Tensorflow矩阵运算（矩阵相乘，点乘，行/列累加）

Tensorflow二维、三维、四维矩阵运算（矩阵相乘，点乘，行/列累加）

1. 矩阵相乘 $A_{a*b}\ast B_{b*c}=C_{a*c}$

根据矩阵相乘的匹配原则，左乘矩阵的列数要等于右乘矩阵的行数。

在多维（三维、四维）矩阵的相乘中，需要最后两维满足匹配原则。

可以将多维矩阵理解成：（矩阵排列，矩阵），即后两维为矩阵，前面的维度为矩阵的排列。

比如对于（2，2，4）来说，视为2个（2，4）矩阵。

对于（2，2，2，4）来说，视为2*2个（2，4）矩阵。

import tensorflow as tf

a_2d = tf.constant([1]*6, shape=[2, 3])
b_2d = tf.constant([2]*12, shape=[3, 4])
c_2d = tf.matmul(a_2d, b_2d)
a_3d = tf.constant([1]*12, shape=[2, 2, 3])
b_3d = tf.constant([2]*24, shape=[2, 3, 4])
c_3d = tf.matmul(a_3d, b_3d)
a_4d = tf.constant([1]*24, shape=[2, 2, 2, 3])
b_4d = tf.constant([2]*48, shape=[2, 2, 3, 4])
c_4d = tf.matmul(a_4d, b_4d)

with tf.Session() as sess:
    tf.global_variables_initializer().run()
    print("# {}*{}={} \n{}".
          format(a_2d.eval().shape, b_2d.eval().shape, c_2d.eval().shape, c_2d.eval()))
    print("# {}*{}={} \n{}".
          format(a_3d.eval().shape, b_3d.eval().shape, c_3d.eval().shape, c_3d.eval()))
    print("# {}*{}={} \n{}".
          format(a_4d.eval().shape, b_4d.eval().shape, c_4d.eval().shape, c_4d.eval()))

2. 点乘 $A_{a*b}\ast B_{a*b}=C_{a*b}$

点乘指的是shape相同的两个矩阵，对应位置元素相乘，得到一个新的shape相同的矩阵。

a_2d = tf.constant([1]*6, shape=[2, 3])
b_2d = tf.constant([2]*6, shape=[2, 3])
c_2d = tf.multiply(a_2d, b_2d)
a_3d = tf.constant([1]*12, shape=[2, 2, 3])
b_3d = tf.constant([2]*12, shape=[2, 2, 3])
c_3d = tf.multiply(a_3d, b_3d)
a_4d = tf.constant([1]*24, shape=[2, 2, 2, 3])
b_4d = tf.constant([2]*24, shape=[2, 2, 2, 3])
c_4d = tf.multiply(a_4d, b_4d)
with tf.Session() as sess:
    tf.global_variables_initializer().run()
    print("# {}*{}={} \n{}".
          format(a_2d.eval().shape, b_2d.eval().shape, c_2d.eval().shape, c_2d.eval()))
    print("# {}*{}={} \n{}".
          format(a_3d.eval().shape, b_3d.eval().shape, c_3d.eval().shape, c_3d.eval()))
    print("# {}*{}={} \n{}".
          format(a_4d.eval().shape, b_4d.eval().shape, c_4d.eval().shape, c_4d.eval()))

另外，点乘的其中一方可以是一个常数，也可以是一个和矩阵行向量等长（即列数）的向量。

即 $k\ast A_{a*b}=B_{a*b}$ 或 $\l_{b}\ast A_{a*b}=B_{a*b}$

因为在点乘过程中，会自动将常数或者向量进行扩维。

a_2d = tf.constant([1]*6, shape=[2, 3])
k = tf.constant(2)
l = tf.constant([2, 3, 4])
b_2d_1 = tf.multiply(k, a_2d)  # tf.multiply(a_2d, k) is also ok
b_2d_2 = tf.multiply(l, a_2d)  # tf.multiply(a_2d, l) is also ok
a_3d = tf.constant([1]*12, shape=[2, 2, 3])
b_3d_1 = tf.multiply(k, a_3d)  # tf.multiply(a_3d, k) is also ok
b_3d_2 = tf.multiply(l, a_3d)  # tf.multiply(a_3d, l) is also ok
a_4d = tf.constant([1]*24, shape=[2, 2, 2, 3])
b_4d_1 = tf.multiply(k, a_4d)  # tf.multiply(a_4d, k) is also ok
b_4d_2 = tf.multiply(l, a_4d)  # tf.multiply(a_4d, l) is also ok

with tf.Session() as sess:
    tf.global_variables_initializer().run()
    print("# {}*{}={} \n{}".
          format(k.eval().shape, a_2d.eval().shape, b_2d_1.eval().shape, b_2d_1.eval()))
    print("# {}*{}={} \n{}".
          format(l.eval().shape, a_2d.eval().shape, b_2d_2.eval().shape, b_2d_2.eval()))
    print("# {}*{}={} \n{}".
          format(k.eval().shape, a_3d.eval().shape, b_3d_1.eval().shape, b_3d_1.eval()))
    print("# {}*{}={} \n{}".
          format(l.eval().shape, a_3d.eval().shape, b_3d_2.eval().shape, b_3d_2.eval()))
    print("# {}*{}={} \n{}".
          format(k.eval().shape, a_4d.eval().shape, b_4d_1.eval().shape, b_4d_1.eval()))
    print("# {}*{}={} \n{}".
          format(l.eval().shape, a_4d.eval().shape, b_4d_2.eval().shape, b_4d_2.eval()))

4. 行/列累加

a_2d = tf.constant([1]*6, shape=[2, 3])
d_2d_1 = tf.reduce_sum(a_2d, axis=0)
d_2d_2 = tf.reduce_sum(a_2d, axis=1)
a_3d = tf.constant([1]*12, shape=[2, 2, 3])
d_3d_1 = tf.reduce_sum(a_3d, axis=1)
d_3d_2 = tf.reduce_sum(a_3d, axis=2)
a_4d = tf.constant([1]*24, shape=[2, 2, 2, 3])
d_4d_1 = tf.reduce_sum(a_4d, axis=2)
d_4d_2 = tf.reduce_sum(a_4d, axis=3)

with tf.Session() as sess:
    tf.global_variables_initializer().run()
    print("# a_2d 行累加得到shape:{}\n{}".format(d_2d_1.eval().shape, d_2d_1.eval()))
    print("# a_2d 列累加得到shape:{}\n{}".format(d_2d_2.eval().shape, d_2d_2.eval()))
    print("# a_3d 行累加得到shape:{}\n{}".format(d_3d_1.eval().shape, d_3d_1.eval()))
    print("# a_3d 列累加得到shape:{}\n{}".format(d_3d_2.eval().shape, d_3d_2.eval()))
    print("# a_4d 行累加得到shape:{}\n{}".format(d_4d_1.eval().shape, d_4d_1.eval()))
    print("# a_4d 列累加得到shape:{}\n{}".format(d_4d_2.eval().shape, d_4d_2.eval()))

Tensorflow矩阵运算（矩阵相乘，点乘，行/列累加）

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