 185}; 9 | double l = -1.0; 10 | double r = 1.0; 11 | 12 | double X(int k, int n) { return (k + 13) * (k + 13); } 13 | 14 | double Y(double x) { return sqrt(x); } 15 | 16 | int main() { 17 | for (int i = 0; i < N2; i++) printf("\tx=%.2lf", x[i]); 18 | printf("\n"); 19 | for (int i = 0; i < N1; i++) { 20 | double a[N3 + 1], b[N3 + 1]; 21 | int n = Ns[i]; 22 | for (int k = 0; k <= n; k++) { 23 | a[k] = X(k, n); // x 24 | b[k] = Y(a[k]); // y 25 | } 26 | printf("n=%d", n); 27 | for (int p = 0; p < N2; p++) { 28 | double y = 0.0; 29 | for (int k = 0; k <= n; k++) { 30 | double l = 1.0; 31 | for (int j = 0; j <= n; j++) { 32 | if (j != k) l *= (x[p] - a[j]) / (a[k] - a[j]); 33 | } 34 | y += l * b[k]; 35 | } 36 | printf("\t%.6lf", y); 37 | } 38 | printf("\n"); 39 | } 40 | printf("Actual"); 41 | for (int p = 0; p < N2; p++) printf("\t%.6lf", Y(x[p])); 42 | return 0; 43 | } -------------------------------------------------------------------------------- /Labs/Lab1/figure.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 6, 6 | "metadata": {}, 7 | "outputs": [], 8 | "source": [ 9 | "import math\n", 10 | "from matplotlib import pyplot as plt\n", 11 | "import seaborn as sns\n", 12 | "import numpy as np\n", 13 | "import pandas as pd\n", 14 | "%matplotlib inline\n", 15 | "sns.set_style(\"darkgrid\")" 16 | ] 17 | }, 18 | { 19 | "cell_type": "code", 20 | "execution_count": 7, 21 | "metadata": {}, 22 | "outputs": [ 23 | { 24 | "output_type": "execute_result", 25 | "data": { 26 | "text/plain": "[]" 27 | }, 28 | "metadata": {}, 29 | "execution_count": 7 30 | }, 31 | { 32 | "output_type": "display_data", 33 | "data": { 34 | "text/plain": "
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37 | }, 38 | "metadata": {} 39 | } 40 | ], 41 | "source": [ 42 | "x = np.linspace(-1, 1, 100)\n", 43 | "plt.plot(x, 1 / (1 + x*x))" 44 | ] 45 | }, 46 | { 47 | "cell_type": "code", 48 | "execution_count": 33, 49 | "metadata": {}, 50 | "outputs": [ 51 | { 52 | "output_type": "execute_result", 53 | "data": { 54 | "text/plain": "([], )" 55 | }, 56 | "metadata": {}, 57 | "execution_count": 33 58 | }, 59 | { 60 | "output_type": "display_data", 61 | "data": { 62 | "text/plain": "
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65 | }, 66 | "metadata": {} 67 | } 68 | ], 69 | "source": [ 70 | "n = 30\n", 71 | "x = np.arange(n+1);\n", 72 | "z = (2*x+1)*math.pi/(2*(n+1))\n", 73 | "y = np.cos(z)\n", 74 | "ax = plt.scatter(y, np.zeros(n+1))\n", 75 | "plt.yticks([])" 76 | ] 77 | }, 78 | { 79 | "cell_type": "code", 80 | "execution_count": null, 81 | "metadata": {}, 82 | "outputs": [], 83 | "source": [] 84 | } 85 | ], 86 | "metadata": { 87 | "language_info": { 88 | "codemirror_mode": { 89 | "name": "ipython", 90 | "version": 3 91 | }, 92 | "file_extension": ".py", 93 | "mimetype": "text/x-python", 94 | "name": "python", 95 | "nbconvert_exporter": "python", 96 | "pygments_lexer": "ipython3", 97 | "version": "3.6.8-final" 98 | }, 99 | "orig_nbformat": 2, 100 | "kernelspec": { 101 | "name": "python36864bit2eb17439148c485399fa2f77fed1b772", 102 | "display_name": "Python 3.6.8 64-bit" 103 | } 104 | }, 105 | "nbformat": 4, 106 | "nbformat_minor": 2 107 | } -------------------------------------------------------------------------------- /Labs/Lab1/~$实验报告1.docx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gzn00417/2020Spring-Computational-Method/11c99df6e18702d6c34556556098b75ead5a6823/Labs/Lab1/~$实验报告1.docx -------------------------------------------------------------------------------- /Labs/Lab1/实验报告1.docx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gzn00417/2020Spring-Computational-Method/11c99df6e18702d6c34556556098b75ead5a6823/Labs/Lab1/实验报告1.docx -------------------------------------------------------------------------------- /Labs/Lab1/实验报告1.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gzn00417/2020Spring-Computational-Method/11c99df6e18702d6c34556556098b75ead5a6823/Labs/Lab1/实验报告1.pdf -------------------------------------------------------------------------------- /Labs/Lab2/Romberg.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #include 4 | using namespace std; 5 | #define N 20 6 | 7 | int n; 8 | long double a, b, e, T[N][N] = {{0.0}}; 9 | 10 | long double f(long double x) { return 1.0 / (1.0 + x); } 11 | long double x(int i, long double h) { return a + h * i; } 12 | 13 | int main() { 14 | scanf("%llf%llf%llf%d", &a, &b, &e, &n); 15 | int k = 0; 16 | for (; k < n; k++) { 17 | long double h = (b - a) / pow(2, k), sum = 0.0; 18 | for (int i = 1; i <= pow(2, k) - 1; i++) sum += f(x(i, h)); 19 | T[k][0] = 0.5 * h * (f(a) + 2 * sum + f(b)); 20 | for (int m = 1; m <= k; m++) 21 | T[k][m] = 22 | (pow(4, m) * T[k][m - 1] - T[k - 1][m - 1]) / (pow(4, m) - 1); 23 | for (int m = 0; m <= k; m++) printf("%.7Lf\t", T[k][m]); 24 | cout << endl; 25 | if (k > 0 && fabs(T[k][0] - T[k][k]) <= e) break; 26 | } 27 | return 0; 28 | } 29 | -------------------------------------------------------------------------------- /Labs/Lab2/实验报告2.docx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gzn00417/2020Spring-Computational-Method/11c99df6e18702d6c34556556098b75ead5a6823/Labs/Lab2/实验报告2.docx -------------------------------------------------------------------------------- /Labs/Lab2/实验报告2.pdf: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gzn00417/2020Spring-Computational-Method/11c99df6e18702d6c34556556098b75ead5a6823/Labs/Lab2/实验报告2.pdf -------------------------------------------------------------------------------- /Labs/Lab3/Runge_Kutta.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #include 4 | using namespace std; 5 | 6 | int n; 7 | double a, b, fa; 8 | 9 | double f(double x, double y) { return -y * y; } 10 | double f_(double x) { return 1.0 / (x + 1.0); } 11 | 12 | int main() { 13 | scanf("%lf%lf%lf%d", &a, &b, &fa, &n); 14 | double x = a, y = fa, h = (b - a) / n; 15 | for (int i = 1; i <= n; i++) { 16 | double k1 = h * f(x, y); 17 | double k2 = h * f(x + h / 2, y + k1 / 2); 18 | double k3 = h * f(x + h / 2, y + k2 / 2); 19 | double k4 = h * f(x + h, y + k3); 20 | x += h; 21 | y += 1.0 / 6.0 * (k1 + 2 * k2 + 2 * k3 + k4); 22 | printf("%.2lf\t%lf\t%.2lf\n", x, y, fabs(f_(x) - y)); 23 | } 24 | return 0; 25 | } -------------------------------------------------------------------------------- /Labs/Lab3/实验报告3.docx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gzn00417/2020Spring-Computational-Method/11c99df6e18702d6c34556556098b75ead5a6823/Labs/Lab3/实验报告3.docx -------------------------------------------------------------------------------- /Labs/Lab4/Newton.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #include 4 | using namespace std; 5 | 6 | double x, e1, e2; 7 | int n; 8 | 9 | double f(double x) { return cos(x) - x; } 10 | double df(double x) { return -sin(x) - 1; } 11 | 12 | int main() { 13 | scanf("%lf%lf%lf%d", &x, &e1, &e2, &n); 14 | for (int i = 1; i <= n; i++) { 15 | double F = f(x), DF = df(x); 16 | if (fabs(F) < e1) { 17 | printf("%lf", x); 18 | return 0; 19 | } 20 | if (fabs(DF) < e2) { 21 | printf("Failed"); 22 | return 0; 23 | } 24 | double x1 = x - F / DF; 25 | double tol = fabs(x - x1); 26 | if (tol < e1) { 27 | printf("%lf", x1); 28 | return 0; 29 | } 30 | x = x1; 31 | printf("%lf, ", x1); 32 | } 33 | printf("Failed"); 34 | return 0; 35 | } -------------------------------------------------------------------------------- /Labs/Lab4/figure.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 7, 6 | "metadata": {}, 7 | "outputs": [], 8 | "source": [ 9 | "import math\n", 10 | "from matplotlib import pyplot as plt\n", 11 | "import seaborn as sns\n", 12 | "import numpy as np\n", 13 | "import pandas as pd\n", 14 | "%matplotlib inline\n", 15 | "sns.set_style(\"darkgrid\")" 16 | ] 17 | }, 18 | { 19 | "cell_type": "code", 20 | "execution_count": 25, 21 | "metadata": {}, 22 | "outputs": [ 23 | { 24 | "output_type": "execute_result", 25 | "data": { 26 | "text/plain": "" 27 | }, 28 | "metadata": {}, 29 | "execution_count": 25 30 | }, 31 | { 32 | "output_type": "display_data", 33 | "data": { 34 | "text/plain": "
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4MPH2q3j13s4UnzvPQ4s38OqyvZSUadlmWzBYrJhRcfbsWcaMGcPx48fx8PBg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\n" 37 | }, 38 | "metadata": {} 39 | } 40 | ], 41 | "source": [ 42 | "x = np.linspace(0.73, 0.79, 100)\n", 43 | "plt.plot(x, np.cos(x) - x)\n", 44 | "plt.plot(x, np.zeros(x.shape))\n", 45 | "a = np.array([0.785398163, 0.739536, 0.739085, 0.739085])\n", 46 | "plt.scatter(a, np.cos(a) - a, s=15, c=\"red\")" 47 | ] 48 | }, 49 | { 50 | "cell_type": "code", 51 | "execution_count": null, 52 | "metadata": {}, 53 | "outputs": [], 54 | "source": [] 55 | } 56 | ], 57 | "metadata": { 58 | "language_info": { 59 | "codemirror_mode": { 60 | "name": "ipython", 61 | "version": 3 62 | }, 63 | "file_extension": ".py", 64 | "mimetype": "text/x-python", 65 | "name": "python", 66 | "nbconvert_exporter": "python", 67 | "pygments_lexer": "ipython3", 68 | "version": "3.6.8-final" 69 | }, 70 | "orig_nbformat": 2, 71 | "kernelspec": { 72 | "name": "python36864bit2eb17439148c485399fa2f77fed1b772", 73 | "display_name": "Python 3.6.8 64-bit" 74 | } 75 | }, 76 | "nbformat": 4, 77 | "nbformat_minor": 2 78 | } -------------------------------------------------------------------------------- /Labs/Lab4/实验报告4.docx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gzn00417/2020Spring-Computational-Method/11c99df6e18702d6c34556556098b75ead5a6823/Labs/Lab4/实验报告4.docx -------------------------------------------------------------------------------- /Labs/Lab5/Gauss_1.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #include 4 | using namespace std; 5 | #define N 10 6 | 7 | int n; 8 | double a[N][N], b[N], x[N]; 9 | 10 | int main() { 11 | scanf("%d", &n); 12 | for (int i = 1; i <= n; i++) 13 | for (int j = 1; j <= n; j++) scanf("%lf", &a[i][j]); 14 | for (int i = 1; i <= n; i++) scanf("%lf", &b[i]); 15 | for (int k = 1; k < n; k++) { 16 | int p = k; 17 | double maxabs = fabs(a[k][k]); 18 | for (int j = k + 1; j <= n; j++) 19 | if (fabs(a[j][k]) - maxabs > 0) { 20 | p = j; 21 | maxabs = fabs(a[j][k]); 22 | } 23 | if (a[p][k] == 0) { 24 | printf("Singular"); 25 | return 0; 26 | } 27 | if (p != k) { 28 | double tmp; 29 | for (int j = 1; j <= n; j++) { 30 | tmp = a[p][j]; 31 | a[p][j] = a[k][j]; 32 | a[k][j] = tmp; 33 | } 34 | tmp = b[p]; 35 | b[p] = b[k]; 36 | b[k] = tmp; 37 | } 38 | for (int i = k + 1; i <= n; i++) { 39 | double m_ik = a[i][k] / a[k][k]; 40 | for (int j = k + 1; j <= n; j++) a[i][j] -= a[k][j] * m_ik; 41 | b[i] -= b[k] * m_ik; 42 | } 43 | } 44 | if (a[n][n] == 0) { 45 | printf("Singular"); 46 | return 0; 47 | } 48 | x[n] = b[n] / a[n][n]; 49 | for (int k = n - 1; k >= 1; k--) { 50 | double sigma = 0.0; 51 | for (int j = k + 1; j <= n; j++) sigma += a[k][j] * x[j]; 52 | x[k] = (b[k] - sigma) / a[k][k]; 53 | } 54 | for (int i = 1; i <= n; i++) printf("%lf\t", x[i]); 55 | return 0; 56 | } -------------------------------------------------------------------------------- /Labs/Lab5/Gauss_2.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #include 4 | #include 5 | 6 | #define N 4 7 | 8 | int main() { 9 | static double a[N][N] = {{0.4096, 0.1234, 0.3678, 0.2943}, 10 | {0.2246, 0.3872, 0.4015, 0.1129}, 11 | {0.3645, 0.1920, 0.3781, 0.0643}, 12 | {0.1784, 0.4002, 0.2786, 0.3927}}; 13 | double b[N] = {1.2951, 1.1262, 0.9989, 1.2499}; 14 | double x[N] = {0, 0, 0}; 15 | double r, s, e; 16 | int k, i, j, p, flag = 1; 17 | 18 | for (k = 0; k < N - 1; k++) { 19 | p = k; 20 | e = a[k][k]; 21 | for (i = k; i < N; i++) 22 | if (fabs(a[i][k]) > e) { 23 | e = fabs(a[i][k]); 24 | p = i; 25 | } 26 | for (j = k; j < N; j++) { 27 | s = a[k][j]; 28 | a[k][j] = a[p][j]; 29 | a[p][j] = s; 30 | } 31 | s = b[k]; 32 | b[k] = b[p]; 33 | b[p] = s; 34 | if (a[k][k] == 0) { 35 | printf("Gauss-Method does not run!"); 36 | flag = 0; 37 | break; 38 | } else { 39 | for (i = k + 1; i < N; i++) { 40 | r = a[i][k] / a[k][k]; 41 | if (a[k][k] != 0) { 42 | for (j = k; j < N; j++) a[i][j] = a[i][j] - r * a[k][j]; 43 | } 44 | b[i] -= r * b[k]; 45 | } 46 | } 47 | } 48 | 49 | if (flag) { 50 | x[N - 1] = b[N - 1] / a[N - 1][N - 1]; 51 | for (i = N - 2; i >= 0; i--) { 52 | s = b[i]; 53 | for (j = i + 1; j < N; j++) s -= a[i][j] * x[j]; 54 | x[i] = s / a[i][i]; 55 | } 56 | for (i = 0; i < N; i++) printf("%lf, ", x[i]); 57 | } 58 | return 0; 59 | } -------------------------------------------------------------------------------- /Labs/Lab5/实验报告5.docx: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/gzn00417/2020Spring-Computational-Method/11c99df6e18702d6c34556556098b75ead5a6823/Labs/Lab5/实验报告5.docx -------------------------------------------------------------------------------- /Labs/流程图/分段线性插值流程图.jpg: -------------------------------------------------------------------------------- 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https://raw.githubusercontent.com/gzn00417/2020Spring-Computational-Method/11c99df6e18702d6c34556556098b75ead5a6823/大作业/1183710109+郭茁宁_课程论文/1183710109+郭茁宁_课程论文.pdf -------------------------------------------------------------------------------- /大作业/1183710109+郭茁宁_课程论文/Gauss_1.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #include 4 | using namespace std; 5 | #define N 10 6 | 7 | int n; 8 | double a[N][N], b[N], x[N]; 9 | 10 | int main() { 11 | scanf("%d", &n); 12 | for (int i = 1; i <= n; i++) 13 | for (int j = 1; j <= n; j++) scanf("%lf", &a[i][j]); 14 | for (int i = 1; i <= n; i++) scanf("%lf", &b[i]); 15 | for (int k = 1; k < n; k++) { 16 | int p = k; 17 | double maxabs = fabs(a[k][k]); 18 | for (int j = k + 1; j <= n; j++) 19 | if (fabs(a[j][k]) - maxabs > 0) { 20 | p = j; 21 | maxabs = fabs(a[j][k]); 22 | } 23 | if (a[p][k] == 0) { 24 | printf("Singular"); 25 | return 0; 26 | } 27 | if (p != k) { 28 | double tmp; 29 | for (int j = 1; j <= n; j++) { 30 | tmp = a[p][j]; 31 | a[p][j] = a[k][j]; 32 | a[k][j] = tmp; 33 | } 34 | tmp = b[p]; 35 | b[p] = b[k]; 36 | b[k] = tmp; 37 | } 38 | for (int i = k + 1; i <= n; i++) { 39 | double m_ik = a[i][k] / a[k][k]; 40 | for (int j = k + 1; j <= n; j++) a[i][j] -= a[k][j] * m_ik; 41 | b[i] -= b[k] * m_ik; 42 | } 43 | } 44 | if (a[n][n] == 0) { 45 | printf("Singular"); 46 | return 0; 47 | } 48 | x[n] = b[n] / a[n][n]; 49 | for (int k = n - 1; k >= 1; k--) { 50 | double sigma = 0.0; 51 | for (int j = k + 1; j <= n; j++) sigma += a[k][j] * x[j]; 52 | x[k] = (b[k] - sigma) / a[k][k]; 53 | } 54 | for (int i = 1; i <= n; i++) printf("%lf\t", x[i]); 55 | return 0; 56 | } -------------------------------------------------------------------------------- /大作业/1183710109+郭茁宁_课程论文/Gauss_2.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #include 4 | #include 5 | 6 | #define N 4 7 | 8 | int main() { 9 | static double a[N][N] = {{0.4096, 0.1234, 0.3678, 0.2943}, 10 | {0.2246, 0.3872, 0.4015, 0.1129}, 11 | {0.3645, 0.1920, 0.3781, 0.0643}, 12 | {0.1784, 0.4002, 0.2786, 0.3927}}; 13 | double b[N] = {1.2951, 1.1262, 0.9989, 1.2499}; 14 | double x[N] = {0, 0, 0}; 15 | double r, s, e; 16 | int k, i, j, p, flag = 1; 17 | 18 | for (k = 0; k < N - 1; k++) { 19 | p = k; 20 | e = a[k][k]; 21 | for (i = k; i < N; i++) 22 | if (fabs(a[i][k]) > e) { 23 | e = fabs(a[i][k]); 24 | p = i; 25 | } 26 | for (j = k; j < N; j++) { 27 | s = a[k][j]; 28 | a[k][j] = a[p][j]; 29 | a[p][j] = s; 30 | } 31 | s = b[k]; 32 | b[k] = b[p]; 33 | b[p] = s; 34 | if (a[k][k] == 0) { 35 | printf("Gauss-Method does not run!"); 36 | flag = 0; 37 | break; 38 | } else { 39 | for (i = k + 1; i < N; i++) { 40 | r = a[i][k] / a[k][k]; 41 | if (a[k][k] != 0) { 42 | for (j = k; j < N; j++) a[i][j] = a[i][j] - r * a[k][j]; 43 | } 44 | b[i] -= r * b[k]; 45 | } 46 | } 47 | } 48 | 49 | if (flag) { 50 | x[N - 1] = b[N - 1] / a[N - 1][N - 1]; 51 | for (i = N - 2; i >= 0; i--) { 52 | s = b[i]; 53 | for (j = i + 1; j < N; j++) s -= a[i][j] * x[j]; 54 | x[i] = s / a[i][i]; 55 | } 56 | for (i = 0; i < N; i++) printf("%lf, ", x[i]); 57 | } 58 | return 0; 59 | } -------------------------------------------------------------------------------- /大作业/1183710109+郭茁宁_课程论文/Lagrange.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #define N1 1 // n amount 4 | #define N2 4 // x amount 5 | #define N3 20 // n max 6 | 7 | int Ns[N1] = {3}; 8 | double x[N2] = {5, 50, 115, 185}; 9 | double l = -1.0; 10 | double r = 1.0; 11 | 12 | double X(int k, int n) { return (k + 13) * (k + 13); } 13 | 14 | double Y(double x) { return sqrt(x); } 15 | 16 | int main() { 17 | for (int i = 0; i < N2; i++) printf("\tx=%.2lf", x[i]); 18 | printf("\n"); 19 | for (int i = 0; i < N1; i++) { 20 | double a[N3 + 1], b[N3 + 1]; 21 | int n = Ns[i]; 22 | for (int k = 0; k <= n; k++) { 23 | a[k] = X(k, n); // x 24 | b[k] = Y(a[k]); // y 25 | } 26 | printf("n=%d", n); 27 | for (int p = 0; p < N2; p++) { 28 | double y = 0.0; 29 | for (int k = 0; k <= n; k++) { 30 | double l = 1.0; 31 | for (int j = 0; j <= n; j++) { 32 | if (j != k) l *= (x[p] - a[j]) / (a[k] - a[j]); 33 | } 34 | y += l * b[k]; 35 | } 36 | printf("\t%.6lf", y); 37 | } 38 | printf("\n"); 39 | } 40 | printf("Actual"); 41 | for (int p = 0; p < N2; p++) printf("\t%.6lf", Y(x[p])); 42 | return 0; 43 | } -------------------------------------------------------------------------------- /大作业/1183710109+郭茁宁_课程论文/Newton.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #include 4 | using namespace std; 5 | 6 | double x, e1, e2; 7 | int n; 8 | 9 | double f(double x) { return cos(x) - x; } 10 | double df(double x) { return -sin(x) - 1; } 11 | 12 | int main() { 13 | scanf("%lf%lf%lf%d", &x, &e1, &e2, &n); 14 | for (int i = 1; i <= n; i++) { 15 | double F = f(x), DF = df(x); 16 | if (fabs(F) < e1) { 17 | printf("%lf", x); 18 | return 0; 19 | } 20 | if (fabs(DF) < e2) { 21 | printf("Failed"); 22 | return 0; 23 | } 24 | double x1 = x - F / DF; 25 | double tol = fabs(x - x1); 26 | if (tol < e1) { 27 | printf("%lf", x1); 28 | return 0; 29 | } 30 | x = x1; 31 | printf("%lf, ", x1); 32 | } 33 | printf("Failed"); 34 | return 0; 35 | } -------------------------------------------------------------------------------- /大作业/1183710109+郭茁宁_课程论文/Romberg.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #include 4 | using namespace std; 5 | #define N 20 6 | 7 | int n; 8 | long double a, b, e, T[N][N] = {{0.0}}; 9 | 10 | long double f(long double x) { return 1.0 / (1.0 + x); } 11 | long double x(int i, long double h) { return a + h * i; } 12 | 13 | int main() { 14 | scanf("%llf%llf%llf%d", &a, &b, &e, &n); 15 | int k = 0; 16 | for (; k < n; k++) { 17 | long double h = (b - a) / pow(2, k), sum = 0.0; 18 | for (int i = 1; i <= pow(2, k) - 1; i++) sum += f(x(i, h)); 19 | T[k][0] = 0.5 * h * (f(a) + 2 * sum + f(b)); 20 | for (int m = 1; m <= k; m++) 21 | T[k][m] = 22 | (pow(4, m) * T[k][m - 1] - T[k - 1][m - 1]) / (pow(4, m) - 1); 23 | for (int m = 0; m <= k; m++) printf("%.7Lf\t", T[k][m]); 24 | cout << endl; 25 | if (k > 0 && fabs(T[k][0] - T[k][k]) <= e) break; 26 | } 27 | return 0; 28 | } 29 | -------------------------------------------------------------------------------- /大作业/1183710109+郭茁宁_课程论文/Runge_Kutta.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #include 4 | using namespace std; 5 | 6 | int n; 7 | double a, b, fa; 8 | 9 | double f(double x, double y) { return -y * y; } 10 | double f_(double x) { return 1.0 / (x + 1.0); } 11 | 12 | int main() { 13 | scanf("%lf%lf%lf%d", &a, &b, &fa, &n); 14 | double x = a, y = fa, h = (b - a) / n; 15 | for (int i = 1; i <= n; i++) { 16 | double k1 = h * f(x, y); 17 | double k2 = h * f(x + h / 2, y + k1 / 2); 18 | double k3 = h * f(x + h / 2, y + k2 / 2); 19 | double k4 = h * f(x + h, y + k3); 20 | x += h; 21 | y += 1.0 / 6.0 * (k1 + 2 * k2 + 2 * k3 + k4); 22 | printf("%.2lf\t%lf\t%.2lf\n", x, y, fabs(f_(x) - y)); 23 | } 24 | return 0; 25 | } -------------------------------------------------------------------------------- /大作业/1183710109+郭茁宁_课程论文/figure_2.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 7, 6 | "metadata": {}, 7 | "outputs": [], 8 | "source": [ 9 | "import math\n", 10 | "from matplotlib import pyplot as plt\n", 11 | "import seaborn as sns\n", 12 | "import numpy as np\n", 13 | "import pandas as pd\n", 14 | "%matplotlib inline\n", 15 | "sns.set_style(\"darkgrid\")" 16 | ] 17 | }, 18 | { 19 | "cell_type": "code", 20 | "execution_count": 25, 21 | "metadata": {}, 22 | "outputs": [ 23 | { 24 | "output_type": "execute_result", 25 | "data": { 26 | "text/plain": "" 27 | }, 28 | "metadata": {}, 29 | "execution_count": 25 30 | }, 31 | { 32 | "output_type": "display_data", 33 | "data": { 34 | "text/plain": "
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4MPH2q3j13s4UnzvPQ4s38OqyvZSUadlmWzBYrJhRcfbsWcaMGcPx48fx8PBg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\n" 37 | }, 38 | "metadata": {} 39 | } 40 | ], 41 | "source": [ 42 | "x = np.linspace(0.73, 0.79, 100)\n", 43 | "plt.plot(x, np.cos(x) - x)\n", 44 | "plt.plot(x, np.zeros(x.shape))\n", 45 | "a = np.array([0.785398163, 0.739536, 0.739085, 0.739085])\n", 46 | "plt.scatter(a, np.cos(a) - a, s=15, c=\"red\")" 47 | ] 48 | }, 49 | { 50 | "cell_type": "code", 51 | "execution_count": null, 52 | "metadata": {}, 53 | "outputs": [], 54 | "source": [] 55 | } 56 | ], 57 | "metadata": { 58 | "language_info": { 59 | "codemirror_mode": { 60 | "name": "ipython", 61 | "version": 3 62 | }, 63 | "file_extension": ".py", 64 | "mimetype": "text/x-python", 65 | "name": "python", 66 | "nbconvert_exporter": "python", 67 | "pygments_lexer": "ipython3", 68 | "version": "3.6.8-final" 69 | }, 70 | "orig_nbformat": 2, 71 | "kernelspec": { 72 | "name": "python36864bit2eb17439148c485399fa2f77fed1b772", 73 | "display_name": "Python 3.6.8 64-bit" 74 | } 75 | }, 76 | "nbformat": 4, 77 | "nbformat_minor": 2 78 | } 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