Add imbalance stats for total perf, hbm and ddr #2040
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Summary:
Add and log 4 ways to measure imbalance of generated sharding plan.
Suppose we have$k$ gpus. Let $s$ be a vector where the $i^{th}$ component is the total size currently allocated to the $i^{th}$ device.
First we normalize vector$s$ such that sum of elements in $p$ equals 1. We can view this as a probability distribution, and to get a measure of imbalance, we can measure its deviation from uniform distribution $p$ using one of the following ways:
Differential Revision: D57465383