Erf and erfinv functions in PyTorch

I have a torch.FloatTensor say A of size u,v,x,y. I have to calculate its erf and erfinv. Is there any way to do this in PyTorch. Please help me.

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What is Erf (and what is it’s inverse)? Is this an abbreviation?

Erf is error function also known as Gauss error function ( and erfinv is its inverse.

I’m actually interested by this as well, could you give us some updates if you find a solution?

import torch
from scipy import special
## reference -

u = 1
v = 2
x = 3
y = 4

A = torch.randn(u,v,x,y)

special.erf( A.numpy() )
special.erfinv( A.numpy())

Thanks Ajay! This is working fine. :blush:

Nope, it does not work, because I also need the error function but as an autograd function; I mean, I would like to insert this function in the computation graph and pytorch to automatically differentiate it !

If the function is not supported for now in pytorch, may I define my own custom autograd function ?

(actually the equivalent of TF function: )

Thank you @Soumith and all devs !

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If you can do it with torchtensors then you can define your own custom autograd function.

It might be a little tedious, but we’ve all written our own custom functions and modules - that’s a lot of the fun :smile: .

It’s definitely worth doing, once you’ve done one, it’s a lot less scary - good luck :slight_smile:

Hello @cerisara,

if you can live with an approximation, you could use the following (in the formula with the square root here: )

import torch
a_for_erf = 8.0/(3.0*numpy.pi)*(numpy.pi-3.0)/(4.0-numpy.pi)
def erf_approx(x):
    return torch.sign(x)*torch.sqrt(1-torch.exp(-x*x*(4/numpy.pi+a_for_erf*x*x)/(1+a_for_erf*x*x)))
def erfinv_approx(x):
    b = -2/(numpy.pi*a_for_erf)-torch.log(1-x*x)/2
    return torch.sign(x)*torch.sqrt(b+torch.sqrt(b*b-torch.log(1-x*x)/a_for_erf))

I must admit I don’t have a particular reason to use x*x for x**2 except that I copy-pasted it from a C version I typed up a couple of years ago.
If you feed Variables that should work as well.

To get an impression of how they look, you could plot it against the scipy.special functions like

from matplotlib import pyplot
%matplotlib inline
import scipy.special
x = numpy.linspace(-2,2,100)
pyplot.plot(x,erf_approx(torch.from_numpy(x)).numpy(), label="approx")
pyplot.plot(x,scipy.special.erf(x),'--', label="scipy")
y = scipy.special.erf(x)
pyplot.plot(y,erfinv_approx(torch.from_numpy(y)).numpy(), label="approx")
pyplot.plot(y,scipy.special.erfinv(y),'--', label="scipy")

(the %matplotlib is for jupyter).

Best regards



Hi @tom,

nice work !!!

I found a very simple implementation of the sinkhorn-knopp matrix normalisation, we were looking at a while ago. It’s in MATLAB, but it’s very understandable,

Hopefully I’ll try to implement it in torch this weekend - that should be a lot of fun, and useful too.

All the best,


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Great !

Thank you, very useful !

One use case that I needed was to sample from a Gaussian VAE and do interpolation in uniform distributed variables. That is because u = erfinv(v) follows normal distribution if v follows uniform distribution via a technique called inverse sampling.

These functions are now in master: :relaxed:


Awesome, thank you!

Best regards


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Can you point me to the current code for erf and erfinv? I want to see how they and their gradients have been approximated.
Many thanks!