;+
; NAME:
;  vt3d_thermwave_nloc_p0_nz
; PURPOSE: (one line)
;  Return thermal wave, multiple locations, phase=0, n depths
; DESCRIPTION:
;  Return thermal wave, multiple locations, phase=0, n depths
; CATEGORY:
;  Volatile Transport
; CALLING SEQUENCE:
;  temp = vt3d_thermwave_nloc_p0_nz(temp_terms, dtemp_dzeta, zeta)
; INPUTS:
;  temp_terms : complex[nloc, n_terms + 1]
;  phase : float[n_t] = 0.
;  dtemp_dzeta : scalar
;  zeta : float[n_z]
; OUTPUTS:
;  temp: float[n_z]
;   
; RESTRICTIONS:
; PROCEDURE:
; MODIFICATION HISTORY:
;  Written 2011 Dec 30, by Leslie Young, SwRI
;  Modified 2012 Sep 30, LAY.  Added m inside sqrt(_i) term.
;-
function vt3d_thermwave_nloc_p0_nz, temp_terms, dtemp_dzeta, zeta

    _i = complex(0,1)

    ; get the dimensions of temp_t, phase, substrate
    n_term = n_elements(temp_terms) - 1
    n_z = n_elements(zeta)
    n_loc = 1
    n_t = 1

    temp_0 = replicate(temp_terms[0],n_z) ; [n_z]
    temp_f = dtemp_dzeta * zeta ; [n_z]
    
    temp = complex(temp_0 + temp_f,0) ; [n_z]
    for m = 1,n_term do begin
       temp_m = temp_terms[m]; scalar
       temp += (temp_m*exp(sqrt(_i*m)*zeta)) ; [n_z]
    endfor

    return, re(temp)

end