57 lines
1.7 KiB
Python
57 lines
1.7 KiB
Python
#模 范数
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def Norm(x,v):
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if len(x[0]) == 1:
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if v == 1:
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return sum([abs(i[0]) for i in x])
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elif v == 2:
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return (sum([i[0]**2 for i in x]))**0.5
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elif v == float("inf"):
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return max([abs(i[0]) for i in x])
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else:
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if v == 1:
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return max([sum([abs(x[i][j]) for i in range(len(x))]) for j in range(len(x[0]))])
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elif v == float("inf"):
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return max([sum([abs(i) for i in x[j]]) for j in range(len(x))])
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return None
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# 计算矩阵的点积
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def Dot(A,B):
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if len(A[0]) != len(B):
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return None
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return [[sum([A[i][j] * B[j][k] for j in range(len(A[0]))]) for k in range(len(B[0]))] for i in range(len(A))]
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# 计算矩阵的行列式
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def Det(A):
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if len(A) == 2:
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return A[0][0] * A[1][1] - A[0][1] * A[1][0]
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det = 0
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for c in range(len(A)):
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sub_matrix = [row[:c] + row[c+1:] for row in A[1:]]
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det += ((-1) ** c) * A[0][c] * Det(sub_matrix)
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return det
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if __name__ == "__main__":
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##########################################################################
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# 把矩阵换成题干的矩阵 #########################
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A = [
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[1,2,-2],
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[1,1,1],
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[2,2,1]
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]
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# 把范数的种类数换成题干的要求，inf是无穷范数 #########################
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LU = A.copy()
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ID = [[0 for _ in range(len(A))] for __ in range(len(A))]
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for i in range(len(A)):
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for j in range(len(A[0])):
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if i == j:
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ID[i][j] = 1/A[i][j]
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LU[i][j] = 0
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else:
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LU[i][j] = -LU[i][j]
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print(f"LU分解的LU矩阵为: {LU}")
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print(f"LU分解的D矩阵的逆矩阵为: {ID}")
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J = Dot(ID, LU)
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print(f"LU分解的J矩阵为: {J}")
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