In South India outside of the chera country the knowledge of hAdi vidyA has largely declined. I recall a gentleman telling me that hAdi vidyA is only used for abhichAra purposes. Of course this is an erroneous view. I was going through R’s manual used for the hAdi krama- pretty distinctive in terms of its vArAhI and mAta~NgI formulae. But the hAdi pa~ncha krama involves the worship of AdyA-kAlI in the morning, tArA at the mid-day ritual, ChinnamastA at the sunset rite, bagalAmukhI at the nocturnal rite and hAdI-vidyA at the mid-night rite. The worship of tArA at the mid-day ritual is shared by the hAdi-mata with the sAdi-mata.
Interestingly the hAdi followers also accept the formula which is believed to be associated with the shAnkhAyana tradition of the R^igveda:
kAmo yoniH kamalA vajrapANir guhA hasA mAtarishvAbhraM indraH |
punar guhA sakalA mAyA cha puruchyeShA vishvamAtA .a.adi-vidyA ||
Interestingly it is also at the heart of the mahAchInAchAra tantra, the kAlachakra.
jjhrIM mahAchaNDe tejaH sa~NkarShiNi kAlamanthane haH ||