在 Python 中提取多个子矩阵

Question

如果我的稀疏矩阵有多个非零值区域，我会尝试提取多个子矩阵。

例如， 假设我有以下矩阵：

x = np.array([0,0,0,0,0,0],
             [0,1,1,0,0,0],
             [0,1,1,0,0,1],
             [0,0,0,0,1,1],
             [0,0,0,0,1,0])

然后我需要能够提取具有非零值的区域，即

x_1 = [[1,1]
       [1,1]]

和

x_2 = [[0,1],
       [1,1],
       [1,0]]

我一直在使用 np.where() 来查找非零值的索引并仅返回一个子矩阵的区域，但是如何将其扩展到我的稀疏矩阵中的所有可能子区域？

谢谢！

Answer 1

程序：

1. 用全零删除前导和尾随行和列。 （不是中间的）
2. 在这些索引上查找所有空行和列并拆分矩阵。这将创建一个矩阵列表
3. 对于每个新创建的矩阵，递归地重复该过程，直到无法进一步拆分

代码：

def delrc(arr):
    while True:     # delete leading rows with all zeros
    if np.all(arr[0]==0):
        arr=np.delete(arr,0,axis=0)
    else: break
    while True:     # delete trailing rows with all zeros
    if np.all(arr[-1]==0):
        arr=np.delete(arr,-1,axis=0)
    else: break
    while True:     # delete leading cols with all zeros
    if np.all(arr[:,0]==0):
        arr=np.delete(arr,0,axis=1)
    else: break
    while True:     # delete trailing cols with all zeros
    if np.all(arr[:,-1]==0):
        arr=np.delete(arr,-1,axis=1)
    else: break
    return arr

def rcsplit(arr):
    if np.all(arr==0): return []    # if all zeros return
    global  res
    arr = delrc(arr)        # delete leading/trailing rows/cols with all zeros
    print arr
    indr = np.where(np.all(arr==0,axis=1))[0]
    indc = np.where(np.all(arr==0,axis=0))[0]
    if not indr and not indc:   # If no further split possible return
    res.append(arr)
    return
    arr=np.delete(arr,indr,axis=0)  #delete empty rows in between non empty rows
    arr=np.delete(arr,indc,axis=1)  #delete empty cols in between non empty cols
    arr=np.split(arr,indc,axis=1)   # split on empty (all zeros) cols 
    print arr
    arr2=[]
    for i in arr:
    z=delrc(i)  
    arr2.extend(np.split(z,indr,axis=0))   # split on empty (all zeros) rows
    for i in arr2:
    rcsplit(np.array(i))        # recursive split again no further splitting is possible

if __name__=="__main__":

    import numpy as np 
    res = []   
    arr = np.array([[0,0,0,0,0,0],
        [0,1,1,0,0,0],
        [0,1,1,0,0,1],
        [0,0,0,0,1,1],
        [0,0,0,0,1,0]])
    rcsplit(arr)
    for i in res: print i

Answer 2

您可以为此使用内置插件。

from scipy.ndimage.measurements import find_objects, label
from scipy.ndimage import generate_binary_structure as gbs

import numpy as np

# create array
x = np.array([[0,0,0,0,0,0],
             [0,1,1,0,0,0],
             [0,1,1,0,0,1],
             [0,0,0,0,1,1],
             [0,0,0,0,1,0]])

# define labeling structure to inlcude adjacent (including diagonal) cells
struc = gbs(2,2)

# generate array of labeled sections labels
x2, numlabels = label(x,struc)

# pull out first group of "ones"
xy1 = find_objects(x2==1)[0]

# pull out second group of "ones"
xy2 = find_objects(x2==2)[0]

现在测试：

>>> x[xy1]
    array([[1, 1],
           [1, 1]])

>>> x[xy2]
    array([[0, 1],
           [1, 1],
           [1, 0]])

瞧！如果你想取出所有可以迭代的小节，它会告诉你数组中有多少个不同的组。