np.ravel()
numpy中的 ravel() 和 flatten()函数功能一致，用于将多维数组降位一维，两者的区别numpy.flatten()返回一份拷贝，对拷贝所做的修改不会影响（reflects）原始矩阵，而numpy.ravel()返回的是视图会影响原始矩阵。
ravel(): 不会产生原来数据的副本
flatten（）：返回源数据副本
squeeze（）：只能对维度为1的维度降维
reshape(-1)：可以拉平多维数组>>>#代码用于生成100*100的网格数据点，后续可用于matplotlib.pyplot.contour画图
>>>import numpy as np
>>>x=np.linspace(0,100,101)#return an 101*1 array from 0 to 101
>>>y=np.linspace(0,100,101)
>>>xx,yy=np.meshgrid(x,y)#生成网格数据
>>>xx
array([[ 0., 1., 2., ..., 98., 99., 100.],
[ 0., 1., 2., ..., 98., 99., 100.],
[ 0., 1., 2., ..., 98., 99., 100.],
...,
[ 0., 1., 2., ..., 98., 99., 100.],
[ 0., 1., 2., ..., 98., 99., 100.],
[ 0., 1., 2., ..., 98., 99., 100.]])
>>>yy
array([[ 0., 0., 0., ..., 0., 0., 0.],
[ 1., 1., 1., ..., 1., 1., 1.],
[ 2., 2., 2., ..., 2., 2., 2.],
...,
[ 98., 98., 98., ..., 98., 98., 98.],
[ 99., 99., 99., ..., 99., 99., 99.],
[100., 100., 100., ..., 100., 100., 100.]])
>>>xx.ravel()
array([ 0., 1., 2., ..., 98., 99., 100.])#len=10201
>>> yy.ravel()
array([ 0., 0., 0., ..., 100., 100., 100.])
>>> np.stack((xx.ravel(), yy.ravel()), axis = 1)
array([[ 0., 0.],
[ 1., 0.],
[ 2., 0.],
...,
[ 98., 100.],
[ 99., 100.],
[100., 100.]])np.meshgrid ()
numpy提供的numpy.meshgrid()函数可以让我们快速生成坐标矩阵XXX，YYY。
语法：X,Y = numpy.meshgrid(x, y)
输入的x，y，就是网格点的横纵坐标列向量（非矩阵）
输出的X，Y，就是坐标矩阵。
import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(0,1000,20)
y = np.linspace(0,500,20)
X,Y = np.meshgrid(x, y)
plt.plot(X, Y,
color='limegreen', # 设置颜色为limegreen
marker='.', # 设置点类型为圆点
linestyle='') # 设置线型为空，也即没有线连接点
plt.grid(True)
plt.show()np.stack ()
np.stack()，输入参数有两个，第一个为arrays，也就是用来作为堆叠的数组，要求形状维度必须相等，第二个参数为axis也就是指定依照哪个维度进行堆叠
>>> x=np.linspace(1,100,100)
>>> y=np.linspace(1,100,100)
>>> x
array([ 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11.,
12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22.,
23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33.,
34., 35., 36., 37., 38., 39., 40., 41., 42., 43., 44.,
45., 46., 47., 48., 49., 50., 51., 52., 53., 54., 55.,
56., 57., 58., 59., 60., 61., 62., 63., 64., 65., 66.,
67., 68., 69., 70., 71., 72., 73., 74., 75., 76., 77.,
78., 79., 80., 81., 82., 83., 84., 85., 86., 87., 88.,
89., 90., 91., 92., 93., 94., 95., 96., 97., 98., 99.,
100.])
>>> y
array([ 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11.,
12., 13., 14., 15., 16., 17., 18., 19., 20., 21., 22.,
23., 24., 25., 26., 27., 28., 29., 30., 31., 32., 33.,
34., 35., 36., 37., 38., 39., 40., 41., 42., 43., 44.,
45., 46., 47., 48., 49., 50., 51., 52., 53., 54., 55.,
56., 57., 58., 59., 60., 61., 62., 63., 64., 65., 66.,
67., 68., 69., 70., 71., 72., 73., 74., 75., 76., 77.,
78., 79., 80., 81., 82., 83., 84., 85., 86., 87., 88.,
89., 90., 91., 92., 93., 94., 95., 96., 97., 98., 99.,
100.])
>>> np.stack((x,y),axis=1)
array([[ 1., 1.],
[ 2., 2.],
[ 3., 3.],
...
[ 99., 99.],
[100., 100.]])Example:
QDA与LDA监督分类
from scipy import linalg
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
from matplotlib import colors
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis
# #############################################################################
# Colormap
cmap = colors.LinearSegmentedColormap(
'red_blue_classes',
{'red': [(0, 1, 1), (1, 0.7, 0.7)],
'green': [(0, 0.7, 0.7), (1, 0.7, 0.7)],
'blue': [(0, 0.7, 0.7), (1, 1, 1)]})
plt.cm.register_cmap(cmap=cmap)
# #############################################################################
# Generate datasets
def dataset_fixed_cov():
'''Generate 2 Gaussians samples with the same covariance matrix'''
n, dim = 300, 2
np.random.seed(0)
C = np.array([[0., -0.23], [0.83, .23]])
X = np.r_[np.dot(np.random.randn(n, dim), C),
np.dot(np.random.randn(n, dim), C) + np.array([1, 1])]
y = np.hstack((np.zeros(n), np.ones(n)))
return X, y
def dataset_cov():
'''Generate 2 Gaussians samples with different covariance matrices'''
n, dim = 300, 2
np.random.seed(0)
C = np.array([[0., -1.], [2.5, .7]]) * 2.
X = np.r_[np.dot(np.random.randn(n, dim), C),
np.dot(np.random.randn(n, dim), C.T) + np.array([1, 4])]
y = np.hstack((np.zeros(n), np.ones(n)))
return X, y
# #############################################################################
# Plot functions
def plot_data(lda, X, y, y_pred, fig_index):
splot = plt.subplot(2, 2, fig_index)
if fig_index == 1:
plt.title('Linear Discriminant Analysis')
plt.ylabel('Data with\n fixed covariance')
elif fig_index == 2:
plt.title('Quadratic Discriminant Analysis')
elif fig_index == 3:
plt.ylabel('Data with\n varying covariances')
tp = (y == y_pred) # True Positive
tp0, tp1 = tp[y == 0], tp[y == 1]
X0, X1 = X[y == 0], X[y == 1]
X0_tp, X0_fp = X0[tp0], X0[~tp0]
X1_tp, X1_fp = X1[tp1], X1[~tp1]
# class 0: dots
plt.scatter(X0_tp[:, 0], X0_tp[:, 1], marker='.', color='red')
plt.scatter(X0_fp[:, 0], X0_fp[:, 1], marker='x',
s=20, color='#990000') # dark red
# class 1: dots
plt.scatter(X1_tp[:, 0], X1_tp[:, 1], marker='.', color='blue')
plt.scatter(X1_fp[:, 0], X1_fp[:, 1], marker='x',
s=20, color='#000099') # dark blue
# class 0 and 1 : areas
nx, ny = 200, 100
x_min, x_max = plt.xlim()
y_min, y_max = plt.ylim()
xx, yy = np.meshgrid(np.linspace(x_min, x_max, nx),
np.linspace(y_min, y_max, ny))
Z = lda.predict_proba(np.c_[xx.ravel(), yy.ravel()])
Z = Z[:, 1].reshape(xx.shape)
plt.pcolormesh(xx, yy, Z, cmap='red_blue_classes',
norm=colors.Normalize(0., 1.), zorder=0)
plt.contour(xx, yy, Z, [0.5], linewidths=2., colors='white')
# means
plt.plot(lda.means_[0][0], lda.means_[0][1],
'*', color='yellow', markersize=15, markeredgecolor='grey')
plt.plot(lda.means_[1][0], lda.means_[1][1],
'*', color='yellow', markersize=15, markeredgecolor='grey')
return splot
def plot_ellipse(splot, mean, cov, color):
v, w = linalg.eigh(cov)
u = w[0] / linalg.norm(w[0])
angle = np.arctan(u[1] / u[0])
angle = 180 * angle / np.pi # convert to degrees
# filled Gaussian at 2 standard deviation
ell = mpl.patches.Ellipse(mean, 2 * v[0] ** 0.5, 2 * v[1] ** 0.5,
180 + angle, facecolor=color,
edgecolor='black', linewidth=2)
ell.set_clip_box(splot.bbox)
ell.set_alpha(0.2)
splot.add_artist(ell)
splot.set_xticks(())
splot.set_yticks(())
def plot_lda_cov(lda, splot):
plot_ellipse(splot, lda.means_[0], lda.covariance_, 'red')
plot_ellipse(splot, lda.means_[1], lda.covariance_, 'blue')
def plot_qda_cov(qda, splot):
plot_ellipse(splot, qda.means_[0], qda.covariance_[0], 'red')
plot_ellipse(splot, qda.means_[1], qda.covariance_[1], 'blue')
plt.figure(figsize=(10, 8), facecolor='white')
plt.suptitle('Linear Discriminant Analysis vs Quadratic Discriminant Analysis',
y=0.98, fontsize=15)
for i, (X, y) in enumerate([dataset_fixed_cov(), dataset_cov()]):
# Linear Discriminant Analysis
lda = LinearDiscriminantAnalysis(solver="svd", store_covariance=True)
y_pred = lda.fit(X, y).predict(X)
splot = plot_data(lda, X, y, y_pred, fig_index=2 * i + 1)
plot_lda_cov(lda, splot)
plt.axis('tight')
# Quadratic Discriminant Analysis
qda = QuadraticDiscriminantAnalysis(store_covariance=True)
y_pred = qda.fit(X, y).predict(X)
splot = plot_data(qda, X, y, y_pred, fig_index=2 * i + 2)
plot_qda_cov(qda, splot)
plt.axis('tight')
plt.tight_layout()
plt.subplots_adjust(top=0.92)
plt.show()
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