Create a tensor from a function that takes indexes as variable

ITensor Julia Questions
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1

Hello everyone, I am trying to create a tensor with a function that should take the indexes as values to produce a specific result for every element for the tensor.
I was able to define it using CartesianIndexes, a function and a map for the case of a simple matrix as listed below :

# fourier transform of call option
function vstate(z, eta, alpha, strike_price)
    z = - eta .* z .- im *alpha
    return  -strike_price^(1 + im * sum(z))/((-1)^length(z) * prod(im .* z) .*(1 + im * sum(z)))
end
alpha = 2.5
eta = 0.5
strike_price = 100
#create the matrix
callp = map(x -> vstate(x.I, -eta, -alpha, strike_price), 
CartesianIndices((-25:25, -25:25)))

Is it possible to do this in Itensors? And do you perhaps know, in case the first response is positive, how to produce an MPS of it? Thank you.

2

The best way to do that is just wrap the Julia Array in an ITensor, i.e.

i = Index(size(callp, 1))
j = Index(size(callp, 2))
t = itensor(callp, i, j) # Creates a view into `callp`
t = ITensor(callp, i, j) # Creates a copy of `callp`

Then you can create an MPS with:

m = MPS(t, [i, j]; cutoff=1e-12) # Create an MPS from the ITensor
m = MPS(callp, [i, j]; cutoff=1e-12) # Create an MPS from the Julia Array
3

So it is not possible to allocate that tensor directly using the function, but I need to instantiate the array first and then convert it to Tensor at the moment?

4

Yeah, but I don’t see how that could be avoided (i.e. we could provide an interface for passing a function that constructs elements of an ITensor, but we would have to allocate an array internally at some point anyway).

5

Ok, thank you!