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Commit b7df6f33 authored by Christophe Geuzaine's avatar Christophe Geuzaine
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Merge branch 'master' of https://gitlab.onelab.info/doc/models

parents bab75432 6dcfb724
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ElectromagneticScattering/scattering.geo
+ 2
− 0
View file @ b7df6f33
...@@ -723,6 +723,7 @@ If(flag_cartpml==0) ...@@ -723,6 +723,7 @@ If(flag_cartpml==0)
Physical Volume(2) = {1073}; // Out - air Physical Volume(2) = {1073}; // Out - air
Physical Volume(3) = {1091}; // pml Physical Volume(3) = {1091}; // pml
Physical Point(2000) = {1}; // PrintPoint Physical Point(2000) = {1}; // PrintPoint
Physical Surface(10) = {1055,1057,1059,1062,1064,1066,1068,1070};
EndIf EndIf
// Mesh.Algorithm = 1; // // 1=MeshAdapt, 5=Delaunay, 6=Frontal // Mesh.Algorithm = 1; // // 1=MeshAdapt, 5=Delaunay, 6=Frontal
...@@ -752,3 +753,4 @@ Printf(Sprintf("n_max = %g;" ,n_max)) >> "scattering_tmp.py"; ...@@ -752,3 +753,4 @@ Printf(Sprintf("n_max = %g;" ,n_max)) >> "scattering_tmp.py";
Printf(Sprintf("p_max = %g;" ,p_max)) >> "scattering_tmp.py"; Printf(Sprintf("p_max = %g;" ,p_max)) >> "scattering_tmp.py";
Printf(Sprintf("siwt = %g;" ,siwt)) >> "scattering_tmp.py"; Printf(Sprintf("siwt = %g;" ,siwt)) >> "scattering_tmp.py";
Mesh.ElementOrder = 2;
ElectromagneticScattering/scattering.pro
+ 71
− 22
View file @ b7df6f33
...@@ -21,6 +21,7 @@ Group { ...@@ -21,6 +21,7 @@ Group {
Domain = Region[{Scat_In,Scat_Out}]; Domain = Region[{Scat_In,Scat_Out}];
PMLs = Region[{PMLxyz,PMLxy,PMLxz,PMLyz,PMLx,PMLy,PMLz}]; PMLs = Region[{PMLxyz,PMLxy,PMLxz,PMLyz,PMLx,PMLy,PMLz}];
All_domains = Region[{Scat_In,Scat_Out,PMLxyz,PMLxy,PMLxz,PMLyz,PMLx,PMLy,PMLz}]; All_domains = Region[{Scat_In,Scat_Out,PMLxyz,PMLxy,PMLxz,PMLyz,PMLx,PMLy,PMLz}];
SurfInt = Region[{}];
EndIf EndIf
If(flag_cartpml==0) If(flag_cartpml==0)
Scat_In = Region[1]; Scat_In = Region[1];
...@@ -28,6 +29,7 @@ Group { ...@@ -28,6 +29,7 @@ Group {
Domain = Region[{Scat_In,Scat_Out}]; Domain = Region[{Scat_In,Scat_Out}];
PMLs = Region[3]; PMLs = Region[3];
All_domains = Region[{Scat_In,Scat_Out,PMLs}]; All_domains = Region[{Scat_In,Scat_Out,PMLs}];
SurfInt = Region[{10}];
EndIf EndIf
PrintPoint = Region[2000]; PrintPoint = Region[2000];
} }
...@@ -37,6 +39,7 @@ Function{ ...@@ -37,6 +39,7 @@ Function{
// For i In {0:#test()-1} // For i In {0:#test()-1}
// Printf("%g",test(i)); // Printf("%g",test(i));
// EndFor // EndFor
I[] = Complex[0,1]; I[] = Complex[0,1];
avoid_sing = 1.e-14; avoid_sing = 1.e-14;
mu0 = 4*Pi*100.0*nm; mu0 = 4*Pi*100.0*nm;
...@@ -192,6 +195,8 @@ Function{ ...@@ -192,6 +195,8 @@ Function{
me = ne*(ne+1) - Floor[pe]; me = ne*(ne+1) - Floor[pe];
Mnm_source~{pe}[] = Mnm[1,ne,me,XYZ[],k_Out]; Mnm_source~{pe}[] = Mnm[1,ne,me,XYZ[],k_Out];
Nnm_source~{pe}[] = Nnm[1,ne,me,XYZ[],k_Out]; Nnm_source~{pe}[] = Nnm[1,ne,me,XYZ[],k_Out];
Mnm_out~{pe}[] = Mnm[4,ne,me,XYZ[],k_Out];
Nnm_out~{pe}[] = Nnm[4,ne,me,XYZ[],k_Out];
source_M~{pe}[] = (omega0/cel)^2*(epsilonr[]-epsilonr1[])*Mnm_source~{pe}[]; source_M~{pe}[] = (omega0/cel)^2*(epsilonr[]-epsilonr1[])*Mnm_source~{pe}[];
source_N~{pe}[] = (omega0/cel)^2*(epsilonr[]-epsilonr1[])*Nnm_source~{pe}[]; source_N~{pe}[] = (omega0/cel)^2*(epsilonr[]-epsilonr1[])*Nnm_source~{pe}[];
EndFor EndFor
...@@ -236,9 +241,9 @@ Integration { ...@@ -236,9 +241,9 @@ Integration {
{ Type Gauss ; { Type Gauss ;
Case { Case {
{ GeoElement Point ; NumberOfPoints 1 ; } { GeoElement Point ; NumberOfPoints 1 ; }
{ GeoElement Line ; NumberOfPoints 4 ; } { GeoElement Line2 ; NumberOfPoints 4 ; }
{ GeoElement Triangle ; NumberOfPoints 6 ; } { GeoElement Triangle2 ; NumberOfPoints 12 ; }
{ GeoElement Tetrahedron ; NumberOfPoints 15 ; } { GeoElement Tetrahedron2 ; NumberOfPoints 17 ; }
} }
} }
} }
...@@ -249,16 +254,16 @@ FunctionSpace { ...@@ -249,16 +254,16 @@ FunctionSpace {
{ Name Hcurl; Type Form1; { Name Hcurl; Type Form1;
BasisFunction { BasisFunction {
{ Name sn; NameOfCoef un; Function BF_Edge; { Name sn; NameOfCoef un; Function BF_Edge;
Support Region[All_domains]; Entity EdgesOf[All]; } Support Region[{All_domains,SurfInt}]; Entity EdgesOf[All]; }
{ Name sn2; NameOfCoef un2; Function BF_Edge_2E; { Name sn2; NameOfCoef un2; Function BF_Edge_2E;
Support Region[All_domains]; Entity EdgesOf[All]; } Support Region[{All_domains,SurfInt}]; Entity EdgesOf[All]; }
If (is_FEM_o2==1) If (is_FEM_o2==1)
{ Name sn3; NameOfCoef un3; Function BF_Edge_3F_b; { Name sn3; NameOfCoef un3; Function BF_Edge_3F_b;
Support Region[All_domains]; Entity FacetsOf[All]; } Support Region[{All_domains,SurfInt}]; Entity FacetsOf[All]; }
{ Name sn4; NameOfCoef un4; Function BF_Edge_3F_c; { Name sn4; NameOfCoef un4; Function BF_Edge_3F_c;
Support Region[All_domains]; Entity FacetsOf[All]; } Support Region[{All_domains,SurfInt}]; Entity FacetsOf[All]; }
{ Name sn5; NameOfCoef un5; Function BF_Edge_4E; { Name sn5; NameOfCoef un5; Function BF_Edge_4E;
Support Region[All_domains]; Entity EdgesOf[All]; } Support Region[{All_domains,SurfInt}]; Entity EdgesOf[All]; }
EndIf EndIf
} }
Constraint { Constraint {
...@@ -316,6 +321,29 @@ Formulation { ...@@ -316,6 +321,29 @@ Formulation {
} }
} }
EndFor EndFor
{Name VPWMN_helmholtz_vector; Type FemEquation;
Quantity {
{ Name u; Type Local; NameOfSpace Hcurl;}
}
Equation {
Galerkin { [-1/mur[]*Dof{Curl u} , {Curl u}]; In All_domains; Jacobian JVol; Integration Int_1; }
Galerkin { [(omega0/cel)^2*epsilonr[]*Dof{u} , {u} ]; In All_domains; Jacobian JVol; Integration Int_1; }
Galerkin { [ (omega0/cel)^2*(epsilonr[]-epsilonr1[])*
($isN ? Nnm[1,$NE,$ME,XYZ[],k_Out] : Mnm[1,$NE,$ME,XYZ[],k_Out])
, {u} ]; In Scat_In; Jacobian JVol; Integration Int_1;}
}
}
{Name VPWN_helmholtz_vector_test; Type FemEquation;
Quantity {
{ Name u; Type Local; NameOfSpace Hcurl;}
}
Equation {
Galerkin { [-1/mur[]*Dof{Curl u} , {Curl u}]; In All_domains; Jacobian JVol; Integration Int_1; }
Galerkin { [(omega0/cel)^2*epsilonr[]*Dof{u} , {u} ]; In All_domains; Jacobian JVol; Integration Int_1; }
Galerkin { [ (omega0/cel)^2*(epsilonr[]-epsilonr1[])*Nnm[1,$NE,$ME,XYZ[],k_Out], {u} ]; In Scat_In; Jacobian JVol; Integration Int_1;}
}
}
EndIf EndIf
If (flag_study==RES_GREEN) If (flag_study==RES_GREEN)
For ncomp In {0:2} For ncomp In {0:2}
...@@ -352,25 +380,33 @@ Resolution { ...@@ -352,25 +380,33 @@ Resolution {
If (flag_study==RES_TMAT) If (flag_study==RES_TMAT)
{ Name res_VPWall_helmholtz_vector; { Name res_VPWall_helmholtz_vector;
System { System {
For pe In {1:p_max} { Name T; NameOfFormulation VPWMN_helmholtz_vector; Type ComplexValue; }
{ Name M~{pe}; NameOfFormulation VPWM_helmholtz_vector~{pe}; Type ComplexValue; Frequency Freq; }
{ Name N~{pe}; NameOfFormulation VPWN_helmholtz_vector~{pe}; Type ComplexValue; Frequency Freq; }
EndFor
} }
Operation { Operation {
CreateDir[Str[myDir]]; CreateDir[Str[myDir]];
Evaluate[Python[]{"scattering_init.py"}]; Evaluate[Python[]{"scattering_init.py"}];
For pe In {1:p_max} For pe In {1:p_max}
Generate[M~{pe}]; Evaluate[ $isN = 0 ];
Solve[M~{pe}]; Evaluate[ $PE = pe ];
Evaluate[ $NE = Floor[Sqrt[$PE]] ];
Evaluate[ $ME = $NE*($NE+1) - Floor[$PE] ];
If (pe==1)
Generate[T];
Solve[T];
EndIf
GenerateRHS[T];
SolveAgain[T];
PostOperation[VPWM_postop~{pe}]; PostOperation[VPWM_postop~{pe}];
Generate[N~{pe}]; Evaluate[$isN=1];
Solve[N~{pe}]; GenerateRHS[T];
SolveAgain[T];
PostOperation[VPWN_postop~{pe}]; PostOperation[VPWN_postop~{pe}];
EndFor EndFor
Evaluate[Python[]{"scattering_post.py"}]; Evaluate[Python[]{"scattering_post.py"}];
} }
} }
EndIf EndIf
If (flag_study==RES_GREEN) If (flag_study==RES_GREEN)
{ Name res_GreenAll_helmholtz_vector; { Name res_GreenAll_helmholtz_vector;
...@@ -439,9 +475,10 @@ PostProcessing { ...@@ -439,9 +475,10 @@ PostProcessing {
} }
} }
EndIf EndIf
If (flag_study==RES_TMAT) If (flag_study==RES_TMAT)
For pe In {1:p_max} For pe In {1:p_max}
{ Name VPWM_postpro~{pe}; NameOfFormulation VPWM_helmholtz_vector~{pe};NameOfSystem M~{pe}; { Name VPWM_postpro~{pe}; NameOfFormulation VPWMN_helmholtz_vector; NameOfSystem T;
Quantity { Quantity {
{ Name E_scat ; Value { Local { [{u}]; In All_domains; Jacobian JVol; } } } { Name E_scat ; Value { Local { [{u}]; In All_domains; Jacobian JVol; } } }
{ Name E_scat_sph ; Value { Local { [Vector[ { Name E_scat_sph ; Value { Local { [Vector[
...@@ -452,9 +489,13 @@ PostProcessing { ...@@ -452,9 +489,13 @@ PostProcessing {
In All_domains; Jacobian JVol; } } } In All_domains; Jacobian JVol; } } }
{ Name H_scat ; Value { Local { [siwt*I[]/(mur[]*mu0*omega0)*{Curl u}]; In All_domains; Jacobian JVol; } } } { Name H_scat ; Value { Local { [siwt*I[]/(mur[]*mu0*omega0)*{Curl u}]; In All_domains; Jacobian JVol; } } }
{ Name Mnm_source~{pe} ; Value { Local { [ Mnm_source~{pe}[] ]; In All_domains; Jacobian JVol; } } } { Name Mnm_source~{pe} ; Value { Local { [ Mnm_source~{pe}[] ]; In All_domains; Jacobian JVol; } } }
For po In {1:p_max}
{ Name a~{pe}~{po} ; Value { Integral { [ {u}*Conj[Mnm_out~{po}[]] ]; In SurfInt; Integration Int_1 ; Jacobian JSur; } } }
{ Name norma~{pe}~{po} ; Value { Integral { [ Mnm_out~{pe}[]*Conj[Mnm_out~{po}[]] ]; In SurfInt; Integration Int_1 ; Jacobian JSur; } } }
EndFor
} }
} }
{ Name VPWN_postpro~{pe}; NameOfFormulation VPWN_helmholtz_vector~{pe};NameOfSystem N~{pe}; { Name VPWN_postpro~{pe}; NameOfFormulation VPWMN_helmholtz_vector; NameOfSystem T;
Quantity { Quantity {
{ Name E_scat ; Value { Local { [{u}]; In All_domains; Jacobian JVol; } } } { Name E_scat ; Value { Local { [{u}]; In All_domains; Jacobian JVol; } } }
{ Name E_scat_sph ; Value { Local { [Vector[ { Name E_scat_sph ; Value { Local { [Vector[
...@@ -469,6 +510,7 @@ PostProcessing { ...@@ -469,6 +510,7 @@ PostProcessing {
} }
EndFor EndFor
EndIf EndIf
If (flag_study==RES_GREEN) If (flag_study==RES_GREEN)
For ncomp In {0:2} For ncomp In {0:2}
{ Name GreenAll_postpro~{ncomp}; NameOfFormulation GreenAll_helmholtz_vector~{ncomp};NameOfSystem M~{ncomp}; { Name GreenAll_postpro~{ncomp}; NameOfFormulation GreenAll_helmholtz_vector~{ncomp};NameOfSystem M~{ncomp};
...@@ -520,6 +562,7 @@ PostOperation { ...@@ -520,6 +562,7 @@ PostOperation {
} }
} }
EndIf EndIf
If (flag_study==RES_PW) If (flag_study==RES_PW)
{Name PW_postop; NameOfPostProcessing PW_postpro ; {Name PW_postop; NameOfPostProcessing PW_postpro ;
Operation { Operation {
...@@ -540,6 +583,7 @@ PostOperation { ...@@ -540,6 +583,7 @@ PostOperation {
} }
} }
EndIf EndIf
If (flag_study==RES_TMAT) If (flag_study==RES_TMAT)
For pe In {1:p_max} For pe In {1:p_max}
{Name VPWM_postop~{pe}; NameOfPostProcessing VPWM_postpro~{pe} ; {Name VPWM_postop~{pe}; NameOfPostProcessing VPWM_postpro~{pe} ;
...@@ -557,6 +601,10 @@ PostOperation { ...@@ -557,6 +601,10 @@ PostOperation {
{sph_scan : 2.0*Pi-sph_scan+(2.0*Pi-2.0*sph_scan)/(10*(npts_plot_phi-1.0)) : (2.0*Pi-2.0*sph_scan)/(npts_plot_phi-1.0)} }, {sph_scan : 2.0*Pi-sph_scan+(2.0*Pi-2.0*sph_scan)/(10*(npts_plot_phi-1.0)) : (2.0*Pi-2.0*sph_scan)/(npts_plot_phi-1.0)} },
File StrCat[myDir,StrCat[StrCat["E_scat_onsphere_cart_M",Sprintf["%g",pe]],Sprintf["_r%g.pos",kr]]], File StrCat[myDir,StrCat[StrCat["E_scat_onsphere_cart_M",Sprintf["%g",pe]],Sprintf["_r%g.pos",kr]]],
Name StrCat["E_scat_onsphere_cart_M",Sprintf["%g",pe]]]; Name StrCat["E_scat_onsphere_cart_M",Sprintf["%g",pe]]];
For po In {1:p_max}
Print[a~{pe}~{po}[SurfInt], OnGlobal , Format Table, File StrCat[myDir,StrCat[StrCat["a_",Sprintf["pe%g",pe]],Sprintf["po%g.dat",po]]]];
Print[norma~{pe}~{po}[SurfInt], OnGlobal , Format Table, File StrCat[myDir,StrCat[StrCat["norma_",Sprintf["pe%g",pe]],Sprintf["po%g.dat",po]]]];
EndFor
} }
} }
{Name VPWN_postop~{pe}; NameOfPostProcessing VPWN_postpro~{pe} ; {Name VPWN_postop~{pe}; NameOfPostProcessing VPWN_postpro~{pe} ;
...@@ -578,6 +626,7 @@ PostOperation { ...@@ -578,6 +626,7 @@ PostOperation {
} }
EndFor EndFor
EndIf EndIf
If (flag_study==RES_GREEN) If (flag_study==RES_GREEN)
For ncomp In {0:2} For ncomp In {0:2}
{Name GreenAll_postop~{ncomp}; NameOfPostProcessing GreenAll_postpro~{ncomp} ; {Name GreenAll_postop~{ncomp}; NameOfPostProcessing GreenAll_postpro~{ncomp} ;
......
ElectromagneticScattering/scattering_init.py
+ 56
− 49
View file @ b7df6f33
...@@ -11,8 +11,8 @@ import sys,os ...@@ -11,8 +11,8 @@ import sys,os
import numpy as np import numpy as np
from scipy.special import jv, yv, hankel1, hankel2 from scipy.special import jv, yv, hankel1, hankel2
sys.path.append(os.getcwd()) sys.path.append(os.getcwd())
from matplotlib import cm # from matplotlib import cm
import pylab as pl # import pylab as pl
from scattering_tmp import * from scattering_tmp import *
np.set_printoptions(precision=2) np.set_printoptions(precision=2)
pi = np.pi pi = np.pi
...@@ -38,7 +38,7 @@ def field_VSH_expansion(post_filename): ...@@ -38,7 +38,7 @@ def field_VSH_expansion(post_filename):
FF_erCrossXnm_p = np.zeros((npts_theta,npts_phi,p_max),dtype=complex) FF_erCrossXnm_p = np.zeros((npts_theta,npts_phi,p_max),dtype=complex)
##################################### #####################################
##### sn, pn ,un ##### sn, pn ,un
##### Brian's recurrence relations ##### Brian Stout's recurrence relations (B_ arrays)
B_Pnpms = np.zeros((npts_theta,m_max+1,n_max+1)) B_Pnpms = np.zeros((npts_theta,m_max+1,n_max+1))
B_unpms = np.zeros((npts_theta,m_max+1,n_max+1)) B_unpms = np.zeros((npts_theta,m_max+1,n_max+1))
B_snpms = np.zeros((npts_theta,m_max+1,n_max+1)) B_snpms = np.zeros((npts_theta,m_max+1,n_max+1))
...@@ -88,7 +88,7 @@ def field_VSH_expansion(post_filename): ...@@ -88,7 +88,7 @@ def field_VSH_expansion(post_filename):
##################################### #####################################
##### sn, pn ,un ##### sn, pn ,un
##### Brian's recurrence relations ##### Brian Stout's recurrence relations (B_ arrays)
m_max = n_max m_max = n_max
p_max = n_max*n_max+2*n_max p_max = n_max*n_max+2*n_max
aM_nm = np.zeros(p_max,dtype=complex) aM_nm = np.zeros(p_max,dtype=complex)
...@@ -218,41 +218,48 @@ def field_VSH_expansion(post_filename): ...@@ -218,41 +218,48 @@ def field_VSH_expansion(post_filename):
orth3 = np.trapz(np.trapz((np.sin(theta_sph)*ZnmconjXnm).transpose(),theta_sph[:,0]),phi_sph[0,:]) orth3 = np.trapz(np.trapz((np.sin(theta_sph)*ZnmconjXnm).transpose(),theta_sph[:,0]),phi_sph[0,:])
aM_nm[int(po)-1] = np.trapz(np.trapz((np.sin(theta_sph)*EdotconjMnm).transpose(),theta_sph[:,0]),phi_sph[0,:]) / normalize_aM_nm2 aM_nm[int(po)-1] = np.trapz(np.trapz((np.sin(theta_sph)*EdotconjMnm).transpose(),theta_sph[:,0]),phi_sph[0,:]) / normalize_aM_nm2
bN_nm[int(po)-1] = np.trapz(np.trapz((np.sin(theta_sph)*EdotconjNnm).transpose(),theta_sph[:,0]),phi_sph[0,:]) / normalize_bN_nm2 bN_nm[int(po)-1] = np.trapz(np.trapz((np.sin(theta_sph)*EdotconjNnm).transpose(),theta_sph[:,0]),phi_sph[0,:]) / normalize_bN_nm2
print('anm not normalized' , np.trapz(np.trapz((np.sin(theta_sph)*EdotconjMnm).transpose(),theta_sph[:,0]),phi_sph[0,:]))
print('normalization ' , normalize_aM_nm2)
# print(np.loadtxt('run_results/a_pe%gpo%g.dat'%(1,int(po))))
# print(aM_nm)
return [fhnm_X,fenm_Y,fenm_Z,aM_nm,bN_nm,FF_Xnm_t,FF_Xnm_p,FF_erCrossXnm_t,FF_erCrossXnm_p] return [fhnm_X,fenm_Y,fenm_Z,aM_nm,bN_nm,FF_Xnm_t,FF_Xnm_p,FF_erCrossXnm_t,FF_erCrossXnm_p]
########################### # # ###########################
def plot_farfield(far_field_sph,filename): # # def plot_farfield(far_field_sph,filename):
vmax_sph = np.max(far_field_sph) # # vmax_sph = np.max(far_field_sph)
vmin_sph = np.min(far_field_sph) # # vmin_sph = np.min(far_field_sph)
x_sph = far_field_sph/vmax_sph*np.sin(theta_sph) * np.cos(phi_sph) # # x_sph = far_field_sph/vmax_sph*np.sin(theta_sph) * np.cos(phi_sph)
y_sph = far_field_sph/vmax_sph*np.sin(theta_sph) * np.sin(phi_sph) # # y_sph = far_field_sph/vmax_sph*np.sin(theta_sph) * np.sin(phi_sph)
z_sph = far_field_sph/vmax_sph*np.cos(theta_sph) # # z_sph = far_field_sph/vmax_sph*np.cos(theta_sph)
fig = pl.figure() # # fig = pl.figure()
ax = fig.add_subplot(111, projection='3d') # # ax = fig.add_subplot(111, projection='3d')
ax.set_aspect('equal') # # ax.set_aspect('equal')
surf=ax.plot_surface(x_sph,y_sph,z_sph,\ # # surf=ax.plot_surface(x_sph,y_sph,z_sph,\
facecolors=cm.viridis(far_field_sph/vmax_sph),\ # # facecolors=cm.viridis(far_field_sph/vmax_sph),\
rstride=2,\ # # rstride=2,\
cstride=2,\ # # cstride=2,\
linewidth=0,\ # # linewidth=0,\
vmin = vmin_sph,\ # # vmin = vmin_sph,\
vmax = vmax_sph,\ # # vmax = vmax_sph,\
shade=True,\ # # shade=True,\
alpha=0.5,\ # # alpha=0.5,\
antialiased=False) # # antialiased=False)
cset = ax.contourf(x_sph, y_sph, z_sph,1,fc='k', zdir='z', offset=-1) # # cset = ax.contourf(x_sph, y_sph, z_sph,1,fc='k', zdir='z', offset=-1)
cset = ax.contourf(x_sph, y_sph, z_sph,1,fc='k', zdir='x', offset=-1) # # cset = ax.contourf(x_sph, y_sph, z_sph,1,fc='k', zdir='x', offset=-1)
cset = ax.contourf(x_sph, y_sph, z_sph,1,fc='k', zdir='y', offset=1 ) # # cset = ax.contourf(x_sph, y_sph, z_sph,1,fc='k', zdir='y', offset=1 )
surf.set_edgecolor('k') # # surf.set_edgecolor('k')
max_range = 0.5*np.max(np.array([x_sph.max()-x_sph.min(), y_sph.max()-y_sph.min(), z_sph.max()-z_sph.min()])) # # max_range = 0.5*np.max(np.array([x_sph.max()-x_sph.min(), y_sph.max()-y_sph.min(), z_sph.max()-z_sph.min()]))
mid_x = (x_sph.max()+x_sph.min())*0.5 # # mid_x = (x_sph.max()+x_sph.min())*0.5
mid_y = (y_sph.max()+y_sph.min())*0.5 # # mid_y = (y_sph.max()+y_sph.min())*0.5
mid_z = (z_sph.max()+z_sph.min())*0.5 # # mid_z = (z_sph.max()+z_sph.min())*0.5
ax.set_xlim(mid_x-max_range, mid_x+max_range) # # ax.set_xlim(mid_x-max_range, mid_x+max_range)
ax.set_ylim(mid_y-max_range, mid_y+max_range) # # ax.set_ylim(mid_y-max_range, mid_y+max_range)
ax.set_zlim(mid_z-max_range, mid_z+max_range) # # ax.set_zlim(mid_z-max_range, mid_z+max_range)
ax.xaxis.set_ticklabels([]);ax.xaxis.set_label('x') # # ax.xaxis.set_ticklabels([]);ax.xaxis.set_label('x')
ax.yaxis.set_ticklabels([]);ax.yaxis.set_label('y') # # ax.yaxis.set_ticklabels([]);ax.yaxis.set_label('y')
ax.zaxis.set_ticklabels([]);ax.zaxis.set_label('z') # # ax.zaxis.set_ticklabels([]);ax.zaxis.set_label('z')
pl.savefig(filename,bbox_inches='tight') # # pl.savefig(filename,bbox_inches='tight')
pl.close('all') # # pl.close('all')
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