Numpy np.linalg.det（）与我的计算结果不同
我试图理解行列式是如何计算的。 我有： 现在，我是这样理解的：Numpy np.linalg.det（）与我的计算结果不同,numpy,Numpy,我试图理解行列式是如何计算的。 我有： 现在，我是这样理解的： >>>>>>> array([[1, 2, 3], [2, 3, 4], [5, 6, 7]]) >>>>>>> |b| = |1 2 3| = 1|3 4| - 2|2 4| + 3|2 3| |2 3 4| |6 7| |5
>>>>>>> array([[1, 2, 3],
[2, 3, 4],
[5, 6, 7]])
>>>>>>> |b| = |1 2 3| = 1|3 4| - 2|2 4| + 3|2 3|
|2 3 4| |6 7| |5 7| |5 6|
|5 6 7|
|b| = 1*(3*7 - 4*6) - 2*(2*7 - 4*5) + 3*(2*6 - 3*5)
|b| = 1*( - 3 ) - 2*( - 6 ) + 3*( - 3 )
|b| = ( - 3 ) - ( - 12 ) + ( - 9 )
|b| = -3 +12 - 9 = 0
det（）1.770>>>>>>> |b| = |1 2 5| = 1|3 6| - 2|2 6| + 5|2 3|
|2 3 6| |4 7| |3 7| |3 4|
|3 4 7|
上述注释的意思是
numpyb = np.array([ [1,2,3], [2,3,4], [5,6,7] ], dtype=np.float64)
np.linalg.det(b)
>>> 1.7763568394002396e-15
0.+/-舍入误差舍入误差np.finfo（np.float64）.eps=2.22e-16float64np.linalg.detbnumpyfrom scipy.linalg import lu_factor
b_LU = lu_factor(b)
def lu_det(A_LU):
# The determinant of a permutation matrix is (-1)**n where n is the number of permutations.
# Recall a permutation matrix is a matrix with a one in each row, and column, and zeros everywhere else.
# => if the elements of the diagonal are not 1, they will be zero, and then there has been a swap
nswaps = len(A_LU[1]) - sum(A_LU[1]==np.arange(len(A_LU[1])))
detP = (-1)**nswaps
# The determinant of a triangular matrix is the product of the elements on the diagonal.
detL = 1 # The unit diagonal elements of L are not stored.
detU = np.prod(np.diag(A_LU[0]))
# Matrix containing U in its upper triangle, and L in its lower triangle.
# The determinant of a product of matrices is equal to the product of the determinant of the matrices.
return detP * detL * detU
lu_det(b_LU)
>>> 4.4408920985006196e-17
sympyimport sympy as sp
sp.Matrix(b).det()
>>> 0
希望您现在能更清楚地理解。以上评论的意思是
numpyb = np.array([ [1,2,3], [2,3,4], [5,6,7] ], dtype=np.float64)
np.linalg.det(b)
>>> 1.7763568394002396e-15
0.+/-舍入误差舍入误差np.finfo（np.float64）.eps=2.22e-16float64np.linalg.detbnumpyfrom scipy.linalg import lu_factor
b_LU = lu_factor(b)
def lu_det(A_LU):
# The determinant of a permutation matrix is (-1)**n where n is the number of permutations.
# Recall a permutation matrix is a matrix with a one in each row, and column, and zeros everywhere else.
# => if the elements of the diagonal are not 1, they will be zero, and then there has been a swap
nswaps = len(A_LU[1]) - sum(A_LU[1]==np.arange(len(A_LU[1])))
detP = (-1)**nswaps
# The determinant of a triangular matrix is the product of the elements on the diagonal.
detL = 1 # The unit diagonal elements of L are not stored.
detU = np.prod(np.diag(A_LU[0]))
# Matrix containing U in its upper triangle, and L in its lower triangle.
# The determinant of a product of matrices is equal to the product of the determinant of the matrices.
return detP * detL * detU
lu_det(b_LU)
>>> 4.4408920985006196e-17
sympyimport sympy as sp
sp.Matrix(b).det()
>>> 0
希望现在对你来说更清楚。数值方法的首要原则之一是，永远不要严格使用
=1.7763568394002396e-150.0=numpy1.77.数值方法的首要原则之一是，永远不要严格使用
==1.7763568394002396e-150.0=numpy1.77.
1.7763568394002396e-15float64sympy.Matrix（[[1,2,3]，[2,3,4]，[5,6,7]]）。det（）1.7763568394002396e-15float64symphy.Matrix（[[1,2,3]，[2,3,4]，[5,6,7]）。det（）1.7763568394002396e-1500e-151.7763568394002396e-1500e-15