99 lines
2.7 KiB
Python
99 lines
2.7 KiB
Python
import math
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# 列主元高斯消元法
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def SovleRowMain(A,b):
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ks = 0.00000001
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n = len(A)
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if len(A[0]) != n:
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print("A要为方阵")
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return None,None,None,None
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if len(b) != n:
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print("b与A的行数不匹配")
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return None,None,None,None
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p = list(range(n))
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for i in range(n):
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row_max = abs(A[i][i])
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row_max_index = i
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for j in range(i + 1, n):
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if abs(A[j][i]) > row_max:
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row_max = abs(A[j][i])
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row_max_index = j
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A[i], A[row_max_index] = A[row_max_index], A[i]
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b[i], b[row_max_index] = b[row_max_index], b[i]
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p[i], p[row_max_index] = p[row_max_index], p[i]
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print(f"第{i+1}次交换，交换行{i+1}和行{row_max_index+1}，A矩阵为：")
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for row in A:
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print(row)
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print(f"b向量为：{b}\n")
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if abs(A[i][i]) < ks:
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print("A矩阵奇异，无法进行高斯消元")
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return None,None,None,None
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for j in range(i + 1, n):
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m = A[j][i] / A[i][i]
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A[j][i] = m
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for k in range(i + 1, n):
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A[j][k] -= m * A[i][k]
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b[j] -= m * b[i]
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print(f"系数为{-1*m}用加号")
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print("消元后的A矩阵：")
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for row in A:
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print(row)
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print(f"消元后的b向量：{b}\n")
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if abs(A[n - 1][n - 1]) < ks:
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print("A矩阵奇异，无法进行高斯消元")
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return None,None,None,None
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# 回代求解
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b[n - 1] /= A[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] -= A[i][j] * b[j]
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b[i] /= A[i][i]
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# 得到L,U和P矩阵
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L = [[0 for i in range(n)] for j in range(n)]
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U = [[0 for i in range(n)] for j in range(n)]
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P = [[0 for i in range(n)] for j in range(n)]
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for i in range(n):
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for j in range(n):
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if i == j:
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L[i][j] = 1
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U[i][j] = A[i][j]
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elif i < j:
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U[i][j] = A[i][j]
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else:
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L[i][j] = A[i][j]
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P[i][p[i]] = 1
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return P,L,U,b
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#打印矩阵
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def prettyPrintMatrix(matrix):
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for row in matrix:
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print(row)
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if __name__ == "__main__":
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##########################################################################
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#把矩阵A和b改成题干要求的#####################################
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A = [
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[0, 3, 4],
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[1, -1, 1],
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[2, 1, 2]
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]
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b = [1, 2, 3]
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P,L,U,x = SovleRowMain(A, b)
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print("P:")
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prettyPrintMatrix(P)
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print("L:")
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prettyPrintMatrix(L)
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print("U:")
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prettyPrintMatrix(U)
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print("x:")
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print(x)
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