Related
Consider the following code fragment:
import numpy as np
mask = np.array([True, True, False, True, True, False])
val = np.array([9, 3])
arr = np.random.randint(1, 9, size = (5,len(mask)))
As expected, we get an array of random integers, 1 to 9, with 5 rows and 6 columns as below. The val array has not been used yet.
[[2, 7, 6, 9, 7, 5],
[7, 2, 9, 7, 8, 3],
[9, 1, 3, 5, 7, 3],
[5, 7, 4, 4, 5, 2],
[7, 7, 9, 6, 9, 8]]
Now I'll introduce val = [9, 3].
Where mask = True, I want the row element to be taken randomly from 1 to 9.
Where mask = False, I want the row element to be taken randomly from 1 to 3.
How can this be done efficiently? A sample output is shown below.
[[2, 7, 2, 9, 7, 1],
[7, 2, 1, 7, 8, 3],
[9, 1, 3, 5, 7, 3],
[5, 7, 1, 4, 5, 2],
[7, 7, 2, 6, 9, 1]]
One idea is to sample randomly between 0 to 1, then multiply with 9 or 3 depending on mask, and finally add 1 to move the sample.
rand = np.random.rand(5,len(mask))
is3 = (1-mask).astype(int)
# out is random from 0-8 or 0-2 depending on `is3`
out = (rand*val[is3]).astype(int)
# move out by `1`:
out = (out + 1)
Output:
array([[4, 9, 3, 6, 2, 1],
[1, 8, 2, 7, 1, 3],
[8, 2, 1, 2, 3, 2],
[4, 3, 2, 2, 3, 2],
[5, 8, 1, 5, 6, 1]])
I have 2 arrays
asc = [0, 1, 2, 3, 4, 5]
dsc = [5, 4, 3, 2, 1, 0]
I want a new array that is results of multiplying each corresponding item in asc and dsc
I'm used to Clojure where I would just map
(map #(* %1 %2) asc dsc) ;=> (0 4 6 6 4 0)
Is their an equivalent in Ruby, what would be the idiomatic way to do this in Ruby?
I'm new to Ruby but it seems to have really nice concise solutions, so I assume I'm missing something.
Do I just write:
i = 0
res = []
while i < asc.length() do
res.append(asc[i] * dsc[i])
end
Use zip to combine each element with its corresponding in two element array and than map
asc.zip(dsc).map { |a, b| a * b }
=> [0, 4, 6, 6, 4, 0]
It appears that dsc ("descending") is derived from asc ("ascending"), in which case you could write:
asc.each_index.map { |i| asc[i] * asc[-i-1] }
#=> [0, 4, 6, 6, 4, 0]
You could also write:
[asc, dsc].transpose.map { |a,d| a*d }
#=> [0, 4, 6, 6, 4, 0]
or:
require 'matrix'
Matrix[asc].hadamard_product(Matrix[dsc]).to_a.first
#=> [0, 4, 6, 6, 4, 0]
See Matrix#hadamard_product.
Use map and with_index:
asc = [0, 1, 2, 3, 4, 5]
dsc = [5, 4, 3, 2, 1, 0]
res = asc.map.with_index{ |el, i| el * dsc[i] }
puts res.inspect
# [0, 4, 6, 6, 4, 0]
Alternatively, use each_index and map:
res = asc.each_index.map{ |i| asc[i] * dsc[i] }
You could also write like below:
asc = [0, 1, 2, 3, 4, 5]
dsc = [5, 4, 3, 2, 1, 0]
p asc.zip(dsc).collect{|z| z.inject(:*)}
[0, 4, 6, 6, 4, 0]
Consider the small sample of a 6-column integer array:
import numpy as np
J = np.array([[1, 3, 1, 3, 2, 5],
[2, 6, 3, 4, 2, 6],
[1, 7, 2, 5, 2, 5],
[4, 2, 8, 3, 8, 2],
[0, 3, 0, 3, 0, 3],
[2, 2, 3, 3, 2, 3],
[4, 3, 4, 3, 3, 4])
I want to remove, from J:
a) all rows where the first and second PAIRS of elements are exact matches
(this remove rows like [1,3, 1,3, 2,5])
b) all rows where the second and third PAIRS of elements are exact matches
(this remove rows like [1,7, 2,5, 2,5])
Matches between any other pairs are OK.
I have a solution, below, but it is handled in two steps. If there is a more direct, cleaner, or more readily extendable approach, I'd be very interested.
K = J[~(np.logical_and(J[:,0] == J[:,2], J[:,1] == J[:,3]))]
L = K[~(np.logical_and(K[:,2] == J[:,4], K[:,3] == K[:,5]))]
K removes the 1st, 5th, and 7th rows from J, leaving
K = [[2, 6, 3, 4, 2, 6],
[1, 7, 2, 5, 2, 5],
[4, 2, 8, 3, 8, 2],
[2, 2, 3, 3, 2, 3]])
L removes the 2nd row from K, giving the final outcome.
L = [[2, 6, 3, 4, 2, 6],
[4, 2, 8, 3, 8, 2],
[2, 2, 3, 3, 2, 3]])
I'm hoping for an efficient solution because, learning from this problem, I need to extend these ideas to 8-column arrays where
I eliminate rows having exact matches between the 1st and 2nd PAIRS, the 2nd and 3rd PAIRS, and the 3rd and 4th PAIRS.
Since we are checking for adjacent pairs for equality, a differencing on 3D reshaped data seems would be one way to do it for a cleaner vectorized one -
# a is input array
In [117]: b = a.reshape(a.shape[0],-1,2)
In [118]: a[~(np.diff(b,axis=1)==0).all(2).any(1)]
Out[118]:
array([[2, 6, 3, 4, 2, 6],
[4, 2, 8, 3, 8, 2],
[2, 2, 3, 3, 2, 3]])
If you are going for performance, skip the differencing and go for sliced equality -
In [142]: a[~(b[:,:-1] == b[:,1:]).all(2).any(1)]
Out[142]:
array([[2, 6, 3, 4, 2, 6],
[4, 2, 8, 3, 8, 2],
[2, 2, 3, 3, 2, 3]])
Generic no. of cols
Extends just as well on generic no. of cols -
In [156]: a
Out[156]:
array([[1, 3, 1, 3, 2, 5, 1, 3, 1, 3, 2, 5],
[2, 6, 3, 4, 2, 6, 2, 6, 3, 4, 2, 6],
[1, 7, 2, 5, 2, 5, 1, 7, 2, 5, 2, 5],
[4, 2, 8, 3, 8, 2, 4, 2, 8, 3, 8, 2],
[0, 3, 0, 3, 0, 3, 0, 3, 0, 3, 0, 3],
[2, 2, 3, 3, 2, 3, 2, 2, 3, 3, 2, 3],
[4, 3, 4, 3, 3, 4, 4, 3, 4, 3, 3, 4]])
In [158]: b = a.reshape(a.shape[0],-1,2)
In [159]: a[~(b[:,:-1] == b[:,1:]).all(2).any(1)]
Out[159]:
array([[4, 2, 8, 3, 8, 2, 4, 2, 8, 3, 8, 2],
[2, 2, 3, 3, 2, 3, 2, 2, 3, 3, 2, 3]])
Of course, we are assuming the number of cols allows pairing.
What you have is quite reasonable. Here's what I would write:
def eliminate_pairs(x: np.ndarray) -> np.ndarray:
first_second = (x[:, 0] == x[:, 2]) & (x[:, 1] == x[:, 3])
second_third = (x[:, 1] == x[:, 3]) & (x[:, 2] == x[:, 4])
return x[~(first_second | second_third)]
You could also apply DeMorgan's theorem and eliminate an extra not operation, but that's less important than clarity.
Let's try a loop:
mask = False
for i in range(0,3,2):
mask = (J[:,i:i+2]==J[:,i+2:i+4]).all(1) | mask
J[~mask]
Output:
array([[2, 6, 3, 4, 2, 6],
[4, 2, 8, 3, 8, 2],
[2, 2, 3, 3, 2, 3]])
I have an numpy array like this with shape (6, 2, 4):
x = np.array([[[0, 3, 2, 0],
[1, 3, 1, 1]],
[[3, 2, 3, 3],
[0, 3, 2, 0]],
[[1, 0, 3, 1],
[3, 2, 3, 3]],
[[0, 3, 2, 0],
[1, 3, 2, 2]],
[[3, 0, 3, 1],
[1, 0, 1, 1]],
[[1, 3, 1, 1],
[3, 1, 3, 3]]])
And I have choices array like this:
choices = np.array([[1, 1, 1, 1],
[0, 1, 1, 0],
[1, 1, 1, 1],
[1, 0, 0, 0],
[1, 0, 1, 1],
[0, 0, 0, 1]])
How can I use choices array to index only the middle dimension with size 2 and get a new numpy array with shape (6, 4) in the most efficient way possible?
The result would be this:
[[1 3 1 1]
[3 3 2 3]
[3 2 3 3]
[1 3 2 0]
[1 0 1 1]
[1 3 1 3]]
I've tried to do it by x[:, choices, :] but this doesn't return what I want. I also tried to do x.take(choices, axis=1) but no luck.
Use np.take_along_axis to index along the second axis -
In [16]: np.take_along_axis(x,choices[:,None],axis=1)[:,0]
Out[16]:
array([[1, 3, 1, 1],
[3, 3, 2, 3],
[3, 2, 3, 3],
[1, 3, 2, 0],
[1, 0, 1, 1],
[1, 3, 1, 3]])
Or with explicit integer-array indexing -
In [22]: m,n = choices.shape
In [23]: x[np.arange(m)[:,None],choices,np.arange(n)]
Out[23]:
array([[1, 3, 1, 1],
[3, 3, 2, 3],
[3, 2, 3, 3],
[1, 3, 2, 0],
[1, 0, 1, 1],
[1, 3, 1, 3]])
as I recently had this issue, found #divakar's answer useful, but still wanted a general functions for that (independent of number of dims etc.), here it is :
def take_indices_along_axis(array, choices, choice_axis):
"""
array is N dim
choices are integer of N-1 dim
with valuesbetween 0 and array.shape[choice_axis] - 1
choice_axis is the axis along which you want to take indices
"""
nb_dims = len(array.shape)
list_indices = []
for this_axis, this_axis_size in enumerate(array.shape):
if this_axis == choice_axis:
# means this is the axis along which we want to choose
list_indices.append(choices)
continue
# else, we want arange(this_axis), but reshaped to match the purpose
this_indices = np.arange(this_axis_size)
reshape_target = [1 for _ in range(nb_dims)]
reshape_target[this_axis] = this_axis_size # replace the corresponding axis with the right range
del reshape_target[choice_axis] # remove the choice_axis
list_indices.append(
this_indices.reshape(tuple(reshape_target))
)
tuple_indices = tuple(list_indices)
return array[tuple_indices]
# test it !
array = np.random.random(size=(10, 10, 10, 10))
choices = np.random.randint(10, size=(10, 10, 10))
assert take_indices_along_axis(array, choices, choice_axis=0)[5, 5, 5] == array[choices[5, 5, 5], 5, 5, 5]
assert take_indices_along_axis(array, choices, choice_axis=2)[5, 5, 5] == array[5, 5, choices[5, 5, 5], 5]
I have a 9x9 multidimensional array that represents a sudoku game. I need to break it into it's 9 3x3 many components. How would this be done? I have absolutely no idea where to begin, here.
game = [
[1, 3, 2, 5, 7, 9, 4, 6, 8],
[4, 9, 8, 2, 6, 1, 3, 7, 5],
[7, 5, 6, 3, 8, 4, 2, 1, 9],
[6, 4, 3, 1, 5, 8, 7, 9, 2],
[5, 2, 1, 7, 9, 3, 8, 4, 6],
[9, 8, 7, 4, 2, 6, 5, 3, 1],
[2, 1, 4, 9, 3, 5, 6, 8, 7],
[3, 6, 5, 8, 1, 7, 9, 2, 4],
[8, 7, 9, 6, 4, 2, 1, 5, 3]
]
Split into chunks, it becomes
chunk_1 = [
[1, 3, 2],
[4, 9, 8],
[7, 5, 6]
]
chunk_2 = [
[5, 7, 9],
[2, 6, 1],
[3, 8, 4]
]
...and so on
That was a fun exercise!
Answer
game.each_slice(3).map{|stripe| stripe.transpose.each_slice(3).map{|chunk| chunk.transpose}}.flatten(1)
It would be cumbersome and not needed to define every chunk_1, chunk_2, ....
If you want chunk_2, you can use extract_chunks(game)[1]
It outputs [chunk_1, chunk_2, chunk_3, ..., chunk_9], so it's an Array of Arrays of Arrays :
1 3 2
4 9 8
7 5 6
5 7 9
2 6 1
3 8 4
4 6 8
3 7 5
2 1 9
6 4 3
5 2 1
...
You can define a method to check if this grid is valid (it is) :
def extract_chunks(game)
game.each_slice(3).map{|stripe| stripe.transpose.each_slice(3).map{|chunk| chunk.transpose}}.flatten(1)
end
class Array # NOTE: Use refinements if you don't want to patch Array
def has_nine_unique_elements?
self.flatten(1).uniq.size == 9
end
end
def valid?(game)
game.has_nine_unique_elements? &&
game.all?{|row| row.has_nine_unique_elements? } &&
game.all?{|column| column.has_nine_unique_elements? } &&
extract_chunks(game).all?{|chunk| chunk.has_nine_unique_elements? }
end
puts valid?(game) #=> true
Theory
The big grid can be sliced in 3 stripes, each containing 3 rows of 9 cells.
The first stripe will contain chunk_1, chunk_2 and chunk_3.
We need to cut the strip vertically into 3 chunks. To do so :
We transpose the strip,
Cut it horizontally with each_slice,
transpose back again.
We do the same for stripes #2 and #3.
To avoid returning an Array of Stripes of Chunks of Rows of Cells, we use flatten(1) to remove one level and return an Array of Chunks of Rows of Cells. :)
The method Matrix#minor is tailor-made for this:
require 'matrix'
def sub3x3(game, i, j)
Matrix[*game].minor(3*i, 3, 3*j, 3).to_a
end
chunk1 = sub3x3(game, 0, 0)
#=> [[1, 3, 2], [4, 9, 8], [7, 5, 6]]
chunk2 = sub3x3(game, 0, 1)
#=> [[5, 7, 9], [2, 6, 1], [3, 8, 4]]
chunk3 = sub3x3(game, 0, 2)
#=> [[4, 6, 8], [3, 7, 5], [2, 1, 9]]
chunk4 = sub3x3(game, 1, 0)
#=> [[6, 4, 3], [5, 2, 1], [9, 8, 7]]
...
chunk9 = sub3x3(game, 2, 2)
#=> [[6, 8, 7], [9, 2, 4], [1, 5, 3]]
Ruby has not concept of "rows" and "columns" of arrays. For convenience, therefore, I will refer to the 3x3 "subarray" of game, at offsets i and j (i = 0,1,2, j = 0,1,2), as the 3x3 submatrix of m = Matrix[*game] whose upper left value is at row offset 3*i and column offset 3*j of m, converted to an array.
This is relatively inefficient as a new matrix is created for the calculation of each "chunk". Considering the size of the array, this is not a problem, but rather than making that more efficient you really need to rethink the overall design. Creating nine local variables (rather than, say, an array of nine arrays) is not the way to go.
Here's a suggestion for checking the validity of game (that uses the method sub3x3 above) once all the open cells have been filled. Note that I've used the Wiki description of the game, in which the only valid entries are the digits 1-9, and I have assumed the code enforces that requirement when players enter values into cells.
def invalid_vector_index(game)
game.index { |vector| vector.uniq.size < 9 }
end
def sub3x3_invalid?(game, i, j)
sub3x3(game, i, j).flatten.uniq.size < 9
end
def valid?(game)
i = invalid_vector_index(game)
return [:ROW_ERR, i] if i
j = invalid_vector_index(game.transpose)
return [:COL_ERR, j] if j
m = Matrix[*game]
(0..2).each do |i|
(0..2).each do |j|
return [:SUB_ERR, i, j] if sub3x3_invalid?(game, i, j)
end
end
true
end
valid?(game)
#=> true
Notice this either returns true, meaning game is valid, or an array that both signifies that the solution is not valid and contains information that can be used to inform the player of the reason.
Now try
game[5], game[6] = game[6], game[5]
so
game
#=> [[1, 3, 2, 5, 7, 9, 4, 6, 8],
# [4, 9, 8, 2, 6, 1, 3, 7, 5],
# [7, 5, 6, 3, 8, 4, 2, 1, 9],
# [6, 4, 3, 1, 5, 8, 7, 9, 2],
# [5, 2, 1, 7, 9, 3, 8, 4, 6],
# [2, 1, 4, 9, 3, 5, 6, 8, 7],
# [9, 8, 7, 4, 2, 6, 5, 3, 1],
# [3, 6, 5, 8, 1, 7, 9, 2, 4],
# [8, 7, 9, 6, 4, 2, 1, 5, 3]]
valid?(game)
#=> [:SUB_ERR, 1, 0]
The rows and columns are obviously still valid, but this return value indicates that at least one 3x3 subarray is invalid and the array
[[6, 4, 3],
[5, 2, 1],
[2, 1, 4]]
was the first found to be invalid.
You could create a method that generates a single 3X3 chunk from a given index. since the sudoku board is of length 9, that will produce 9 3X3 chunks for you. see below.
#steps
#you'll loop through each index of the board
#to get the x value
#you divide the index by 3 and multiply by 3
#to get the y value
#you divide the index by 3, take remainder and multiply by 3
#for each x value, you can get 3 y values
#this will give you a single 3X3 box from one index so
def three_by3(index, sudoku)
#to get x value
x=(index/3)*3
#to get y value
y=(index%3)*3
(x...x+3).each_with_object([]) do |x,arr|
(y...y+3).each do |y|
arr<<sudoku[x][y]
end
end
end
sudoku = [ [1,2,3,4,5,6,7,8,9],
[2,3,4,5,6,7,8,9,1],
[3,4,5,6,7,8,9,1,2],
[1,2,3,4,5,6,7,8,9],
[2,3,4,5,6,7,8,9,1],
[3,4,5,6,7,8,9,1,2],
[1,2,3,4,5,6,7,8,9],
[2,3,4,5,6,7,8,9,1],
[3,4,5,6,7,8,9,1,2]]
p (0...sudoku.length).map {|i| three_by3(i,sudoku)}
#output:
#[[1, 2, 3, 2, 3, 4, 3, 4, 5],
# [4, 5, 6, 5, 6, 7, 6, 7, 8],
# [7, 8, 9, 8, 9, 1, 9, 1, 2],
# [1, 2, 3, 2, 3, 4, 3, 4, 5],
# [4, 5, 6, 5, 6, 7, 6, 7, 8],
# [7, 8, 9, 8, 9, 1, 9, 1, 2],
# [1, 2, 3, 2, 3, 4, 3, 4, 5],
# [4, 5, 6, 5, 6, 7, 6, 7, 8],
# [7, 8, 9, 8, 9, 1, 9, 1, 2]]