计算梯度的方法

计算梯度的三种方法： 数值法(numerical gradient)，解析法(analytic gradient)，反向传播法(Back propagation gradient)

一个简单的函数：

Python:

f(x,y,z)=(x+y)z

# coding=gbk

"""
function : f(x,y,z) = (x+y)z
"""
# first method   解析法
def grad1(x,y,z):
    dx = z
    dy = z
    dz = (x+y)
    return (dx,dy,dz)
# second method  数值法
def grad2(x,y,z,epi): 
    # dx
    fx1 = (x+epi+y)*z
    fx2 = (x-epi+y)*z
    dx = (fx1-fx2)/(2*epi)
    # dy
    fy1 = (x+y+epi)*z
    fy2 = (x+y-epi)*z
    dy = (fy1-fy2)/(2*epi)
    # dz
    fz1 = (x+y)*(z+epi)
    fz2 = (x+y)*(z-epi)
    dz = (fz1-fz2)/(2*epi)
    return (dx,dy,dz)
# third method 反向传播法
def grad3(x,y,z): 
    # forward
    p = x+y;
    f = p*z;    
    # backward
    dp = z
    dz = p
    dx = 1 * dp
    dy = 1 * dp
    return (dx,dy,dz)

print ("<df/dx,df/dy,df/dz>: %.2f %.2f %.2f"%(grad1(1,2,3)))       
print ("<df/dx,df/dy,df/dz>: %.2f %.2f %.2f"%(grad2(1,2,3,1e-5)))
print ("<df/dx,df/dy,df/dz>: %.2f %.2f %.2f"%(grad3(1,2,3)))
 
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结果：

<df/dx,df/dy,df/dz>: 3.00 3.00 3.00
<df/dx,df/dy,df/dz>: 3.00 3.00 3.00
<df/dx,df/dy,df/dz>: 3.00 3.00 3.00