Dot matrix multiplication and differentiation of:
1) dot (ie, "*") ---- multiply each matrix corresponding element
If w is m * 1 matrix, x is an m * n matrix, we will obtain a multiplication result by the point m * n matrix.
If w is a m * n matrix, x is an m * n matrix, the multiplication results obtained will point a m * n matrix.
w is the number of columns can only be 1 or equal to the number of columns of x (i.e., n), the number of rows the number of rows w and x equal to multiplication.
2) matrix multiplication ---- do operations in accordance with the rules of matrix multiplication
If w is an m * p matrix, x is p * n matrix, the matrix multiplication result will be obtained by a m * n matrix.
Only the number of columns w == x number of lines of time before multiplication
1. numpy
1) dot
1 import numpy as np
2
3 w = np.array([[0.4], [1.2]])
4 x = np.array([range(1,6), range(5,10)])
5
6 print w
7 print x
8 print w*xFIG results are as follows:
2) matrix multiplication
1 import numpy as np
2
3 w = np.array([[0.4, 1.2]])
4 x = np.array([range(1,6), range(5,10)])
5
6 print w
7 print x
8 print np.dot(w,x)Results are as follows:
2. tensorflow
1) dot
1 import tensorflow as tf
2
3 w = tf.Variable([[0.4], [1.2]], dtype=tf.float32) # w.shape: [2, 1]
4 x = tf.Variable([range(1,6), range(5,10)], dtype=tf.float32) # x.shape: [2, 5]
5 y = w * x # 等同于 y = tf.multiply(w, x) y.shape: [2, 5]
6
7 sess = tf.Session()
8 init = tf.global_variables_initializer()
9 sess.run(init)
10
11 print sess.run(w)
12 print sess.run(x)
13 print sess.run(y)Results are as follows:
2) matrix multiplication
1 # coding:utf-8
2 import tensorflow as tf
3
4 w = tf.Variable([[0.4, 1.2]], dtype=tf.float32) # w.shape: [1, 2]
5 x = tf.Variable([range(1,6), range(5,10)], dtype=tf.float32) # x.shape: [2, 5]
6 y = tf.matmul(w, x) # y.shape: [1, 5]
7
8 sess = tf.Session()
9 init = tf.global_variables_initializer()
10 sess.run(init)
11
12 print sess.run(w)
13 print sess.run(x)
14 print sess.run(y)Results are as follows:
