在keras中有batch_dot函數,用於計算兩個多維矩陣,官方註釋如下:
def batch_dot(x, y, axes=None):
"""Batchwise dot product.
`batch_dot` is used to compute dot product of `x` and `y` when
`x` and `y` are data in batches, i.e. in a shape of
`(batch_size, :)`.
`batch_dot` results in a tensor or variable with less dimensions
than the input. If the number of dimensions is reduced to 1,
we use `expand_dims` to make sure that ndim is at least 2.
這個函數是用於計算批次數據‘x’和‘y'的內積,兩個數據的batch_size必須相同。
函數的輸出張量的維度數量會少於輸入的維度數量和。如果輸出的維度數量減少到1,就會使用
’expand_dim‘函數來確保維度數量至少爲2。
# Arguments
x: Keras tensor or variable with `ndim >= 2`. 維度數量 >= 2
y: Keras tensor or variable with `ndim >= 2`. 維度數量 >= 2
axes: int or tuple(int, int). Target dimensions to be reduced.
要減少的目標維度。理論上從0開始(即shape首位),但batch_size是忽略的,故從1開始。若是一
個整數,則表示兩個輸入的shape的同一位。若是一個tuple或list,則分別指向不同位置。
注意:無論axes是那種類型,指向的兩個位置上的數值必須一致。
# Returns
A tensor with shape equal to the concatenation of `x`'s shape
(less the dimension that was summed over) and `y`'s shape
(less the batch dimension and the dimension that was summed over).
If the final rank is 1, we reshape it to `(batch_size, 1)`.
"""
下面對例子進行說明。
>>> x_batch = K.ones(shape=(32, 20, 1))
>>> y_batch = K.ones(shape=(32, 30, 20))
>>> xy_batch_dot = K.batch_dot(x_batch, y_batch, axes=(1, 2))
>>> K.int_shape(xy_batch_dot)
(32, 1, 30)
首先我認爲,該函數進行還是普通的矩陣乘法,但是兩個輸入矩陣的格式明顯不符合,所以進行了類似reshape的操作,具體就是將左邊的矩陣的目標位移動到末尾,將右邊矩陣的目標位移動到首位。如上例,去掉batch_size,原規格爲(20,1)和(30,20),因爲axes=(1,2),故變爲(1,20)和(20,30)的矩陣乘法,結果爲(1,30),加上batch_size即爲(32,1,30)。