When generating a new block, how is the nbits field in block header calculated? Is nbits calculated for every new block like:

nbits=nbits of last block * (timstamp of lastblock-timestamp of (lastblocknum-2016))/20160 

Or, nbits is only updated every 2016 blocks like:

if(currentblocknum%2016==0)
    nbits=nbits of last block * (timstamp of lastblock-timestamp of (lastblocknum-2016))/20160 
else
    nbits=nbits of lastblock

And when a node receives a new block, it will calculate the correct nbits itself for the new block (instead of using the nbits in the received block) before verifying the hash result, right?

I have not read the source code of bitcoin, and am confused by the introduction of nbits in some books.