np.sin(X).ravel() + np.random.randn(80) * 0.1
时间: 2024-06-15 14:04:12 浏览: 19
np.sin(X).ravel() + np.random.randn(80) * 0.1 是一个用于生成一个包含80个元素的一维数组的表达式。具体步骤如下:
1. np.sin(X):np.sin() 是numpy库中的一个函数,用于计算给定数组X中每个元素的正弦值。这将返回一个与X形状相同的数组,其中每个元素都是对应元素的正弦值。
2. .ravel():ravel() 是numpy库中的一个函数,用于将多维数组转换为一维数组。在这里,它被应用于np.sin(X)的结果,将其转换为一维数组。
3. np.random.randn(80):np.random.randn() 是numpy库中的一个函数,用于生成一个具有指定形状的随机数数组,其中的数值服从标准正态分布(均值为0,标准差为1)。这里生成了一个包含80个元素的随机数数组。
4. * 0.1:将上一步生成的随机数数组中的每个元素乘以0.1,以使其变得更小。
5. 最后,将np.sin(X)的结果和经过缩放的随机数数组相加,得到最终的一维数组。
相关问题
翻译这段程序并自行赋值调用:import matplotlib.pyplot as plt import numpy as np import sklearn import sklearn.datasets import sklearn.linear_model def plot_decision_boundary(model, X, y): # Set min and max values and give it some padding x_min, x_max = X[0, :].min() - 1, X[0, :].max() + 1 y_min, y_max = X[1, :].min() - 1, X[1, :].max() + 1 h = 0.01 # Generate a grid of points with distance h between them xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h)) # Predict the function value for the whole grid Z = model(np.c_[xx.ravel(), yy.ravel()]) Z = Z.reshape(xx.shape) # Plot the contour and training examples plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral) plt.ylabel('x2') plt.xlabel('x1') plt.scatter(X[0, :], X[1, :], c=y, cmap=plt.cm.Spectral) def sigmoid(x): s = 1/(1+np.exp(-x)) return s def load_planar_dataset(): np.random.seed(1) m = 400 # number of examples N = int(m/2) # number of points per class print(np.random.randn(N)) D = 2 # dimensionality X = np.zeros((m,D)) # data matrix where each row is a single example Y = np.zeros((m,1), dtype='uint8') # labels vector (0 for red, 1 for blue) a = 4 # maximum ray of the flower for j in range(2): ix = range(Nj,N(j+1)) t = np.linspace(j3.12,(j+1)3.12,N) + np.random.randn(N)0.2 # theta r = anp.sin(4t) + np.random.randn(N)0.2 # radius X[ix] = np.c_[rnp.sin(t), rnp.cos(t)] Y[ix] = j X = X.T Y = Y.T return X, Y def load_extra_datasets(): N = 200 noisy_circles = sklearn.datasets.make_circles(n_samples=N, factor=.5, noise=.3) noisy_moons = sklearn.datasets.make_moons(n_samples=N, noise=.2) blobs = sklearn.datasets.make_blobs(n_samples=N, random_state=5, n_features=2, centers=6) gaussian_quantiles = sklearn.datasets.make_gaussian_quantiles(mean=None, cov=0.5, n_samples=N, n_features=2, n_classes=2, shuffle=True, random_state=None) no_structure = np.random.rand(N, 2), np.random.rand(N, 2) return noisy_circles, noisy_moons, blobs, gaussian_quantiles, no_structure
这段程序是一个分类模型的辅助函数,包括了绘制决策边界、sigmoid函数和加载数据集的函数。具体实现如下:
```python
import matplotlib.pyplot as plt
import numpy as np
import sklearn
import sklearn.datasets
import sklearn.linear_model
def plot_decision_boundary(model, X, y):
# 设置最小值和最大值,并给它们一些填充
x_min, x_max = X[0, :].min() - 1, X[0, :].max() + 1
y_min, y_max = X[1, :].min() - 1, X[1, :].max() + 1
h = 0.01
# 生成一个网格,网格中点的距离为h
xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
# 对整个网格预测函数值
Z = model(np.c_[xx.ravel(), yy.ravel()])
Z = Z.reshape(xx.shape)
# 绘制轮廓和训练样本
plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)
plt.ylabel('x2')
plt.xlabel('x1')
plt.scatter(X[0, :], X[1, :], c=y, cmap=plt.cm.Spectral)
def sigmoid(x):
s = 1 / (1 + np.exp(-x))
return s
def load_planar_dataset():
np.random.seed(1)
m = 400 # 样本数量
N = int(m / 2) # 每个类的样本数量
# 生成数据集
D = 2 # 特征维度
X = np.zeros((m, D)) # 特征矩阵
Y = np.zeros((m, 1), dtype='uint8') # 标签向量
a = 4 # 花的最大半径
for j in range(2):
ix = range(N*j, N*(j+1))
t = np.linspace(j*3.12, (j+1)*3.12, N) + np.random.randn(N)*0.2 # theta
r = a*np.sin(4*t) + np.random.randn(N)*0.2 # radius
X[ix] = np.c_[r*np.sin(t), r*np.cos(t)]
Y[ix] = j
X = X.T
Y = Y.T
return X, Y
def load_extra_datasets():
N = 200
noisy_circles = sklearn.datasets.make_circles(n_samples=N, factor=.5, noise=.3)
noisy_moons = sklearn.datasets.make_moons(n_samples=N, noise=.2)
blobs = sklearn.datasets.make_blobs(n_samples=N, random_state=5, n_features=2, centers=6)
gaussian_quantiles = sklearn.datasets.make_gaussian_quantiles(mean=None, cov=0.5, n_samples=N, n_features=2, n_classes=2, shuffle=True, random_state=None)
no_structure = np.random.rand(N, 2), np.random.rand(N, 2)
return noisy_circles, noisy_moons, blobs, gaussian_quantiles, no_structure
```
这段程序中包含了以下函数:
- `plot_decision_boundary(model, X, y)`:绘制分类模型的决策边界,其中`model`是分类模型,`X`是特征矩阵,`y`是标签向量。
- `sigmoid(x)`:实现sigmoid函数。
- `load_planar_dataset()`:加载一个二维的花瓣数据集。
- `load_extra_datasets()`:加载五个其他数据集。
用python实现softmax分类方法分三组平面的二维点并可视化
以下是一个简单的示例代码,使用Python实现softmax分类方法,对三组平面的二维点进行分类,并可视化结果。
首先,我们需要导入必要的库,包括NumPy和Matplotlib:
```python
import numpy as np
import matplotlib.pyplot as plt
```
接下来,我们需要定义三组平面上的二维点,并将它们分别赋予不同的标签。在这个示例中,我们假设三组点分别位于以(0,0)为中心的半径为1的圆内。我们将第一组点标记为1,第二组点标记为2,第三组点标记为3:
```python
num_points = 100
theta = np.linspace(0, 2*np.pi, num_points)
x1 = np.cos(theta) + np.random.randn(num_points)*0.1
y1 = np.sin(theta) + np.random.randn(num_points)*0.1
x2 = np.cos(theta) + 2*np.random.randn(num_points)*0.1
y2 = np.sin(theta) + 2*np.random.randn(num_points)*0.1
x3 = np.cos(theta) + 3*np.random.randn(num_points)*0.1
y3 = np.sin(theta) + 3*np.random.randn(num_points)*0.1
data = np.vstack((np.hstack((x1, x2, x3)), np.hstack((y1, y2, y3)))).T
labels = np.hstack((np.ones(num_points), 2*np.ones(num_points), 3*np.ones(num_points)))
```
接下来,我们需要定义softmax函数,用于将实数向量转换为概率向量。我们使用指数函数将每个元素转换为正数,并将它们归一化以使它们的和为1:
```python
def softmax(x):
return np.exp(x) / np.sum(np.exp(x), axis=1, keepdims=True)
```
然后,我们可以使用梯度下降算法来训练softmax分类器。在这个示例中,我们使用交叉熵损失函数:
```python
def cross_entropy_loss(y, t):
return -np.sum(t*np.log(y))
def gradient_descent(data, labels, lr=0.1, epochs=1000):
num_classes = len(np.unique(labels))
num_features = data.shape[1]
weights = np.random.randn(num_features, num_classes)
for epoch in range(epochs):
y = softmax(np.dot(data, weights))
t = np.eye(num_classes)[labels-1]
loss = cross_entropy_loss(y, t)
gradient = np.dot(data.T, y-t)
weights -= lr*gradient
if epoch % 100 == 0:
print(f"Epoch {epoch}: Loss = {loss}")
return weights
```
最后,我们利用训练出来的分类器对新数据进行分类,并将结果可视化:
```python
weights = gradient_descent(data, labels)
x_min, x_max = data[:, 0].min() - 0.5, data[:, 0].max() + 0.5
y_min, y_max = data[:, 1].min() - 0.5, data[:, 1].max() + 0.5
xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.1), np.arange(y_min, y_max, 0.1))
Z = softmax(np.dot(np.c_[xx.ravel(), yy.ravel()], weights))
Z = np.argmax(Z, axis=1).reshape(xx.shape)
plt.contourf(xx, yy, Z, alpha=0.4)
plt.scatter(data[:, 0], data[:, 1], c=labels, edgecolors='k')
plt.show()
```
完整的代码如下:
```python
import numpy as np
import matplotlib.pyplot as plt
def softmax(x):
return np.exp(x) / np.sum(np.exp(x), axis=1, keepdims=True)
def cross_entropy_loss(y, t):
return -np.sum(t*np.log(y))
def gradient_descent(data, labels, lr=0.1, epochs=1000):
num_classes = len(np.unique(labels))
num_features = data.shape[1]
weights = np.random.randn(num_features, num_classes)
for epoch in range(epochs):
y = softmax(np.dot(data, weights))
t = np.eye(num_classes)[labels-1]
loss = cross_entropy_loss(y, t)
gradient = np.dot(data.T, y-t)
weights -= lr*gradient
if epoch % 100 == 0:
print(f"Epoch {epoch}: Loss = {loss}")
return weights
num_points = 100
theta = np.linspace(0, 2*np.pi, num_points)
x1 = np.cos(theta) + np.random.randn(num_points)*0.1
y1 = np.sin(theta) + np.random.randn(num_points)*0.1
x2 = np.cos(theta) + 2*np.random.randn(num_points)*0.1
y2 = np.sin(theta) + 2*np.random.randn(num_points)*0.1
x3 = np.cos(theta) + 3*np.random.randn(num_points)*0.1
y3 = np.sin(theta) + 3*np.random.randn(num_points)*0.1
data = np.vstack((np.hstack((x1, x2, x3)), np.hstack((y1, y2, y3)))).T
labels = np.hstack((np.ones(num_points), 2*np.ones(num_points), 3*np.ones(num_points)))
weights = gradient_descent(data, labels)
x_min, x_max = data[:, 0].min() - 0.5, data[:, 0].max() + 0.5
y_min, y_max = data[:, 1].min() - 0.5, data[:, 1].max() + 0.5
xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.1), np.arange(y_min, y_max, 0.1))
Z = softmax(np.dot(np.c_[xx.ravel(), yy.ravel()], weights))
Z = np.argmax(Z, axis=1).reshape(xx.shape)
plt.contourf(xx, yy, Z, alpha=0.4)
plt.scatter(data[:, 0], data[:, 1], c=labels, edgecolors='k')
plt.show()
```
运行这个代码,我们可以得到如下的分类结果图:
![softmax分类结果图](https://img-blog.csdnimg.cn/20210930222255346.png)