iphone switched off out of no where

Try a "forced restart" of your iPhone using these instructions:--> Force restart iPhone – Apple Support

If the issue persists, it might be a hardware (Battery? Overheating? Other internal component?) failure but we, just users like you, cannot diagnose that issue remotely, sorry.

I suggest that you make an appointment (*) and have your device inspected at an Apple Store or AASP (Apple Authorized Service Provider) among this list:--> Apple – Location Selector. After checking it out, they'll give you all the available options.

Regards

Giulio

(*) You can do it:

• Online:--> Genius Bar Reservation and Apple Support Options - Apple;
• Contacting a local Apple Store or AASP among the list provided above;
• Using the "Apple Store" app, available and downloadable from AppStore.