Tensorflow矩陣運(yùn)算實(shí)例(矩陣相乘,點(diǎn)乘,行/列累加)

更新時(shí)間：2020年02月05日 16:15:02 作者：Kenn7

今天小編就為大家分享一篇Tensorflow矩陣運(yùn)算實(shí)例(矩陣相乘,點(diǎn)乘,行/列累加)，具有很好的參考價(jià)值，希望對(duì)大家有所幫助。一起跟隨小編過(guò)來(lái)看看吧

Tensorflow二維、三維、四維矩陣運(yùn)算（矩陣相乘，點(diǎn)乘，行/列累加）

1. 矩陣相乘

根據(jù)矩陣相乘的匹配原則，左乘矩陣的列數(shù)要等于右乘矩陣的行數(shù)。

在多維（三維、四維）矩陣的相乘中，需要最后兩維滿(mǎn)足匹配原則。

可以將多維矩陣?yán)斫獬桑海ň仃嚺帕?，矩陣），即后兩維為矩陣，前面的維度為矩陣的排列。

比如對(duì)于（2，2，4）來(lái)說(shuō)，視為2個(gè)（2，4）矩陣。

對(duì)于（2，2，2，4）來(lái)說(shuō)，視為2*2個(gè)（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(diǎn)乘

點(diǎn)乘指的是shape相同的兩個(gè)矩陣，對(duì)應(yīng)位置元素相乘，得到一個(gè)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(diǎn)乘的其中一方可以是一個(gè)常數(shù)，也可以是一個(gè)和矩陣行向量等長(zhǎng)（即列數(shù)）的向量。

即

因?yàn)樵邳c(diǎn)乘過(guò)程中，會(huì)自動(dòng)將常數(shù)或者向量進(jìn)行擴(kuò)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()))