

In [35]:

    
fig = plt.figure(figsize=(1.5*6.5,1.5*3.8))
gs = matplotlib.gridspec.GridSpec( 1,1)

ax0 = fig.add_subplot( gs[0,0])

for ax in [ax0]:
    ax.set_xlabel("$V_{0} (E_{R})$",fontsize=16)
    ax.grid()
    ax.set_ylim(0.,15.)
    ax.set_xlim(0.,20.)
    
ax0.set_ylabel("$E_{R}$",fontsize=16,rotation=0)

v0 = np.linspace(0.1,40,80.)
v03d = np.outer( v0, np.ones(3))
c = ['blue', 'red', 'green']
fc = ['lightblue','pink','limegreen']
for i in range(3):
    if i>1: continue
    Eb = bands3dinterpvec(v03d,i)
    ax.fill_between( v0 , Eb[:,0], Eb[:,1], \
          color=c[i], facecolor=c[i], alpha=0.7, zorder=4) 
    ax.plot( v0, Eb[:,1], color=c[i])
    ax.plot( v0, Eb[:,0], color=c[i],\
          label="Band = %d"%i)
    if i==2: labelstr = 'h.osc.'
    else: labelstr = None
    ax.plot( v0, hosc3d(i,v0), color='black', label=labelstr, zorder=1 )

    
    zfit = np.polyfit( v0, Eb[:,0] - (3.+i)*np.sqrt(v0) , 4) 
    #print zfit
    z = np.poly1d( zfit  )
    ax0.plot( v0, z(v0) + (3.+i)*np.sqrt(v0), '--', lw=4, color=c[i]) 
    
    print "Band %d Bottom"%i 
    for ci,coef in enumerate(zfit): 
        print "( %+0.4e )* v0^%d" % ( coef, len(zfit)-1-ci )
        
    
    zfit = np.polyfit( v0, Eb[:,1] , 5)
    #print zfit
    z = np.poly1d( zfit  )
    ax0.plot( v0, z(v0) , '--', lw=4, color=c[i]) 
    
    print "Band %d Top"%i 
    for ci,coef in enumerate(zfit): 
        print "( %+0.4e )* v0^%d" % ( coef, len(zfit)-1-ci )
        
    print "\n--------------" 
        
    ax0.legend( bbox_to_anchor=(1.03,1.00), \
                loc='upper left', numpoints=1, \
                 prop={'size':12}, handlelength=1.1, handletextpad=0.5 )
             
            


#ax0.plot( v0, 3.*np.sqrt(v0), lw=5, color='black' )


gs.tight_layout(fig, rect=[0.,0.,0.8,1.0])
#fig.savefig('BandStructure_figures/bands3d_V0_interp.png',dpi=240)
ax0.set_xlim(0., 20)
ax0.set_ylim(0.,  10.)









    



Band 0 Bottom
( +1.1080e-06 )* v0^4
( -5.9045e-05 )* v0^3
( -3.9164e-04 )* v0^2
( +5.8301e-02 )* v0^1
( -1.5032e+00 )* v0^0
Band 0 Top
( +7.0144e-08 )* v0^5
( -9.9790e-06 )* v0^4
( +6.0294e-04 )* v0^3
( -2.1721e-02 )* v0^2
( +7.4294e-01 )* v0^1
( +3.0057e+00 )* v0^0

--------------
Band 1 Bottom
( +9.3920e-06 )* v0^4
( -7.8060e-04 )* v0^3
( +1.8631e-02 )* v0^2
( +4.9235e-02 )* v0^1
( -1.2629e+00 )* v0^0
Band 1 Top
( +3.9194e-08 )* v0^5
( -6.0709e-06 )* v0^4
( +4.2764e-04 )* v0^3
( -1.9971e-02 )* v0^2
( +9.9644e-01 )* v0^1
( +6.0027e+00 )* v0^0

--------------






    Out[35]:





(0.0, 10.0)