update

2021.06.24_sympy_example/sympy_example.py

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+"""
+This code is supported by the website: https://www.guanjihuan.com
+The newest version of this code is on the web page: https://www.guanjihuan.com/archives/14684
+"""
+
+import sympy
+
+
+# 定义符号
+print()
+print('定义符号：')
+x, y, z = sympy.symbols('x y z')  # 使用sympy.symbols
+print(x)
+print(y+1)
+print(z**2)
+print()
+
+
+# 替换（Substitution）
+print('变量替换：')
+expression_1 = x**2+1
+value_1 = expression_1.subs(x, 3)  # 使用.subs()方法
+print(value_1)
+print()
+
+
+# 字符串转成符号表达式
+print('字符串转成符号表达式：')
+expression_string = 'x**3+1'
+print(expression_string)
+expression_2 = sympy.sympify(expression_string)  # 使用sympy.sympify()
+print(expression_2)
+value_2 = expression_2.subs(x, 2)
+print(value_2)
+print()
+
+
+# 简化表达式
+print('简化表达式：')
+expression_3 = sympy.simplify(sympy.sin(x)**2 + sympy.cos(x)**2)  # 使用sympy.simplify()
+print(expression_3)
+print()
+
+
+# 符号矩阵
+print('符号矩阵：')
+a, b = sympy.symbols('a b')
+matrix = sympy.Matrix([[1, a], [0, b]])   # 使用sympy.Matrix()
+print(matrix)
+print()
+
+
+sympy.init_printing(use_unicode=True)
+# 符号矩阵的特征值和特征向量
+print('符号矩阵的特征值和特征向量：')
+eigenvalue = matrix.eigenvals()  # 使用.eigenvals()方法
+print('特征值\n', eigenvalue, '\n')
+sympy.pprint(eigenvalue)               # 使用sympy.pprint()输出
+print('\n', sympy.pretty(eigenvalue))  # 使用sympy.pretty()美化后输出
+print()
+
+eigenvector = matrix.eigenvects() # 使用.eigenvects()方法
+print('特征向量\n', eigenvector, '\n')
+sympy.pprint(eigenvector)
+print('\n', sympy.pretty(eigenvector)) 
+print()
+
+P, D = matrix.diagonalize()  # 使用.diagonalize()方法
+print('特征值\n', D, '\n')
+print(sympy.pretty(D), '\n')
+print('特征向量\n', P, '\n')
+print(sympy.pretty(P), '\n')
+print()
+
+print('特征值\n', D.subs(a, -4).subs(b, 2), '\n')
+print(sympy.pretty(D.subs(a, -4).subs(b, 2)), '\n')
+print('特征向量\n', P.subs(a, -4).subs(b, 2), '\n')
+print(sympy.pretty(P.subs(a, -4).subs(b, 2)), '\n')
+print()
+
+# 和numpy对比
+print('和numpy对比：')
+import numpy as np
+matrix = np.array([[1, -4], [0, 2]])
+eigenvalue, eigenvector = np.linalg.eig(matrix) 
+print('特征值\n', eigenvalue)
+print('特征向量\n', eigenvector)
+print()