tensorflow求导和梯度计算

1.函数求一阶导

import tensorflow as tf tf.enable_eager_execution() tfe=tf.contrib.eager from math import  pi def f(x):     return tf.square(tf.sin(x)) assert f(pi/2).numpy()==1.0 sess=tf.Session() grad_f=tfe.gradients_function(f) print(grad_f(np.zeros(1))[0].numpy()) 

2.高阶函数求导

import numpy as np def  f(x):     return tf.square(tf.sin(x))  def grad(f):     return lambda x:tfe.gradients_function(f)(x)[0]  x=tf.lin_space(-2*pi,2*pi,100) # print(grad(f)(x).numpy()) x=x.numpy() import matplotlib.pyplot as plt plt.plot(x,f(x).numpy(),label="f") plt.plot(x,grad(f)(x).numpy(),label="first derivative")#一阶导 plt.plot(x,grad(grad(f))(x).numpy(),label="second derivative")#二阶导 plt.plot(x,grad(grad(grad(f)))(x).numpy(),label="third derivative")#三阶导 plt.legend() plt.show()

def f(x,y):     output=1     for i in range(int(y)):         output=tf.multiply(output,x)     return output  def g(x,y):     return tfe.gradients_function(f)(x,y)[0]  print(f(3.0,2).numpy()) #f(x)=x^2 print(g(3.0,2).numpy()) #f'(x)=2*x print(f(4.0,3).numpy())#f(x)=x^3 print(g(4.0,3).numpy())#f(x)=3x^2

3.函数求一阶偏导

x=tf.ones((2,2)) with tf.GradientTape(persistent=True) as t:     t.watch(x)     y=tf.reduce_sum(x)     z=tf.multiply(y,y)      dz_dy=t.gradient(z,y) print(dz_dy.numpy()) dz_dx=t.gradient(z,x) print(dz_dx.numpy()) for i in [0, 1]:   for j in [0, 1]:    print(dz_dx[i][j].numpy() )

4.函数求二阶偏导

x=tf.constant(2.0) with tf.GradientTape() as t:     with tf.GradientTape() as t2:         t2.watch(x)         y=x*x*x     dy_dx=t2.gradient(y,x) d2y_dx2=t.gradient(dy_dx,x)  print(dy_dx.numpy()) print(d2y_dx2.numpy())