;+
; NAME:
;  vt3d_step_cn_1loc
; PURPOSE: (one line)
;  step the temperature one time step at a single location
; DESCRIPTION:
;  step the temperature one time step at a single location
; CATEGORY:
;  Volatile Transport
; CALLING SEQUENCE:
;  vt3d_step_cn_1loc, alpha_i, beta_0, beta_i, gamma_0, gamma_J, temp_0, temp_i
; INPUTS:
;  alpha_i: dependance of temp[1..J] on temp[0..J-1], unitless, float[J]
;  beta_0:  dependance of temp[0] on temp[1], unitless, float
;  beta_i:  dependance of temp[1..J] on temp[2..J+1], unitless, float[J]
;  gamma_0: net flux at upper boundary, K, float
;  gamma_J: net flux at lower boundary, K, float
; INPUT-OUTPUTS:
;  temp_0 : temperature at layer 0, K, float
;  temp_i : temperature at layer 1..J, K, float[J]
; PROCEDURE:
;  Solve Crank-Nicholson equation
;  Young, L. A. 2016, Volatile transport on inhomogeneous surfaces: II. Numerical calculations (VT3D)
;   Resubmitted to Icarus.
;   Eq. 3.4-9a, 3.4-9b
; MODIFICATION HISTORY:
;  Written 2011 Feb 6, by Leslie Young, SwRI
;  2016 Mar 24 LAY. Modified for inclusion in vt3d library.
;-

pro vt3d_step_cn_1loc, alpha_i, beta_0, beta_i, gamma_0, gamma_J, temp_0, temp_i

    ; first get the right-hand side
    vt3d_step_expl_1loc, alpha_i/2., beta_0/2., beta_i/2., gamma_0, gamma_J, temp_0, temp_i

    ; then solve for the final temperature
    vt3d_step_impl_1loc, alpha_i/2., beta_0/2., beta_i/2., 0., 0., temp_0, temp_i

end