I have a question

From my past tax returns, I have the impression that for first partial year when you used the property for personal use, there is limit on deduction, but I can't find the rule for it.  If anyone knows, please let me know.

For example,  let's say I lived 6 months in the house, then rent it out for 6 months,  the income is 10K, the expense is 9K, the depreciation (for 6 months) is 2K.  

You would expect my income/loss would be 10K-9K-2K = -1K

But actually according to my tax software, my income/loss is limited to 0, and my depreciation that year is 1K instead of 2K to ensure I don't have a loss.

So my question is, is there a rule says that if you use a property for both rental and personal use, your depreciation is limited to whatever the income - expense, but could not generate a loss.