的numpy的数组的固定大小的子矩阵索引 [英] Indexes of fixed size sub-matrices of numpy array
问题描述
我实现它要求我看不重叠的连续子矩阵A(严格二维)numpy的阵列内的算法。例如,对于12 12
I am implementing an algorithm which requires me to look at non-overlapping consecutive submatrices within a (strictly two dimensional) numpy array. eg, for the 12 by 12
>>> a = np.random.randint(20, size=(12, 12)); a
array([[ 4, 0, 12, 14, 3, 8, 14, 12, 11, 18, 6, 6],
[15, 13, 2, 18, 15, 15, 16, 2, 9, 16, 6, 4],
[18, 18, 3, 8, 1, 15, 14, 13, 13, 13, 7, 0],
[ 1, 9, 3, 6, 0, 4, 3, 15, 0, 9, 11, 12],
[ 5, 15, 5, 6, 4, 4, 18, 13, 10, 17, 11, 8],
[13, 17, 8, 15, 17, 12, 7, 1, 13, 15, 0, 18],
[ 2, 1, 11, 12, 3, 16, 11, 9, 10, 15, 4, 16],
[19, 11, 10, 7, 10, 19, 7, 13, 11, 9, 17, 8],
[14, 14, 17, 0, 0, 0, 11, 1, 10, 14, 2, 7],
[ 6, 15, 6, 7, 15, 19, 2, 4, 6, 16, 0, 3],
[ 5, 10, 7, 5, 0, 8, 5, 8, 9, 14, 4, 3],
[17, 2, 0, 3, 15, 10, 14, 1, 0, 7, 16, 2]])
和看3x3的子矩阵,我想第一个3×3子矩阵是从左上角:
and looking at 3x3 submatrices, I would want the first 3x3 submatrix to be from the upper left corner:
>>> a[0:3, 0:3]
array([[ 4, 0, 12],
[15, 13, 2],
[18, 18, 3]])
接下来一起通过 A [0:3,3:6] 给予
等。如果最后一次集中的每一行或列中指数的运行了数组的结束不要紧 - 简单地给存在足以片内的部分numpy的行为
The next along to be given by a[0:3, 3:6]
and so on. It doesn't matter if the last such set of indices in each row or column runs off the end of the array - numpy's behavior of simply giving the portion within the slice that exists is sufficient.
我想要的方式来编程生成这些切片指数任意大小的矩阵和子矩阵。目前,我有这样的:
I want a way to generate these slice indices programatically for arbitrarily sized matrices and submatrices. I currently have this:
size = 3
x_max = a.shape[0]
xcoords = range(0, x_max, size)
xcoords = zip(xcoords, xcoords[1:])
和同样产生 y_coords
,使该系列指数是由给出itertools.product(xcoords,ycoords)
。
and similarly to generate y_coords
, so that the series of indices is given by itertools.product(xcoords, ycoords)
.
我的问题是:是否有一个更直接的方式做到这一点,可能使用<一个href=\"http://docs.scipy.org/doc/numpy/reference/generated/numpy.mgrid.html#numpy.mgrid\"><$c$c>numpy.mgrid$c$c>或其他一些numpy的技术?
My question is: is there a more direct way to do this, perhaps using numpy.mgrid
or some other numpy technique?
推荐答案
下面是一个快速的方法来获取特定的尺寸X尺寸
块:
Getting the indexes
Here's a quick way to get a specific size x size
block:
base = np.arange(size) # Just the base set of indexes
row = 1 # Which block you want
col = 0
block = a[base[:, np.newaxis] + row * size, base + col * size]
如果你想你可以建立类似矩阵你的 xcoords
这样的:
If you wanted you could build up matrices similar to your xcoords
like:
y, x = np.mgrid[0:a.shape[0]/size, 0:a.shape[1]/size]
y_coords = y[..., np.newaxis] * size + base
x_coords = x[..., np.newaxis] * size + base
然后,你可以访问一个块是这样的:
Then you could access a block like this:
block = a[y_coords[row, col][:, np.newaxis], x_coords[row, col]]
直接获取块
如果你只是想获得块(和块条目不是索引),我会使用的 np.split
(两次):
blocks = map(lambda x : np.split(x, a.shape[1]/size, 1), # Split the columns
np.split(a, a.shape[0]/size, 0)) # Split the rows
那么你有尺寸X尺寸
块的二维列表:
>>> blocks[0][0]
array([[ 4, 0, 12],
[15, 13, 2],
[18, 18, 3]])
>>> blocks[1][0]
array([[ 1, 9, 3],
[ 5, 15, 5],
[13, 17, 8]])
您可以再此做一个numpy的数组,并使用相同的索引风格如上:
You could then make this a numpy array and use the same indexing style as above:
>>> blocks = np.array(blocks)
>>> blocks.shape
(4, 4, 3, 3)
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