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fcn_activate_function_plt_sean.py
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import numpy as np
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
def sigmoid(x):
return 1 / (1 + np.exp(-x))
def ddx_sigmoid(x):
return sigmoid(x)*(1-sigmoid(x))
def tanh(x):
return np.tanh(x)
def ddx_tanh(x):
return 1 - tanh(x)*tanh(x)
def relu(x):
res = []
for item in x:
if item > 0:
res.append(item)
else:
res.append(0)
return np.asarray(res)
def ddx_relu(x):
res = []
for item in x:
if item > 0:
res.append(1)
else:
res.append(0)
return np.asarray(res)
def leaky_relu(x, alpha):
res = []
for item in x:
if item > 0:
res.append(item)
else:
res.append(item*alpha)
return np.asarray(res)
def ddx_leaky_relu(x, alpha):
res = []
for item in x:
if item > 0:
res.append(1)
else:
res.append(alpha)
return np.asarray(res)
def softplus(x):
return np.log(1+np.exp(x))
def ddx_softplus(x):
return 1/(1+np.exp(-x))
if __name__ == '__main__':
# evenly sampled time at 200ms intervals
input_range = np.arange(-3., 3., 0.025)
out_sigmoid = sigmoid(input_range)
out_tanh = tanh(input_range)
out_relu = relu(input_range)
out_lrelu = leaky_relu(input_range,0.2)
out_softplus = softplus(input_range)
out_ddx_sigmoid = ddx_sigmoid(input_range)
out_ddx_tanh = ddx_tanh(input_range)
out_ddx_relu = ddx_relu(input_range)
out_ddx_lrelu = ddx_leaky_relu(input_range,0.2)
out_ddx_softplus = ddx_softplus(input_range)
# --- Functions ---
# Fig size
figPres = plt.figure(figsize=(8, 6))
axPres = figPres.add_subplot(111)
fig_size = plt.rcParams["figure.figsize"]
fig_size[0] = 8
fig_size[1] = 6
plt.rcParams["figure.figsize"] = fig_size
# Axis lines
plt.axhline(0, color='black', linewidth=0.5, alpha=0.5)
plt.axvline(0, color='black', linewidth=0.5, alpha=0.5)
relu_pos = len(input_range)//2
# Lines
plt.plot(input_range, out_sigmoid, '-', linewidth=2, c='#bca72d')
plt.plot(input_range[relu_pos:], out_relu[relu_pos:], '-', linewidth=5, c='darkblue', alpha=1)
plt.plot(input_range[:relu_pos+1], out_relu[:relu_pos+1], '-', linewidth=2, c='darkblue', alpha=1)
plt.plot(input_range, out_tanh, '-', linewidth=2, c='#258458')
# plt.plot(input_range, out_lrelu, '-', linewidth=2, c='red', alpha=1)
# plt.plot(input_range, out_softplus, '-', linewidth=2, c='orange', alpha=1)
# Legend
p_sig = mpatches.Patch(facecolor='#bca72d', label='Sigmoid', lw=1, edgecolor='black')
p_rel = mpatches.Patch(facecolor='darkblue', label='ReLU', lw=1, edgecolor='black')
p_tan = mpatches.Patch(facecolor='#258458', label='Tanh', lw=1, edgecolor='black')
#p_lrel = mpatches.Patch(facecolor='red', label='Leaky ReLU', lw=1, edgecolor='black')
#p_soft = mpatches.Patch(facecolor='orange', label='Softplus', lw=1, edgecolor='black')
plt.legend(handles = [p_sig, p_tan, p_rel], loc='upper left')
# Plot properties, axis etc
plt.gca().yaxis.grid(True, linestyle='-', linewidth=0.5, alpha=0.2)
plt.gca().xaxis.grid(True, linestyle='-', linewidth=0.5, alpha=0.2)
plt.xticks([-3, -2, -1, 0, 1, 2, 3], [-3, -2, -1, 0, 1, 2, 3], rotation='horizontal', fontsize=13)
plt.yticks([-3, -2, -1, 0, 1, 2, 3], [-3, -2, -1, 0, 1, 2, 3], rotation='horizontal', fontsize=13)
axes = plt.gca()
axes.set_xlim([-3, 3])
axes.set_ylim([-3, 3])
axPres.yaxis.set_label_coords(-0.06,0.475)
axPres.yaxis.tick_right()
plt.xlabel('x', fontsize=17)
plt.ylabel('f(x)', fontsize=17, rotation='horizontal')
plt.axhline(0, color='black', linewidth=1, alpha=0.5)
plt.axvline(0, color='black', linewidth=1, alpha=0.5)
plt.savefig('Activation.png')
plt.show()
# --- Derivatives ---
# Fig size
figPres = plt.figure(figsize=(8, 6))
axPres = figPres.add_subplot(111)
fig_size = plt.rcParams["figure.figsize"]
fig_size[0] = 8
fig_size[1] = 6
plt.rcParams["figure.figsize"] = fig_size
# Axis lines
plt.axhline(0, color='black', linewidth=1, alpha=0.5)
plt.axvline(0, color='black', linewidth=1, alpha=0.5)
# Lines
plt.plot(input_range, out_ddx_softplus, '-', linewidth=2, c='orange')
plt.plot(input_range[relu_pos+1:], out_ddx_relu[relu_pos+1:], '-', linewidth=5, c='darkblue', alpha=1)
plt.plot(input_range[:relu_pos+1], out_ddx_relu[:relu_pos+1], '-', linewidth=2, c='darkblue', alpha=1)
plt.plot(input_range[:relu_pos+1], out_ddx_lrelu[:relu_pos+1], '-', linewidth=2, c='red', alpha=1)
#plt.plot(input_range, out_ddx_lrelu, '-', linewidth=2, c='red', alpha=1)
plt.plot(input_range, out_ddx_tanh, '-', linewidth=2, c='#258458')
plt.plot(input_range, out_ddx_sigmoid, '-', linewidth=2, c='#bca72d')
plt.plot(input_range[relu_pos+1:], out_ddx_lrelu[relu_pos+1:], '-', linewidth=2, c='red', alpha=1)
# Legend
p_sig = mpatches.Patch(facecolor='#bca72d', label='Sigmoid', lw=1, edgecolor='black')
p_rel = mpatches.Patch(facecolor='darkblue', label='ReLU', lw=1, edgecolor='black')
p_tan = mpatches.Patch(facecolor='#258458', label='Tanh', lw=1, edgecolor='black')
p_lrel = mpatches.Patch(facecolor='red', label='Leaky ReLU', lw=1, edgecolor='black')
p_soft = mpatches.Patch(facecolor='orange', label='Softplus', lw=1, edgecolor='black')
plt.legend(handles = [p_sig, p_tan, p_rel, p_lrel, p_soft], loc='upper left')
# Plot properties, axis etc
plt.gca().yaxis.grid(True, linestyle='-', linewidth=0.5, alpha=0.2)
plt.gca().xaxis.grid(True, linestyle='-', linewidth=0.5, alpha=0.2)
plt.xticks([-3, -2, -1, 0, 1, 2, 3], [-3, -2, -1, 0, 1, 2, 3], rotation='horizontal', fontsize=13)
plt.yticks([-0.5, 0, 0.5, 1, 1.5],[-0.5, 0, 0.5, 1, 1.5], rotation='horizontal', fontsize=13)
axes = plt.gca()
axes.set_xlim([-3, 3])
axes.set_ylim([-0.5, 1.5])
axPres.yaxis.set_label_coords(-0.06,0.475)
axPres.yaxis.tick_right()
plt.xlabel('x', fontsize=17)
plt.ylabel('f \'(x)', fontsize=17, rotation='horizontal')
plt.savefig('Activation_Derivative.png')
plt.show()