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引子
Matlab中有一個函數叫做find,可以很方便地尋找數組內特定元素的下標,即:Find indices and values of nonzero elements。
這個函數非常有用。比如,我們想計算圖1中點Q(x0, y0)拋物線的最短距離。一個可以實施的方法是:計算出拋物線上所有點到Q點的距離,找到最小值,用find函數找到最小值對應的下標,即M點橫坐標和縱坐標對應的元素的下標,M點到Q點的距離就是最短距離。
首先給出Matlab使用find函數實現的代碼:
a = linspace(-5,5,1000); b = a .^2; x0 = 4; y0 = 4; dis = sqrt((a - x0).^2 + (b - y0).^2); mm = find (dis == min(dis)); a0 = a(mm); b0 = b(mm); disMin = sqrt((a0 - x0).^2 + (b0 - y0).^2); plot(a, b); hold on; scatter(x0, y0, 'k*'); scatter(a0, b0, 'k*'); xx = [a0, x0]; yy = [b0, y0]; plot(xx, yy);
NumPy中的where函數
Syntax: np.where(conditions, [x,y])
具體實現代碼如下:
import numpy as np import math import matplotlib.pyplot as plt a = np.linspace(-5, 5, 10000) b = a * a x0 = 4 y0 =4 num = np.linspace(0, len(a) - 1, len(a)) dis = np.linspace(0, 0, len(a)) for k in num: k = int(k) dis[k] = dis[k] + math.sqrt((a[k] -x0) **2 + (b[k] - y0) **2) disMin = min(dis) disMinIndex = np.where(dis == disMin) disMin0 = math.sqrt((a[disMinIndex] - x0) **2 + (b[disMinIndex] - y0) **2) print('The mininum distance:',disMin) print('The mininum distance:',disMin0) print(type(dis)) a0 = a[disMinIndex] b0 = b[disMinIndex] fig = plt.figure(figsize = (6,6), dpi = 200) ax1 = plt.subplot(1,1,1) line11 = ax1.scatter(a,b,s = 1) line12 = ax1.scatter(x0, y0, s = 100, marker = '*', color = 'darkorange') line13 = ax1.scatter(a0, b0, s = 100, marker = '*', color = 'darkorange') line14 = ax1.plot([x0,a0],[y0,b0], color = 'darkorange') line15 = ax1.text(4.2,4,'Q(x0,y0)') line16 = ax1.text(0.6,5, 'M(a0,b0)') line18 = plt.xlim(-5,5) line17 = plt.ylim(0,25) plt.savefig('C:/Users/BRIAR/Desktop/index.png') plt.show()
The mininum distance: 1.943317035
The mininum distance: 1.9433170350024023
class ‘numpy.ndarray'
List中的index函數
Syntax: List.index(aimElement)
注意:此處需將NumPy數組轉換成List格式的數據。
具體實現代碼如下:
import numpy as np import math import matplotlib.pyplot as plt a = np.linspace(-5, 5, 10000) b = a * a x0 = 4 y0 =4 num = np.linspace(0, len(a) - 1, len(a)) dis = np.linspace(0, 0, len(a)) for k in num: k = int(k) dis[k] = dis[k] + math.sqrt((a[k] -x0) **2 + (b[k] - y0) **2) disMin = min(dis) disList = dis.tolist() disMinIndex = disList.index(disMin) disMin0 = math.sqrt((a[disMinIndex] - x0) **2 + (b[disMinIndex] - y0) **2) print('The mininum distance:',disMin) print('The mininum distance:',disMin0) print(type(disList)) a0 = a[disMinIndex] b0 = b[disMinIndex] fig = plt.figure(figsize = (6,6), dpi = 200) ax1 = plt.subplot(1,1,1) line11 = ax1.scatter(a,b,s = 1) line12 = ax1.scatter(x0, y0, s = 100, marker = '*', color = 'darkorange') line13 = ax1.scatter(a0, b0, s = 100, marker = '*', color = 'darkorange') line14 = ax1.plot([x0,a0],[y0,b0], color = 'darkorange') line15 = ax1.text(4.2,4,'Q(x0,y0)') line16 = ax1.text(0.6,5, 'M(a0,b0)') line18 = plt.xlim(-5,5) line17 = plt.ylim(0,25) plt.savefig('C:/Users/BRIAR/Desktop/index.png') plt.show()
The mininum distance: 1.943317035
The mininum distance: 1.9433170350024023
class ‘list'
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