I want to access a specific row and column restriction of a 2d numpy array.
> x
array([[1, 2, 0],
[3, 4, 0],
[0, 0, 1]])
If I do what seems natural, I just get the diagonal elements of the restricted array.
> x[[0,1], [0,1]]
array([1, 4])
Instead I can do this to read what I want -
> x[[0,1],:][:,[0,1]]
array([[1, 2],
[3, 4]])
..but it doesn't let me write/assign the values.
> x[[0,1],:][:,[0,1]] = np.array([[1,0],[0,1]])
> x
array([[1, 2, 0],
[3, 4, 0],
[0, 0, 1]])
How can I write to a matrix here?
Use np.ix_ to map that grid of elements and then assign -
x[np.ix_([0,1], [0,1])] = np.array([[1,0],[0,1]])
This works too:
x[:2, :2] = np.array([[1, 0], [0, 1]])
Related
I want to compare each element against all others like following. The number of variables like a, b, c is dynamic. However, each variable's array size is uniform.
let a = [1, 2, 3]
let b = [3, 4, 5]
let c = [4, 5, 6]
for i in a {
for j in b {
for k in c {
/// comparison
}
}
}
Instead looping from start to finish at once, what would be a way to make each comparison on call? For example:
compare(iteration: 0)
/// compares a[0], b[0], c[0]
compare(iteration: 1)
/// compares a[0], b[0], c[1]
/// all the way to
/// compares a[2], b[2], c[2]
Or it could even be like following:
next()
/// compares a[0], b[0], c[0]
next()
/// compares a[0], b[0], c[1]
almost like an iterator stepping through each cycle dictated by my invocation.
Let the number of arrays be n. And let the number of elements in each array, which is guaranteed the same for all of them, be k.
Then create an array consisting of the integers 0 through k-1, repeated n times. For example, in your case, n is 3, and k is 3, so generate the array
[0, 1, 2, 0, 1, 2, 0, 1, 2]
Now obtain all combinations of n elements of that array. You can do this using the algorithm at https://github.com/apple/swift-algorithms/blob/main/Guides/Combinations.md. Unique the result (by, for example, coercing to a Set and then back to an Array). This will give you a result equivalent, in some order or other, to
[[0, 1, 2], [0, 1, 0], [0, 1, 1], [0, 2, 0], [0, 2, 1], [0, 2, 2], [0, 0, 1], [0, 0, 2], [0, 0, 0], [1, 2, 0], [1, 2, 1], [1, 2, 2], [1, 0, 1], [1, 0, 2], [1, 0, 0], [1, 1, 2], [1, 1, 0], [1, 1, 1], [2, 0, 1], [2, 0, 2], [2, 0, 0], [2, 1, 2], [2, 1, 0], [2, 1, 1], [2, 2, 0], [2, 2, 1], [2, 2, 2]]
You can readily see that those are all 27 possible combinations of the numbers 0, 1, and 2. But that is exactly what you were doing with your for loops! So now, use those subarrays as indexes into each of your original arrays respectively.
So for instance, using my result and your original example, the first subarray [0, 1, 2] yields [1, 4, 6] — the first value from the first array, the second value from the second array, and the third value from the third array. And so on.
In this way you will have generated all possible n-tuples by choosing one value from each of your original arrays, which is the desired result; and we are in no way bound to fixed values of n and k, which was what you wanted to achieve. You will then be able to "compare" the elements of each n-tuple, whatever that may mean to you (you did not say in your question what it means).
In the case of your original values, we will get these n-tuples (expressed as arrays):
[1, 4, 6]
[1, 4, 4]
[1, 4, 5]
[1, 5, 4]
[1, 5, 5]
[1, 5, 6]
[1, 3, 5]
[1, 3, 6]
[1, 3, 4]
[2, 5, 4]
[2, 5, 5]
[2, 5, 6]
[2, 3, 5]
[2, 3, 6]
[2, 3, 4]
[2, 4, 6]
[2, 4, 4]
[2, 4, 5]
[3, 3, 5]
[3, 3, 6]
[3, 3, 4]
[3, 4, 6]
[3, 4, 4]
[3, 4, 5]
[3, 5, 4]
[3, 5, 5]
[3, 5, 6]
Those are precisely the triples of values you are after.
Actual code:
// your original conditions
let a = [1, 2, 3]
let b = [3, 4, 5]
let c = [4, 5, 6]
let originals = [a, b, c]
// The actual solution starts here. Note that I never use any hard
// coded numbers.
let n = originals.count
let k = originals[0].count
var indices = [Int]()
for _ in 0..<n {
for i in 0..<k {
indices.append(i)
}
}
let combos = Array(indices.combinations(ofCount: n))
var combosUniq = [[Int]]()
var combosSet = Set<[Int]>()
for combo in combos {
let success = combosSet.insert(combo)
if success.inserted {
combosUniq.append(combo)
}
}
// And here's how to generate your actual desired values.
for combo in combosUniq {
var tuple = [Int]()
for (outerIndex, innerIndex) in combo.enumerated() {
tuple.append(originals[outerIndex][innerIndex])
}
print(tuple) // in real life, do something useful here
}
}
How would I replace values less than 4 with 0 in this array without triggering a SparseEfficiencyWarning and without reducing its sparsity?
from scipy import sparse
x = sparse.csr_matrix(
[[0, 1, 2, 3, 4],
[1, 2, 3, 4, 5],
[0, 0, 0, 2, 5]])
x[x < 4] = 0
x.toarray() # verifies that this works
Note also that the sparsity between the initial version of x is 11 stored elements, which rises to 15 stored elements after doing the masking.
Manipulate the data array directly
from scipy import sparse
x = sparse.csr_matrix(
[[0, 1, 2, 3, 4],
[1, 2, 3, 4, 5],
[0, 0, 0, 2, 5]])
x.data[x.data < 4] = 0
>>> x.toarray()
array([[0, 0, 0, 0, 4],
[0, 0, 0, 4, 5],
[0, 0, 0, 0, 5]])
>>> x.data
array([0, 0, 0, 4, 0, 0, 0, 4, 5, 0, 5])
Note that the sparsity is unchanged and there are zero values unless you run x.eliminate_zeros().
x.eliminate_zeros()
>>> x.data
array([4, 4, 5, 5])
If for some reason you don't want to use a boolean mask & fancy indexing in numpy, you can loop over the array with numba:
import numba
#numba.jit(nopython=True)
def _set_array_less_than_to_zero(array, value):
for i in range(len(array)):
if array[i] < value:
array[i] = 0
This should also be faster than the numpy indexing by a fairly substantial degree.
array = np.arange(10)
_set_array_less_than_to_zero(array, 5)
>>> array
array([0, 0, 0, 0, 0, 5, 6, 7, 8, 9])
i have written the code below,it works for shortest distance but not for shortest path,
import math
def floyd(dist_mat):
n=len(dist_mat)
p=[[0]*n]*n
for k in range(n):
for i in range(n):
for j in range(n):
if dist_mat[i][j]>dist_mat[i][k]+dist_mat[k][j]:
dist_mat[i][j] = dist_mat[i][k] + dist_mat[k][j]
p[i][j] = k+1
return p
if __name__ == '__main__':
print(floyd([[0,5,9999,9999],
[50,0,15,5],
[30,9999,0,15],
[15,9999,5,0]]))
result of this code is: [[4, 1, 4, 2], [4, 1, 4, 2], [4, 1, 4, 2], [4, 1, 4, 2]]
true result is: [[0, 0, 4, 2], [4, 0, 4, 0], [0, 1, 0, 0], [0, 1, 0, 0]],
I will be happy to receive your ideas about why it works wrong soon
A=2;
for x=0:2:4
A=[A, A*x];
end
A
I'd appreciate any help! The for loop condition as well as the 3rd line and how they work together I can't quite piece together
So, here comes the walktrough.
A = 2;
A is an array of length 1, with 2 as the only element.
for x = 0:2:4
Have a look at the Examples section of the for help. You create an "iteration variable" x, which iterates through an array with the values [0, 2, 4]. See also the Examples section of the : operator help.
A = [A, A*x];
Concatenate array A with the value of A*x (multiplying an array with a scalar results in an array of the same length, in which each element is multiplied by the given scalar), and re-assign the result to A. See also the help on Concatenating Matrices.
Initially, A = [2].
For x = 0: A = [[2], [2] * 0], i.e. A = [2, 0].
For x = 2: A = [[2, 0], [2, 0] * 2], i.e. A = [2, 0, 4, 0].
For x = 4: A = [[2, 0, 4, 0], [2, 0, 4, 0] * 4], i.e. A = [2, 0, 4, 0, 8, 0, 16, 0].
end
End of for loop.
A
Output content of A by implicitly calling the display function by omitting the semicolon at the end of the line, see here for explanation.
Let's say I have a vector that looks as so (the numbers will always be > 0)...
[1, 2, 1, 4, 1, 2, 4, 3]
I need a vectorized implementation that sums the numbers together and uses the original number as the index to store the number. So if I run it I would get...
% step 1
[1+1+1, 2+2, 3, 4+4]
% step 2
[3, 4, 3, 8]
I have already implemented this using for loops, but I feel like there is a vectorized way to achieve this. I am still quite new at vectorizing functions so any help is appreciated.
This sounds like a job for accumarray:
v = [1, 2, 1, 4, 1, 2, 4, 3];
result = accumarray(v(:), v(:)).'
result =
3 4 3 8
Other approaches:
Using histcounts:
x = [1, 2, 1, 4, 1, 2, 4, 3];
u = unique(x);
result = u.*histcounts(x, [u inf]);
Using bsxfun (may be more memory-intensive):
x = [1, 2, 1, 4, 1, 2, 4, 3];
u = unique(x);
result = u .* sum(bsxfun(#eq, x(:), u(:).' ), 1);