  We invert directly the redshift - luminosity distribution of observed long
Swift GRBs to obtain their rate and luminosity function. Our best fit rate is
described by a broken power law that rises like (1+z)^2.1{+0.5-0.6} for 0<z<3
and decrease like (1+z)^-1.4{+2.4-1.0} for z>3. The local rate is
1.3^{+0.6-0.7} [Gpc^-3 yr^-1]. The luminosity function is well described by a
broken power law with a break at L* = 10^52.5{+-0.2}[erg/sec] and with indices
alpha = 0.2^{+0.2-0.1} and beta = 1.4^{+0.3-0.6}. The recently detected GRB
090423, with redshift ~8, fits nicely into the model's prediction, verifying
that we are allowed to extend our results to high redshifts. While there is a
possible agreement with the star formation rate (SFR) for z<3, the high
redshift slope is shallower than the steep decline in the SFR for 4<z. However
we cannot rule out a GRB rate that follows one of the recent SFR models.
