Returns a list containing
f1function 1
f2_qregistered function using quotient space
gam_qwarping function quotient space
f2_aregistered function using ambient space
q2_awarping function ambient space
match_collectposterior samples from warping function (returned if extrainfo=TRUE)
dist_collectposterior samples from the distances (returned if extrainfo=TRUE)
kappa_collectposterior samples from kappa (returned if extrainfo=TRUE)
log_collectlog-likelihood of each sample (returned if extrainfo=TRUE)
pct_acceptvector of acceptance ratios for the warping function (returned if extrainfo=TRUE)