Given the following code:
import numpy as np
mat = np.arange(1,26).reshape(5,5)
My understanding was the following lines are identical:
mat[:3][1:2]
mat[:3,1:2]
But they are not. Why?
3 Answers
If you only specify one dimension in your slicing syntax, only one dimension will be sliced. In NumPy, dimensions in indexing are typically separated by ",".
For a 2d array, you may substitute "row" with "dimension 1" and "column" with "dimension 2". In your example, mat[:3] slices the first 3 rows. The subsequent indexer [1:2], slices the first of those 3 rows.
With your second example, [:3, 1:2] slices rows and columns simultaneously.
You may find it helpful to look at the shapes of your results:
mat[:3].shape # (3, 5)
mat[:3][1:2].shape # (1, 5)
mat[:3,1:2].shape # (3, 1)
Comments
Your matrix:
array([[ 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]])
The first one mat[:3][1:2] will first take mat[:3] and then apply [1:2]:
mat[:3]
array([[ 1, 2, 3, 4, 5],
[ 6, 7, 8, 9, 10],
[11, 12, 13, 14, 15]])
# mat[:3][1:2] => array([[ 6, 7, 8, 9, 10]])
While the second one (mat[:3,1:2]) states:
lines up to 3
array([[ 1, 2, 3, 4, 5],
[ 6, 7, 8, 9, 10],
[11, 12, 13, 14, 15]])
Columns 1 to 2
array([[ 2],
[ 7],
[12]])
Conclusion, the main difference is that the first one is applying [1:2] after the [:3]
Comments
Here's why:
> mat
# output:
array([[ 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]])
> mat[:3] # you are selecting the first 3 rows
#output:
array([[ 1, 2, 3, 4, 5],
[ 6, 7, 8, 9, 10],
[11, 12, 13, 14, 15]])
> mat[:3][1:2] # you are selecting the second row only
Output:
array([[ 6, 7, 8, 9, 10]])
> mat[:3,1:2] # you are selecting from the first 3 rows and the second column
Output:
array([[ 2],
[ 7],
[12]])
mat[x][y]is the same asmat[x, y]only ifxis a scalar, i.e. if it selects one item on the first dimension.