I want to take the logarithm of a tensor, what do I do
Do you mean element by element? How do you define the operation?
What does your input look like?
Let’s say I have A tensor of third order ,then,I want to know how to calculate e^A or log(A)
I believe this is because tensor multiplication is not defined, unlike a square matrix (where the matrix multiplication is defined)
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Have a look at my tensor package
https://github.com/chakravala/Grassmann.jl
It supports expnentiation and log of arbitrary tensors, although the fully general log method is not as well implemented as the exp method yet.
It uses a Clifford algebra representation for tensors.
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If you want element-wise operations, those are written as log.(A) and exp.(A) in Julia.
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I don’t mean element by element
I can’t find a logarithm operation in this package
It’s not clear to me what you mean by the log of a tensor. Logs are defined when you have an algebra, ie you can square a tensor. I imagine you mean that you contract A*B with the two last indices of A and the two first of B? If that is the case then you can get your log by reshaping your tensor as a matrix (with reshape) and reshaping back.
It’s in there in src/composite.jl
https://github.com/chakravala/Grassmann.jl/blob/master/src/composite.jl
Tensor multiplication is actually defined, if you use the Clifford product to multiply the tensors representation. The logarithm can be defined in terms of a series expansion with Clifford multiplication. In this case, using qlog:
Base.log(t::T) where T<:TensorAlgebra = qlog((t-1)/(t+1))
Base.log1p(t::T) where T<:TensorAlgebra = qlog(t/(t+2))
After first applying a transformation to the input. However, this method can diverge with some input.
In the Grassmann.jl package, there are several options, including an approximate but faster log_fast along with the slightly more robust Base.log with qlog.