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Replace column by 0 based on probability

How to replace column in the numpy array be certain number based on probability, if it is (1,X,X) shape.
I found code to replace rows, but cannot figure out how to modify it, so it is applicable for columns replacement.
grid_example = np.random.rand(1,5,5)
probs = np.random.random((1,5))
grid_example[probs < 0.25] = 0
grid_example
Thanks!

Use:
import numpy as np
rng = np.random.default_rng(42)
grid_example = rng.random((1, 5, 5))
probs = rng.random((1, 5))
grid_example[..., (probs < 0.25).flatten()] = 0
print(grid_example)
Output
[[[0. 0.43887844 0. 0. 0.09417735]
[0. 0.7611397 0. 0. 0.45038594]
[0. 0.92676499 0. 0. 0.4434142 ]
[0. 0.55458479 0. 0. 0.6316644 ]
[0. 0.35452597 0. 0. 0.7783835 ]]]
The notation [..., (probs < 0.25).flatten()] applies the boolean indexing to the last index. More on the documentation.

Create Jordan matrix from eigenvalues using NumPy

I have ndarray of eigenvalues and their multiplicities (for instance, np.array([(2.2, 2), (3, 3), (5, 1)])). I need to compute Jordan matrix for this eigenvalues without using Python cycles and iterables (list comprehensions, for loops etc.), only by using NumPy's functions.
I decided to build the matrix by this steps:
Create this blocks using np.vectorize and np.eye with np.fill_diagonal:
Combine blocks into one matrix using hstack and vstack.
But I've got two problems:
Here's snippet of my block creating code:
def eye(t):
eye = np.eye(t[1].astype(int),k=1)
return eye
def jordan_matrix(X: np.ndarray) -> np.ndarray:
dim = np.sum(X[:,1].astype(int))
eyes = np.vectorize(eye, signature='(x)->(n,m)')(X)
return eyes
And I'm getting error ValueError: could not broadcast input array from shape (3,3) into shape (2,2)
I need to create extra zero matrices to fill space which is not used by created blocks, but their sizes are variable and I can't figure out how to create them without using Python's for and its equivalents.
Am I on the right way? How can I get out of this problems?

np.vectorize would basically loop under the hoods. We could use NumPy funcs for actual vectorization at Python level. Here's one such way -
def blockwise_jordan(a):
r = a[:,1].astype(int)
v = np.repeat(a[:,0],r)
out = np.diag(v)
n = out.shape[1]
fillvals = np.ones(n, dtype=out.dtype)
fillvals[r[:-1].cumsum()-1] = 0
out.flat[1::out.shape[1]+1] = fillvals
return out
Sample run -
In [52]: X = np.array([(2.2, 2), (3, 3), (5, 1)])
In [53]: blockwise_jordan(X)
Out[53]:
array([[2.2, 1. , 0. , 0. , 0. , 0. ],
[0. , 2.2, 0. , 0. , 0. , 0. ],
[0. , 0. , 3. , 1. , 0. , 0. ],
[0. , 0. , 0. , 3. , 1. , 0. ],
[0. , 0. , 0. , 0. , 3. , 0. ],
[0. , 0. , 0. , 0. , 0. , 5. ]])
Optimization #1
We can replace the final three steps to perform the conditional assignment of 1s and 0s, like so -
out.flat[1::n+1] = 1
c = r[:-1].cumsum()-1
out[c,c+1] = 0

Here's my solution:
def jordan(a):
e = a[:,0] # eigenvalues
m = a[:,1].astype('int') # multiplicities
d = np.repeat(e, m) # main diagonal
ones = np.ones(d.size - 1)
ones[np.cumsum(m)[:-1] -1] = 0
j = np.diag(d) + np.diag(ones, k=1)
return j
Edit: just realized that my solution is almost the same as Divakar's.

Creating random Variables in Python with one third of the array to be zero

I want to create random variables in python and used the following below code
weights = np.random.random(10) but I want to create random variables such that one third of the weights should be zero. Is there any way possible? I have also tried below code but this is not what I want
weights = np.random.random(7)
weights.append(0, 0, 0)

With the clarification that you want the 0's to appear randomly, you can just use shuffle:
weights = np.random.random(7)
weights = np.append(weights,[0, 0, 0])
np.random.shuffle(weights)

One simple way:
>>> import numpy as np
>>>
>>> a = np.clip(np.random.uniform(-0.5, 1, (100,)), 0, np.inf)
>>> a
array([0.39497669, 0.65003362, 0. , 0. , 0. ,
0.75545815, 0.30772786, 0.1805628 , 0. , 0. ,
0. , 0.82527704, 0. , 0.63983682, 0.89283051,
0.25173721, 0.18409163, 0.63631959, 0.59095185, 0. ,
0.85817311, 0. , 0.06769175, 0. , 0.67807471,
0.29805637, 0.03429861, 0.53077809, 0.32317273, 0.52346321,
0.22966515, 0.98175502, 0.54615167, 0. , 0.88853359,
0. , 0.70622272, 0.08106305, 0. , 0.8767082 ,
0.52920044, 0. , 0. , 0.29394736, 0.4097331 ,
0.77977164, 0.62860222, 0. , 0. , 0.14899124,
0.81880283, 0. , 0.1398242 , 0. , 0.50113732,
0. , 0.68872893, 0.15582668, 0. , 0.34789122,
0.18510949, 0.60281713, 0.21097922, 0.77419626, 0.29588479,
0.18890799, 0.9781896 , 0.96220508, 0.52201816, 0.71087763,
0. , 0.43540516, 0.99297503, 0. , 0.69248893,
0.05157044, 0. , 0.75131066, 0. , 0. ,
0.25627591, 0.53367521, 0.58151298, 0.85662171, 0.455367 ,
0. , 0. , 0.21293519, 0.52337335, 0. ,
0.68644488, 0. , 0. , 0.39695189, 0. ,
0.40860821, 0.84549468, 0. , 0.21247807, 0.59054669])
>>> np.count_nonzero(a)
67
It draws uniformly from [-0.5, 1] and then sets everything below zero to zero.

Set Approximately 1/3 of weights
This will guarantee that approximately one third of your weights are 0:
weights = np.random.random(10)/np.random.choice([0,1],10,p=[0.3,0.7])
weights[np.isinf(weights)] = 0
# or
# weights[weights == np.inf] = 0
>>> weights
array([0. , 0.25715864, 0. , 0.80958258, 0.12880619,
0.48781856, 0.52278911, 0.76541417, 0.87736431, 0. ])
What it does is divides about 1/3 of your values by 0, giving you inf, then just replace the inf by 0
Set Exactly 1/3 of weights
Alternatively, if you need it to be exactly 1/3 (or in your case, 3 out of 10), you can replace 1/3 of your weights with 0:
weights = np.random.random(10)
# Replace 3 with however many indices you want changed...
weights[np.random.choice(range(len(weights)),3,replace=False)] = 0
>>> weights
array([0. , 0.36839012, 0. , 0.51468295, 0.45694205,
0.23881473, 0.1223229 , 0.68440171, 0. , 0.15542469])
That selects 3 random indices from weights and replaces them with 0

size = 10
v = np.random.random(size)
v[np.random.randint(0, size, size // 3)] = 0
A little bit more optimized (because random number generation is not "cheap"):
v = np.zeros(size)
nnonzero = size - size // 3
idx = np.random.choice(size, nnonzero, replace=False)
v[idx] = np.random.random(nnonzero)

What about replacing the first third of items with 0 then shuffle it as following
weights = np.random.random(10)
weights[: weights.size / 3] = 0
np.random.shuffle(weights)

Raise diagonal matrix to the negative power 1/2

I am trying to compute the matrix which has the following equation.
S = (D^−1/2) * W * (D^−1/2)
where D is a diagonal matrix of this form:
array([[ 0.59484625, 0. , 0. , 0. ],
[ 0. , 0.58563893, 0. , 0. ],
[ 0. , 0. , 0.58280472, 0. ],
[ 0. , 0. , 0. , 0.58216725]])
and W:
array([[ 0. , 0.92311635, 0.94700586, 0.95599748],
[ 0.92311635, 0. , 0.997553 , 0.99501248],
[ 0.94700586, 0.997553 , 0. , 0.9995501 ],
[ 0.95599748, 0.99501248, 0.9995501 , 0. ]])
I tried to compute D^-1/2 by using numpy function linalg.matrix_power(D,-1/2) and numpy.power(D,-1/2) and matrix_power function raises TypeError: exponent must be an integer and numpy.power function raises RuntimeWarning: divide by zero encountered in power.
How to compute negative power -1/2 for diagonal matrix. Please help.

If you can update D(like in your own answer) then simply update the items at its diagonal indices and then call np.dot:
>>> D[np.diag_indices(4)] = 1/ (D.diagonal()**0.5)
>>> np.dot(D, W).dot(D)
array([[ 0. , 0.32158153, 0.32830723, 0.33106193],
[ 0.32158153, 0. , 0.34047794, 0.33923936],
[ 0.32830723, 0.34047794, 0. , 0.33913717],
[ 0.33106193, 0.33923936, 0.33913717, 0. ]])
Or create a new zeros array and then fill its diagonal elements with 1/ (D.diagonal()**0.5):
>>> arr = np.zeros(D.shape)
>>> np.fill_diagonal(arr, 1/ (D.diagonal()**0.5))
>>> np.dot(arr, W).dot(arr)
array([[ 0. , 0.32158153, 0.32830723, 0.33106193],
[ 0.32158153, 0. , 0.34047794, 0.33923936],
[ 0.32830723, 0.34047794, 0. , 0.33913717],
[ 0.33106193, 0.33923936, 0.33913717, 0. ]])

I got the answer by computing thro' mathematical terms but would love to see any straight forward one liners :)
def compute_diagonal_to_negative_power():
for i in range(4):
for j in range(4):
if i == j:
element = D[i][j]
numerator = 1
denominator = math.sqrt(element)
D[i][j] = numerator / denominator
return D
diagonal_matrix = compute_diagonal_to_negative_power()
S = np.dot(diagonal_matrix, W).dot(diagonal_matrix)
print(S)
"""
[[ 0. 0.32158153 0.32830723 0.33106193]
[ 0.32158153 0. 0.34047794 0.33923936]
[ 0.32830723 0.34047794 0. 0.33913718]
[ 0.33106193 0.33923936 0.33913718 0. ]]
"""
Source: https://math.stackexchange.com/questions/340321/raising-a-square-matrix-to-a-negative-half-power

You can do the following:
numpy.power(D,-1/2, where=(D!=0))
And then you will avoid getting the warning:
RuntimeWarning: divide by zero encountered in power
numpy will divide every value on the matrix element-wise by it's own square root, which is not zero, so basically you won't try to divide by zero anymore.

From list of indices to one-hot matrix

What is the best (elegant and efficient) way in Theano to convert a vector of indices to a matrix of zeros and ones, in which every row is the one-of-N representation of an index?
v = t.ivector() # the vector of indices
n = t.scalar() # the width of the matrix
convert = <your code here>
f = theano.function(inputs=[v, n], outputs=convert)
Example:
n_val = 4
v_val = [1,0,3]
f(v_val, n_val) = [[0,1,0,0],[1,0,0,0],[0,0,0,1]]

I didn't compare the different option, but you can also do it like this. It don't request extra memory.
import numpy as np
import theano
n_val = 4
v_val = np.asarray([1,0,3])
idx = theano.tensor.lvector()
z = theano.tensor.zeros((idx.shape[0], n_val))
one_hot = theano.tensor.set_subtensor(z[theano.tensor.arange(idx.shape[0]), idx], 1)
f = theano.function([idx], one_hot)
print f(v_val)[[ 0. 1. 0. 0.]
[ 1. 0. 0. 0.]
[ 0. 0. 0. 1.]]

It's as simple as:
convert = t.eye(n,n)[v]
There still might be a more efficient solution that doesn't require building the whole identity matrix. This might be problematic for large n and short v's.

There's now a built in function for this theano.tensor.extra_ops.to_one_hot.
y = tensor.as_tensor([3,2,1])
fn = theano.function([], tensor.extra_ops.to_one_hot(y, 4))
print fn()
# [[ 0. 0. 0. 1.]
# [ 0. 0. 1. 0.]
# [ 0. 1. 0. 0.]]