Calculates area under the curve (no fitting)

   Parameters
   ----------
   spectrum : array of shape (n_transients, n_points)
      Typically the difference of the on/off spectra in each transient.

   center, bandwidth : float
      Determine the limits for the part of the spectrum for which we want
      to calculate the AUC.
      e.g. if center = 3.0, bandwidth = 0.3, lower and upper bounds will be
      2.85 and 3.15 respectively (center +/- bandwidth/2).

   Notes
   -----
   Default center and bandwidth are 3.0 and 0.3ppm respectively
    because of Sanacora 1999 pg 1045:
   "The GABA signal was integrated over a 0.30-ppm bandwidth at 3.00ppm"

   Ref: Sanacora, G., Mason, G. F., Rothman, D. L., Behar, K. L., Hyder, F.,
   Petroff, O. A., ... & Krystal, J. H. (1999). Reduced cortical
   {gamma}-aminobutyric acid levels in depressed patients determined by proton
   magnetic resonance spectroscopy. Archives of general psychiatry, 56(11),
   1043.

def simple_auc(spectrum, f_ppm, center=3.00, bandwidth=0.30):
   """
   Calculates area under the curve (no fitting)

   Parameters
   ----------
   spectrum : array of shape (n_transients, n_points)
      Typically the difference of the on/off spectra in each transient.

   center, bandwidth : float
      Determine the limits for the part of the spectrum for which we want
      to calculate the AUC.
      e.g. if center = 3.0, bandwidth = 0.3, lower and upper bounds will be
      2.85 and 3.15 respectively (center +/- bandwidth/2).

   Notes
   -----
   Default center and bandwidth are 3.0 and 0.3ppm respectively
    because of Sanacora 1999 pg 1045:
   "The GABA signal was integrated over a 0.30-ppm bandwidth at 3.00ppm"

   Ref: Sanacora, G., Mason, G. F., Rothman, D. L., Behar, K. L., Hyder, F.,
   Petroff, O. A., ... & Krystal, J. H. (1999). Reduced cortical
   {gamma}-aminobutyric acid levels in depressed patients determined by proton
   magnetic resonance spectroscopy. Archives of general psychiatry, 56(11),
   1043.

   """
   range = np.max(f_ppm)-np.min(f_ppm)
   dx=float(range)/float(len(f_ppm))
   
   lb = np.floor((np.max(f_ppm)-float(center)+float(bandwidth)/2)/dx)
   ub = np.ceil((np.max(f_ppm)-float(center)-float(bandwidth)/2)/dx)

   auc = trapz(spectrum[ub:lb].real, dx=dx)

   return auc, ub, lb