引子

Matlab中有一個函式叫做find,可以很方便地尋找陣列內特定元素的下標，即：Find indices and values of nonzero elements。
這個函式非常有用。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函式找到最小值對應的下標，即M點橫座標和縱座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函式實現的程式碼：

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函式

Syntax: np.where(conditions, [x,y])
具體實現程式碼如下：

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函式

Syntax: List.index(aimElement)
注意：此處需將NumPy陣列轉換成List格式的資料。
具體實現程式碼如下：

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’