山东大学人工智能导论实验1工程文件-numpy的基本操作

import os import numpy as np import math def sigmoid(x): """ Compute the sigmoid of x Arguments: x -- A scalar or numpy array of any size Return: s -- sigmoid(x) """ # write your code here fx = [] for num in x: fx.append(1 / (1 + math.exp(-num))) return fx def sigmoid_derivative(x): """ 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. """ # write your code here y = [] fx = [] for num in x: y.append(1 / (1 + math.exp(-num))) for n in y: fx.append(n * (1 - n)) return fx def softmax(x): """Calculates the softmax for the input x. Argument: x -- A numpy matrix of shape (n,) Returns: s -- A numpy matrix equal to the softmax of x, of shape (n,) """ # write your code here x_exp = np.exp(x) x_sum = np.sum(x_exp, axis=0, keepdims=True) fx = x_exp / x_sum return fx def cross_entropy_loss(target, prediction): """ Compute the cross entropy loss between target and prediction Arguments: target -- the real label, a scalar or numpy array size = (n,) prediction -- the output of model, a scalar or numpy array, size=(n, c) Return: mean loss -- cross_entropy_loss(target, prediction) """ # write your code here batch_loss = 0. for i in range(prediction.shape[0]): numerator = np.exp(prediction[i, target[i]]) # 分子 denominator = np.sum(np.exp(prediction[i, :])) # 分母 # Calculating individual losses loss = -np.log(numerator / denominator) # 损失累加 batch_loss += loss return batch_loss if __name__ == '__main__': ## don't edit x = np.array([-1, 0, 5]) print("sigmoid(x) = ", sigmoid(x)) print("sigmoid_derivative(x) = ", sigmoid_derivative(x)) print("softmax(x) = ", softmax(x)) prediction = np.array([[0.093, 0.1939, -1.0649, 0.4476, -2.0769], [-1.8024, 0.3696, 0.7796, -1.0346, 0.473], [0.5593, -2.5067, -2.1275, 0.5548, -1.6639]]) target = np.array([2, 1, 4]) print("cross entropy loss = ", cross_entropy_loss(target, prediction))