Efficient negation of subdiagonal values of a 2d numpy array - numpy

How would one efficiently negate the subdiagonal entries of a 2d numpy array?

You may use numpy.tril_indices to compute the indices of the subdiagonal entries, considering a diagonal offset of k = -1, and negate them with a mask, for instance:
import numpy as np
a = np.arange(16).reshape(4, 4)
>>> array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11],
[12, 13, 14, 15]])
idx_low_tri = np.tril_indices(a.shape[0], k=-1)
a[idx_low_tri] = -a[idx_low_tri]
>>> array([[ 0, 1, 2, 3],
[ -4, 5, 6, 7],
[ -8, -9, 10, 11],
[-12, -13, -14, 15]])
Hope this helps !

Related

Can I create a view from a boolean selection of a numpy array?

If I create a numpy array, and another to serve as a selective index into it:
>>> x
array([[ 2, 3, 4],
[ 5, 6, 7],
[ 6, 7, 8],
[11, 12, 13]])
>>> nz
array([ True, True, False, True], dtype=bool)
then direct use of nz returns a view of the original array:
>>> x[nz,:]
array([[ 2, 3, 4],
[ 5, 6, 7],
[11, 12, 13]])
>>> x[nz,:] += 2
>>> x
array([[ 4, 5, 6],
[ 7, 8, 9],
[ 6, 7, 8],
[13, 14, 15]])
however, naturally, an assignment makes a copy:
>>> v = x[nz,:]
Any operation on v is on the copy, and has no effect on the original array.
Is there any way to create a named view, from x[nz,:], simply to abbreviate code, or which I can pass around, so operations on the named view will affect only the selected elements of x?
Numpy has masked_array, which might be what you are looking for:
import numpy as np
x = np.asarray([[ 2, 3, 4],[ 5, 6, 7],[ 6, 7, 8],[11, 12, 13]])
nz = np.asarray([ True, True, False, True], dtype=bool)
mx = np.ma.masked_array(x, ~nz.repeat(3)) # True means masked, so "~" is needed
mx += 2
# x changed as well because it is the base of mx
print(x)
print(x is mx.base)

Splitting a number and assigning to elements in a row in a numpy array

How to place a list of numbers in to a 2D numpy array, where the second dimension of the array is equal to the number of digits of the largest number of that list? I also want the elements that don't belong to the original number to be zero in each row of the returning array.
Example:
From the list a = range(0,1001), how to get the numpy array of the below form:
[[0,0,0,0],
[0,0,0,1],
[0,0,0,2],
...
[0,9,9,8]
[0,9,9,9],
[1,0,0,0]]
Please note how the each number is placed in-place in a np.zeros((1000,4)) array at the end of the each row.
NB: A pythonic, vectorized implementation is expected
Broadcasting again!
def split_digits(a):
N = int(np.log10(np.max(a))+1) # No. of digits
r = 10**np.arange(N,-1,-1) # 10-powered range array
return (np.asarray(a)[:,None]%r[:-1])//r[1:]
Sample runs -
In [224]: a = range(0,1001)
In [225]: split_digits(a)
Out[225]:
array([[0, 0, 0, 0],
[0, 0, 0, 1],
[0, 0, 0, 2],
...,
[0, 9, 9, 8],
[0, 9, 9, 9],
[1, 0, 0, 0]])
In [229]: a = np.random.randint(0,1000000,(7))
In [230]: a
Out[230]: array([431921, 871855, 636144, 541186, 410562, 89356, 476258])
In [231]: split_digits(a)
Out[231]:
array([[4, 3, 1, 9, 2, 1],
[8, 7, 1, 8, 5, 5],
[6, 3, 6, 1, 4, 4],
[5, 4, 1, 1, 8, 6],
[4, 1, 0, 5, 6, 2],
[0, 8, 9, 3, 5, 6],
[4, 7, 6, 2, 5, 8]])
Another concept using pandas str
def pir(a):
z = int(np.log10(np.max(a)))
s = pd.Series(a.astype(str))
zfilled = s.str.zfill(z + 1).sum()
a_ = np.array(list(zfilled)).reshape(-1, z + 1)
return a_.astype(int)
Using #Divakar's random array
a = np.random.randint(0,1000000,(7))
array([ 57190, 29950, 392317, 592062, 460333, 639794, 983647])
pir(a)
array([[0, 5, 7, 1, 9, 0],
[0, 2, 9, 9, 5, 0],
[3, 9, 2, 3, 1, 7],
[5, 9, 2, 0, 6, 2],
[4, 6, 0, 3, 3, 3],
[6, 3, 9, 7, 9, 4],
[9, 8, 3, 6, 4, 7]])

Split last dimension of arrays in lower dimensional arrays

Assume we have an array with NxMxD shape. I want to get a list with D NxM arrays.
The correct way of doing it would be:
np.dsplit(myarray, D)
However, this returns D NxMx1 arrays.
I can achieve the desired result by doing something like:
[myarray[..., i] for i in range(D)]
Or:
[np.squeeze(subarray) for subarray in np.dsplit(myarray, D)]
However, I feel like it is a bit redundant to need to perform an additional operation. Am I missing any numpy function that returns the desired result?
Try D.swapaxes(1,2).swapaxes(1,0)
>>>import numpy as np
>>>a = np.arange(24).reshape(2,3,4)
>>>a
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]]])
>>>[a[:,:,i] for i in range(4)]
[array([[ 0, 4, 8],
[12, 16, 20]]),
array([[ 1, 5, 9],
[13, 17, 21]]),
array([[ 2, 6, 10],
[14, 18, 22]]),
array([[ 3, 7, 11],
[15, 19, 23]])]
>>>a.swapaxes(1,2).swapaxes(1,0)
array([[[ 0, 4, 8],
[12, 16, 20]],
[[ 1, 5, 9],
[13, 17, 21]],
[[ 2, 6, 10],
[14, 18, 22]],
[[ 3, 7, 11],
[15, 19, 23]]])
Edit: As pointed out by ajcr (thanks again), the transpose command is more convenient since the two swaps can be done in one step by using
D.transpose(2,0,1)
np.dsplit uses np.array_split, the core of which is:
sub_arys = []
sary = _nx.swapaxes(ary, axis, 0)
for i in range(Nsections):
st = div_points[i]; end = div_points[i+1]
sub_arys.append(_nx.swapaxes(sary[st:end], axis, 0))
with axis=-1, this is equivalent to:
[x[...,i:(i+1)] for i in np.arange(x.shape[-1])] # or
[x[...,[i]] for i in np.arange(x.shape[-1])]
which accounts for the singleton dimension.
So there's nothing wrong or inefficient about your
[x[...,i] for i in np.arange(x.shape[-1])]
Actually in quick time tests, any use of dsplit is slow. It's generality costs. So adding squeeze is relatively cheap.
But by accepting the other answer, it looks like you are really looking for an array of the correct shape, rather than a list of arrays. For many operations that makes sense. split is more useful when the subarrays have more than one 'row' along the split axis, or even an uneven number of 'rows'.

Select elements of a numpy array based on the elements of a second array

Consider a numpy array A of shape (7,6)
A = array([[0, 1, 2, 3, 5, 8],
[4, 100, 6, 7, 8, 7],
[8, 9, 10, 11, 5, 4],
[12, 13, 14, 15, 1, 2],
[1, 3, 5, 6, 4, 8],
[12, 23, 12, 24, 4, 3],
[1, 3, 5, 7, 89, 0]])
together with a second numpy array r of the same shape which contains the radius of A starting from a central point A(3,2)=0:
r = array([[3, 3, 3, 3, 3, 4],
[2, 2, 2, 2, 2, 3],
[2, 1, 1, 1, 2, 3],
[2, 1, 0, 1, 2, 3],
[2, 1, 1, 1, 2, 3],
[2, 2, 2, 2, 2, 3],
[3, 3, 3, 3, 3, 4]])
I would like to pick up all the elements of A which are located at the position 1 of r, i.e. [9,10,11,15,4,6,5,13], all the elements of A located at position 2 of r and so on. I there some numpy function to do that?
Thank you
You can select a section of A by doing something like A[r == 1], to get all the sections as a list you could do [A[r == i] for i in range(r.max() + 1)]. This will work, but may be inefficient depending on how big the values in r go because you need to compute r == i for every i.
You could also use this trick, first sort A based on r, then simply split the sorted A array at the right places. That looks something like this:
r_flat = r.ravel()
order = r_flat.argsort()
A_sorted = A.ravel()[order]
r_sorted = r_flat[order]
edges = r_sorted.searchsorted(np.arange(r_sorted[-1] + 1), 'right')
sections = []
start = 0
for end in edges:
sections.append(A_sorted[start:end])
start = end
I get a different answer to the one you were expecting (3 not 4 from the 4th row) and the order is slightly different (strictly row then column), but:
>>> A
array([[ 0, 1, 2, 3, 5, 8],
[ 4, 100, 6, 7, 8, 7],
[ 8, 9, 10, 11, 5, 4],
[ 12, 13, 14, 15, 1, 2],
[ 1, 3, 5, 6, 4, 8],
[ 12, 23, 12, 24, 4, 3],
[ 1, 3, 5, 7, 89, 0]])
>>> r
array([[3, 3, 3, 3, 3, 4],
[2, 2, 2, 2, 2, 3],
[2, 1, 1, 1, 2, 3],
[2, 1, 0, 1, 2, 3],
[2, 1, 1, 1, 2, 3],
[2, 2, 2, 2, 2, 3],
[3, 3, 3, 3, 3, 4]])
>>> A[r==1]
array([ 9, 10, 11, 13, 15, 3, 5, 6])
Alternatively, you can get column then row ordering by transposing both arrays:
>>> A.T[r.T==1]
array([ 9, 13, 3, 10, 5, 11, 15, 6])

numpy custom array element retrieval

I have a question regarding how to extract certain values from a 2D numpy array
Foo =
array([[ 1, 2, 3],
[ 4, 5, 6],
[ 7, 8, 9],
[10, 11, 12]])
Bar =
array([[0, 0, 1],
[1, 2, 3]])
I want to extract elements from Foo using the values of Bar as indices, such that I end up with an 2D matrix/array Baz of the same shape as Bar. The ith column in Baz correspond is Foo[(np.array(each j in Bar[:,i]),np.array(i,i,i,i ...))]
Baz =
array([[ 1, 2, 6],
[ 4, 8, 12]])
I could do a couple nested for-loops but I was wondering if there is a more elegant, numpy-ish way to do this.
Sorry if this is a bit convoluted. Let me know if I need to explain further.
Thanks!
You can use Bar as the row index and an array [0, 1, 2] as the column index:
# for easy copy-pasting
import numpy as np
Foo = np.array([[ 1, 2, 3], [ 4, 5, 6], [ 7, 8, 9], [10, 11, 12]])
Bar = np.array([[0, 0, 1], [1, 2, 3]])
# now use Bar as the `i` coordinate and 0, 1, 2 as the `j` coordinate:
Foo[Bar, [0, 1, 2]]
# array([[ 1, 2, 6],
# [ 4, 8, 12]])
# OR, to automatically generate the [0, 1, 2]
Foo[Bar, xrange(Bar.shape[1])]