避免 for 循环在 3d 数组上运行线性回归

Question

我需要在 3d-Array 中运行线性回归，例如：-

数组 = np.arange(3*4*5).reshape(3,4,5)

array([[[ 0,  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]]])

我需要在 [0,20,40], [1,21,41] ....[5,25,45]....[19,39, 59] 上运行 LR 我正在使用以下代码：-

LrCalcRate = np.array([])
col_nums = 3
for j in range(Array.shape[1]):
    for i in range(Array.shape[2]):
        y = Array[:, j, i].T
        x = np.arange(col_nums)
        A = np.vstack([x, np.ones(len(x))]).T
        m, c = np.linalg.lstsq(A, y)[0]
        LrCalcRate = np.append(LrCalcRate, -m)

两个for循环很费时间，不使用for循环可以优化吗？

Answer 1

你写的等价于

x = np.arange(col_nums)
A = np.vstack([x, np.ones(len(x))]).T
-np.linalg.lstsq(A, a.reshape(a.shape[0], -1))[0][0]

例如，使用为每个目标生成不同斜率的数据：

In [9]: a = (np.linspace(0, 2, num=3*4*5)**2).reshape(3,4,5)                                

In [11]: lr_calc_rate = np.array([]) 
    ...: col_nums = 3 
    ...: for j in range(a.shape[1]): 
    ...:     for i in range(a.shape[2]): 
    ...:         y = a[:, j, i].T 
    ...:         x = np.arange(col_nums) 
    ...:         A = np.vstack([x, np.ones(len(x))]).T 
    ...:         m, c = np.linalg.lstsq(A, y)[0] 
    ...:         lr_calc_rate = np.append(lr_calc_rate, -m) 
    ...: lr_calc_rate

Out[11]: 
array([-0.91927607, -0.96523987, -1.01120368, -1.05716748, -1.10313128,
       -1.14909509, -1.19505889, -1.24102269, -1.2869865 , -1.3329503 ,
       -1.37891411, -1.42487791, -1.47084171, -1.51680552, -1.56276932,
       -1.60873312, -1.65469693, -1.70066073, -1.74662453, -1.79258834])

In [12]: x = np.arange(col_nums)
    ...: A = np.vstack([x, np.ones(len(x))]).T
    ...: -np.linalg.lstsq(A, a.reshape(3, -1))[0][0]

Out[12]: 
array([-0.91927607, -0.96523987, -1.01120368, -1.05716748, -1.10313128,
       -1.14909509, -1.19505889, -1.24102269, -1.2869865 , -1.3329503 ,
       -1.37891411, -1.42487791, -1.47084171, -1.51680552, -1.56276932,
       -1.60873312, -1.65469693, -1.70066073, -1.74662453, -1.79258834])