我对numpy.dot乘积有一些疑问。
我定义了一个6x6的矩阵,如下所示:
矩阵是正交的(尽管数值精度不完美):
但是,如果我执行以下操作,为什么会这样呢:
我得到了c_mat(等于c)的期望值,但对于c_mat1没有。在多维数组上使用点运算符有什么微妙之处吗?
我定义了一个6x6的矩阵,如下所示:
C=np.zeros((6,6))
C[0,0], C[1,1], C[2,2] = 129.5, 129.5, 129.5
C[3,3], C[4,4], C[5,5] = 25, 25, 25
C[0,1], C[0,2] = 82, 82
C[1,0], C[1,2] = 82, 82
C[2,0], C[2,1] = 82, 82
然后我使用多维数组将其重构为4阶张量
def long2short(m, n):
"""
Given two indices m and n of the stiffness tensor the function
return i the index of the Voigt matrix
i = long2short(m,n)
"""
if m == n:
i = m
elif (m == 1 and n == 2) or (m == 2 and n == 1):
i = 3
elif (m == 0 and n == 2) or (m == 2 and n == 0):
i = 4
elif (m == 0 and n == 1) or (m == 1 and n == 0):
i = 5
return i
c=np.zeros((3,3,3,3))
for m in range(3):
for n in range(3):
for o in range(3):
for p in range(3):
i = long2short(m, n)
j = long2short(o, p)
c[m, n, o, p] = C[i, j]
接下来我想通过使用我定义的旋转矩阵来改变张量的坐标参考系:
Q=np.array([[sqrt(2.0/3), 0, 1.0/sqrt(3)], [-1.0/sqrt(6), 1.0/sqrt(2), 1.0/sqrt(3)], [-1.0/sqrt(6), -1.0/sqrt(2), 1.0/sqrt(3)]])
Qt = Q.transpose()
矩阵是正交的(尽管数值精度不完美):
In [157]: np.dot(Q, Qt)
Out[157]:
array([[ 1.00000000e+00, 4.28259858e-17, 4.28259858e-17],
[ 4.28259858e-17, 1.00000000e+00, 2.24240114e-16],
[ 4.28259858e-17, 2.24240114e-16, 1.00000000e+00]])
但是,如果我执行以下操作,为什么会这样呢:
In [158]: a=np.dot(Q,Qt)
In [159]: c_mat=np.dot(a, c)
In [160]: a1 = np.dot(Qt, c)
In [161]: c_mat1=np.dot(Q, a1)
我得到了c_mat(等于c)的期望值,但对于c_mat1没有。在多维数组上使用点运算符有什么微妙之处吗?
numpy.tensordot()
函数。 - Saullo G. P. Castro