Inverting the phase response of a biquad all-pass filter

Greetings!

I need an algorithm for inverting the phase response of a biquad all-pass filter. Thank you to everyone who can help with this issue.

What do you mean with inverting ?

Run your signal backwards through the same filter - everything else is doomed to fail because it requires exchanging poles/zeros, and one pole will end up outside the unit circle, rendering your inverse filter unstable.

By inverting the phase of an all-pass filter, I mean changing what would be +90 degrees of phase shift to -90 degrees of phase shift. An all-pass filter alters phase according to algorithms that occur in nature. I want to reverse these algorithms that occur in nature, in order to cancel types of phase shift that occur in nature.

Could you elaborate on those algorithms? However, your desired filter sounds quite noncausal to me

My math skills are only in the 63rd percentile for the United States. This means that I know nothing about calculus.

It is my understanding that the peaks in the frequency response of rooms have the same phase shift characteristics as boosted biquad peaking filters.

Consider a two-way loudspeaker system with a 4th order crossover network. There will be 360 degrees of phase shift at the crossover frequency. I am exploring the idea of an all-pass filter that would change this to 0 degrees of phase shift after the correction has been applied.

Sometimes audio software developers tell audio engineers that the technology they are requesting is a bad idea. Am I being that kind of an audio engineer right now?