What I have is the following tensor:
a = np.array([[1,1], [2,2], [3,3]])
t = torch.from_numpy(a)
I need an operation that gets me to the following matrix:
enter image description here
This matrix contains the element-wise dot product of the tensor if it gets multiplied by its transposed version, i.e., the first element on the diagonal is
1x1 + 1x1 = 2, the 2nd element on the diagonal is
2x2 + 2x2 = 8, and the 2nd element in the first column is 1x2 + 1x2 = 4,
and so on. How do I get this matrix in torch, starting from tensor t? Thank you!
I tried various combinations of torch.tensordot, torch.transpose, etc.
einsum it!
print(torch.einsum("ik,jk->ij", t, t))
print(torch.einsum("ki,kj->ij", t, t))
tensor([[ 2, 4, 6],
[ 4, 8, 12],
[ 6, 12, 18]], dtype=torch.int32)
tensor([[14, 14],
[14, 14]], dtype=torch.int32)
Related
I have a tensor Aof sizetorch.Size([32, 32, 3, 3]) and I want to split it and extract a tensor B of size torch.Size([16, 16, 3, 3]) from it. The tensor can be 1d or 4d and split has to be according to the given new tensor dimensions. I have been able to generate the target dimensions but I'm unable to split and extract the values from the source tensor. I ave tried torch.narrow but it takes only 3 arguments and I need 4 in many cases. torch.split takes dim as an int due to which tensor is split along one dimension only. But I want to split it along multiple dimensions.
You have multiple options:
use .split multiple times
use .narrow multiple times
use slicing
e.g.:
t = torch.rand(32, 32, 3, 3)
t0, t1 = t.split((16, 16), 0)
print(t0.shape, t1.shape)
>>> torch.Size([16, 32, 3, 3]) torch.Size([16, 32, 3, 3])
t00, t01 = t0.split((16, 16), 1)
print(t00.shape, t01.shape)
>>> torch.Size([16, 16, 3, 3]) torch.Size([16, 16, 3, 3])
t00_alt, t01_alt = t[:16, :16, :, :], t[16:, 16:, :, :]
print(t00_alt.shape, t01_alt.shape)
>>> torch.Size([16, 16, 3, 3]) torch.Size([16, 16, 3, 3])
I am trying to use numpy to multiply two matrices:
import numpy as np
A = np.array([[1, 3, 2], [4, 0, 1]])
B = np.array([[1, 0, 5], [3, 1, 2]])
I tested the process and ran the calculations manually, utilizing the formula for matrix multiplications. So, in this case, I would first multiply [1, 0, 5] x A, which resulted in [11, 9] and then multiply [3, 1, 2] x B, which resulted in [10, 14]. Finally, the product of this multiplication is [[11, 9], [10, 14]]
nevertheless, when I use numpy to multiply these matrices, I am getting an error:
ValueError: shapes (2,3) and (2,3) not aligned: 3 (dim 1) != 2 (dim 0)
Is there a way to do this with python, successfully?
Read the docs on matrix multiplication in numpy, specifically on behaviours.
The behavior depends on the arguments in the following way.
If both arguments are 2-D they are multiplied like conventional
matrices. If either argument is N-D, N > 2, it is treated as a stack
of matrices residing in the last two indexes and broadcast
accordingly. If the first argument is 1-D, it is promoted to a matrix
by prepending a 1 to its dimensions. After matrix multiplication the
prepended 1 is removed. If the second argument is 1-D, it is promoted
to a matrix by appending a 1 to its dimensions. After matrix
multiplication the appended 1 is removed.
to get your output, try transposing one before multiplying?
c=np.matmul(A,B.transpose())
array([[11, 10],
[ 9, 14]])
I have the following tensor :
ts = torch.tensor([[1,2,3],[4,6,7],[8,9,10]])
> tensor([[ 1, 2, 3],
[ 4, 6, 7],
[ 8, 9, 10]])
I am looking for a pytorch generic operation that adds all rows element-wise like that:
ts2 = ts[0]+ts[1]+ts[2]
print(ts2)
> tensor([13, 17, 20])
In reality, the number of rows corresponds to the batch size that vary.
You can sum over an axis/dimension like so:
torch.sum(ts, dim=0)
I have a 2D tensor and an index tensor. The 2D tensor has a batch dimension, and a dimension with 3 values. I have an index tensor that selects exactly 1 element of the 3 values. What is the "best" way to product a slice containing just the elements in the index tensor?
t = torch.tensor([[1,2,3], [4,5,6], [7,8,9]])
t = tensor([[1, 2, 3],
[4, 5, 6],
[7, 8, 9]])
i = torch.tensor([0,0,1], dtype=torch.int64)
tensor([0, 0, 1])
Expected output...
tensor([1, 4, 8])
An example of the answer is as follows.
import torch
t = torch.tensor([[1,2,3], [4,5,6], [7,8,9]])
col_i = [0, 0, 1]
row_i = range(3)
print(t[row_i, col_i])
# tensor([1, 4, 8])
I am trying to extract the unique values in each row of a matrix and returning them into the same matrix (with repeated values set to say, 0) For example, I would like to transform
torch.Tensor(([1, 2, 3, 4, 3, 3, 4],
[1, 6, 3, 5, 3, 5, 4]])
to
torch.Tensor(([1, 2, 3, 4, 0, 0, 0],
[1, 6, 3, 5, 0, 0, 4]])
or
torch.Tensor(([1, 2, 3, 4, 0, 0, 0],
[1, 6, 3, 5, 4, 0, 0]])
I.e. the order does not matter in the rows. I have tried using pytorch.unique() and in the documentation it is mentioned that the dimension to take the unique values can be specified with the parameter dim. However, It doesn't seem to work for this case.
I've tried:
output= torch.unique(torch.Tensor([[4,2,52,2,2],[5,2,6,6,5]]), dim = 1)
output
Which gives
tensor([[ 2., 2., 2., 4., 52.],
[ 2., 5., 6., 5., 6.]])
Does anyone have a particular fix for this? If possible, I'm trying to avoid for loops.
One must admit the unique function can sometimes be very confusing without given proper examples and explanations.
The dim parameter specifies which dimension on the matrix tensor you want to apply on.
For instance, in a 2D matrix, dim=0 will let operation perform vertically where dim=1 means horizontally.
Example, let's consider a 4x4 matrix with dim=1. As you can see from my code below, the unique operation is applied row by row.
You notice the double occurrence of the number 11 in the first and last row. Numpy and Torch does this to preserve the shape of the final matrix.
However, if you do not specify any dimension, torch will automatically flatten your matrix and then apply unique to it and you will get a 1D array that contains unique data.
import torch
m = torch.Tensor([
[11, 11, 12,11],
[13, 11, 12,11],
[16, 11, 12, 11],
[11, 11, 12, 11]
])
output, indices = torch.unique(m, sorted=True, return_inverse=True, dim=1)
print("Ori \n{}".format(m.numpy()))
print("Sorted \n{}".format(output.numpy()))
print("Indices \n{}".format(indices.numpy()))
# without specifying dimension
output, indices = torch.unique(m, sorted=True, return_inverse=True)
print("Sorted (no dim) \n{}".format(output.numpy()))
Result (dim=1)
Ori
[[11. 11. 12. 11.]
[13. 11. 12. 11.]
[16. 11. 12. 11.]
[11. 11. 12. 11.]]
Sorted
[[11. 11. 12.]
[11. 13. 12.]
[11. 16. 12.]
[11. 11. 12.]]
Indices
[1 0 2 0]
Result (no dimension)
Sorted (no dim)
[11. 12. 13. 16.]
I was confused when using torch.unique the first time. After doing some experiments I have finally figured out how the dim argument works.
Docs of torch.unique says that:
counts (Tensor): (optional) if return_counts is True, there will be an additional returned tensor (same shape as output or output.size(dim), if dim was specified) representing the number of occurrences for each unique value or tensor.
For example, if your input tensor is a 3D tensor of size n x m x k and dim=2, unique will work separately on k matrices of size n x m. In other words, it will treat all dimensions other than the dim 2 as a single tensor.