63 lines
2.0 KiB
Python
63 lines
2.0 KiB
Python
import math
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# 获取下三角矩阵的索引
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# 列 行
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def getIndexFromDownMatrix(col, row):
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if row > col:
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row, col = col, row
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return (1+col)*col//2+row
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# 平方根法求解
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def SqrtSolve(A,b):
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n = len(b)
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L = [0]*(n*(n+1)//2)
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for j in range(n):
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for i in range(j,n):
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if i == j:
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L[getIndexFromDownMatrix(i,j)] = A[getIndexFromDownMatrix(i,j)]
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for k in range(j):
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L[getIndexFromDownMatrix(i,j)] -= L[getIndexFromDownMatrix(j,k)]**2
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L[getIndexFromDownMatrix(i,j)] = L[getIndexFromDownMatrix(i,j)]**0.5
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else:
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L[getIndexFromDownMatrix(i,j)] = A[getIndexFromDownMatrix(i,j)]
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for k in range(j):
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L[getIndexFromDownMatrix(i,j)] -= L[getIndexFromDownMatrix(i,k)]*L[getIndexFromDownMatrix(j,k)]
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L[getIndexFromDownMatrix(i,j)] /= L[getIndexFromDownMatrix(j,j)]
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# 打印下三角矩阵
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print("下三角矩阵 L:")
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for i in range(n):
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L_row = []
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for j in range(n):
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if j <= i:
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L_row.append(L[getIndexFromDownMatrix(i,j)])
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else:
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L_row.append(0)
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print(L_row)
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# print(L)
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for i in range(n):
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for k in range(i):
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b[i] -= L[getIndexFromDownMatrix(i,k)]*b[k]
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b[i] /= L[getIndexFromDownMatrix(i,i)]
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# 打印 b 向量
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print("y 向量:")
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print(b)
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for i in range(n-1,-1,-1):
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for k in range(i+1,n):
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b[i] -= L[getIndexFromDownMatrix(k,i)]*b[k]
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b[i] /= L[getIndexFromDownMatrix(i,i)]
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return b
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#把A,b换成题干的数值###########################################
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if __name__ == "__main__":
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##########################################################################
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# 储存下三角矩阵 a11, a21, a22, a31, a32, a33 ...，按照这个格式写
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A = [4,2,2,-2,-3,14]
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b = [10,5,4] # b向量，常数项
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# print("x:")
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print("x: \n",SqrtSolve(A,b))
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