先验知识：张量可以按照不同阶展开成不同的矩阵
具体可以参考：如何加单理解和实现张量展开
但是查到的资料都不是python的，我根据matlab版本的代码做了一些转换
在这里共享给大家（目前应该只适用三阶张量）
# Author--Zoe
# 2022/06/02
'''
tensor 张量
mat 矩阵
mode 分解的阶
tensor_size 张量每维的大小构成的数组
'''
# 张量转矩阵
def ten2mat(tensor, mode):
return np.reshape(np.moveaxis(tensor, mode, 0), (tensor.shape[mode], -1), order = 'F')
# 矩阵转张量
def mat2ten(mat, tensor_size, mode):
index = list()
index.append(tensor_size[mode])
for i in range(tensor_size.shape[0]):
if i != mode:
index.append(tensor_size[i])
return np.moveaxis(np.reshape(mat, list(index), order = 'F'), 0, mode)
# 这里只举例mode-1展开 其他也是类似的
def mode1Unfolding(X):
print('模态1展开矩阵 (mode-1 tensor unfolding):')
M1 = ten2mat(X, 0)
print(M1)
return M1
def mode1Folding(X,tensor_size):
print('模态1合并张量 (mode-1 tensor folding):')
T1= mat2ten(X, tensor_size, 0)
print(T1)
return T1
if __name__ == '__main__':
X=np.array([[[1,13,25],[2,14,26],[3,15,27]],
[[4,16,28],[5,17,29],[6,18,30]],
[[7,19,31],[8,20,32],[9,21,33]],
[[10,22,34],[11,23,35],[12,24,36]]])
M1 = mode1Unfolding(X)
print()
mode1Folding(M1, np.array([X.shape[0],X.shape[1],X.shape[2]]))
