Chrome has native date picker for <input type="date">:

I like it, and it's totally ok with me to have it work only in chrome.
The question is how can I invoke date picker for this input field in javascript?
Normally there is only input field until user focus it and click little black triangle to open small calendar. I want to open it from javascript.
I would like to avoid 3rd party date picker implementations if possible.
I've tried element.focus(), element.click(), etc.
inputdoesn't cause it. And you can't move the mouse pointer with JS, no API for it, not that I know of.