[ENHANCEMENT] Defined loginner(::ITensor, ::ITensor) methods

[sotashimozono]

Description

I implemented loginner and logdot methods.
Fixes #1552

In the previous implementation for MPS/MPO, the contraction order was well-defined, and we utilized a specialized method to compute the inner product in the logarithmic scale.

For general ITensor objects, however, the optimal contraction sequence is not uniquely determined. Therefore, I have implemented a straightforward fallback as follows:

inner(y::ITensor, x::ITensor) = (dag(y) * x)[]
loginner(A::ITensor, B::ITensor) = log(complex(inner(A, B)))

example code:

i = Index(2)
j = Index(2)
A = random_itensor(ElType, i', j', i, j)
x = random_itensor(ElType, i, j)
y = random_itensor(ElType, i, j)


val2 = inner(x, y)
val3 = inner(x', A, y)

@assert loginner(x, y) ≈ log(complex(val2))
@assert logdot(x, y) ≈ log(complex(val2))

How Has This Been Tested?

I added testcode in test_itensor.jl

Checklist:

• My code follows the style guidelines of this project. Please run the ITensorFormatter in the base directory of the repository (~/.julia/dev/ITensors) to format your code according to our style guidelines.
• I have performed a self-review of my own code.
• I have commented my code, particularly in hard-to-understand areas.
• I have added tests that verify the behavior of the changes I made.
• I have made corresponding changes to the documentation.
• My changes generate no new warnings.
• Any dependent changes have been merged and published in downstream modules.

[github-actions]

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