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import numpy as npimport matplotlib.pyplot as plth = 0.001 #空间步长N = 1000 #空间步数dt = 0.0001 #时间步长M = 10000

#龙贝格积分法函数import numpy as npfrom matplotlib import pyplot as pltfrom mpl_toolkits.axes_grid1.inset_locator import inset_axesdef romberg(fun, a, b): sum = 0 t1 = ((b - a)*(fun(a)+fun(b)))/2 for i in range(1, 2): sum = sum + fun(a+(

import numpy as npfrom matplotlib import pyplot as pltdef fgauss(A, b): n = A.shape[0] zengguan = np.hstack((A, b.T)) ra = np.linalg.matrix_rank(A) rz = np.linalg.matrix_rank(zengguan) temp1 = rz - ra if temp1 > 0: pr

这里对三次样条插值函数，拉格朗日插值多项式，牛顿插值多项式这三种插值方法进行比较代码import numpy as npfrom sympy import *from matplotlib import pyplot as pltdef lagrange(x, y): p, la = symbols('p la') n = len(x) s = 0 for k in range(n): la = y[k] for j in ra

代码import numpy as npfrom sympy import *from matplotlib import pyplot as pltdef spline(x, y, t): n = len(x) h = [x[i]-x[i-1] for i in range(1, n)] A = np.eye(n-2) A = A*2 u1 = [h[i]/(h[i]+h[i+1]) for i in range(n-2)] la1 = [1-u

代码在这里插入代码片结果如下图所示

代码import numpy as npfrom sympy import *from matplotlib import pyplot as pltdef hermite(x, y, dy): p, la = symbols('p la') f = 0 n = len(x) for i in range(n): la = 1 lp = 0 for j in range(n): if j !

代码import numpy as npfrom sympy import *from matplotlib import pyplot as pltdef newton(x, y): n = len(x) c = np.zeros((n, n)) print(c) for i in range(n): c[i, 0] = y[i] for i in range(1, n): for j in range(i, n):

#代码

引言SymPy是用于符号数学的 Python 库。详细教程见目录引言加载sympy库定义符号,替换代码结果代码结果展开代码结果加载sympy库from sympy import *定义符号,替换代码x = symbols('x ')str_expr = 'x**2 + 2*x + 1'expr = sympify(str_expr)y = expr*expr+1print(expand(y))print(y.subs(x, 1))结果代码x = symbols('x ')

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基于豪斯霍尔德变换的QR分解# Householderimport numpy as npdef householder(a): temp = 1 m = a.shape[0] n = a.shape[1] for i in range(0, n-1): x = a[i:n, i] print("x向量为：") print(x) e = np.mat(np.zeros((n-i, 1), dtype

基于吉文斯变换的QR分解# 基于吉文斯变换的QR分解import numpy as npdef givens(A): m = A.shape[0] n = A.shape[1] P = np.mat(np.eye(n)) p1 = P for i in range(0, n-1): for j in range(i+1, n): if A[i, j] == 0: continue

基于豪斯霍尔德变换的QR分解

基于吉文斯变换的QR分解

矩阵的LU分解

列主元素高斯-若当消去法import numpy as npdef fgauss(A, b): n = A.shape[0] zengguan = np.hstack((A, b.T)) ra = np.linalg.matrix_rank(A) rz = np.linalg.matrix_rank(zengguan) temp1 = rz - ra if temp1 > 0: print("无一般意义下的解，系数矩阵与增广矩阵的

高斯列元主元素消去法import numpy as npdef fgauss(A, b): n = A.shape[0] zengguan = np.hstack((A, b.T)) ra = np.linalg.matrix_rank(A) rz = np.linalg.matrix_rank(zengguan) temp1 = rz - ra if temp1 > 0: print("无一般意义下的解，系数矩阵与增广矩阵的秩不

高斯消元法import numpy as npdef fgauss(A, b): n = A.shape[0] zengguan = np.hstack((A, b.T)) ra = np.linalg.matrix_rank(A) rz = np.linalg.matrix_rank(zengguan) temp1 = rz - ra if temp1 > 0: print("无一般意义下的解，系数矩阵与增广矩阵的秩不同")