diff --git a/README.md b/README.md
index 6172939..e87be84 100644
--- a/README.md
+++ b/README.md
@@ -1,8 +1,23 @@
 # pytorch study
 
-## ENV
+## BASE ENV
 ```shell
 conda create -n pt python=3.10 -y
 
 conda activate pt
+```
+
+## MAC
+```shell
+# 安装 pytorch v1.12版本已经正式支持了用于mac m1芯片gpu加速的mps后端
+conda install pytorch::pytorch torchvision torchaudio -c pytorch -y
+
+pip install numpy
+pip install pandas
+pip install matplotlib
+```
+
+## gpt4free
+```
+pip install -U g4f[all]
 ```
\ No newline at end of file
diff --git a/autograd.py b/autograd.py
new file mode 100644
index 0000000..21556e4
--- /dev/null
+++ b/autograd.py
@@ -0,0 +1,15 @@
+import torch
+from torch import autograd
+
+device = torch.device('mps')
+
+x = torch.tensor(1.)
+a = torch.tensor(2., requires_grad=True)
+b = torch.tensor(2., requires_grad=True)
+c = torch.tensor(3., requires_grad=True)
+
+y = a ** 2 * x + b * x + c ** 3
+
+print('before:', a.grad, b.grad, c.grad)
+grads = autograd.grad(y, [a, b, c])
+print('after:', grads[0], grads[1], grads[2])
diff --git a/gpt.py b/gpt.py
new file mode 100644
index 0000000..4a7a0a2
--- /dev/null
+++ b/gpt.py
@@ -0,0 +1,11 @@
+from g4f.client import Client
+
+content = "张量在机器学习中的主要用途"
+
+
+client = Client()
+response = client.chat.completions.create(
+    model="gpt-4o",
+    messages=[{"role": "user", "content": content}],
+)
+print(response.choices[0].message.content)
\ No newline at end of file
diff --git a/linear regression/1.py b/linear regression/1.py
new file mode 100644
index 0000000..dc455ef
--- /dev/null
+++ b/linear regression/1.py	
@@ -0,0 +1,56 @@
+import numpy as np
+import torch
+
+
+def compute_error_for_line_given_points(b, w, points):
+    totalError = 0
+    N = float(len(points))
+    for i in range(len(points)):
+        x = points[i][0]
+        y = points[i][1]
+        totalError += (y - (w * x + b)) ** 2
+    return totalError / N
+
+
+def step_gradient(b_current, w_current, points, learningRate):
+    b_gradient = torch.tensor(0.0, device=points.device, dtype=torch.float32)
+    w_gradient = torch.tensor(0.0, device=points.device, dtype=torch.float32)
+    N = float(len(points))
+    for i in range(len(points)):
+        x = points[i][0]
+        y = points[i][1]
+        b_gradient += -(2 / N) * (y - (w_current * x + b_current) + b_current)
+        w_gradient += -(2 / N) * x * (y - (w_current * x + b_current + b_current))
+    new_b = b_current - (learningRate * b_gradient)
+    new_w = w_current - (learningRate * w_gradient)
+    return [new_b, new_w]
+
+
+def gradient_descent_runner(points, starting_b, starting_w, learningRate, num_iterations):
+    b = torch.tensor(starting_b, device=points.device, dtype=torch.float32)
+    w = torch.tensor(starting_w, device=points.device, dtype=torch.float32)
+    for i in range(num_iterations):
+        b, w = step_gradient(b, w, points, learningRate)
+    return [b, w]
+
+
+def run():
+    # 修改为生成数据的文件路径
+    points_np = np.genfromtxt("data1.csv", delimiter=',').astype(np.float32)
+    points = torch.tensor(points_np, device='mps')
+    learning_rate = 0.0001  # 使用较小的学习率
+    initial_b = 0.0
+    initial_w = 0.0
+    num_iterations = 1000
+    print("Starting gradient descent at b={0},w={1},error={2}".format(initial_b, initial_w,
+                                                                      compute_error_for_line_given_points(initial_b,
+                                                                                                          initial_w,
+                                                                                                          points)))
+    print("running...")
+    [b, w] = gradient_descent_runner(points, initial_b, initial_w, learning_rate, num_iterations)
+    print("After gradient descent at b={0},w={1},error={2}".format(b.item(), w.item(),
+                                                                   compute_error_for_line_given_points(b, w, points)))
+
+
+if __name__ == '__main__':
+    run()
diff --git a/linear regression/data1.csv b/linear regression/data1.csv
new file mode 100644
index 0000000..338b71d
--- /dev/null
+++ b/linear regression/data1.csv	
@@ -0,0 +1,100 @@
+0.0,2.4360562173289115
+0.10101010101010101,2.4288710820592065
+0.20202020202020202,3.677943201375977
+0.30303030303030304,3.5029234515863217
+0.40404040404040403,4.007715980839878
+0.5050505050505051,3.95999321461469
+0.6060606060606061,3.220853916066527
+0.7070707070707071,3.2211460206798623
+0.8080808080808081,4.2516957270374505
+0.9090909090909091,4.311826715084292
+1.0101010101010102,4.153966583608258
+1.1111111111111112,4.224290328721461
+1.2121212121212122,4.551324602105953
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+1.9191919191919191,5.7260434379514065
+2.0202020202020203,5.607446671816119
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+8.98989898989899,15.526107019435932
+9.09090909090909,14.352357736719853
+9.191919191919192,15.843742065895144
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+9.595959595959595,15.622518083688107
+9.696969696969697,15.589081237426006
+9.797979797979798,15.511248085690712
+9.8989898989899,16.27050774059862
+10.0,16.1105549896166
diff --git a/linear regression/np_genPoints.py b/linear regression/np_genPoints.py
new file mode 100644
index 0000000..70fd9e2
--- /dev/null
+++ b/linear regression/np_genPoints.py	
@@ -0,0 +1,30 @@
+import numpy as np
+import csv
+
+# 定义回归方程参数
+w = 1.35
+b = 2.89
+
+# 生成x值范围
+x_min = 0
+x_max = 10
+
+# 生成100个在x轴附近的点
+x = np.linspace(x_min, x_max, 100)
+
+# 根据回归方程计算y值
+y = w * x + b
+
+# 添加一些噪声，使数据更真实
+y += np.random.normal(scale=0.5, size=y.shape)
+
+# 将x和y合并成一个二维数组
+data = np.column_stack((x, y))
+
+# 将数据保存到CSV文件
+with open('data1.csv', 'w', newline='') as csvfile:
+    writer = csv.writer(csvfile)
+    # 写入表头
+    # writer.writerow(['x', 'y'])
+    # 写入数据
+    writer.writerows(data)
diff --git a/linear regression/plt_print.py b/linear regression/plt_print.py
new file mode 100644
index 0000000..2e1d90c
--- /dev/null
+++ b/linear regression/plt_print.py	
@@ -0,0 +1,22 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+# 原始数据
+points = np.genfromtxt("data1.csv", delimiter=',')
+x = points[:, 0]
+y = points[:, 1]
+
+# 拟合直线
+x_range = np.linspace(min(x), max(x), 100)
+y_pred = 1.6455038785934448 * x_range + 1.827562689781189
+
+# 绘图
+plt.figure(figsize=(8, 6))
+plt.scatter(x, y, color='blue', label='Original data')
+plt.plot(x_range, y_pred, color='red', label='Fitted line')
+plt.xlabel('X')
+plt.ylabel('Y')
+plt.title('Fitting a line to random data')
+plt.legend()
+plt.grid(True)
+plt.savefig('print1.png')
diff --git a/linear regression/print1.png b/linear regression/print1.png
new file mode 100644
index 0000000..a008b51
Binary files /dev/null and b/linear regression/print1.png differ
diff --git a/requirements.txt b/requirements.txt
new file mode 100644
index 0000000..11027f8
--- /dev/null
+++ b/requirements.txt
@@ -0,0 +1,7 @@
+pytorch::pytorch
+torchvision
+torchaudio
+pandas
+matplotlib
+numpy
+g4f
\ No newline at end of file
diff --git a/test/macTest.py b/test/macTest.py
new file mode 100644
index 0000000..c4fc7d3
--- /dev/null
+++ b/test/macTest.py
@@ -0,0 +1,6 @@
+import torch
+
+print(torch.backends.mps.is_available())
+print(torch.backends.mps.is_built())
+
+print(torch.device("mps"))
\ No newline at end of file
diff --git a/test/performance.py b/test/performance.py
new file mode 100644
index 0000000..356a313
--- /dev/null
+++ b/test/performance.py
@@ -0,0 +1,29 @@
+import torch
+import time
+
+print(torch.__version__)
+print(torch.backends.mps.is_available())
+print(torch.cuda.is_available())
+
+a = torch.randn(10000,1000)
+b = torch.randn(1000,2000)
+
+t0 = time.time()
+c = torch.matmul(a, b)
+t1 = time.time()
+print(a.device,t1-t0,c.norm(2))
+
+device = torch.device('mps')
+
+a = a.to(device)
+b = b.to(device)
+
+t0 = time.time()
+c = torch.matmul(a, b)
+t1 = time.time()
+print(a.device,t1-t0,c.norm(2))
+
+t0 = time.time()
+c = torch.matmul(a, b)
+t1 = time.time()
+print(a.device,t1-t0,c.norm(2))
\ No newline at end of file