This is a comparison of the Gaussian fitters using their default settings. This was just a sanity test. But I did find the omission of the Jacobian because of strange problems with EMPsfApprox doing these simple tests.

nGauss1: ngmix EMPsfApprox, nGauss = 1
nGauss2: ngmix EMPsfApprox, nGauss = 2
SingleGaussian: PsfShapeletApprox
DoubleGaussian: PsfShapeletApprox

Models running on a Single Gaussian:
component 0: amp = 1.000000, sigma = 4.000000

Using model nGauss1
DIFFS: (-0.00015829129176376792, 0.0011888552335592665)
PSF: (ixx=15.9990375642, iyy=15.9990375678, ixy=-1.59644452847e-08),
(-5.7088e-13, 7.2717e-14))
[ 0.27003514]

Using model SingleGaussian
DIFFS: (-0.00015541221422079763, 0.0012018456926277991)
PSF: (ixx=15.9999987904, iyy=15.9999994105, ixy=-2.88753774136e-07),
(7.0562e-10, 5.9369e-10))
[ 0.28209478]

Using model nGauss2
DIFFS: (-0.00015828218642075919, 0.0011889808463263511)
PSF: (ixx=15.437239682, iyy=15.4376494832, ixy=-0.000212610070082),
(0.0019808, -0.0022363))
[ 0.15543501]
PSF: (ixx=16.7722790887, iyy=16.7717162863, ixy=0.000298129770636),
(-0.0027039, 0.003053))
[ 0.11461417]

Using model DoubleGaussian
DIFFS: (-0.0001554122121517216, 0.0012018456811670592)
PSF: (ixx=15.9999999845, iyy=16.0000010528, ixy=-2.86920951877e-07),
(1.1837e-09, 9.7758e-10))
[ 0.28209478]
PSF: (ixx=63.9982986901, iyy=63.9982986901, ixy=1.49369523773e-12),
(-1.9056e-17, -2.3531e-17))
[ 1.48330137e-08]

-------------------------------------
-------------------------------------
Models running on a double gaussian
component 0: amp = 1.000000, sigma = 4.000000
component 1: amp = 0.500000, sigma = 8.000000

Using model nGauss1
DIFFS: (-0.00016236985259901842, 0.00093493041720977275)
PSF: (ixx=26.4048038208, iyy=26.4048038208, ixy=-8.42381887074e-13),
(-3.7257e-16, -6.1202e-19))
[ 0.26343557]

Using model SingleGaussian
DIFFS: (-0.00016284465841898458, 0.00095982776760274104)
PSF: (ixx=20.3547972164, iyy=20.2284155693, ixy=0.0631870250436),
(-0.00017337, -9.5825e-05))
[ 0.25573096]

Using model nGauss2
DIFFS: (-0.0001595243252360783, 0.00095397063580048111)
PSF: (ixx=15.9668132914, iyy=15.9668132914, ixy=0.0),
(3.8047e-16, -5.4508e-17))
[ 0.18150405]
PSF: (ixx=63.7248239325, iyy=63.7248239325, ixy=-3.79858632292e-16),
(2.0634e-16, 2.0936e-17))
[ 0.09142004]

Using model DoubleGaussian
DIFFS: (-0.0001572490117598259, 0.0009619403876283553)
PSF: (ixx=16.169975098, iyy=16.1699215778, ixy=-1.24287220881e-05),
(7.8807e-07, 2.8255e-06))
[ 0.19159612]
PSF: (ixx=67.2220132981, iyy=67.2225928636, ixy=0.000126914960634),
(2.2892e-07, 4.0119e-07))
[ 0.09126995]

Note that nGauss2 finds a two Gaussian fit to a single gaussian which splits the flux between two gaussians of nearly equal sigma and flux.

Yes, I was just sending you email about that. The EmPsfApprox algorithm seems fine now. Note comparison with ShapeletPsfApprox models of similar order.

I think that all the questions for 6124 and 6125 were answered by the timing information I sent you. Yes, I think the plugin is working well now, and is faster. It is about as good as the comparable lower order ShapeletPsfApprox models at reproducing the input Psf. And the CModel + EmPsfApprox pair seems to work comparably.