I am a novice programmer.
I would like to create a "subtraction matrix." (I lack the vocabulary to describe it). I would like to create a matrix from all the combination of subtractions.
v = [1, 5, 10]
0 4 9
4 0 5
9 5 0
I think I am missing something very basic with numpy but I do know what it is.
Thank you
You can use the outer method of the subtract ufunc. outer applies the operation (in this case subtraction) to every possible pair and arranges the result in a matrix:
v = [1, 5, 10]
np.absolute(np.subtract.outer(v, v))
# array([[0, 4, 9],
# [4, 0, 5],
# [9, 5, 0]])
Conveniently, it accepts lists etc. without you having to explicitly cast them to array.
You can utilize numpy broadcasting:
v = np.array([1, 5, 10])
# v[:, None] creates a 2d array, when subtracted by a 1d array, the broadcasting rule will
# make a cartesian subtraction
np.abs(v[:, None] - v)
#array([[0, 4, 9],
# [4, 0, 5],
# [9, 5, 0]])
If you don't want to use numpy, you could use nested for loops:
v = [1, 5, 10]
vLen = len(v)
subMatrix = [[0]*vLen for x in range(vLen)] //creates empty matrix
for i in range(vLen):
for j in range(vLen):
subMatrix[j][i] = abs(v[i] - v[j])
# [[0, 4, 9],
# [4, 0, 5],
# [9, 5, 0]]
Edit: @aryamccarthy pointed out that for loops are less efficient than numpy broadcasting. Another alternative that he gave would be to use list comprehension for the same result:
v = [1, 5, 10]
subMatrix = [[abs(i - j) for i in v] for j in v]
numpy broadcasting, this is terribly inefficient. Python's for-loops are super slow. Further, the asker only shows non-negative values in the intended output.
[[abs(i - j) for i in v] for j in v]