Merging LoRA and getting unexpected results (Is my math wrong?)

[AI-Casanova]

I'm attempting to use Automatic1111 to test the strengths at which I want to merge two LoRA.

In A1111:
<Lora:X:.5> <Lora:Y:.5> yields result A

Using merge_lora.py --ratios .5 .5 gives similar but different results if I do <Lora:Merge:2> in A1111

merge_lora.py --ratios 1 1, gives the same results as the last merge if I do <Lora:Merge:.5>

Is Automatic1111 calculating the LoRA addition differently, which results in the slight differences?

At what ratio should I merge to arrive at a LoRA normalizes to alpha=1?
(I tried 0.75 0.75 but that results in a 3rd outcome)

[AI-Casanova]

Alright, I verified that loading the LoRAs via Automatic1111 and the Additional Networks extension produce the same results.

Also, merging at 0.5*√2 (ie 0.7071) produces the exact same results at weight 1 as .5 at strength 2

However I'm not sure how to generalize that to dissimilar ratios (ie 0.4 and 0.6) though I will test 0.4√2 0.6√2

This solves one of my issues, normalizing to weight 1

However, I still am getting somewhat different results than what using both LoRA at 0.5 weight produces.