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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:
 Buchdahl equation of state example for O$_2$sclpy
See the O$_2$sclpy documentation at https
Step1:  Link the O$_2$scl library
Step2:  Get a copy (a pointer to) the O$_2$scl unit conversion object
Step3:  Create the Buchdahl EOS object
Step4:  Create the TOV solve object, set the EOS and compute the M-R curve
Step5:  Get the table for the TOV results
Step6:  The compactness of a 1.4 solar mass NS
Step7:  Construct two lists, a radius grid and a list containing the
relative difference of the exact and calculated enclosed
gravitational mass
Step8:  Initialize the plotting object
Step9:  Plot the enclosed gravitational mass as a function of
radius for a 1.4 solar mass neutron star
Step10:  For the enclosed gravitational mass, plot the relative
difference of the exact results and that computed from
the tov_solve class
Step11:  For testing using pytest
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Python Code:
import o2sclpy
import matplotlib.pyplot as plot
import ctypes
import numpy
import sys
plots=True
if 'pytest' in sys.modules:
    plots=False
Explanation: Buchdahl equation of state 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
cu=link.o2scl_settings.get_convert_units()
Explanation: Get a copy (a pointer to) the O$_2$scl unit conversion object:
End of explanation
b=o2sclpy.eos_tov_buchdahl(link)
Explanation: Create the Buchdahl EOS object:
End of explanation
ts=o2sclpy.tov_solve(link)
ts.set_eos(b);
ts.fixed(1.4,1.0e-4)
print('Exact radius is %7.6e, computed radius is %7.6e.' %
      (b.rad_from_gm(1.4),ts.rad))
print('Relative difference %7.6e.' %
      (abs(b.rad_from_gm(1.4)-ts.rad)/ts.rad))
Explanation: Create the TOV solve object, set the EOS and compute the M-R curve:
End of explanation
tov_table=ts.get_results()
Explanation: Get the table for the TOV results:
End of explanation
beta=ts.mass*b.G_km_Msun/ts.rad
Explanation: The compactness of a 1.4 solar mass NS:
End of explanation
radial_grid=[]
rel_diff=[]
for i in range(1,tov_table.get_nlines()):
    r=tov_table['r'][i]
    radial_grid.append(r)
    enc_mass=r*(1.0-1.0/b.exp2lam_from_r_gm(tov_table['r'][i],
                                            beta))/2.0/b.G_km_Msun
    enc_mass2=tov_table['gm'][i]
    rel_diff.append(abs(enc_mass-enc_mass2)/enc_mass)
Explanation: Construct two lists, a radius grid and a list containing the
relative difference of the exact and calculated enclosed
gravitational mass:
End of explanation
if plots:
    pl=o2sclpy.plotter()
Explanation: Initialize the plotting object:
End of explanation
    pl.canvas()
    plot.plot(tov_table['r'][0:tov_table.get_nlines()],
              tov_table['gm'][0:tov_table.get_nlines()])
    pl.xtitle('radius (km)')
    pl.ytitle('gravitational mass (Msun)')
    plot.show()
Explanation: Plot the enclosed gravitational mass as a function of
radius for a 1.4 solar mass neutron star:
End of explanation
    pl.canvas_flag=False
    pl.canvas()
    plot.plot(radial_grid,rel_diff)
    pl.xtitle('radius (km)')
    pl.ytitle('rel. error in enclosed grav. mass')
    plot.show()
Explanation: For the enclosed gravitational mass, plot the relative
difference of the exact results and that computed from
the tov_solve class:
End of explanation
def test_fun():
    assert numpy.allclose(b.rad_from_gm(1.4),ts.rad,rtol=1.0e-9,atol=0)
    for i in range(0,len(rel_diff)):
        assert numpy.allclose(rel_diff[i],0.0,atol=5.0e-11)
    return
Explanation: For testing using pytest:
End of explanation
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