def test_disk_derivative_bin():
# Read the data to fit
data_root = remote_data_file()
kin = manga.MaNGAStellarKinematics.from_plateifu(8138, 12704, cube_path=data_root,
maps_path=data_root)
disk = AxisymmetricDisk(rc=HyperbolicTangent(), dc=Exponential())
# Ensure that center is offset from 0,0 because of derivative calculation when r==0.
disk.par[:2] = 0.1
# Use a slowly rising rotation curve. More quickly rising rotation curves
# show a greater difference between the finite-difference and direct
# derivative calculations after the convolution.
disk.par[-3] = 20.
# Finite difference test steps
# x0 y0 pa inc vsys vinf hv sig0 hsig
dp = numpy.array([0.0001, 0.0001, 0.001, 0.001, 0.001, 0.001, 0.0001, 0.001, 0.0001])
# Include the beam-smearing
try:
cnvfftw = ConvolveFFTW(kin.spatial_shape)
except:
cnvfftw = None
v, sig, dv, dsig = disk.deriv_model(disk.par, x=kin.grid_x, y=kin.grid_y, sb=kin.grid_sb,
beam=kin.beam_fft, is_fft=True, cnvfftw=cnvfftw)
# Now also include the binning
bv, dbv = kin.deriv_bin(v, dv)
bsig, dbsig = kin.deriv_bin(sig, dsig)
vp = numpy.empty(v.shape+(disk.par.size,), dtype=float)
sigp = numpy.empty(v.shape+(disk.par.size,), dtype=float)
bvp = numpy.empty(bv.shape+(disk.par.size,), dtype=float)
bsigp = numpy.empty(bv.shape+(disk.par.size,), dtype=float)
p = disk.par.copy()
for i in range(disk.par.size):
_p = p.copy()
_p[i] += dp[i]
# These calls to `model` reuse the previously provided x, y, sb, beam,
# and cnvfftw
vp[...,i], sigp[...,i] = disk.model(_p)
bvp[...,i] = kin.bin(vp[...,i])
bsigp[...,i] = kin.bin(sigp[...,i])
disk._set_par(p)
fd_dbv = (bvp - bv[...,None])/dp[None,:]
fd_dbsig = (bsigp - bsig[...,None])/dp[None,:]
for i in range(disk.par.size):
assert numpy.allclose(dbv[...,i], fd_dbv[...,i], rtol=0., atol=1e-4), \
f'Finite difference produced different derivative for parameter {i+1}!'
# The difference is relatively large (again) for the dispersion data
assert numpy.allclose(dbsig[...,i], fd_dbsig[...,i], rtol=0., atol=3e-3), \
f'Finite difference produced different sigma derivative for parameter {i+1}!'
def test_disk_derivative_nosig():
disk = AxisymmetricDisk()
# Ensure that center is offset from 0,0 because of derivative calculation when r==0.
disk.par[:2] = 0.1
# Use a slowly rising rotation curve. More quickly rising rotation curves
# show a greater difference between the finite-difference and direct
# derivative calculations after the convolution.
disk.par[-1] = 20.
# Finite difference test steps
# x0 y0 pa inc vsys vinf hv
dp = numpy.array([0.0001, 0.0001, 0.001, 0.001, 0.001, 0.001, 0.0001])
n = 101
x = numpy.arange(n, dtype=float)[::-1] - n//2
y = numpy.arange(n, dtype=float) - n//2
x, y = numpy.meshgrid(x, y)
v, dv = disk.deriv_model(disk.par, x=x, y=y)
vp = numpy.empty(v.shape+(disk.par.size,), dtype=float)
p = disk.par.copy()
for i in range(disk.par.size):
_p = p.copy()
_p[i] += dp[i]
# These calls to `model` reuse the previously provided x and y
vp[...,i] = disk.model(_p)
disk._set_par(p)
fd_dv = (vp - v[...,None])/dp[None,:]
for i in range(disk.par.size):
assert numpy.allclose(dv[...,i], fd_dv[...,i], rtol=0., atol=1e-4), \
f'Finite difference produced different derivative for parameter {i+1}!'
# Now include the beam-smearing
beam = gauss2d_kernel(n, 3.)
try:
cnvfftw = ConvolveFFTW(beam.shape)
except:
cnvfftw = None
v, dv = disk.deriv_model(disk.par, x=x, y=y, beam=beam, cnvfftw=cnvfftw)
vp = numpy.empty(v.shape+(disk.par.size,), dtype=float)
p = disk.par.copy()
for i in range(disk.par.size):
_p = p.copy()
_p[i] += dp[i]
# These calls to `model` reuse the previously provided x, y, beam, and
# cnvfftw
vp[...,i] = disk.model(_p)
disk._set_par(p)
fd_dv = (vp - v[...,None])/dp[None,:]
for i in range(disk.par.size):
assert numpy.allclose(dv[...,i], fd_dv[...,i], rtol=0., atol=1e-4), \
f'Finite difference produced different derivative for parameter {i+1}!'
def test_disk_fit_derivative():
# Read the data to fit
data_root = remote_data_file()
kin = manga.MaNGAStellarKinematics.from_plateifu(8138, 12704, cube_path=data_root,
maps_path=data_root)
disk = AxisymmetricDisk(rc=HyperbolicTangent(), dc=Exponential())
# Set the parameters close to the best-fitting parameters from a previous
# run
p0 = numpy.array([-0.2, -0.08, 166.3, 53.0, 25.6, 217.0, 2.82, 189.7, 16.2])
# Finite difference test steps
# x0 y0 pa inc vsys vinf hv sig0 hsig
dp = numpy.array([0.0001, 0.0001, 0.001, 0.001, 0.001, 0.001, 0.0001, 0.001, 0.0001])
# Run the fit preparation
disk._fit_prep(kin, p0, None, None, True, True, True, None)
# Get the method used to generate the figure-of-merit and the jacobian
fom = disk._get_fom()
jac = disk._get_jac()
# Get the fom and the jacobian
chi = fom(p0)
dchi = jac(p0)
# Brute force it
chip = numpy.empty(dchi.shape, dtype=float)
p = disk.par.copy()
for i in range(disk.par.size):
_p = p.copy()
_p[i] += dp[i]
chip[...,i] = fom(_p)
disk._set_par(p)
# Compare them
fd_dchi = (chip - chi[...,None])/dp[None,:]
for i in range(disk.par.size):
# diff = numpy.absolute(dchi[...,i]-fd_dchi[...,i])
# print(i, numpy.amax(diff), numpy.amin(diff))
# continue
assert numpy.allclose(dchi[...,i], fd_dchi[...,i], rtol=0., atol=1e-3), \
f'Finite difference produced different derivative for parameter {i+1}!'
def test_disk_derivative():
disk = AxisymmetricDisk(rc=HyperbolicTangent(), dc=Exponential())
# Ensure that center is offset from 0,0 because of derivative calculation when r==0.
disk.par[:2] = 0.1
# Use a slowly rising rotation curve. More quickly rising rotation curves
# show a greater difference between the finite-difference and direct
# derivative calculations after the convolution.
disk.par[-3] = 20.
# Finite difference test steps
# x0 y0 pa inc vsys vinf hv sig0 hsig
dp = numpy.array([0.0001, 0.0001, 0.001, 0.001, 0.001, 0.001, 0.0001, 0.001, 0.0001])
n = 101
x = numpy.arange(n, dtype=float)[::-1] - n//2
y = numpy.arange(n, dtype=float) - n//2
x, y = numpy.meshgrid(x, y)
v, sig, dv, dsig = disk.deriv_model(disk.par, x=x, y=y)
vp = numpy.empty(v.shape+(disk.par.size,), dtype=float)
sigp = numpy.empty(v.shape+(disk.par.size,), dtype=float)
p = disk.par.copy()
for i in range(disk.par.size):
_p = p.copy()
_p[i] += dp[i]
# These calls to `model` reuse the previously provided x and y
vp[...,i], sigp[...,i] = disk.model(_p)
disk._set_par(p)
fd_dv = (vp - v[...,None])/dp[None,:]
fd_dsig = (sigp - sig[...,None])/dp[None,:]
for i in range(disk.par.size):
assert numpy.allclose(dv[...,i], fd_dv[...,i], rtol=0., atol=1e-4), \
f'Finite difference produced different velocity derivative for parameter {i+1}!'
# The precision is worse for dsig/dx0 and dsig/dy0 at x=y=0.0. Not sure
# why. The larger atol is to account for this.
assert numpy.allclose(dsig[...,i], fd_dsig[...,i], rtol=0., atol=3e-3), \
f'Finite difference produced different sigma derivative for parameter {i+1}!'
# Now include the beam-smearing
beam = gauss2d_kernel(n, 3.)
try:
cnvfftw = ConvolveFFTW(beam.shape)
except:
cnvfftw = None
v, sig, dv, dsig = disk.deriv_model(disk.par, x=x, y=y, beam=beam, cnvfftw=cnvfftw)
vp = numpy.empty(v.shape+(disk.par.size,), dtype=float)
sigp = numpy.empty(v.shape+(disk.par.size,), dtype=float)
p = disk.par.copy()
for i in range(disk.par.size):
_p = p.copy()
_p[i] += dp[i]
# These calls to `model` reuse the previously provided x, y, beam, and
# cnvfftw
vp[...,i], sigp[...,i] = disk.model(_p)
disk._set_par(p)
fd_dv = (vp - v[...,None])/dp[None,:]
fd_dsig = (sigp - sig[...,None])/dp[None,:]
for i in range(disk.par.size):
assert numpy.allclose(dv[...,i], fd_dv[...,i], rtol=0., atol=1e-4), \
f'Finite difference produced different derivative for parameter {i+1}!'
# Apparently the convolution smooths out the difference seen in the test above
assert numpy.allclose(dsig[...,i], fd_dsig[...,i], rtol=0., atol=1e-4), \
f'Finite difference produced different sigma derivative for parameter {i+1}!'