B = np.array([0.0, 0, 1]).transpose()
def sig(x):
s = 1 / (1 + np.exp(-x))
return s
def f(p):
X = p
Y = np.dot(A, X)
return norm(Y - B)
p = np.array([0.0, 0, 0])
p = gd.gradientDescendent(f, p)
print(
"\n==================================================================================\n"
)
print("p = {}".format(p))
weights = np.array([p[0], p[1]])
bias = p[2]
inputArr = np.array([[0, 0], [0, 1], [1, 0], [1, 1]])
B = np.dot(inputArr, weights) + bias
print("Inputs: \n{}".format(inputArr))
print("\u03A3(in⋅w) + b = {}".format(B))
print("sig(\u03A3) = {}".format(sig(B)))
#1 0 | 0 x2 y2 o2
#1 1 | 1 x3 y3 o3
#sig(w1*x + w2*y + b) = o
#sig(w1*0 + w2*0 + b) = o0 => 0
#sig(w1*0 + w2*1 + b) = o1 => 0
#sig(w1*1 + w2*0 + b) = o2 => 0
#sig(w1*1 + w2*1 + b) = o3 => 1
#f(x,y,w) = (o0-0)^2 + (o1-0)^2 + (o2-0)^2 + (o3-1)^2
import gd2 as gd
import numpy as np
from numpy.linalg import norm # 縣代
B = np.array([0.0, 0, 1]) # B=[w1, w2, b]
def loss(B):
A = np.array([[0, 0, 1], [0, 1, 1], [1, 0, 1], [1, 1, 1]])
O = np.array([0.0, 0, 0, 1]) # 輸出
dot = np.dot(A, B) # A、B 內積
return np.linalg.norm(sigmoid(dot) - O,
2) # (o0-0)^2 + (o1-0)^2 + (o2-0)^2 + (o3-1)^2
def sigmoid(dot):
return 1.0 / (1 + np.exp(-dot)) # dot >= 0.5 -> 1; dot < 0.5 -> 0
gd.gradientDescendent(loss, B)
"""
A X = B ，求 X 是多少？
3x+2y=5
1x+1y=2
"""
import gd2 as gd
import numpy as np
A = np.array([[3.0, 2],[1, 1]])
B = np.array([5.0, 2]) # np.array([[5.0, 2]]).transpose()
def f(p): # 能量函數:計算 ||AX-B||，也就是 ||Y-B||
X = p.transpose()
Y = A.dot(X)
return np.linalg.norm(Y-B, 1)
p = np.array([0.0, 0])
gd.gradientDescendent(f, p, step=0.001)
Y = np.dot(A, X)
for i in Y:
i = sig(i)
i = 1 if i >= 0.5 else 0
return (np.linalg.norm(Y - B, 2))**2
A = np.array([
[0, 0, 1], # A矩陣為輸入
[0, 1, 1],
[1, 0, 1],
[1, 1, 1]
])
B = np.array([[0.0, 0, 0, 1]]) # B矩陣為標準答案
p = np.array([0.0, 0, 0]) # 設定 w1、w2、b 的初始值
p = gd2.gradientDescendent(f, p) # 用梯度下降法找最低點
print("\n\nw1 = {}, w2 = {}, b = {}".format(p[0], p[1], p[2]))
C = np.dot(A, p)
result = []
for i in C:
result.append(1) if i >= 0.5 else result.append(0)
print("\tx y | o")
print("\t----|--")
for i in range(len(result)):
print("\t{} {} | {}".format(A[i][0], A[i][1], result[i]))