Multiplication of MultivariateNormal with vector

[pabloprf]

The MultivariateNormal distribution allows to pass a mean in the form of a matrix to represent a batch of multivariate normals (as indicated in the class description). The __mul__ method, however, only allows multiplication of the distribution by a scalar.
I'm interested in multiplying each of the multivariate normals in the batch by a different scalar.
How would you do that?

[Balandat]

You'd basically just have to extend the __mul__ method to also accept a tensor as the other argument, and then make sure to properly apply the broadcasted (across batch dims) multiplication to the mean as well as the lazy covariance matrix.

[Balandat]

happy to review a PR for this.

[pabloprf]

Thanks @Balandat. I will work on it and submit a PR