Flight Crew Air Transport Pilot (ATP)
Human-Machine Interface; Situational Awareness
Aircraft Equipment Problem Less Severe; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Air Traffic Control Issued New Clearance; Flight Crew Became Reoriented; Flight Crew FLC complied w / Automation / Advisory
Aircraft; Procedure
We had just taken off from runway 01R at SFO and were assigned the NITE1 RNAV departure.  We entered the departure; route and arrival after receiving the clearance.   I was the pilot flying and shortly after takeoff the Flight Director commanded a left turn; which I followed.  The NITE1 turns slightly to the right on a 014 heading and then proceeds to MOSAY out of 520 feet.  I remember thinking that it was strange that the Flight Director was commanding a left turn when the Controller called and asked us to confirm that we were on the NITE1.  My First Officer responded with 'Yes.'  The Controller then came back with turn right to 020 degrees. We complied and continued on our trip. There was no traffic on Runway 01L which was fortunate.  We kept going over what went wrong as we were at cruise altitude. We had followed SOP when finishing the taxi checklist and confirming that the FMS and the runway we were taking were the same.  As to what I would do differently; I would be more vigilant in making sure the flight director is taking me where I want to go and not blindly following it.  I trust that this is a wakeup call for me to never become complacent.  I realize that is always a danger.  As to why it happened; as we continued our flight; the First Officer lost his FMC.  I don't know if that had anything to do with what happened or not.  It doesn't make sense that it would have.  Bottom line; fly the airplane to where it is supposed to go is first priority and never think that because you have the FMC telling you where you are going that it is correct.
[Report narrative contained no additional information].
After entering the correct runway and departure an Airbus flight crew followed the incorrect left turn indicated by the flight director on the NITE1 RNAV departure out of SFO. ATC issued a vector for a right turn back on course.