35 lines
1.3 KiB
Python
35 lines
1.3 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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#改成题干的矩阵##########################
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if __name__ == "__main__":
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A = [[1, 3], [-2, 4]] # 注意储存形式
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x = [[1], [-1]] # 注意储存形式，单独一列的相量，每个数字都要中括号
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print("Norm of x with v=1:", Norm(x, 1))
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print("Norm of x with v=inf:", Norm(x, float("inf"))) # 1 1范数；2 2范数；float('inf') 无穷范数
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print("Norm of x with v=2:", Norm(x, 2))
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print("Dot product of A and x:", Dot(A, x))
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print("Norm of Ax with v=2:", Norm(Dot(A, x), 2))
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print("Norm of A with v=inf:", Norm(A, float("inf")))
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print("Norm of A with v=1:", Norm(A, 1))
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