我尝试使用此http://www.irma-international.org/viewtitle/41011/算法来反转nxn矩阵。
我在这个矩阵上运行了这个函数
[[1.0, -0.5],
[-0.4444444444444444, 1.0]]
并获得输出
[[ 1.36734694, 0.64285714]
[ 0.57142857, 1.28571429]]
正确的输出是
[[ 1.28571429, 0.64285714]
[ 0.57142857, 1.28571429]]
我的功能:
def inverse(m):
n = len(m)
P = -1
D = 1
mI = m
while True:
P += 1
if m[P][P] == 0:
raise Exception("Not Invertible")
else:
D = D * m[P][P]
for j in range(n):
if j != P:
mI[P][j] = m[P][j] / m[P][P]
for i in range(n):
if i != P:
mI[i][P] = -m[i][P] / m[P][P]
for i in range(n):
for j in range(n):
if i != P and j != P:
mI[i][j] = m[i][j] + (m[P][j] * mI[i][P])
mI[P][P] = 1 / m[P][P]
if P == n - 1: # All elements have been looped through
break
return mI
我在哪里弄错了?
答案 0 :(得分:2)
https://repl.it/repls/PowerfulOriginalOpensoundsystem
输出
逆:[[十进制('1.285714285714285693893862813'), 十进制( '0.6428571428571428469469314065')], [十进制( '0.5714285714285713877877256260'), 十进制( '1.285714285714285693893862813')]] numpy:[[1.28571429 0.64285714] [0.57142857 1.28571429]]
from decimal import Decimal
import numpy as np
def inverse(m):
m = [[Decimal(n) for n in a] for a in m]
n = len(m)
P = -1
D = Decimal(1)
mI = [[Decimal(0) for n in a] for a in m]
while True:
P += 1
if m[P][P] == 0:
raise Exception("Not Invertible")
else:
D = D * m[P][P]
for j in range(n):
if j != P:
mI[P][j] = m[P][j] / m[P][P]
for i in range(n):
if i != P:
mI[i][P] = -m[i][P] / m[P][P]
for i in range(n):
for j in range(n):
if i != P and j != P:
mI[i][j] = m[i][j] + (m[P][j] * mI[i][P])
mI[P][P] = 1 / m[P][P]
m = [[Decimal(n) for n in a] for a in mI]
mI = [[Decimal(0) for n in a] for a in m]
if P == n - 1: # All elements have been looped through
break
return m
m = [[1.0, -0.5],
[-0.4444444444444444, 1.0]]
print(inverse(m))
print(np.linalg.inv(np.array(m)))
我的思考过程:
起初,我认为你可能潜伏着浮点出现错误。事实证明这不是真的。这就是Decimal爵士乐的用途。
你的错误就在这里
mI = m # this just creates a pointer that points to the SAME list as m
在这里
for i in range(n):
for j in range(n):
if i != P and j != P:
mI[i][j] = m[i][j] + (m[P][j] * mI[i][P])
mI[P][P] = 1 / m[P][P]
# you are not copying mI to m for the next iteration
# you are also not zeroing mI
if P == n - 1: # All elements have been looped through
break
return mI
遵循算法,每次迭代都会创建一个NEW a'矩阵,它不会继续修改相同的旧a。我推断这意味着在循环不变量中,a变为'。适用于您的测试用例,结果证明是真的。