Note
Click here to download the full example code
2. Halite liquidus
Calculate halite liquidus and compare result with [Driesner, 2007].
Python code
import os
import numpy as np
import time
import linecache
import matplotlib.pyplot as plt
import matplotlib as mpl
from matplotlib import patches
import matplotlib.ticker as ticker
from matplotlib.ticker import MultipleLocator
from tabulate import tabulate
import warnings
warnings.filterwarnings("ignore", category=RuntimeWarning)
# 3d plot
import helpfunc
mpl.rcParams['font.family'] = 'Arial' # default font family
mpl.rcParams['mathtext.fontset'] = 'cm' # font for math
fmt_figs = [] # ['svg','pdf']
figpath = '.'
result_path='../../../gallery_H2ONaCl/pT'
def savefig(figname):
for fmt_fig in fmt_figs:
figname_full = '%s/%s.%s' % (figpath, figname, fmt_fig)
plt.savefig(figname_full, bbox_inches='tight')
print('figure saved: ', figname_full)
compare = lambda a,b : float(str('%.6e'%(a)))-float(str('%.6e'%(b)))
# Import package of xThermo
from xThermo import H2O
from xThermo import NaCl
from xThermo import H2ONaCl
sw_84 = H2ONaCl.cH2ONaCl("IAPS84")
sw_95 = H2ONaCl.cH2ONaCl("IAPWS95")
def plot_3d(sw,style='linear'):
fig=plt.figure(figsize=(14,14))
ax = fig.add_subplot(111,projection='3d',facecolor='None')
helpfunc.set_axis_diagram_3D(ax)
# plot
if(style=='linear'):
pb = sw.PhaseBoundary_HaliteLiquidus_DeformLinear()
TT,PP,XX = np.array(pb.T), np.array(pb.p), np.array(pb.X)
ax.plot_wireframe(XX*100,TT-273.15,PP/1E5, color='green',lw=0.5,label='Halite liquidus')
ax.plot_wireframe(ax.get_xlim()[1],TT-273.15,PP/1E5, color='orange',lw=0.3,label='Halite liquidus: p-X plane')
ax.plot_wireframe(XX*100,ax.get_ylim()[1],PP/1E5, color='cyan',lw=0.3,label='Halite liquidus: p-T plane')
elif(style=='triangle'):
# halite liquidus surface mesh
pb = sw.PhaseBoundary_HaliteLiquidus()
T,p,X,connection = np.array(pb.x),np.array(pb.y),np.array(pb.z), np.array(pb.connection)
ax.plot_trisurf(X*100, T-273.15, connection,p/1E5, color='green',lw=0.1,label='Halite liquidus')
ax.plot_trisurf(X*100, T*0 + ax.get_ylim()[1], connection,p/1E5,color='orange',lw=0.1)
ax.plot_trisurf(X*0 + ax.get_xlim()[1], T-273.15, connection,p/1E5,color='cyan',lw=0.1)
# ax.legend(ncol=3)
savefig('HaliteLiquidus_3D_%s'%(style))
Benchmark comparison
Compare result of xThermo and [Driesner, 2007], and also compare result based on different EOS of water.
Python code
def plot_props(TT,PP,XX,rho_,h_,unit_H='MJ/kg'):
wspace=0.1
fig,axes=plt.subplots(1,4,figsize=(21,5),gridspec_kw={'wspace':wspace}, sharey=True)
cmap_rho, cmap_h = 'YlGnBu_r','rainbow'
# 1. Rho
axes[0].contourf(TT-273.15,PP/1E5,rho_.reshape(TT.shape),levels=50,cmap=cmap_rho)
CS=axes[1].contourf(XX*100,PP/1E5,rho_.reshape(TT.shape),levels=50,cmap=cmap_rho)
ax_cb_rho = axes[0].inset_axes([0,1.03,2+wspace,0.05])
plt.colorbar(CS,cax=ax_cb_rho,orientation='horizontal',label='Density (kg/m$^{\mathregular{3}}$)')
# 2. H
scale_H = 1
if(unit_H=='MJ/kg'): scale_H=1E-6
axes[2].contourf(TT-273.15,PP/1E5,h_.reshape(TT.shape)*scale_H,levels=50,cmap=cmap_h)
CS=axes[3].contourf(XX*100,PP/1E5,h_.reshape(TT.shape)*scale_H,levels=50,cmap=cmap_h)
ax_cb_h = axes[2].inset_axes([0,1.03,2+wspace,0.05])
plt.colorbar(CS,cax=ax_cb_h,orientation='horizontal',label='Specific enthalpy (%s)'%(unit_H))
for ax_cb in [ax_cb_rho,ax_cb_h]:
ax_cb.xaxis.set_ticks_position('top')
ax_cb.xaxis.set_label_position('top')
for ax in [axes[0],axes[2]]: ax.set_xlabel('Temperature ($^{\circ}$C)')
for ax in [axes[1],axes[3]]: ax.set_xlabel('X$_{\mathregular{NaCl}}$ (wt.% NaCl)')
axes[0].set_ylabel('Pressure (bar)')
def plot_props_HaliteLiquidus(sw):
# calculate
pb = sw.PhaseBoundary_HaliteLiquidus_DeformLinear()
TT,PP,XX = np.array(pb.T), np.array(pb.p), np.array(pb.X)
rho_ = np.array(sw.Rho_phase(TT.reshape(-1,), PP.reshape(-1,), XX.reshape(-1,), H2ONaCl.Liquid))
h_ = np.array(sw.H_phase(TT.reshape(-1,), PP.reshape(-1,), XX.reshape(-1,), H2ONaCl.Liquid))
# plot
plot_props(TT,PP,XX,rho_,h_)
savefig('HaliteLiquidus_props_%s'%(sw.name_backend()))
return TT,PP,XX,rho_,h_
def plot_err(ax,x,y,data,label='',cmap='rainbow'):
# plot difference between xThermo and Driesner(2007b)
CS=ax.scatter(x, y,c=data,cmap=cmap)
ax_cb=ax.inset_axes([0,1.02,1,0.05])
plt.colorbar(CS,cax=ax_cb,label=label,orientation='horizontal')
ax_cb.xaxis.set_label_position('top')
ax_cb.xaxis.set_ticks_position('top')
def benchmark_HaliteLiquidus(sw,mmc1='../Driesner2007b/1-s2.0-S0016703707002955-mmc1.txt'):
# compare
if(not os.path.exists(mmc1)):
print('Please set correct mmc1 file path: %s'%(mmc1))
exit()
data=np.loadtxt(mmc1, skiprows=7)
T0,P0,X0,rho0,h0=data[:,0]+273.15,data[:,1]*1E5,data[:,2],data[:,3],data[:,4]
# 1. calculate halite liquidus
X_=sw.X_HaliteLiquidus(T0,P0)
X_mol = sw.Wt2Mol(X_)
# 2. calculate liquid density on halite liquidus
rho_ = np.array(sw.Rho_phase(T0, P0, sw.Mol2Wt(X0), H2ONaCl.Liquid))
h_ = np.array(sw.H_phase(T0, P0, sw.Mol2Wt(X0), H2ONaCl.Liquid))
# compare result dict
Data0 = {'X':X0,'rho':rho0,'h':h0}
Data_={'X':X_mol,'rho':rho_,'h':h_}
Err,RErr={},{}
for key in Data0.keys(): Err[key],RErr[key] = Data0[key]-Data_[key], np.abs(Data0[key]-Data_[key])/(Data0[key])*100.0
# print to file
fpout = open('%s/mmc1_%s.csv'%(result_path,sw.name_backend()),'w')
fpout.write('T[C],P[bar],X(Driesner)[mol],X(xThermo)[mol],X(diff)[mol],Rho(Driesner)[kg/m3],Rho(xThermo),Rho(err),H(Driesner)[J/kg],H(xThermo),H(err)\n')
for i in range(0,len(T0)):
fpout.write('%.6e,%.6e'%(T0[i]-273.15,P0[i]))
for key in Data0.keys():
fpout.write(',%.6e,%.6e,%.6e'%(Data0[key][i], Data_[key][i],compare(Data0[key][i],Data_[key][i])))
fpout.write('\n')
fpout.close()
# plot difference
fig,axes=plt.subplots(1,3,figsize=(21,5),sharey=True,gridspec_kw={'wspace':0.1})
plot_err(axes[0], T0, P0/1E5, RErr['X'],'Relative difference: Composition (%)')
plot_err(axes[1], T0, P0/1E5, RErr['rho'],'Relative difference: Density (%)')
plot_err(axes[2], T0, P0/1E5, RErr['h'],'Relative difference: Specific enthalpy (%)')
for ax in axes: ax.set_xlabel('Temperature ($^{\circ}$C)')
axes[0].set_ylabel('Pressure (bar)')
# statistics of the difference
table=[]
for key,name in zip(list(Err.keys()),['Composition (mole fraction)','Density (kg/m3)','Specific enthalpy (J/kg)']):
RErr[key] = RErr[key][~(np.isnan(RErr[key]) | np.isinf(RErr[key]))]
table.append([name,Err[key].min(),Err[key].max(),RErr[key].min(),RErr[key].max()])
print(tabulate(table, headers=['Critical property', 'Err. Min', 'Err. Max','RE. Min(%)','RE. Max(%)'],numalign="right",floatfmt=".6f"))
Based on IAPS84 EOS
TT,PP,XX,rho_84,h_84=plot_props_HaliteLiquidus(sw_84)
benchmark_HaliteLiquidus(sw_84)
Out:
Critical property Err. Min Err. Max RE. Min(%) RE. Max(%)
--------------------------- ---------- ---------- ------------ ------------
Composition (mole fraction) -0.000000 0.000000 0.000000 0.000049
Density (kg/m3) 0.004662 2.143326 0.000385 0.175167
Specific enthalpy (J/kg) -0.535427 0.511738 0.000000 0.000047
Based on IAPWS95 EOS
TT,PP,XX,rho_95,h_95=plot_props_HaliteLiquidus(sw_95) benchmark_HaliteLiquidus(sw_95)
Difference between IAPS84 and IAPWS95 EOS
plot_props(TT,PP,XX, rho_84-rho_95, (h_84-h_95),unit_H=’J/kg’)
Result table
Result data calculated by xThermo based on both water EOS of IAPS84 and IAPWS95.
See also
Electronic Annex EA-1 in [Driesner, 2007] and Fig. 1,5,6 in [Driesner & Heinrich, 2007].
T[C] |
P[bar] |
X(Driesner)[mol] |
X(xThermo)[mol] |
X(diff)[mol] |
Rho(Driesner)[kg/m3] |
Rho(xThermo) |
Rho(err) |
H(Driesner)[J/kg] |
H(xThermo) |
H(err) |
---|---|---|---|---|---|---|---|---|---|---|
1.000000e+01 |
5.000000e+07 |
1.006877e-01 |
1.006877e-01 |
0.000000e+00 |
1.223591e+03 |
1.221448e+03 |
2.143000e+00 |
1.151070e+05 |
1.151070e+05 |
0.000000e+00 |
2.000000e+01 |
5.000000e+07 |
1.010120e-01 |
1.010120e-01 |
0.000000e+00 |
1.218549e+03 |
1.217436e+03 |
1.113000e+00 |
1.471303e+05 |
1.471303e+05 |
0.000000e+00 |
3.000000e+01 |
5.000000e+07 |
1.014886e-01 |
1.014886e-01 |
0.000000e+00 |
1.214057e+03 |
1.213485e+03 |
5.720000e-01 |
1.792355e+05 |
1.792355e+05 |
0.000000e+00 |
4.000000e+01 |
5.000000e+07 |
1.021042e-01 |
1.021042e-01 |
0.000000e+00 |
1.209867e+03 |
1.209577e+03 |
2.900000e-01 |
2.113515e+05 |
2.113515e+05 |
0.000000e+00 |
5.000000e+01 |
5.000000e+07 |
1.028475e-01 |
1.028475e-01 |
0.000000e+00 |
1.205844e+03 |
1.205697e+03 |
1.470000e-01 |
2.434245e+05 |
2.434245e+05 |
0.000000e+00 |
6.000000e+01 |
5.000000e+07 |
1.037088e-01 |
1.037088e-01 |
0.000000e+00 |
1.201909e+03 |
1.201835e+03 |
7.400000e-02 |
2.754190e+05 |
2.754190e+05 |
0.000000e+00 |
7.000000e+01 |
5.000000e+07 |
1.046797e-01 |
1.046797e-01 |
0.000000e+00 |
1.198018e+03 |
1.197980e+03 |
3.800000e-02 |
3.073134e+05 |
3.073134e+05 |
0.000000e+00 |
8.000000e+01 |
5.000000e+07 |
1.057537e-01 |
1.057537e-01 |
0.000000e+00 |
1.194149e+03 |
1.194129e+03 |
2.000000e-02 |
3.390943e+05 |
3.390943e+05 |
0.000000e+00 |
9.000000e+01 |
5.000000e+07 |
1.069254e-01 |
1.069254e-01 |
0.000000e+00 |
1.190289e+03 |
1.190277e+03 |
1.200000e-02 |
3.707527e+05 |
3.707527e+05 |
0.000000e+00 |
1.000000e+02 |
5.000000e+07 |
1.081911e-01 |
1.081911e-01 |
0.000000e+00 |
1.186431e+03 |
1.186423e+03 |
8.000000e-03 |
4.022809e+05 |
4.022809e+05 |
0.000000e+00 |
1.100000e+02 |
5.000000e+07 |
1.095484e-01 |
1.095484e-01 |
0.000000e+00 |
1.182573e+03 |
1.182567e+03 |
6.000000e-03 |
4.336706e+05 |
4.336706e+05 |
0.000000e+00 |
1.200000e+02 |
5.000000e+07 |
1.109960e-01 |
1.109960e-01 |
0.000000e+00 |
1.178718e+03 |
1.178712e+03 |
6.000000e-03 |
4.649125e+05 |
4.649125e+05 |
0.000000e+00 |
1.300000e+02 |
5.000000e+07 |
1.125343e-01 |
1.125343e-01 |
0.000000e+00 |
1.174868e+03 |
1.174863e+03 |
5.000000e-03 |
4.959956e+05 |
4.959956e+05 |
0.000000e+00 |
1.400000e+02 |
5.000000e+07 |
1.141646e-01 |
1.141646e-01 |
0.000000e+00 |
1.171029e+03 |
1.171024e+03 |
5.000000e-03 |
5.269073e+05 |
5.269073e+05 |
0.000000e+00 |
1.500000e+02 |
5.000000e+07 |
1.158895e-01 |
1.158895e-01 |
0.000000e+00 |
1.167210e+03 |
1.167205e+03 |
5.000000e-03 |
5.576337e+05 |
5.576337e+05 |
0.000000e+00 |
1.600000e+02 |
5.000000e+07 |
1.177126e-01 |
1.177126e-01 |
0.000000e+00 |
1.163418e+03 |
1.163412e+03 |
6.000000e-03 |
5.881596e+05 |
5.881596e+05 |
0.000000e+00 |
1.700000e+02 |
5.000000e+07 |
1.196389e-01 |
1.196389e-01 |
0.000000e+00 |
1.159664e+03 |
1.159659e+03 |
5.000000e-03 |
6.184686e+05 |
6.184685e+05 |
1.000000e-01 |
1.800000e+02 |
5.000000e+07 |
1.216740e-01 |
1.216740e-01 |
0.000000e+00 |
1.155961e+03 |
1.155956e+03 |
5.000000e-03 |
6.485429e+05 |
6.485429e+05 |
0.000000e+00 |
1.900000e+02 |
5.000000e+07 |
1.238248e-01 |
1.238248e-01 |
0.000000e+00 |
1.152322e+03 |
1.152317e+03 |
5.000000e-03 |
6.783639e+05 |
6.783639e+05 |
0.000000e+00 |
2.000000e+02 |
5.000000e+07 |
1.260990e-01 |
1.260990e-01 |
0.000000e+00 |
1.148762e+03 |
1.148756e+03 |
6.000000e-03 |
7.079116e+05 |
7.079115e+05 |
1.000000e-01 |
2.100000e+02 |
5.000000e+07 |
1.285052e-01 |
1.285052e-01 |
0.000000e+00 |
1.145296e+03 |
1.145291e+03 |
5.000000e-03 |
7.371645e+05 |
7.371644e+05 |
1.000000e-01 |
2.200000e+02 |
5.000000e+07 |
1.310528e-01 |
1.310528e-01 |
0.000000e+00 |
1.141943e+03 |
1.141937e+03 |
6.000000e-03 |
7.660999e+05 |
7.660999e+05 |
0.000000e+00 |
2.300000e+02 |
5.000000e+07 |
1.337522e-01 |
1.337522e-01 |
0.000000e+00 |
1.138721e+03 |
1.138715e+03 |
6.000000e-03 |
7.946933e+05 |
7.946933e+05 |
0.000000e+00 |
2.400000e+02 |
5.000000e+07 |
1.366141e-01 |
1.366141e-01 |
0.000000e+00 |
1.135649e+03 |
1.135643e+03 |
6.000000e-03 |
8.229188e+05 |
8.229188e+05 |
0.000000e+00 |
2.500000e+02 |
5.000000e+07 |
1.396504e-01 |
1.396504e-01 |
0.000000e+00 |
1.132749e+03 |
1.132743e+03 |
6.000000e-03 |
8.507483e+05 |
8.507483e+05 |
0.000000e+00 |
2.600000e+02 |
5.000000e+07 |
1.428732e-01 |
1.428732e-01 |
0.000000e+00 |
1.130043e+03 |
1.130037e+03 |
6.000000e-03 |
8.781522e+05 |
8.781523e+05 |
-1.000000e-01 |
2.700000e+02 |
5.000000e+07 |
1.462955e-01 |
1.462955e-01 |
0.000000e+00 |
1.127553e+03 |
1.127547e+03 |
6.000000e-03 |
9.050988e+05 |
9.050988e+05 |
0.000000e+00 |
2.800000e+02 |
5.000000e+07 |
1.499306e-01 |
1.499306e-01 |
0.000000e+00 |
1.125302e+03 |
1.125296e+03 |
6.000000e-03 |
9.315545e+05 |
9.315546e+05 |
-1.000000e-01 |
2.900000e+02 |
5.000000e+07 |
1.537925e-01 |
1.537925e-01 |
0.000000e+00 |
1.123315e+03 |
1.123309e+03 |
6.000000e-03 |
9.574840e+05 |
9.574839e+05 |
1.000000e-01 |
3.000000e+02 |
5.000000e+07 |
1.578954e-01 |
1.578954e-01 |
0.000000e+00 |
1.121617e+03 |
1.121611e+03 |
6.000000e-03 |
9.828499e+05 |
9.828499e+05 |
0.000000e+00 |
3.100000e+02 |
5.000000e+07 |
1.622541e-01 |
1.622541e-01 |
0.000000e+00 |
1.120232e+03 |
1.120226e+03 |
6.000000e-03 |
1.007614e+06 |
1.007614e+06 |
0.000000e+00 |
3.200000e+02 |
5.000000e+07 |
1.668838e-01 |
1.668838e-01 |
0.000000e+00 |
1.119187e+03 |
1.119181e+03 |
6.000000e-03 |
1.031735e+06 |
1.031735e+06 |
0.000000e+00 |
3.300000e+02 |
5.000000e+07 |
1.717996e-01 |
1.717996e-01 |
0.000000e+00 |
1.118507e+03 |
1.118500e+03 |
7.000000e-03 |
1.055172e+06 |
1.055172e+06 |
0.000000e+00 |
3.400000e+02 |
5.000000e+07 |
1.770173e-01 |
1.770173e-01 |
0.000000e+00 |
1.118217e+03 |
1.118210e+03 |
7.000000e-03 |
1.077883e+06 |
1.077883e+06 |
0.000000e+00 |
3.500000e+02 |
5.000000e+07 |
1.825527e-01 |
1.825527e-01 |
0.000000e+00 |
1.118343e+03 |
1.118336e+03 |
7.000000e-03 |
1.099824e+06 |
1.099824e+06 |
0.000000e+00 |
3.600000e+02 |
5.000000e+07 |
1.884216e-01 |
1.884216e-01 |
0.000000e+00 |
1.118909e+03 |
1.118902e+03 |
7.000000e-03 |
1.120953e+06 |
1.120953e+06 |
0.000000e+00 |
3.700000e+02 |
5.000000e+07 |
1.946401e-01 |
1.946401e-01 |
0.000000e+00 |
1.119940e+03 |
1.119933e+03 |
7.000000e-03 |
1.141227e+06 |
1.141227e+06 |
0.000000e+00 |
3.800000e+02 |
5.000000e+07 |
2.012243e-01 |
2.012244e-01 |
-1.000000e-07 |
1.121459e+03 |
1.121452e+03 |
7.000000e-03 |
1.160602e+06 |
1.160602e+06 |
0.000000e+00 |
3.900000e+02 |
5.000000e+07 |
2.081904e-01 |
2.081904e-01 |
0.000000e+00 |
1.123489e+03 |
1.123481e+03 |
8.000000e-03 |
1.179038e+06 |
1.179038e+06 |
0.000000e+00 |
4.000000e+02 |
5.000000e+07 |
2.155542e-01 |
2.155542e-01 |
0.000000e+00 |
1.126050e+03 |
1.126042e+03 |
8.000000e-03 |
1.196494e+06 |
1.196494e+06 |
0.000000e+00 |
4.100000e+02 |
5.000000e+07 |
2.233318e-01 |
2.233318e-01 |
0.000000e+00 |
1.129162e+03 |
1.129154e+03 |
8.000000e-03 |
1.212933e+06 |
1.212933e+06 |
0.000000e+00 |
4.200000e+02 |
5.000000e+07 |
2.315390e-01 |
2.315390e-01 |
0.000000e+00 |
1.132842e+03 |
1.132834e+03 |
8.000000e-03 |
1.228320e+06 |
1.228320e+06 |
0.000000e+00 |
4.300000e+02 |
5.000000e+07 |
2.401912e-01 |
2.401912e-01 |
0.000000e+00 |
1.137107e+03 |
1.137098e+03 |
9.000000e-03 |
1.242621e+06 |
1.242621e+06 |
0.000000e+00 |
4.400000e+02 |
5.000000e+07 |
2.493038e-01 |
2.493039e-01 |
-1.000000e-07 |
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1.850807e+06 |
1.850807e+06 |
0.000000e+00 |
8.000000e+02 |
5.000000e+08 |
7.460619e-01 |
7.460619e-01 |
0.000000e+00 |
1.525499e+03 |
1.525478e+03 |
2.100000e-02 |
1.863698e+06 |
1.863698e+06 |
0.000000e+00 |
8.100000e+02 |
5.000000e+08 |
7.664171e-01 |
7.664171e-01 |
0.000000e+00 |
1.536035e+03 |
1.536014e+03 |
2.100000e-02 |
1.877464e+06 |
1.877464e+06 |
0.000000e+00 |
8.200000e+02 |
5.000000e+08 |
7.869073e-01 |
7.869073e-01 |
0.000000e+00 |
1.546636e+03 |
1.546615e+03 |
2.100000e-02 |
1.892119e+06 |
1.892119e+06 |
0.000000e+00 |
8.300000e+02 |
5.000000e+08 |
8.075018e-01 |
8.075018e-01 |
0.000000e+00 |
1.557286e+03 |
1.557265e+03 |
2.100000e-02 |
1.907677e+06 |
1.907677e+06 |
0.000000e+00 |
8.400000e+02 |
5.000000e+08 |
8.281680e-01 |
8.281680e-01 |
0.000000e+00 |
1.567968e+03 |
1.567947e+03 |
2.100000e-02 |
1.924142e+06 |
1.924142e+06 |
0.000000e+00 |
8.500000e+02 |
5.000000e+08 |
8.488713e-01 |
8.488713e-01 |
0.000000e+00 |
1.578663e+03 |
1.578641e+03 |
2.200000e-02 |
1.941517e+06 |
1.941517e+06 |
0.000000e+00 |
8.600000e+02 |
5.000000e+08 |
8.695752e-01 |
8.695752e-01 |
0.000000e+00 |
1.589350e+03 |
1.589327e+03 |
2.300000e-02 |
1.959797e+06 |
1.959797e+06 |
0.000000e+00 |
8.700000e+02 |
5.000000e+08 |
8.902412e-01 |
8.902412e-01 |
0.000000e+00 |
1.600005e+03 |
1.599982e+03 |
2.300000e-02 |
1.978972e+06 |
1.978972e+06 |
0.000000e+00 |
8.800000e+02 |
5.000000e+08 |
9.108288e-01 |
9.108288e-01 |
0.000000e+00 |
1.610604e+03 |
1.610581e+03 |
2.300000e-02 |
1.999028e+06 |
1.999028e+06 |
0.000000e+00 |
8.900000e+02 |
5.000000e+08 |
9.312953e-01 |
9.312953e-01 |
0.000000e+00 |
1.621117e+03 |
1.621094e+03 |
2.300000e-02 |
2.019944e+06 |
2.019944e+06 |
0.000000e+00 |
9.000000e+02 |
5.000000e+08 |
9.515959e-01 |
9.515959e-01 |
0.000000e+00 |
1.631515e+03 |
1.631491e+03 |
2.400000e-02 |
2.041692e+06 |
2.041692e+06 |
0.000000e+00 |
9.100000e+02 |
5.000000e+08 |
9.716837e-01 |
9.716837e-01 |
0.000000e+00 |
1.641765e+03 |
1.641740e+03 |
2.500000e-02 |
2.064242e+06 |
2.064242e+06 |
0.000000e+00 |
9.200000e+02 |
5.000000e+08 |
9.915095e-01 |
9.915096e-01 |
-1.000000e-07 |
1.651829e+03 |
1.651805e+03 |
2.400000e-02 |
2.087552e+06 |
2.087552e+06 |
0.000000e+00 |
9.243300e+02 |
5.000000e+08 |
1.000000e+00 |
1.000000e+00 |
0.000000e+00 |
1.656120e+03 |
1.656095e+03 |
2.500000e-02 |
2.097870e+06 |
2.097870e+06 |
0.000000e+00 |
Tip
The help function for 3D plot can be downloaded at here: helpfunc.py
Total running time of the script: ( 0 minutes 17.214 seconds)