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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 SFHo/SFHx example for O$_2$sclpy
See the O$_2$sclpy documentation at
https
Step1:  Link the O$_2$scl library
Step2:  Get the value of $\hbar c$ from an O$_2$scl find_constants object
Step3:  Get a copy (a pointer to) the O$_2$scl unit conversion object
Step4:  Compute nuclear saturation and output the saturation density
and binding energy
Step5:  Baryon density grid in $1/\mathrm{fm}^3$. The O$_2$scl object
uniform_grid_end_width is like numpy.arange() but is numerically
stable.
Step6:  Temperature grid in MeV
Step7:  Store the EOS in a table3d object
Step8:  Create a new slice for the energy per baryon
Step9:  Instead of creating new fermion objects, just get the default
neutron and proton from the EOS object. Similarly, we need a
'thermo' object to store the energy density, pressure, and entropy.
Step10:  By default, the O2scl EOS objects work in units of
$\mathrm{fm}^{-1}$, so we multiply by ħc to get MeV.
Step11:  The solver works much better with an initial guess, so
we store the values of the meson fields
Step12:  The EOS at finite temperature for isospin-symmetric matter, with
equal numbers of neutrons and protons. Our temperature grid is in
MeV, but again the EOS objects expect $\mathrm{fm}^{-1}$ so we have
to divide the temperature by ħc.
Step13:  Now plot the results. Raw matplotlib works, but o2sclpy has
a couple functions which make it easier.
Step14:  For testing purposes
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Python Code:
import o2sclpy
import matplotlib.pyplot as plot
import numpy
import sys
plots=True
if 'pytest' in sys.modules:
    plots=False
Explanation: SFHo/SFHx example for O$_2$sclpy
See the O$_2$sclpy documentation at
https://neutronstars.utk.edu/code/o2sclpy for more information.
End of explanation
link=o2sclpy.linker()
link.link_o2scl()
Explanation: Link the O$_2$scl library:
End of explanation
fc=o2sclpy.find_constants(link)
ħc=fc.find_unique('ħc','MeV*fm')
print('ħc = %7.6e\n' % (ħc))
Explanation: Get the value of $\hbar c$ from an O$_2$scl find_constants object:
End of explanation
cu=link.o2scl_settings.get_convert_units()
sfho=o2sclpy.eos_had_rmf(link)
o2sclpy.rmf_load(link,sfho,'SFHo')
sfhx=o2sclpy.eos_had_rmf(link)
o2sclpy.rmf_load(link,sfhx,'SFHx')
Explanation: Get a copy (a pointer to) the O$_2$scl unit conversion object:
End of explanation
sfho.saturation()
print(('SFHo: n0=%7.6e 1/fm^3, E/A=%7.6e MeV, K=%7.6e MeV, '+
       'M*/M=%7.6e, S=%7.6e MeV, L=%7.6e MeV\n') % 
      (sfho.n0,sfho.eoa*ħc,sfho.comp*ħc,sfho.msom,sfho.esym*ħc,
       sfho.fesym_slope(sfho.n0)*ħc))
sfhx.saturation()
print(('SFHx: n0=%7.6e 1/fm^3, E/A=%7.6e MeV, K=%7.6e MeV, '+
       'M*/M=%7.6e, S=%7.6e MeV, L=%7.6e MeV\n') % 
      (sfhx.n0,sfhx.eoa*ħc,sfhx.comp*ħc,sfhx.msom,sfhx.esym*ħc,
       sfhx.fesym_slope(sfhx.n0)*ħc))
Explanation: Compute nuclear saturation and output the saturation density
and binding energy:
End of explanation
ug_nb=o2sclpy.uniform_grid_end_width.init(link,0.01,0.32,0.01)
Explanation: Baryon density grid in $1/\mathrm{fm}^3$. The O$_2$scl object
uniform_grid_end_width is like numpy.arange() but is numerically
stable.
End of explanation
ug_T=o2sclpy.uniform_grid_end_width.init(link,0.1,10.0,0.1)
Explanation: Temperature grid in MeV
End of explanation
t3d=o2sclpy.table3d(link)
t3d.set_xy_grid('nB',ug_nb,'T',ug_T)
Explanation: Store the EOS in a table3d object
End of explanation
t3d.new_slice('EoA')
Explanation: Create a new slice for the energy per baryon
End of explanation
n=sfho.get_def_neutron()
p=sfho.get_def_proton()
th=sfho.get_def_thermo()
Explanation: Instead of creating new fermion objects, just get the default
neutron and proton from the EOS object. Similarly, we need a
'thermo' object to store the energy density, pressure, and entropy.
End of explanation
print('Neutron mass is %7.6e MeV.' % (n.m*ħc))
print('Proton mass is %7.6e MeV.\n' % (p.m*ħc))
Explanation: By default, the O2scl EOS objects work in units of
$\mathrm{fm}^{-1}$, so we multiply by ħc to get MeV.
End of explanation
sigma=0.0
omega=0.0
rho=0.0
Explanation: The solver works much better with an initial guess, so
we store the values of the meson fields
End of explanation
for i in range(0,t3d.get_nx()):
    print(i+1,'of',t3d.get_nx())
    # At the lowest temperature point we always need a new initial
    # guess.
    first_point=True
    for j in range(0,t3d.get_ny()):
        n.n=ug_nb[i]/2.0
        p.n=ug_nb[i]/2.0
        # If we're not at the lowest temperature point, use the
        # previous solution to the field equations to generate
        # the next solution.
        if first_point==False:
            sfho.set_fields(sigma,omega,rho)
        sfho.calc_temp_e(n,p,ug_T[j]/ħc,th)
        if first_point==True:
            first_point=False
        ret,sigma,omega,rho=sfho.get_fields()
        # Divide the energy density by the baryon density to
        # get the energy per baryon, and then subtract out the
        # rest mass contribution from both the neutrons and
        # the protons.
        t3d.set(i,j,'EoA',th.ed/ug_nb[i]*ħc-n.m*n.n/ug_nb[i]*ħc-
                p.m*p.n*ħc/ug_nb[i])
Explanation: The EOS at finite temperature for isospin-symmetric matter, with
equal numbers of neutrons and protons. Our temperature grid is in
MeV, but again the EOS objects expect $\mathrm{fm}^{-1}$ so we have
to divide the temperature by ħc.
End of explanation
if plots:
    pl=o2sclpy.plotter()
    pl.colbar=True
    pl.xtitle(r'$ n_B~(\mathrm{fm}^{-3}) $')
    pl.ytitle(r'$ T~(\mathrm{MeV}) $')
    pl.ttext(1.25,0.5,r'$ E/A~(\mathrm{MeV}) $',rotation=90)
    pl.den_plot_direct(t3d,'EoA')
    plot.show()
Explanation: Now plot the results. Raw matplotlib works, but o2sclpy has
a couple functions which make it easier.
End of explanation
def test_fun():
    assert numpy.allclose(sfho.n0,0.1582415,rtol=1.0e-4)
    assert numpy.allclose(sfhx.n0,0.1600292,rtol=1.0e-4)
    return
Explanation: For testing purposes
End of explanation
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