用数组表达式完成数据操作任务，无需写大量循环。向量化的数组操作会比纯 Python 的等价实现快一到两个数量级。
In [42]: points = np.arange(-5, 5, 0.01) # 1000 equally spaced points
In [44]: xs, ys = np.meshgrid(points, points) # np.meshgrid 接受两个一维数组,(x,y)对生成一个二维矩阵
In [45]: xs
Out[45]:
array([[-5. , -4.99, -4.98, ..., 4.97, 4.98, 4.99],
[-5. , -4.99, -4.98, ..., 4.97, 4.98, 4.99],
[-5. , -4.99, -4.98, ..., 4.97, 4.98, 4.99],
...,
[-5. , -4.99, -4.98, ..., 4.97, 4.98, 4.99],
[-5. , -4.99, -4.98, ..., 4.97, 4.98, 4.99],
[-5. , -4.99, -4.98, ..., 4.97, 4.98, 4.99]])
In [46]: ys
Out[46]:
array([[-5. , -5. , -5. , ..., -5. , -5. , -5. ],
[-4.99, -4.99, -4.99, ..., -4.99, -4.99, -4.99],
[-4.98, -4.98, -4.98, ..., -4.98, -4.98, -4.98],
...,
[ 4.97, 4.97, 4.97, ..., 4.97, 4.97, 4.97],
[ 4.98, 4.98, 4.98, ..., 4.98, 4.98, 4.98],
[ 4.99, 4.99, 4.99, ..., 4.99, 4.99, 4.99]])
In [65]: z = np.sqrt(xs ** 2 + ys ** 2)
In [66]: z
Out[66]:
array([[7.07106781, 7.06400028, 7.05693985, ..., 7.04988652, 7.05693985,
7.06400028],
[7.06400028, 7.05692568, 7.04985815, ..., 7.04279774, 7.04985815,
7.05692568],
[7.05693985, 7.04985815, 7.04278354, ..., 7.03571603, 7.04278354,
7.04985815],
...,
[7.04988652, 7.04279774, 7.03571603, ..., 7.0286414 , 7.03571603,
7.04279774],
[7.05693985, 7.04985815, 7.04278354, ..., 7.03571603, 7.04278354,
7.04985815],
[7.06400028, 7.05692568, 7.04985815, ..., 7.04279774, 7.04985815,
7.05692568]])
In [67]: import matplotlib.pyplot as plt
In [68]: plt.imshow(z, cmap=plt.cm.gray); plt.colorbar()
Out[68]:
In [69]: plt.title("Image plot of $\sqrt{x^2 + y^2}$ for a grid of values")
Out[69]: Text(0.5, 1.0, 'Image plot of $\\sqrt{x^2 + y^2}$ for a grid of values')
In [70]: plt.show()
