Is it possible to turn a 3D array to coordinate system? - python

Is it possible to take a 3D array and and turn it into a coordinate system? My array consists of 0s and 1s. If the value is 1 I want to take the xyz coordinate. In the end I want to output all coordinates to a csv file.
import nibabel as nib
coord = []
img = nib.load('test.nii').get_fdata().astype(int)
test.nii array:
[[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 1 ... 1 1 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 1 1 1]
[0 1 0 ... 0 0 0]]
[[1 0 0 ... 0 0 0]
[0 0 1 ... 0 0 0]
[0 1 0 ... 0 0 0]
...
[0 1 0 ... 0 0 0]
[0 1 0 ... 0 0 0]
[0 0 0 ... 1 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 1 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 1 0 ... 0 1 1]]
...
[[0 0 0 ... 1 0 0]
[0 0 1 ... 0 0 0]
[0 0 1 ... 0 0 0]
...
[0 0 0 ... 1 0 0]
[0 0 0 ... 1 0 0]
[0 0 0 ... 1 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 1]
...
[0 1 0 ... 0 0 0]
[1 0 0 ... 0 0 0]
[1 0 0 ... 0 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 1 0]
[0 1 0 ... 0 0 0]]]

That might not necessarily be the best solution, but let's keep it simple (would be great if framework did that for us, but...well):
data = [[[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 1, 1],
[0, 1, 0, 0, 0, 0]],
[[1, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0]]]
for x in range(len(data)):
for y in range(len(data[x])):
for z in range(len(data[x][y])):
if data[x][y][z] == 1:
print(f"{x} {y} {z}")
yields:
0 2 2
0 2 3
0 2 4
0 4 3
0 4 4
0 4 5
0 5 1
1 0 0
1 1 2
1 2 1
1 3 1
1 4 1
1 5 3

Using np.where() you can get the row, col and depth index of elements that satisfy you condition.
Try this:
row_idx, col_idx, depth_idx = np.where(img==1)

Related

Is It possible to switch rows or columns between numpy arrays?

I have the following numpy arrays
[[[0 0 1 0 0]
[1 0 0 0 0]
[0 0 1 0 0]]
[[1 0 0 0 0]
[0 0 1 0 0]
[0 0 0 1 0]]]
am trying to switch rows between them, 1 row 2 rows it doesn't matter am trying to see if it's possible.
The output can be for the 1st row or 2nd row or 2 first rows respectively:
[[[0 0 1 0 0] [[[0 0 1 0 0] [[[1 0 0 0 0]x
[1 0 0 0 0] [0 0 1 0 0]x [0 0 1 0 0]x
[0 0 0 1 0]]x [0 0 1 0 0]] [0 0 1 0 0]]
[[1 0 0 0 0] [[1 0 0 0 0] [[0 0 1 0 0]x
[0 0 1 0 0] [1 0 0 0 0]x [1 0 0 0 0]x
[0 0 1 0 0]]]x [0 0 0 1 0]]] [0 0 0 1 0]]]
Is it possible? If so How?
You can switch values like rows on NumPy arrays with Python variable swap operator:
import numpy as np
m = np.array([[0, 0, 1, 0, 0],
[1, 0 ,0, 0, 0],
[0, 0, 1, 0, 0]])
n = np.array([[1, 0, 0, 0, 0],
[0, 0, 1, 0, 0],
[0, 0, 0, 1, 0]])
#m[:, 0], n[:, 0] = n[:, 0].copy(), m[:, 0].copy() #Only for columns
m[0], n[0] = n[0].copy(), m[0].copy() #For rows
print(m, n)
Output:
[[1 0 0 0 0]
[1 0 0 0 0]
[0 0 1 0 0]]
[[0 0 1 0 0]
[0 0 1 0 0]
[0 0 0 1 0]]

Use Numpy arrays for large data file

I have a numpy array which is of the following type:-
[[[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
...
[[0 0 0 ... 0 0 0]
[0 0 1 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 1 1]
[0 0 0 ... 0 1 0]]
[[1 1 1 ... 0 0 0]
[1 1 0 ... 0 0 0]
[1 1 1 ... 0 0 0]
...
[0 1 1 ... 1 1 1]
[1 0 0 ... 0 0 0]
[1 0 0 ... 0 0 0]]]
[[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
...
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 1 1]
[0 0 0 ... 0 1 0]]
[[0 0 0 ... 1 1 0]
[0 0 0 ... 1 0 0]
[0 0 0 ... 1 0 0]
...
[0 0 0 ... 0 0 0]
[1 0 1 ... 0 0 0]
[0 0 0 ... 0 0 0]]]
[[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
...
[[0 0 0 ... 0 0 0]
[0 0 1 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 1 1]
[0 0 0 ... 0 0 0]]
[[1 1 1 ... 0 0 0]
[1 1 0 ... 1 1 1]
[0 1 1 ... 1 1 1]
...
[1 0 0 ... 0 0 0]
[1 0 0 ... 1 0 0]
[1 0 0 ... 0 1 0]]]
...
[[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 1 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 1 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
...
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[0 1 0 ... 0 0 0]
[1 1 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 1 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 1 0 ... 1 1 0]
...
[0 1 0 ... 0 0 0]
[0 1 0 ... 0 0 0]
[1 0 1 ... 1 1 1]]]
[[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 1 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 1 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
...
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[1 1 1 ... 1 1 0]
[1 1 0 ... 0 1 1]
[0 0 0 ... 1 0 1]
...
[0 0 1 ... 0 0 0]
[0 1 0 ... 0 0 0]
[1 0 0 ... 0 0 0]]
[[0 0 0 ... 1 0 0]
[1 1 1 ... 0 1 1]
[0 0 1 ... 1 0 1]
...
[1 0 0 ... 1 0 1]
[0 1 0 ... 1 0 0]
[0 0 0 ... 1 0 0]]]
[[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 1 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 1 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
...
[[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 1 0 0]
...
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]
[[1 1 0 ... 0 0 0]
[1 1 0 ... 0 0 0]
[1 0 0 ... 0 0 0]
...
[1 0 0 ... 0 1 0]
[1 0 0 ... 1 1 0]
[0 1 1 ... 1 1 1]]
[[0 0 0 ... 0 0 0]
[0 1 0 ... 1 1 0]
[1 0 0 ... 0 1 0]
...
[0 0 0 ... 0 0 1]
[0 0 0 ... 0 0 0]
[0 0 0 ... 0 0 0]]]]
I want to extract only 1/4th of the array but the file is too big to be loaded in RAM. I have tried to use mmap but couldn't understand how to do it because it is giving completely different values than that of my numpy array. Even when I loaded the code using the mem map it gives wrong shape and values. I have noticed that on changing dtype the values also change and cannot understand it. My Method for mem map:-
load = np.memmap("dataset/b.npy", mode='r', shape=(14,8,8))

Python lineage naming with clustered dataframe

I have a dataframe
sample1 0 0 0 0 0 1 1 1 1 1 1 1 1 L1
sample2 0 0 0 0 0 1 1 1 1 1 0 0 0 L1-1
sample3 0 0 0 0 0 1 1 0 0 0 0 0 0 L1-1-1
sample4 0 0 0 0 0 1 0 0 0 0 0 0 0 L1-1-1-1
sample5 0 0 0 0 0 0 0 1 1 0 0 0 0 L1-1-2
sample6 0 0 0 0 0 0 0 1 0 0 0 0 0 L1-1-2-1
sample7 0 0 0 0 0 0 0 0 0 1 0 0 0 L1-1-3
sample8 0 0 0 0 0 0 0 0 0 0 1 1 1 L1-2
sample9 0 0 0 0 0 0 0 0 0 0 1 1 0 L1-2-1
sample10 0 0 0 0 0 0 0 0 0 0 0 0 1 L1-2-2
sample11 1 1 1 1 1 0 0 0 0 0 0 0 0 L2
sample12 1 1 1 0 0 0 0 0 0 0 0 0 0 L2-1
sample13 1 1 0 0 0 0 0 0 0 0 0 0 0 L2-1-1
sample14 1 0 0 0 0 0 0 0 0 0 0 0 0 L2-1-1-1
sample15 0 0 0 1 0 0 0 0 0 0 0 0 0 L2-2
sample16 0 0 0 0 1 0 0 0 0 0 0 0 0 L2-3
As you can see, each row is clustered.
I want to name "lineage-based" labeling to each sample.
For example, sample1 will be lin1 because it is first to appear, sample2 will be lin1-1.
Sample3 will be lin1-1-1, sample4 will be lin1-1-1-1.
Next, sample5 will be lin1-2, sample6 will be lin1-2-1...
Sample11 will be a new start for the lineage, lin2.
My original idea for the naming was.
"sample1 is lin1, if next sample is included in the previous sample, lin1 + "-1"
if not, lin(1+1)"
sample1 -> lin1
sample2 -> lin1-1 (sample2 is included in sample1)
sample3 -> lin1-1-1 (sample3 is included in sample2)
sample4 -> lin1-1-1-1 (sample4 is included in sample3)
sample5 -> lin1-1-2 (sample5 is not included in sample4)
.... logic like this.
I couldn't make this logic into a python script.
This can be done in several steps.
Step 1. Data preprocessing
Sort the data in descending order and remove duplicate, otherwise it may not work. Assume done.
import numpy as np
data = '''sample1 0 0 0 0 0 1 1 1 1 1 1 1 1
sample2 0 0 0 0 0 1 1 1 1 1 0 0 0
sample3 0 0 0 0 0 1 1 0 0 0 0 0 0
sample4 0 0 0 0 0 1 0 0 0 0 0 0 0
sample5 0 0 0 0 0 0 0 1 1 0 0 0 0
sample6 0 0 0 0 0 0 0 1 0 0 0 0 0
sample7 0 0 0 0 0 0 0 0 0 1 0 0 0
sample8 0 0 0 0 0 0 0 0 0 0 1 1 1
sample9 0 0 0 0 0 0 0 0 0 0 1 1 0
sample10 0 0 0 0 0 0 0 0 0 0 0 0 1
sample11 1 1 1 1 1 0 0 0 0 0 0 0 0
sample12 1 1 1 0 0 0 0 0 0 0 0 0 0
sample13 1 1 0 0 0 0 0 0 0 0 0 0 0
sample14 1 0 0 0 0 0 0 0 0 0 0 0 0
sample15 0 0 0 1 0 0 0 0 0 0 0 0 0
sample16 0 0 0 0 1 0 0 0 0 0 0 0 0'''
data = [x.split() for x in data.split('\n')]
data = [x[1:] for x in data]
data = np.array(data, dtype=int)
data
array([[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],
[1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0]])
Step 2. Encode the sample to position. Each element is a frozenset.
nrow, ncol = data.shape
def to_position(sample):
ncol = len(sample)
return frozenset(i for i in range(ncol) if sample[i] == 1)
position = [to_position(data[i]) for i in range(nrow)]
# print(position)
Step 3. Assign each sample position to a cluster, where the cluster is represented as a tuple for now.
def assign_cluster(sample, clusters, parent):
if parent not in clusters:
clusters[parent] = sample
elif sample < clusters[parent]:
# Find child
parent = parent + (0,)
assign_cluster(sample, clusters, parent)
else:
# Find siblings
parent = parent[:-1] + (parent[-1] + 1, )
assign_cluster(sample, clusters, parent)
clusters = {}
root = (0,)
clusters[root] = position[0]
for i in range(1, nrow):
sample = position[i]
assign_cluster(sample, clusters, parent=root)
# print(clusters)
Step 4. Convert cluster to string and show result.
def cluster_to_string(c):
c = [str(_ + 1) for _ in c]
return 'L' + '-'.join(c)
position_dict = {v: k for k, v in clusters.items()}
for sample in data:
sample = to_position(sample)
c = position_dict[sample]
print(cluster_to_string(c))
L1
L1-1
L1-1-1
L1-1-1-1
L1-1-2
L1-1-2-1
L1-1-3
L1-2
L1-2-1
L1-2-2
L2
L2-1
L2-1-1
L2-1-1-1
L2-2
L2-3

Numpy way to integer-mask an array

I have a multi-class segmentation mask
eg.
[1 1 1 2 2 2 2 3 3 3 3 3 3 2 2 2 2 4 4 4 4 4 4]
And going to need to get binary segmentation masks for each value
i.e.
[1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1]
Any elegant numpy way to do this?
Ideally an example, where I can set 0 and 1 to other values, if I have to.
Just do "==" as this
import numpy as np
a = np.array([1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4])
mask1 = (a==1)*5
mask2 = (a==2)*5
mask3 = (a==3)*5
mask4 = (a==4)*5
for mask in [mask1,mask2,mask3,mask4]:
print(mask)
This gives
[5 5 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 5 5 5 5 0 0 0 0 0 0 5 5 5 5 0 0 0 0 0 0]
[0 0 0 0 0 0 0 5 5 5 5 5 5 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 5 5 5 5 5]
You can manipulate the masks further in the same manner, i. e.
mask1[mask1==0] = 3
Native python approach:
You can use comprehension and get the equality values for each unique value using set(<sequence>), then convert the boolean to int to get 0,1 values.
>>> ls =[1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4]
>>> {v:[int(v==i) for i in ls] for v in set(ls)}
{1: [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
2: [0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0],
3: [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
4: [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1]}
Numpy approach:
Get the unique values for the list using np.unique then expand the axis and transpose the array, then expand the axis for the list also and repeat it n times where n is the number of unique values, finally do the equality comparison and convert it to integer type:
import numpy as np
ls = [1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4]
uniques = np.expand_dims(np.unique(ls), 0).T
result = (np.repeat(np.expand_dims(ls, 0), uniques.shape[0], 0)==uniques).astype(int)
OUTPUT:
print(result)
[[1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0]
[0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1]]
You can build the mask using np.arange and .repeat() and then use broadcasting and the == operator to generate the arrays:
a = np.array([1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 4, 4, 4, 4, 4, 4])
mask = np.arange(a.min(), a.max()+1).repeat(a.size).reshape(-1, a.size)
a_masked = (a == m).astype(int)
print(a_masked.shape) # (4, 23)
print(a_masked)
# [[1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
# [0 0 0 1 1 1 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0]
# [0 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0]
# [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1]]
Setting 0 and 1 to other values can be done via normal indexing:
a_masked[a_masked == 0] = 7
a_masked[a_masked == 1] = 42

All possible binary matrices with some properties

I need to generate all possible 4x4 binary matrices that have zeros along the main diagonal, are symmetric, and have six entries equal to 1. Some examples:
[[0,0,0,0],
[0,0,1,1],
[0,1,0,1],
[0,1,1,0]],
[[0,1,1,0],
[1,0,1,0],
[1,1,0,0],
[0,0,0,0]],
[[0,1,0,1],
[1,0,0,1],
[0,0,0,0],
[1,1,0,0]]
How could I do that in Python?
This amounts to choosing which three of the six entries
above the diagonal are 1.
From the list of above-the-diagonal positions in a 4 by 4 matrix:
sage: positions = [(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)]
use Sage's Subsets to get all subsets of size 3 of those positions.
sage: S = Subsets([(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)], 3)
Then build the corresponding matrices.
sage: [matrix(ZZ, 4, lambda i, j: (i, j) in s or (j, i) in s) for s in S]
[
[0 1 1 1] [0 1 1 0] [0 1 1 0] [0 1 1 0] [0 1 0 1] [0 1 0 1]
[1 0 0 0] [1 0 1 0] [1 0 0 1] [1 0 0 0] [1 0 1 0] [1 0 0 1]
[1 0 0 0] [1 1 0 0] [1 0 0 0] [1 0 0 1] [0 1 0 0] [0 0 0 0]
[1 0 0 0], [0 0 0 0], [0 1 0 0], [0 0 1 0], [1 0 0 0], [1 1 0 0],
[0 1 0 1] [0 1 0 0] [0 1 0 0] [0 1 0 0] [0 0 1 1] [0 0 1 1]
[1 0 0 0] [1 0 1 1] [1 0 1 0] [1 0 0 1] [0 0 1 0] [0 0 0 1]
[0 0 0 1] [0 1 0 0] [0 1 0 1] [0 0 0 1] [1 1 0 0] [1 0 0 0]
[1 0 1 0], [0 1 0 0], [0 0 1 0], [0 1 1 0], [1 0 0 0], [1 1 0 0],
[0 0 1 1] [0 0 1 0] [0 0 1 0] [0 0 1 0] [0 0 0 1] [0 0 0 1]
[0 0 0 0] [0 0 1 1] [0 0 1 0] [0 0 0 1] [0 0 1 1] [0 0 1 0]
[1 0 0 1] [1 1 0 0] [1 1 0 1] [1 0 0 1] [0 1 0 0] [0 1 0 1]
[1 0 1 0], [0 1 0 0], [0 0 1 0], [0 1 1 0], [1 1 0 0], [1 0 1 0],
[0 0 0 1] [0 0 0 0]
[0 0 0 1] [0 0 1 1]
[0 0 0 1] [0 1 0 1]
[1 1 1 0], [0 1 1 0]
]
Note that these are the adjacency matrices for all graphs
with three edges on four labeled vertices.
If you want un-labeled vertices, or equivalently the list
of adjacency matrices of equivalence classes of graphs
with three edges on four vertices, you could use Nauty
to enumerate them. Here is how to do that from Sage:
sage: G = graphs.nauty_geng("4 3:3")
sage: G
<generator object nauty_geng at 0x21c89a0f0>
sage: [g.adjacency_matrix() for g in G]
[
[0 0 0 1] [0 0 1 1] [0 0 1 1]
[0 0 0 1] [0 0 0 1] [0 0 0 0]
[0 0 0 1] [1 0 0 0] [1 0 0 1]
[1 1 1 0], [1 1 0 0], [1 0 1 0]
]

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