I have a pytorch tensor k x (n+k-1) tensor w with requires_grad=True. I want to transform it into a kxn tensor p also with as such: p[i] = w[i][i:i+n]. How do I do this, such that by calling backward() on a loss function of p in the end, I will learn w?
Any sort of indexing operation would do, with the backward function being <CopySlices>
A naive way of doing this would be using simple python indexing:
w_unrolled = torch.zeros(p.size())
for i in range(w.shape[0]):
w_unrolled[i] = w[i][i:i+n]
loss = criterion(w_unrolled, p)
You can then reduce your loss via mean/sum on whichever axis. Note that while this will work, it is inefficient; the optimal way would be to use a native indexing function to speed things up.
Related
I have there tensors with shapes a = (B,12,512,512), b= (B,12,512,512), c = (B,2,512,512).
I want to multiply a* c[:,0,:,:] + b*c[:,1,:,:]
As far as I know, gradient calculation does not support indexing operation, so I need to implement this calculation without using indexing. How can I implement it in a vectorized way with Pytorch?
Thanks.
I want to minimize an equation. The equation consists of elements which are all tensors.
f=alpha + (vnorm/2) #Equation to minimize
where, vnorm=norm(v)*norm(v)
v is a tensor vector of n*1 and alpha is a tensor of 1*1
Now I need to minimize f with respect to a contraint, that is–
(A # v)+alpha<=0 #Constraint involve in the minimization
where A is a tensor of 2*n.
How should I formulate the above equation and the the constraint to minimize the same in Pytorch ? I was successful in doing the same with 'scipy' but I want to do it in Pytorch so that I can make the minimization process faster taking the help of the tensors.
I'm new in PyTorch and I come from functional programming languages(where map function is used everywhere). The problem is that I have a tensor and I want to do some operations on each element of the tensor. The operation may be various so I need a function like this:
map : (Numeric -> Numeric) -> Tensor -> Tensor
e.g. map(lambda x: x if x < 255 else -1, tensor) # the example is simple, but the lambda may be very complex
Is there such a function in PyTorch? How should I implement such function?
Most mathematical operations that are implemented for tensors (and similarly for ndarrays in numpy) are actually applied element wise, so you could write for instance
mask = tensor < 255
result = tensor * mask + (-1) * ~mask
This is a quite general appraoch. For the case that you have right now where you only want to modify certain elements, you can also apply "logical indexing" that let's you overwrite the current tensor:
tensor[mask < 255] = -1
So in python there actually is a map() function but usually there are better ways to do it (better in python; in other languages - like Haskell - map/fmap is obviously prefered in most contexts).
So the key take-away here is that the preferred method is taking advantage of the vectorization. This also makes the code more efficient as those tensor operations are implemented in a low level language, while map() is nothing but a python-for loop that is a lot slower.
I am trying to multiply two complex matrices in PyTorch and it seems the torch.matmul functions is not added yet to PyTorch library for complex numbers.
Do you have any recommendation or is there another method to multiply complex matrices in PyTorch?
Currently torch.matmul is not supported for complex tensors such as ComplexFloatTensor but you could do something as compact as the following code:
def matmul_complex(t1,t2):
return torch.view_as_complex(torch.stack((t1.real # t2.real - t1.imag # t2.imag, t1.real # t2.imag + t1.imag # t2.real),dim=2))
When possible avoid using for loops as these will result in much slower implementations.
Vectorization is achieved by using built-in methods as demonstrated in the code I have attached.
For example, your code takes roughly 6.1s on CPU while the vectorized version takes only 101ms (~60 times faster) for 2 random complex matrices with dimensions 1000 X 1000.
Update:
Since PyTorch 1.7.0 (as #EduardoReis mentioned) you can do matrix multiplication between complex matrices similarly to real-valued matrices as follows:
t1 # t2
(for t1, t2 complex matrices).
I implemented this function for pytorch.matmul for complex numbers using torch.mv and it's working fine for time-being:
def matmul_complex(t1, t2):
m = list(t1.size())[0]
n = list(t2.size())[1]
t = torch.empty((1,n), dtype=torch.cfloat)
t_total = torch.empty((m,n), dtype=torch.cfloat)
for i in range(0,n):
if i == 0:
t_total = torch.mv(t1,t2[:,i])
else:
t_total = torch.cat((t_total, torch.mv(t1,t2[:,i])), 0)
t_final = torch.reshape(t_total, (m,n))
return t_final
I am new to PyTorch, so please correct me if I am wrong.
I've been trying to implement a custom objective function in Keras (the negative log likelihood of the normal distribution)
Keras expects one argument for the ground truth tensor, and one for the predictions tensor; for y_pred,I'm passing a tensor that should represent a nx2 matrix where the first column is the mean of the distribution, and the second the precision.
My problem is that I haven't been able to get a clear idea how I properly slice y_pred before passing it into the likelihood function without yielding the error
'Expected an array-like object, but found a Variable: maybe you are trying to call a function on a (possibly shared) variable instead of a numeric array?'
While I understand that I'm feeding l_func arguments of the variable type when it expects an array,I don't seem to be able to grok how to properly split the input y_pred variable into its mean and precision components to plug into the likelihood function. Here are some attempts; if someone could enlighten me about how to proceed, I would greatly appreciate it.
def log_likelihood(y_true,y_pred):
mu = T.vector('mu')
beta = T.vector('beta')
x=T.vector('x')
likelihood = .5*(beta*(x-mu)**2)-T.log(beta/(2*np.pi))
l_func = function([mu,beta,x], likelihood)
return(l_func(y_pred[:,0],y_pred[:,1],y_true))
def log_likelihood(y_true,y_pred):
likelihood = .5*(y_pred[:,1]*(y_true-y_pred[:,0])**2)-T.log(y_pred[:,1]/(2*np.pi))
l_func = function([y_true,y_pred], likelihood)
return(l_func(y_true,y_pred))
def log_likelihood(y_true,y_pred):
mu=y_pred[:,0]
beta=y_pred[:,1]
x=y_true
mu_function=function([y_pred],mu)
beta_function=function([y_pred],beta)
id_function=function([y_true],x)
likelihood = .5*(beta_function(y_pred)*(id_function(y_true)-mu_function(y_pred))**2)-T.log(beta_function(y_pred)/(2*np.pi))
l_func = function([y_true,y_pred], likelihood)
return(l_func(y_true,y_pred))