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Merging matrices
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* TOC {:toc}Top
Questions to David Rotermund
Choose vs select:
- Choose: One Matrix with integer values 0,...N-1
- Select: N binary matrices
numpy.choose
numpy.choose(a, choices, out=None, mode='raise')
Construct an array from an index array and a list of arrays to choose from.
First of all, if confused or uncertain, definitely look at the Examples - in its full generality, this function is less simple than it might seem from the following code description (below ndi = numpy.lib.index_tricks):
np.choose(a,c) == np.array([c[a[I]][I] for I in ndi.ndindex(a.shape)]).
But this omits some subtleties. Here is a fully general summary:
Given an “index” array (a) of integers and a sequence of n arrays (choices), a and each choice array are first broadcast, as necessary, to arrays of a common shape; calling these Ba and Bchoices[i], i = 0,…,n-1 we have that, necessarily, Ba.shape == Bchoices[i].shape for each i. Then, a new array with shape Ba.shape is created as follows:
- if mode='raise' (the default), then, first of all, each element of a (and thus Ba) must be in the range [0, n-1]; now, suppose that i (in that range) is the value at the (j0, j1, ..., jm) position in Ba - then the value at the same position in the new array is the value in Bchoices[i] at that same position;
- if mode='wrap', values in a (and thus Ba) may be any (signed) integer; modular arithmetic is used to map integers outside the range [0, n-1] back into that range; and then the new array is constructed as above;
- if mode='clip', values in a (and thus Ba) may be any (signed) integer; negative integers are mapped to 0; values greater than n-1 are mapped to n-1; and then the new array is constructed as above.
Example
| chosen_mask == 0 | use a |
| chosen_mask == 1 | use b |
| chosen_mask == 2 | use c |
import numpy as np
a = np.arange(0, 9).reshape((3, 3))
print(a)
print()
b = np.arange(10, 19).reshape((3, 3))
print(b)
print()
c = np.arange(20, 29).reshape((3, 3))
print(c)
print()
rng = np.random.default_rng()
chosen_mask = rng.integers(size=c.shape, low=0, high=3)
print(chosen_mask)
print()
d = chosen_mask.choose((a, b, c))
print(d)
Output:
[[0 1 2]
[3 4 5]
[6 7 8]]
[[10 11 12]
[13 14 15]
[16 17 18]]
[[20 21 22]
[23 24 25]
[26 27 28]]
[[1 2 2]
[0 0 1]
[1 2 2]]
[[10 21 22]
[ 3 4 15]
[16 27 28]]
numpy.select
numpy.select(condlist, choicelist, default=0)[source]
Return an array drawn from elements in choicelist, depending on conditions.
Example
| chosen_mask == 0 | use a |
| chosen_mask == 1 | use b |
| chosen_mask == 2 | use c |
import numpy as np
a = np.arange(0, 9).reshape((3, 3))
print(a)
print()
b = np.arange(10, 19).reshape((3, 3))
print(b)
print()
c = np.arange(20, 29).reshape((3, 3))
print(c)
print()
rng = np.random.default_rng()
chosen_mask = rng.integers(size=c.shape, low=0, high=3)
print(chosen_mask)
print()
d = np.select([chosen_mask == 0, chosen_mask == 1, chosen_mask == 2], (a, b, c))
print(d)
Output:
[[0 1 2]
[3 4 5]
[6 7 8]]
[[10 11 12]
[13 14 15]
[16 17 18]]
[[20 21 22]
[23 24 25]
[26 27 28]]
[[2 2 0]
[0 0 2]
[0 1 0]]
[[20 21 2]
[ 3 4 25]
[ 6 17 8]]
numpy.place and numpy.extract and numpy.copyto
numpy.place(arr, mask, vals)
Change elements of an array based on conditional and input values.
Similar to np.copyto(arr, vals, where=mask), the difference is that place uses the first N elements of vals, where N is the number of True values in mask, while copyto uses the elements where mask is True.
Note that extract does the exact opposite of place.
numpy.extract(condition, arr)
Return the elements of an array that satisfy some condition.
This is equivalent to np.compress(ravel(condition), ravel(arr)). If condition is boolean np.extract is equivalent to arr[condition].
Note that place does the exact opposite of extract.
numpy.copyto(dst, src, casting='same_kind', where=True)
Copies values from one array to another, broadcasting as necessary.
Raises a TypeError if the casting rule is violated, and if where is provided, it selects which elements to copy.