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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
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.
import numpy as np
a = np.arange(1, 10).reshape((3, 3))
print(a)
print()
np.place(a, a >= 7, 99)
print(a)
print()
np.place(a, a >= 7, [70, 71, 72, 73])
print(a)
print()
Output:
[[1 2 3]
[4 5 6]
[7 8 9]]
[[ 1 2 3]
[ 4 5 6]
[99 99 99]]
[[ 1 2 3]
[ 4 5 6]
[70 71 72]]
numpy.extract
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.
import numpy as np
a = np.arange(1, 10).reshape((3, 3))
print(a)
print()
b = np.extract(a >= 7, a)
print(b)
Output:
[[1 2 3]
[4 5 6]
[7 8 9]]
[7 8 9]
numpy.copyto
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.
import numpy as np
a = np.arange(1, 10).reshape((3, 3))
b = np.zeros_like(a)
print(a)
print()
np.copyto(b, a, where=(a >= 7))
print(b)
Output:
[[1 2 3]
[4 5 6]
[7 8 9]]
[[0 0 0]
[0 0 0]
[7 8 9]]