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()
Categories: numpyPython

0 Comments

Leave a Reply

Your email address will not be published.