Merging matrices

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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

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

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]]

numpy.put

This is an optional topic!

numpy.put(a, ind, v, mode='raise')[source]

Replaces specified elements of an array with given values.

The indexing works on the flattened target array. put is roughly equivalent to:

a.flat[ind] = v

numpy.take

This is an optional topic!

numpy.take(a, indices, axis=None, out=None, mode='raise')

Take elements from an array along an axis.

When axis is not None, this function does the same thing as “fancy” indexing (indexing arrays using arrays); however, it can be easier to use if you need elements along a given axis. A call such as np.take(arr, indices, axis=3) is equivalent to arr[:,:,:,indices,…].

Explained without fancy indexing, this is equivalent to the following use of ndindex, which sets each of ii, jj, and kk to a tuple of indices:

Ni, Nk = a.shape[:axis], a.shape[axis+1:]
Nj = indices.shape
for ii in ndindex(Ni):
    for jj in ndindex(Nj):
        for kk in ndindex(Nk):
            out[ii + jj + kk] = a[ii + (indices[jj],) + kk]

numpy.put_along_axis

This is an optional topic!

numpy.put_along_axis(arr, indices, values, axis)

Put values into the destination array by matching 1d index and data slices.

This iterates over matching 1d slices oriented along the specified axis in the index and data arrays, and uses the former to place values into the latter. These slices can be different lengths.

Functions returning an index along an axis, like argsort and argpartition, produce suitable indices for this function.

numpy.take_along_axis

This is an optional topic!

numpy.take_along_axis(arr, indices, axis)

Take values from the input array by matching 1d index and data slices.

This iterates over matching 1d slices oriented along the specified axis in the index and data arrays, and uses the former to look up values in the latter. These slices can be different lengths.

Functions returning an index along an axis, like argsort and argpartition, produce suitable indices for this function.

The source code is Open Source and can be found on GitHub.