Q: How to analyze Precision rectifier op amp configuration
As a general rule, an op amp in a negative feedback configuration as above will do its best to keep the negative input the same as the positive.  During the negative half cycle on your input, that's exactly what happens--it goes positive just enough to keep the negative input at zero.

On the positive half cycle, the diode (in conjunction with the lack of a negative supply voltage) prevents the op amp from compensating for the input.  It tries its best, driving the output to the negative rail (ground), but it just can't push the needed current through the diode.  Therefore, the output voltage will reflect the input directly.  Thus, rectifier.