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I not sure is about battery problem or other problem. I charged my xperia Z untill 100% before i go to sleep but when i wake up i check it dropped to 50% already. No one using the phone but it dropped to 50% in 4hours and the stamina mode is on. Is there any problem about this?
first few times after a major update is normal. It happened to me, the next time I charged it and left it idle it was fine.
the battery and software just needs some time to get along 
if the problem still persist, i advise you to
Backup your files and
repair it with Sony PC Companion, or Sony Update Service or flash another FTF file. (wipe everything) Do a clean install.
As said above it can happen right after the update. If you experience problem with this again. Check what's draining the battery under settings > power management > battery.