I have two square matrices of the same size and the dimensions of a square patch. I'd like to compute the dot product between every pair of patches. Essentially I would like to implement the following operation:
def patch_dot(A, B, patch_dim):
res_dim = A.shape[0] - patch_dim + 1
res = np.zeros([res_dim, res_dim, res_dim, res_dim])
for i in xrange(res_dim):
for j in xrange(res_dim):
for k in xrange(res_dim):
for l in xrange(res_dim):
res[i, j, k, l] = (A[i:i + patch_dim, j:j + patch_dim] *
B[k:k + patch_dim, l:l + patch_dim]).sum()
return res
Obviously this would be an extremely inefficient implementation. Tensorflow's tf.nn.conv2d seems like a natural solution to this as I'm essentially doing a convolution, however my filter matrix isn't fixed. Is there a natural solution to this in Tensorflow, or should I start looking at implementing my own tf-op?
The natural way to do this is to first extract overlapping image patches of matrix B using tf.extract_image_patches, then to apply the tf.nn.conv2D function on A and each B sub-patch using tf.map_fn.
Note that prior to use tf.extract_image_patches and tf.nn.conv2D you need to reshape your matrices as 4D tensors of shape [1, width, height, 1] using tf.reshape.
Also, prior to use tf.map_fn, you would also need to use the tf.transpose op so that the B sub-patches are indexed by the first dimension of the tensor you use as the elems argument of tf.map_fn.
Related
let’s say I have a Tensor X with dimensions [batch, channels, H, W]
then I have another tensor b that holds bias values for each channel which has dims [channels,]
I want y = x + b (per sample)
Is there a nice way to broadcast this over H and W for each channel for each sample in the batch without using a loop.
If i’m convolving I know I can use the bias field in the function to achieve this, but I’m just wondering if this can be achieved just with primitive ops (not using explicit looping)
Link to PyTorch forum question
y = x + b[None, :, None, None] (basically expand b into x's axis template)
My pytorch code is running too slow due to it not being vectorized and I am unsure how to go about vectorizing it as I am relatively new to PyTorch. Can someone help me do this or point me in the right direction?
level_stride = 8
loc = torch.zeros(H * W, 2)
for i in range(H):
for j in range(W):
loc[i * H + j][0] = level_stride * (j + 0.5)
loc[i * H + j][1] = level_stride * (i + 0.5)
First of all, you defined the tensor to be of size (H*W, 2). This is of course entirely optional, but it might be more expressive to preserve the dimensionality explicitly, by having H and W be separate dimension in the tensor. That makes some operations later on easier as well.
The values you compute to fill the tensor with originate from ranges. We can use the torch.arange function to get the same ranges, already in form of a tensor, ready to be put into your loc tensor. If that is done, you could see it as, completely leaving out the for loops, and just treating j and i as different tensors.
If you're not familiar with tensors, this might seem confusing, but operations between single number values and tensors work just as well, so not much of the rest of the code has to be changed.
I'll give you a expression of how your code could look like with these changes applied:
level_stride = 8
loc = torch.zeros(H, W, 2)
j = torch.arange(W).expand((H, W))
loc[:, :, 0] = level_stride * (j + 0.5)
i = torch.arange(H).expand((W, H)).T
loc[:,:,1] = level_stride * (i + 0.5)
The most notable changes are the assignments to j and i, and the usage of slicing to fill the data into loc.
For completeness, let's go over the expressions that are assigned to i and j.
j starts as a torch.arange(W) which is just like a regular range, just in form of a tensor. Then .expand is applied, which you could see as the tensor being repeated. For example, if H had been 5 and W 2, then a range of 2 would have been created, and expanded to a size of (5, 2). The size of this tensor thereby matches the first two sizes in the loc tensor.
i starts just the same, only that W and H swap positions. This is due to i originating from a range based on H rather then W. Notable here is that .T is applied at the end of that expression. The reason for this is that the i tensor still has to match the first two dimensions of loc. .T transposes the tensor for this reason.
If you have a subject specific reason to have the loc tensor in the (H*W, 2) shape, but are otherwise happy with this solution, you could reshape the tensor in the end with loc.reshape(H*W,2).
I'm trying to assemble a tensor based on the contents of two other tensors, like so:
I have a 2D tensor called A, with shape I * J, and another 2D tensor called B, with shape M * N, whose elements are indices into the 1st dimension of A.
I want to obtain a 3D tensor C with shape M * N * J such that C[m,n,:] == A[B[m,n],:] for all m in [0, M) and n in [0, N).
I could do this using nested for-loops to iterate over all indices in M and N, assigning the right values to C at each one, but M and N are large so this is quite slow. I suspect there's some nicer, faster way of doing this using clever slicing or a built-in pytorch function, but I don't know what it would be. It looks a bit like somewhere one would use torch.gather(), but that requires all tensors to have the same number of dimensions. Does anyone know how this ought to be done?
EDIT: torch.index_select(input, dim, index) is almost what I want, but it won't work here because it requires that index be a 1D tensor, while my tensor of indices is 2D.
You could achieve this by flattening the first dimensions which let's you index A. A broadcast will be required to recover the final shape
>>> A[B.flatten(),:].reshape(*B.shape, A.size(-1))
Indexing with A[B.flatten(),:] is equivalent to torch.index_select(A, 0, B.flatten()).
I am trying to generate a matrix (tensor object on PyTorch) that is similar to Gram matrix except I need to apply a kernel function instead of inner product on my input matrix.
For loops like the one below works:
N = x.shape[0] # x.shape = (N,d)
G = torch.zeros((N,N))
for i in range(N):
for j in range(N):
G[i][j] = K(x[i], x[j])
where x is my input tensor whose shape is (N,d) and the kernel function K(a,b) yields a real value after performing some math. For example:
def K(a,b):
return ((1+(a*b)).sum()).pow(2) #second degree polynomial.
I want to generate this matrix, G without having to change the kernel function K() and of course, without for-loops!
My initial attempt is to use a lambda approach but this code below obviously doesn't work as it only yields a list of k(x[i],x[i]).
G = torch.tensor(list(map(lambda a,b: K(a,b),x,x))
How can I use the lambda function to yield N-by-N matrix?
What would be some other ways to tackle this problem?
Any insight would be appreciated.
You can calculate G from x simply with:
G = (1 + torch.matmul(x, x.T)).pow(2)
I'm trying to vectorize a loop with NumPy but I'm stuck
I have a matrix A of shape (NN,NN) I define the A-dot product by
def scalA(u,v):
return v.T # A # u
Then I have two matrices B and C (B has a shape (N,NN) and C has a shape (K,NN) the loop I'm trying to vectorize is
res = np.zeros((N,K))
for n in range(N):
for k in range(K):
res[n,k] = scalA(B[n,:], C[k,:])
I found during my research functions like np.tensordot or np.einsum, but I haven't really understood how they work, and (if I have well understood) tensordot will compute the canonical dot product (that would correspond to A = np.eye(NN) in my case).
Thanks !
np.einsum('ni,ji,kj->nk', B,A,C)
I think this works. I wrote it 'by eye' without testing.
Probably you're looking for this:
def scalA(u,v):
return u # A # v.T
If shape of A is (NN,NN), shape of B is (N,NN), and shape of C is (K,NN), the result of scalA(B,C) has shape (N,K)
If shape of A is (NN,NN), shape of B is (NN,), and shape of C is (NN,), the result of scalA(B,C) is just a scalar.
However, if you're expecting B and C to have even higher dimensionality (greater than 2), this may need further tweaking. (I could not tell from your question whether that's the case)