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55 lines
1.4 KiB
55 lines
1.4 KiB
'''
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Author: SJ2050
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Date: 2021-10-29 18:46:40
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LastEditTime: 2021-10-29 22:41:31
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Version: v0.0.1
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Description: Solution for homework1.4.
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Copyright © 2021 SJ2050
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'''
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import numpy as np
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from scipy.linalg import lu_factor, lu_solve
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def gauss_eliminate(K, b):
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K = np.array(K)
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b = np.array(b)
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n = len(K)
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x = np.zeros(n)
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for i in range(0, n-1):
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for j in range(i+1,n):
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c = -K[j][i]/K[i][i]
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for k in range(0, n):
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K[j][k] += K[i][k]*c
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b[j] += b[i]*c
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x[n-1]=b[n-1]/K[n-1][n-1]
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for i in range(n-2, -1, -1):
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for j in range(i+1, n):
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b[i] -= K[i][j]*x[j]
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x[i] = b[i]/K[i][i]
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return x
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if __name__ == '__main__':
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K = np.mat([[3, 4, 2],
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[5, 3, 4],
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[8, 2, 7]])
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b = np.mat([[10], [14], [20]])
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# 1. 系数矩阵求逆求解线性方程组
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s1 = K**(-1)*b
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print('1.系数矩阵求逆求解：\n', s1)
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# 2. 直接求解法求解线性方程组
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s2 = np.linalg.solve(K, b)
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print('2.直接求解法解线性方程组：\n', s2)
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# 3. 使用LU分解求解线性方程组
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lu, piv = lu_factor(K)
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s3 = lu_solve((lu, piv), b)
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print('3.LU分解求解线性方程组: \n', s3)
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# 4. 使用高斯消元法求解线性方程组
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s4 = gauss_eliminate(K[:, :]*1.0, [x[0]*1.0 for x in b])
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print('4.高斯消元法求解线性方程组: \n', s4)
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