#coding=utf-8
import numpy as np
import matplotlib.pyplot as plt
import h5py
import scipy
from PIL import Image
from scipy import ndimage
from lr_utils import load_dataset
def sigmoid(x):#啟用函式
"""
Compute the sigmoid of x
Arguments:
x -- A scalar or numpy array of any size
Return:
s -- sigmoid(x)
"""
### START CODE HERE ### (≈ 1 line of code)
s = 1 / (1+np.exp(-x))
### END CODE HERE ###
return s
# GRADED FUNCTION: sigmoid_derivative
def sigmoid_derivative(x):#啟用函式的導數
"""
Compute the gradient (also called the slope or derivative) of the sigmoid function with respect to its input x.
You can store the output of the sigmoid function into variables and then use it to calculate the gradient.
Arguments:
x -- A scalar or numpy array
Return:
ds -- Your computed gradient.
"""
### START CODE HERE ### (≈ 2 lines of code)
s = 1/(1+np.exp(-x))
ds = s*(1-s)
### END CODE HERE ###
return ds
# GRADED FUNCTION: image2vector
def image2vector(image):#圖片畫素矩陣轉置成一個列向量
"""
Argument:
image -- a numpy array of shape (length, height, depth)
Returns:
v -- a vector of shape (length*height*depth, 1)
"""
### START CODE HERE ### (≈ 1 line of code)
v = image.reshape((image.shape[0]*image.shape[1], image.shape[2])) # v.shape[0] = a ; v.shape[1] = b ; v.shape[2] = c
### END CODE HERE ###
return v
# GRADED FUNCTION: normalizeRows
def normalizeRows(x):#正則化，使用第二範數
"""
Implement a function that normalizes each row of the matrix x (to have unit length).
Argument:
x -- A numpy matrix of shape (n, m)
Returns:
x -- The normalized (by row) numpy matrix. You are allowed to modify x.
"""
### START CODE HERE ### (≈ 2 lines of code)
# Compute x_norm as the norm 2 of x. Use np.linalg.norm(..., ord = 2, axis = ..., keepdims = True)
x_norm = np.linalg.norm(x, ord = 2, axis = 1, keepdims = True)
# Divide x by its norm.
x = x / x_norm
### END CODE HERE ###
return x
# GRADED FUNCTION: softmax
def softmax(x):#計算softmax函式值
"""Calculates the softmax for each row of the input x.
Your code should work for a row vector and also for matrices of shape (n, m).
Argument:
x -- A numpy matrix of shape (n,m)
Returns:
s -- A numpy matrix equal to the softmax of x, of shape (n,m)
"""
### START CODE HERE ### (≈ 3 lines of code)
# Apply exp() element-wise to x. Use np.exp(...).
x_exp = np.exp(x)
# Create a vector x_sum that sums each row of x_exp. Use np.sum(..., axis = 1, keepdims = True).
x_sum = np.sum(x_exp, axis = 1, keepdims = True)
# Compute softmax(x) by dividing x_exp by x_sum. It should automatically use numpy broadcasting.
s = x_exp / x_sum
### END CODE HERE ###
return s
# GRADED FUNCTION: L1
def L1(yhat, y):#計算L1損失函式
"""
Arguments:
yhat -- vector of size m (predicted labels)
y -- vector of size m (true labels)
Returns:
loss -- the value of the L1 loss function defined above
"""
### START CODE HERE ### (≈ 1 line of code)
loss = np.sum(np.abs(y-yhat))
### END CODE HERE ###
return loss
# GRADED FUNCTION: L2
def L2(yhat, y):#計算L2損失函式
"""
Arguments:
yhat -- vector of size m (predicted labels)
y -- vector of size m (true labels)
Returns:
loss -- the value of the L2 loss function defined above
"""
### START CODE HERE ### (≈ 1 line of code)
loss = np.sum((y-yhat) * (y-yhat))
### END CODE HERE ###
return loss
if __name__=='__main__':#測試用例
x = np.array([1, 2, 3])
print sigmoid(x)
x = np.array([1, 2, 3])
print ("sigmoid_derivative(x) = " + str(sigmoid_derivative(x)))
# This is a 3 by 3 by 2 array, typically images will be (num_px_x, num_px_y,3) where 3 represents the RGB values
image = np.array([[[ 0.67826139, 0.29380381],
[ 0.90714982, 0.52835647],
[ 0.4215251 , 0.45017551]],
[[ 0.92814219, 0.96677647],
[ 0.85304703, 0.52351845],
[ 0.19981397, 0.27417313]],
[[ 0.60659855, 0.00533165],
[ 0.10820313, 0.49978937],
[ 0.34144279, 0.94630077]]])
print ("image2vector(image) = " + str(image2vector(image)))
x = np.array([
[0, 3, 4],
[1, 6, 4]])
print("normalizeRows(x) = " + str(normalizeRows(x)))
x = np.array([
[9, 2, 5, 0, 0],
[7, 5, 0, 0 ,0]])
print("softmax(x) = " + str(softmax(x)))
yhat = np.array([.9, 0.2, 0.1, .4, .9])
y = np.array([1, 0, 0, 1, 1])
print("L1 = " + str(L1(yhat,y)))
yhat = np.array([.9, 0.2, 0.1, .4, .9])
y = np.array([1, 0, 0, 1, 1])
print("L2 = " + str(L2(yhat,y)))
