Tensorflow二維、三維、四維矩陣運算（矩陣相乘，點乘，行/列累加）

1. 矩陣相乘 

根據矩陣相乘的匹配原則，左乘矩陣的列數要等於右乘矩陣的行數。

在多維（三維、四維）矩陣的相乘中，需要最後兩維滿足匹配原則。

可以將多維矩陣理解成：（矩陣排列，矩陣），即後兩維為矩陣，前面的維度為矩陣的排列。

比如對於（2，2，4）來說，視為2個（2，4）矩陣。

對於（2，2，2，4）來說，視為2*2個（2，4）矩陣。

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. 點乘 

點乘指的是shape相同的兩個矩陣，對應位置元素相乘，得到一個新的shape相同的矩陣。

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，點乘的其中一方可以是一個常數，也可以是一個和矩陣行向量等長（即列數）的向量。

即或

因為在點乘過程中，會自動將常數或者向量進行擴維。

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()))