code: def sphergal_to_rectgal(l,b,d,vr,pmll,pmbb,degree=False):
      
      XYZ= lbd_to_XYZ(l,b,d,degree=degree)
      vxvyvz= vrpmllpmbb_to_vxvyvz(vr,pmll,pmbb,l,b,d,XYZ=False,degree=degree)
      if sc.array(l).shape == ():
          return sc.array([XYZ[0],XYZ[1],XYZ[2],vxvyvz[0],vxvyvz[1],vxvyvz[2]])
      else:
          out=sc.zeros((len(l),6))
          out[:,0:3]= XYZ
          out[:,3:6]= vxvyvz
          return out
docs: NAME:
  
         sphergal_to_rectgal
  
      PURPOSE:
  
         transform phase-space coordinates in spherical Galactic coordinates to rectangular Galactic coordinates (can take vector inputs)
  
      INPUT:
  
         l - Galactic longitude (rad)
  
         b - Galactic lattitude (rad)
  
         d - distance (kpc)
  
         vr - line-of-sight velocity (km/s)
  
         pmll - proper motion in the Galactic longitude direction (mu_l*cos(b) ) (mas/yr)
  
         pmbb - proper motion in the Galactic lattitude (mas/yr)
  
         degree - (bool) if True, l and b are in degrees
  
      OUTPUT:
  
         (X,Y,Z,vx,vy,vz) in (kpc,kpc,kpc,km/s,km/s,km/s)
  
      HISTORY:
  
         2009-10-25 - Written - Bovy (NYU)