From 21a726e134b2b6295655f5307726d88645db3dcf Mon Sep 17 00:00:00 2001
From: p4w2aybsf <2363061197@qq.com>
Date: Thu, 29 Apr 2021 17:15:40 +0800
Subject: [PATCH] Add 'functions.py'

---
 functions.py | 61 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 61 insertions(+)
 create mode 100644 functions.py

diff --git a/functions.py b/functions.py
new file mode 100644
index 0000000..ec02dd0
--- /dev/null
+++ b/functions.py
@@ -0,0 +1,61 @@
+# coding: utf-8
+import numpy as np
+
+
+def identity_function(x):
+    return x
+
+
+def step_function(x):
+    return np.array(x > 0, dtype=np.int)
+
+
+def sigmoid(x):
+    return 1 / (1 + np.exp(-x))    
+
+
+def sigmoid_grad(x):
+    return (1.0 - sigmoid(x)) * sigmoid(x)
+    
+
+def relu(x):
+    return np.maximum(0, x)
+
+
+def relu_grad(x):
+    grad = np.zeros(x)
+    grad[x>=0] = 1
+    return grad
+    
+
+def softmax(x):
+    if x.ndim == 2:
+        x = x.T
+        x = x - np.max(x, axis=0)
+        y = np.exp(x) / np.sum(np.exp(x), axis=0)
+        return y.T 
+
+    x = x - np.max(x) # 溢出对策
+    return np.exp(x) / np.sum(np.exp(x))
+
+
+def mean_squared_error(y, t):
+    return 0.5 * np.sum((y-t)**2)
+
+
+def cross_entropy_error(y, t):
+    if y.ndim == 1:
+        t = t.reshape(1, t.size)
+        y = y.reshape(1, y.size)
+        
+    # 监督数据是one-hot-vector的情况下，转换为正确解标签的索引
+    if t.size == y.size:
+        t = t.argmax(axis=1)
+             
+    batch_size = y.shape[0]
+    return -np.sum(np.log(y[np.arange(batch_size), t] + 1e-7)) / batch_size
+
+
+def softmax_loss(X, t):
+    y = softmax(X)
+    return cross_entropy_error(y, t)