This notebook runs various solvers for a single step and dumps out some variables -- it is intended for unit testing.

At the moment, it is required to be at the top-level pyro/ directory, because not all the functions find pyro's home directory on their own.



In [1]:

    
from pyro import Pyro

advection



In [2]:

    
solver = "advection"
problem_name = "smooth"
param_file = "inputs.smooth"
other_commands = ["driver.max_steps=1", "mesh.nx=8",  "mesh.ny=8"]



In [3]:

    
pyro_sim = Pyro(solver)
pyro_sim.initialize_problem(problem_name, param_file, other_commands=other_commands)
pyro_sim.run_sim()









    



pyro ...
initializing the smooth advection problem...






    












    



    1    0.10000    0.10000






    












    



outputting...
main:  0.3755648136138916
   vis:  0.11605525016784668






    Out[3]:





<advection.simulation.Simulation at 0x7fa0b58dc860>






    





<Figure size 432x288 with 0 Axes>



In [4]:

    
dens = pyro_sim.sim.cc_data.get_var("density")
dens.pretty_print(show_ghost=False)









    



         1         1         1    1.0004    1.0014    1.0013    1.0002         1 
         1         1    1.0003    1.0162    1.0626    1.0579    1.0077    1.0002 
         1    1.0002    1.0116     1.185    1.5348    1.4466    1.0579    1.0013 
         1    1.0001    1.0064    1.2169    1.6258    1.5348    1.0626    1.0014 
         1   0.99994    0.9985     1.085    1.2169     1.185    1.0162    1.0004 
         1   0.99995   0.99797    0.9985    1.0064    1.0116    1.0003         1 
         1         1   0.99995   0.99994    1.0001    1.0002         1         1 
         1         1         1         1         1         1         1         1 

         ^ y
         |
         +---> x

advection_nonuniform



In [5]:

    
solver = "advection_nonuniform"
problem_name = "slotted"
param_file = "inputs.slotted"
other_commands = ["driver.max_steps=1", "mesh.nx=8",  "mesh.ny=8"]



In [6]:

    
pyro_sim = Pyro(solver)
pyro_sim.initialize_problem(problem_name, param_file, other_commands=other_commands)
pyro_sim.run_sim()









    



pyro ...
initializing the slotted advection problem...
extrema:  0.46875 -0.46875






    












    



    1    0.45714    0.45714
outputting...






    












    



outputting...
parameter particles.n_particles never used
parameter particles.particle_generator never used
parameter advection.u never used
parameter advection.v never used
main:  0.3078031539916992
   vis:  0.10725545883178711






    Out[6]:





<advection_nonuniform.simulation.Simulation at 0x7fa0b5323f60>






    





<Figure size 432x288 with 0 Axes>



In [7]:

    
dens = pyro_sim.sim.cc_data.get_var("density")
dens.pretty_print(show_ghost=False)









    



         0         0         0  0.035918  0.045714         0         0         0 
         0         0         0   0.44163   0.91837   0.44082         0         0 
         0         0         0   0.58204   0.98041   0.38204         0         0 
         0         0         0         0   0.10776  0.065306         0         0 
         0         0         0         0         0         0         0         0 
         0         0         0         0         0         0         0         0 
         0         0         0         0         0         0         0         0 
         0         0         0         0         0         0         0         0 

         ^ y
         |
         +---> x

advection_fv4



In [8]:

    
solver = "advection_fv4"
problem_name = "smooth"
param_file = "inputs.smooth"
other_commands = ["driver.max_steps=1", "mesh.nx=8",  "mesh.ny=8"]



In [9]:

    
pyro_sim = Pyro(solver)
pyro_sim.initialize_problem(problem_name, param_file, other_commands=other_commands)
pyro_sim.run_sim()









    



pyro ...
initializing the smooth FV advection problem...






    












    



    1    0.05000    0.05000






    












    



outputting...
parameter particles.n_particles never used
parameter particles.particle_generator never used
main:  1.5392191410064697
   evolve:  1.2681171894073486
   vis:  0.10479354858398438






    Out[9]:





<advection_fv4.simulation.Simulation at 0x7fa0b590fc88>






    





<Figure size 432x288 with 0 Axes>



In [10]:

    
dens = pyro_sim.sim.cc_data.get_var("density")
dens.pretty_print(show_ghost=False)









    



         1         1   0.99983   0.99859   0.99773   0.99854   0.99976         1 
   0.99997    1.0001     1.002    1.0275    1.0421    1.0212    1.0024   0.99976 
   0.99969    1.0009    1.0174    1.2163    1.3164     1.157    1.0212   0.99854 
   0.99921     1.002    1.0357    1.4336    1.6289    1.3164    1.0421   0.99773 
   0.99952    1.0008    1.0228    1.2966    1.4336    1.2163    1.0275   0.99859 
         1         1    1.0025    1.0228    1.0357    1.0174     1.002   0.99983 
         1    1.0001         1    1.0008     1.002    1.0009    1.0001         1 
         1         1         1   0.99952   0.99921   0.99969   0.99997         1 

         ^ y
         |
         +---> x

advection_rk



In [11]:

    
solver = "advection_rk"
problem_name = "tophat"
param_file = "inputs.tophat"
other_commands = ["driver.max_steps=1", "mesh.nx=8",  "mesh.ny=8"]



In [12]:

    
pyro_sim = Pyro(solver)
pyro_sim.initialize_problem(problem_name, param_file, other_commands=other_commands)
pyro_sim.run_sim()









    



pyro ...
initializing the tophat advection problem...






    












    



    1    0.05000    0.05000






    












    



outputting...
parameter particles.n_particles never used
parameter particles.particle_generator never used
main:  0.3059535026550293
   evolve:  0.003072977066040039
   vis:  0.11471986770629883






    Out[12]:





<advection_rk.simulation.Simulation at 0x7fa0b5170668>






    





<Figure size 432x288 with 0 Axes>



In [13]:

    
dens = pyro_sim.sim.cc_data.get_var("density")
dens.pretty_print(show_ghost=False)









    



         0         0         0         0         0         0         0         0 
         0         0         0 0.0030222 0.0040889 0.00278520.00071111         0 
         0         0         0    0.2403   0.39295   0.15301 0.0027852         0 
         0         0         0   0.60178   0.99111   0.39295 0.0040889         0 
         0         0         0   0.36533   0.60178    0.2403 0.0030222         0 
         0         0         0         0         0         0         0         0 
         0         0         0         0         0         0         0         0 
         0         0         0         0         0         0         0         0 

         ^ y
         |
         +---> x

compressible



In [14]:

    
solver = "compressible"
problem_name = "rt"
param_file = "inputs.rt"
other_commands = ["driver.max_steps=1", "mesh.nx=8",  "mesh.ny=24", "driver.verbose=0", "compressible.riemann=CGF"]



In [15]:

    
pyro_sim = Pyro(solver)
pyro_sim.initialize_problem(problem_name, param_file, other_commands=other_commands)
pyro_sim.run_sim()









    



pyro ...
initializing the rt problem...






    



/home/alice/Documents/pyro2/compressible/problems/rt.py:69: RuntimeWarning: invalid value encountered in true_divide
  0.5*(xmom[:, :]**2 + ymom[:, :]**2)/dens[:, :]
/home/alice/Documents/pyro2/compressible/simulation.py:61: RuntimeWarning: invalid value encountered in true_divide
  q[:, :, ivars.iu] = U[:, :, ivars.ixmom]/U[:, :, ivars.idens]
/home/alice/Documents/pyro2/compressible/simulation.py:62: RuntimeWarning: invalid value encountered in true_divide
  q[:, :, ivars.iv] = U[:, :, ivars.iymom]/U[:, :, ivars.idens]






    












    












    Out[15]:





<compressible.simulation.Simulation at 0x7fa08bad7a58>






    





<Figure size 432x288 with 0 Axes>



In [16]:

    
dens = pyro_sim.sim.cc_data.get_var("density")
dens.pretty_print(show_ghost=False)









    



         2         2         2         2         2         2         2         2 
         2         2         2         2         2         2         2         2 
         2         2         2         2         2         2         2         2 
         2         2         2         2         2         2         2         2 
         2         2         2         2         2         2         2         2 
         2         2         2         2         2         2         2         2 
         2         2         2         2         2         2         2         2 
         2         2         2         2         2         2         2         2 
         2         2         2         2         2         2         2         2 
         2         2         2         2         2         2         2         2 
    2.0004    2.0002    1.9999    1.9997    1.9997    1.9999    2.0002    2.0004 
         2         2    1.9999    1.9997    1.9997    1.9999         2         2 
   0.99984   0.99993    1.0002    1.0005    1.0005    1.0002   0.99993   0.99984 
   0.99983   0.99993    1.0001    1.0002    1.0002    1.0001   0.99993   0.99983 
         1         1         1         1         1         1         1         1 
         1         1         1         1         1         1         1         1 
         1         1         1         1         1         1         1         1 
         1         1         1         1         1         1         1         1 
         1         1         1         1         1         1         1         1 
         1         1         1         1         1         1         1         1 
         1         1         1         1         1         1         1         1 
         1         1         1         1         1         1         1         1 
         1         1         1         1         1         1         1         1 
         1         1         1         1         1         1         1         1 

         ^ y
         |
         +---> x

compressible_fv4



In [17]:

    
solver = "compressible_fv4"
problem_name = "kh"
param_file = "inputs.kh"
other_commands = ["driver.max_steps=1", "mesh.nx=8",  "mesh.ny=8", "driver.verbose=0"]



In [18]:

    
pyro_sim = Pyro(solver)
pyro_sim.initialize_problem(problem_name, param_file, other_commands=other_commands)
pyro_sim.run_sim()









    



pyro ...
warning, key: driver.splitting not defined
warning, key: io.tplot not defined
initializing the Kelvin-Helmholtz problem...






    












    












    Out[18]:





<compressible_fv4.simulation.Simulation at 0x7fa0b534f940>






    





<Figure size 432x288 with 0 Axes>



In [19]:

    
e = pyro_sim.sim.cc_data.get_var("eint")
e.pretty_print(show_ghost=False)









    



    6.2377    6.2377    6.2377    6.2377    6.2377    6.2377    6.2377    6.2377 
    5.8296    5.8296    5.8296    5.8296    5.8296    5.8296    5.8296    5.8296 
    3.2605    3.2605    3.2605    3.2605    3.2605    3.2605    3.2605    3.2605 
    3.1281    3.1281    3.1281    3.1281    3.1281    3.1281    3.1281    3.1281 
    3.1281    3.1281    3.1281    3.1281    3.1281    3.1281    3.1281    3.1281 
    3.2605    3.2605    3.2605    3.2605    3.2605    3.2605    3.2605    3.2605 
    5.8296    5.8296    5.8296    5.8296    5.8296    5.8296    5.8296    5.8296 
    6.2377    6.2377    6.2377    6.2377    6.2377    6.2377    6.2377    6.2377 

         ^ y
         |
         +---> x

compressible_rk



In [20]:

    
solver = "compressible_rk"
problem_name = "quad"
param_file = "inputs.quad"
other_commands = ["driver.max_steps=1", "mesh.nx=16",  "mesh.ny=16", "driver.verbose=0"]



In [21]:

    
pyro_sim = Pyro(solver)
pyro_sim.initialize_problem(problem_name, param_file, other_commands=other_commands)
pyro_sim.run_sim()









    



pyro ...
initializing the quadrant problem...






    












    












    Out[21]:





<compressible_rk.simulation.Simulation at 0x7fa0a8ce8828>






    





<Figure size 432x288 with 0 Axes>



In [22]:

    
p = pyro_sim.sim.cc_data.get_var("pressure")
p.pretty_print(show_ghost=False)









    



       0.3       0.3       0.3       0.3       0.3       0.3       0.3       0.3       0.3       0.3       0.3       0.3   0.30292    1.4997       1.5       1.5 
       0.3       0.3       0.3       0.3       0.3       0.3       0.3       0.3       0.3       0.3       0.3       0.3   0.30292    1.4997       1.5       1.5 
   0.29994   0.29994   0.29994   0.29994   0.29994   0.29994   0.29994   0.29994   0.29994   0.29994   0.29994   0.29994   0.30304    1.4991    1.4997    1.4997 
  0.029558  0.029558  0.029558  0.029558  0.029558  0.029558  0.029558  0.029558  0.029558  0.029558  0.029558  0.029559  0.030208   0.30304   0.30292   0.30292 
  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029559   0.29994       0.3       0.3 
  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029558   0.29994       0.3       0.3 
  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029558   0.29994       0.3       0.3 
  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029558   0.29994       0.3       0.3 
  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029558   0.29994       0.3       0.3 
  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029558   0.29994       0.3       0.3 
  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029558   0.29994       0.3       0.3 
  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029558   0.29994       0.3       0.3 
  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029558   0.29994       0.3       0.3 
  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029558   0.29994       0.3       0.3 
  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029558   0.29994       0.3       0.3 
  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029032  0.029558   0.29994       0.3       0.3 

         ^ y
         |
         +---> x

compressible_sdc



In [23]:

    
solver = "compressible_sdc"
problem_name = "sod"
param_file = "inputs.sod.y"
other_commands = ["driver.max_steps=1", "mesh.nx=4",  "mesh.ny=16", "driver.verbose=0"]



In [24]:

    
pyro_sim = Pyro(solver)
pyro_sim.initialize_problem(problem_name, param_file, other_commands=other_commands)
pyro_sim.run_sim()









    



pyro ...
initializing the sod problem...






    



/home/alice/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_base.py:3471: UserWarning: Attempting to set identical bottom==top results
in singular transformations; automatically expanding.
bottom=0.0, top=0.0
  'bottom=%s, top=%s') % (bottom, top))






    












    












    



          The script analysis/sod_compare.py can be used to compare
          this output to the exact solution.  Some sample exact solution
          data is present as analysis/sod-exact.out
          






    Out[24]:





<compressible_sdc.simulation.Simulation at 0x7fa08ba9e9b0>






    





<Figure size 432x288 with 0 Axes>



In [25]:

    
p = pyro_sim.sim.cc_data.get_var("pressure")
p.pretty_print(show_ghost=False)









    



       0.1       0.1       0.1       0.1 
       0.1       0.1       0.1       0.1 
       0.1       0.1       0.1       0.1 
       0.1       0.1       0.1       0.1 
       0.1       0.1       0.1       0.1 
       0.1       0.1       0.1       0.1 
  0.099996  0.099996  0.099996  0.099996 
   0.10175   0.10175   0.10175   0.10175 
   0.99825   0.99825   0.99825   0.99825 
         1         1         1         1 
         1         1         1         1 
         1         1         1         1 
         1         1         1         1 
         1         1         1         1 
         1         1         1         1 
         1         1         1         1 

         ^ y
         |
         +---> x

diffusion



In [26]:

    
solver = "diffusion"
problem_name = "gaussian"
param_file = "inputs.gaussian"
other_commands = ["driver.max_steps=1", "mesh.nx=16",  "mesh.ny=16", "driver.verbose=0"]



In [27]:

    
pyro_sim = Pyro(solver)
pyro_sim.initialize_problem(problem_name, param_file, other_commands=other_commands)
pyro_sim.run_sim()









    



pyro ...
initializing the Gaussian diffusion problem...






    












    












    



          The solution can be compared to the analytic solution with
          the script analysis/gauss_diffusion_compare.py
          






    Out[27]:





<diffusion.simulation.Simulation at 0x7fa0a8a3d828>






    





<Figure size 432x288 with 0 Axes>



In [28]:

    
dens = pyro_sim.sim.cc_data.get_var("phi")
dens.pretty_print(show_ghost=False)









    



         1         1         1         1         1         1         1         1         1         1         1         1         1         1         1         1 
         1         1         1         1         1         1         1         1         1         1         1         1         1         1         1         1 
         1         1         1         1         1         1         1         1         1         1         1         1         1         1         1         1 
         1         1         1         1         1         1    1.0001    1.0001    1.0001    1.0001         1         1         1         1         1         1 
         1         1         1         1         1    1.0001    1.0001    1.0002    1.0002    1.0001    1.0001         1         1         1         1         1 
         1         1         1         1    1.0001    1.0002    1.0004    1.0007    1.0007    1.0004    1.0002    1.0001         1         1         1         1 
         1         1         1    1.0001    1.0001    1.0004     1.001     1.002     1.002     1.001    1.0004    1.0001    1.0001         1         1         1 
         1         1         1    1.0001    1.0002    1.0007     1.002   0.99881   0.99881     1.002    1.0007    1.0002    1.0001         1         1         1 
         1         1         1    1.0001    1.0002    1.0007     1.002   0.99881   0.99881     1.002    1.0007    1.0002    1.0001         1         1         1 
         1         1         1    1.0001    1.0001    1.0004     1.001     1.002     1.002     1.001    1.0004    1.0001    1.0001         1         1         1 
         1         1         1         1    1.0001    1.0002    1.0004    1.0007    1.0007    1.0004    1.0002    1.0001         1         1         1         1 
         1         1         1         1         1    1.0001    1.0001    1.0002    1.0002    1.0001    1.0001         1         1         1         1         1 
         1         1         1         1         1         1    1.0001    1.0001    1.0001    1.0001         1         1         1         1         1         1 
         1         1         1         1         1         1         1         1         1         1         1         1         1         1         1         1 
         1         1         1         1         1         1         1         1         1         1         1         1         1         1         1         1 
         1         1         1         1         1         1         1         1         1         1         1         1         1         1         1         1 

         ^ y
         |
         +---> x

incompressible



In [29]:

    
solver = "incompressible"
problem_name = "shear"
param_file = "inputs.shear"
other_commands = ["driver.max_steps=1", "mesh.nx=8",  "mesh.ny=8", "driver.verbose=0"]



In [30]:

    
pyro_sim = Pyro(solver)
pyro_sim.initialize_problem(problem_name, param_file, other_commands=other_commands)
pyro_sim.run_sim()









    



pyro ...
initializing the incompressible shear problem...
y_half =  0.5
delta_s =  0.05
rho_s =  42.0
extrema:  -1.0 0.9999997110039925






    












    












    Out[30]:





<incompressible.simulation.Simulation at 0x7fa0a8b23cf8>






    





<Figure size 432x288 with 0 Axes>



In [31]:

    
u = pyro_sim.sim.cc_data.get_var("x-velocity")
u.pretty_print(show_ghost=False)









    



        -1   -1.0001   -1.0001        -1  -0.99995  -0.99992  -0.99992  -0.99995 
  -0.98937  -0.98915  -0.98915  -0.98937   -0.9894  -0.98929  -0.98929   -0.9894 
    0.9894   0.98929   0.98929    0.9894   0.98937   0.98915   0.98915   0.98937 
   0.99995   0.99992   0.99992   0.99995         1    1.0001    1.0001         1 
         1    1.0001    1.0001         1   0.99995   0.99992   0.99992   0.99995 
   0.98937   0.98915   0.98915   0.98937    0.9894   0.98929   0.98929    0.9894 
   -0.9894  -0.98929  -0.98929   -0.9894  -0.98937  -0.98915  -0.98915  -0.98937 
  -0.99995  -0.99992  -0.99992  -0.99995        -1   -1.0001   -1.0001        -1 

         ^ y
         |
         +---> x

lm_atm



In [32]:

    
solver = "lm_atm"
problem_name = "bubble"
param_file = "inputs.bubble"
other_commands = ["driver.max_steps=1", "mesh.nx=16",  "mesh.ny=16", "driver.verbose=0"]



In [33]:

    
pyro_sim = Pyro(solver)
pyro_sim.initialize_problem(problem_name, param_file, other_commands=other_commands)
pyro_sim.run_sim()









    



pyro ...
initializing the bubble problem...






    












    












    Out[33]:





<lm_atm.simulation.Simulation at 0x7fa0a8b55e10>






    





<Figure size 432x288 with 0 Axes>



In [34]:

    
v = pyro_sim.sim.cc_data.get_var("y-velocity")
v.pretty_print(show_ghost=False, fmt="%10.3g")









    



 -4.31e-05 -3.83e-05 -2.87e-05 -1.44e-05  3.88e-06  2.41e-05  4.25e-05  5.39e-05  5.39e-05  4.25e-05  2.41e-05  3.88e-06 -1.44e-05 -2.87e-05 -3.83e-05 -4.31e-05 
  -4.7e-05 -4.23e-05 -3.28e-05  -1.8e-05  1.86e-06  2.54e-05  4.86e-05  6.42e-05  6.42e-05  4.86e-05  2.54e-05  1.86e-06  -1.8e-05 -3.28e-05 -4.23e-05  -4.7e-05 
 -5.51e-05 -5.09e-05 -4.18e-05 -2.65e-05 -3.73e-06  2.69e-05  6.19e-05  8.92e-05  8.92e-05  6.19e-05  2.69e-05 -3.73e-06 -2.65e-05 -4.18e-05 -5.09e-05 -5.51e-05 
 -6.73e-05  -6.4e-05 -5.65e-05 -4.22e-05 -1.69e-05  2.42e-05  8.24e-05   0.00014   0.00014  8.24e-05  2.42e-05 -1.69e-05 -4.22e-05 -5.65e-05  -6.4e-05 -6.73e-05 
 -8.22e-05 -8.11e-05 -7.75e-05 -6.81e-05 -4.53e-05  4.76e-06  0.000103  0.000247  0.000247  0.000103  4.76e-06 -4.53e-05 -6.81e-05 -7.75e-05 -8.11e-05 -8.22e-05 
 -9.77e-05 -9.99e-05 -0.000104 -0.000106 -9.99e-05 -6.11e-05  7.66e-05  0.000492  0.000492  7.66e-05 -6.11e-05 -9.99e-05 -0.000106 -0.000104 -9.99e-05 -9.77e-05 
 -6.65e-05 -7.26e-05 -8.57e-05 -0.000108  -0.00014 -0.000178 -0.000178 -0.000209 -0.000209 -0.000178 -0.000178  -0.00014 -0.000108 -8.57e-05 -7.26e-05 -6.65e-05 
  -0.00016 -0.000169 -0.000189 -0.000229 -0.000305  -0.00046 -0.000809   0.00331   0.00331 -0.000809  -0.00046 -0.000305 -0.000229 -0.000189 -0.000169  -0.00016 
 -0.000159 -0.000168 -0.000188 -0.000228 -0.000303 -0.000457 -0.000806   0.00336   0.00336 -0.000806 -0.000457 -0.000303 -0.000228 -0.000188 -0.000168 -0.000159 
 -6.09e-05 -6.71e-05 -8.04e-05 -0.000103 -0.000135 -0.000174 -0.000179 -0.000211 -0.000211 -0.000179 -0.000174 -0.000135 -0.000103 -8.04e-05 -6.71e-05 -6.09e-05 
 -8.68e-05 -8.95e-05 -9.41e-05 -9.82e-05 -9.43e-05 -6.03e-05  6.65e-05  0.000457  0.000457  6.65e-05 -6.03e-05 -9.43e-05 -9.82e-05 -9.41e-05 -8.95e-05 -8.68e-05 
 -6.77e-05 -6.76e-05 -6.62e-05 -6.02e-05 -4.24e-05  2.28e-07  8.69e-05  0.000217  0.000217  8.69e-05  2.28e-07 -4.24e-05 -6.02e-05 -6.62e-05 -6.76e-05 -6.77e-05 
 -4.93e-05 -4.78e-05 -4.38e-05 -3.47e-05 -1.66e-05  1.56e-05  6.37e-05  0.000113  0.000113  6.37e-05  1.56e-05 -1.66e-05 -3.47e-05 -4.38e-05 -4.78e-05 -4.93e-05 
 -3.28e-05 -3.11e-05  -2.7e-05  -1.9e-05 -5.48e-06  1.49e-05     4e-05  6.06e-05  6.06e-05     4e-05  1.49e-05 -5.48e-06  -1.9e-05  -2.7e-05 -3.11e-05 -3.28e-05 
 -1.86e-05 -1.73e-05 -1.45e-05 -9.35e-06 -1.36e-06  9.48e-06  2.14e-05  3.01e-05  3.01e-05  2.14e-05  9.48e-06 -1.36e-06 -9.35e-06 -1.45e-05 -1.73e-05 -1.86e-05 
 -5.95e-06 -5.51e-06 -4.51e-06 -2.78e-06 -1.91e-07  3.17e-06  6.68e-06   9.1e-06   9.1e-06  6.68e-06  3.17e-06 -1.91e-07 -2.78e-06 -4.51e-06 -5.51e-06 -5.95e-06 

         ^ y
         |
         +---> x



In [ ]: