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How to slice 2D Torch tensor individually per row?

I have a 2D tensor in Pytorch that I would like to slice:
x = torch.rand((3, 5))
In this example, the tensor has 3 rows and I want to slice x, creating a new tensor y that also has 3 rows and num_col cols.
What's challenging for me is that I want to slice different columns per row. All I have is x, num_cols, and idx, which is a tensor holding the start index from where to slice.
Example:
What I have is num_cols=2, idx=[1,2,3] and
x=torch.arange(15).reshape((3,-1)) =
tensor([[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14]])
What I want is
y=
tensor([[ 1, 2],
[ 7, 8],
[13, 14]])
What's the "torch"-way of doing this? I know, I can slice if I get a boolean mask somehow, but I don't know how to construct that with idx and num_cols without normal Python loops.

You could use fancy indexing together with broadcasting. Another solution might be to use torch.gather which is similar to numpy's take_along_axis. Your idx array would need to be extended with the extra column:
x = torch.arange(15).reshape(3,-1)
idx = torch.tensor([1,2,3])
idx = torch.column_stack([idx, idx+1])
torch.gather(x, 1, idx)
output:
tensor([[ 1, 2],
[ 7, 8],
[13, 14]])

indexing rows and columns in numpy

a = np.array(list(range(16).reshape((4,4))
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15]])
Say I want the middle square. It'd seem reasonable to do this:
a[[1,2],[1,2]]
but I get this:
array([5, 10])
This works, but seems inelegant:
a[[1,2],:][:,[1,2]]
array([[5, 6],
[9, 10]])
So my questions are:
Why is it this way? What premises are required to make the implemented way sensible?
Is there a canonical way to select along more than one index at once?

I think you can read more details on advanced indexing. Basically, when you slice the array by lists/arrays, the arrays will be broadcast and iterate together.
In your case, you can do:
idx = np.array([1,3])
a[idx,idx[:,None]]
Or as in the doc above:
a[np.ix_(idx, idx)]
Output:
array([[ 5, 13],
[ 7, 15]])

You can do both slicing operations at once instead of creating a view and indexing that again:
import numpy as np
a = np.arange(16).reshape((4, 4))
# preferred if possible
print(a[1:3, 1:3])
# [[ 5 6]
# [ 9 10]]
# otherwise add a second dimension to the first index to make it broadcastable
index1 = np.asarray([1, 2])
index2 = np.asarray([1, 2])
print(a[index1[:, None], index2])
# [[ 5 6]
# [ 9 10]]

You could use multiple np.take to select indices from multiple axes
a = np.arange(16).reshape((4, 4))
idx = np.array([1,2])
np.take(np.take(a, idx, axis=1), idx, axis=0)
Or (slightly more readable)
a.take(idx, axis=1).take(idx, axis=0)
Output:
array([[ 5, 6],
[ 9, 10]])
np.take also allows you to conveniently wrap around out-of-bound indices and such.

How to split numpy array vertically from any column index

I want to split a numpy array into two subarrays where the splitting point is based on a column id, i.e., vertical split. For instance, if I generate a numpy array of shape [10,16] and I want to create two subarrays by splitting it from the column's index 11, then I should get one subarray of size [10,10] and the other one is from [10,15]. Therefore, I am following numpy.hsplit here but it seems it only does an even split (the subarrays need to be equal). I want to be able to:
Split any numpy array vertically, no matter what is the size of subarrays.
Extract both subarrays.
To simulate my request, the following is my code:
import numpy as np
C = [[1,2,3,4],[5,6,7,8],[9,10,11,12], [13,14,15,16]]
C = np.asarray(C)
C = np.hsplit(C, 3)
print(C)
As you can see, np.hsplit(C, 3) doesn't work unless the splitting generates similar subarrays. Even if I did np.hsplit(C, 2), I don't know how to extract both subarrays into separate numpy arrays.
To achieve my goals, how can I modify this code?

Use the array indexing.
C[:,:3] # All rows , columns 0 to 2
Out[29]:
array([[ 1, 2, 3],
[ 5, 6, 7],
[ 9, 10, 11],
[13, 14, 15]])
C[:,3:] # All rows column 3 (to end in this case also 3).
Out[30]:
array([[ 4],
[ 8],
[12],
[16]])

You need to specify the indices as list:
import numpy as np
C = [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]]
C = np.asarray(C)
C = np.hsplit(C, [3])
print(C)
Output
[array([[ 1, 2, 3],
[ 5, 6, 7],
[ 9, 10, 11],
[13, 14, 15]]), array([[ 4],
[ 8],
[12],
[16]])]

Remove/delete each minimum value in each row of a NxM matrix?

Is it possible to remove/delete each minimum value in each row of a NxM matrix
creating a new matrix?
I´ve tried this so far without any luck:
for n in range(0,len(matrix_name)):
Ma = grades.remove(np.min(matrix_name[n,:]))
and this too:
for n in range(0,len(matrix_name)):
Ma = np.delete(matrix_name,np.min(matrix_name[n,:]))

If duplicates are not an issue or if deleting only one of them per row is acceptable:
m, n = a.shape
np.where(np.arange(n-1) < a.argmin(axis=1)[:, None], a[:, :-1], a[:, 1:])

If reconstructing the desired result from the original array instead of modifying the original array by deleting the min values, is allowed then this approach should do the job:
# some test array
In [19]: arr
Out[19]:
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15],
[16, 17, 18, 19]])
In [20]: r, c = arr.shape
# find the minimum along axis 1 (i.e. along rows)
In [21]: min_vals = np.min(arr, axis=1, keepdims=True)
# reshape the result to 2D array
In [22]: (arr[np.where(arr != min_vals)]).reshape(r, c-1)
Out[22]:
array([[ 1, 2, 3],
[ 5, 6, 7],
[ 9, 10, 11],
[13, 14, 15],
[17, 18, 19]])
Note: This approach assumes that there's only one minimum value in each row.

Numpy array slicing using colons

I am trying to learn numpy array slicing.
But this is a syntax i cannot seem to understand.
What does
a[:1] do.
I ran it in python.
a = np.array([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16])
a = a.reshape(2,2,2,2)
a[:1]
Output:
array([[[ 5, 6],
[ 7, 8]],
[[13, 14],
[15, 16]]])
Can someone explain to me the slicing and how it works. The documentation doesn't seem to answer this question.
Another question would be would there be a way to generate the a array using something like
np.array(1:16) or something like in python where
x = [x for x in range(16)]

The commas in slicing are to separate the various dimensions you may have. In your first example you are reshaping the data to have 4 dimensions each of length 2. This may be a little difficult to visualize so if you start with a 2D structure it might make more sense:
>>> a = np.arange(16).reshape((4, 4))
>>> a
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15]])
>>> a[0] # access the first "row" of data
array([0, 1, 2, 3])
>>> a[0, 2] # access the 3rd column (index 2) in the first row of the data
2
If you want to access multiple values using slicing you can use the colon to express a range:
>>> a[:, 1] # get the entire 2nd (index 1) column
array([[1, 5, 9, 13]])
>>> a[1:3, -1] # get the second and third elements from the last column
array([ 7, 11])
>>> a[1:3, 1:3] # get the data in the second and third rows and columns
array([[ 5, 6],
[ 9, 10]])
You can do steps too:
>>> a[::2, ::2] # get every other element (column-wise and row-wise)
array([[ 0, 2],
[ 8, 10]])
Hope that helps. Once that makes more sense you can look in to stuff like adding dimensions by using None or np.newaxis or using the ... ellipsis:
>>> a[:, None].shape
(4, 1, 4)
You can find more here: http://docs.scipy.org/doc/numpy/reference/arrays.indexing.html

It might pay to explore the shape and individual entries as we go along.
Let's start with
>>> a = np.array([1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16])
>>> a.shape
(16, )
This is a one-dimensional array of length 16.
Now let's try
>>> a = a.reshape(2,2,2,2)
>>> a.shape
(2, 2, 2, 2)
It's a multi-dimensional array with 4 dimensions.
Let's see the 0, 1 element:
>>> a[0, 1]
array([[5, 6],
[7, 8]])
Since there are two dimensions left, it's a matrix of two dimensions.
Now a[:, 1] says: take a[i, 1 for all possible values of i:
>>> a[:, 1]
array([[[ 5, 6],
[ 7, 8]],
[[13, 14],
[15, 16]]])
It gives you an array where the first item is a[0, 1], and the second item is a[1, 1].

To answer the second part of your question (generating arrays of sequential values) you can use np.arange(start, stop, step) or np.linspace(start, stop, num_elements). Both of these return a numpy array with the corresponding range of values.