fixed doctest, including bug-fix of two es_mxd*

Fixed the call and expected outcome statements of the doctest strings in
the funciton documentation.  In doing noticed that for the mixed
supersaturations we should use the minimum, not maximum values, which
reverts a false correction from a previous commit.

moist_thermodynamics/functions.py

@@ -35,8 +35,8 @@ def es_liq(T):
 def es_ice(T):
     """ Returns the saturation vapor pressure of water over ice following Wagner et al., (2011) 
     fits for saturation over ice, these also define the IAPWS standard for ice.
-    >>> mt.es_ice(np.asarray([273.16,260.]))
-    [611.65706974, 222.66896149]
+    >>> es_ice(np.asarray([273.16,260.]))
+    array([611.655     , 195.80103377])
     """
     TvT = constants.temperature_water_vapor_triple_point
     PvT = constants.pressure_water_vapor_triple_point
@@ -54,10 +54,10 @@ def es_ice(T):
 def es_mxd(T):
     """ Saturation vapor pressure of water over liquid (T>Tmelt) or ice (T>Tmel) following the
     Wagner and Pruss (2002) and Wagner et al (2011) formuations for each of these.
-    >>> mt.es_mxd(np.asarray([305.,260.]))
-    [4719.32683147,  222.66896149]
+    >>> es_mxd(np.asarray([305.,260.]))
+    array([4719.32683147,  195.80103377])
     """
-    return np.maximum(es_liq(T),es_ice(T))
+    return np.minimum(es_liq(T),es_ice(T))
 
 def es_liq_analytic(T, delta_cl=constants.delta_cl):
     """ Returns an analytic approximation to the saturation vapor pressure over liquid
@@ -103,7 +103,7 @@ def es_mxd_analytic(T, delta_cl=constants.delta_cl, delta_ci=constants.delta_ci)
     >>> es_ice_analytic(np.asarray([273.16,260.]))
     array([611.655     , 195.99959431])
     """
-    return np.maximum(es_liq_analytic(T,delta_cl),es_ice_analytic(T,delta_ci))
+    return np.minimum(es_liq_analytic(T,delta_cl),es_ice_analytic(T,delta_ci))
 
 def vaporization_enthalpy(TK,delta_cl=constants.delta_cl):
     """ Returns the enthlapy [J/g] of vaporization (default) of water vapor or
@@ -296,8 +296,8 @@ def theta_rho(TK,PPa,qt,es=es_liq):
 def T_from_Te(Te,P,qt,es=es_liq):
     """ Given theta_e solves implicitly for the temperature at some other pressure,
     so that theta_e(T,P,qt) = Te
-	>>> T_from_Te(350.,1000.,17)
-	304.4761977
+	>>> T_from_Te(350.,100000.,17.e-3)
+	array([304.49321301])
     """
     def zero(T,Te,P,qt,es=es):
         return  np.abs(Te-theta_e(T,P,qt,es=es))
@@ -326,8 +326,8 @@ def T_from_Ts(Ts,P,qt,es=es_liq):
 def P_from_Te(Te,T,qt,es=es_liq):
     """ Given Te solves implicitly for the pressure at some temperature and qt
     so that theta_e(T,P,qt) = Te
-	>>> P_from_Te(350.,305.,17)
-	100464.71590478
+	>>> P_from_Te(350.,305.,17e-3)
+	array([100586.3357635])
     """
     def zero(P,Te,T,qt,es=es_liq):
         return np.abs(Te-theta_e(T,P,qt,es=es))
@@ -346,7 +346,7 @@ def P_from_Tl(Tl,T,qt,es=es_liq):
 def plcl(TK,PPa,qt,es=es_liq):
     """ Iteratively solve for the pressure [Pa] of the LCL, allows for saturate air.
 	>>> plcl(300.,102000.,17e-3)
-	array([95971.6975098])
+	array([95971.69750248])
     """
     p2r  = partial_pressure_to_mixing_ratio
 
@@ -356,7 +356,7 @@ def plcl(TK,PPa,qt,es=es_liq):
         return np.abs(qs/qt-1.)
 
     Tl   = theta_l(TK,PPa,qt)
-    return optimize.fsolve(zero, 80000., args=(Tl,qt), xtol=1.e-10)
+    return optimize.fsolve(zero, 80000., args=(Tl,qt), xtol=1.e-5)
 
 def plcl_bolton(TK,PPa,qt):
     """ Returns the pressure [Pa] of the LCL using the Bolton formula. Usually accurate to
@@ -380,8 +380,8 @@ def zlcl(Plcl,T,P,qt,z):
     """ Returns the height of the LCL assuming temperature changes following a
     dry adiabat with vertical displacements from the height where the ambient
     temperature is measured.
-	>>> Zlcl(300.,1020.,17)
-	96007.495
+	>>> zlcl(95000.,300.,90000.,17.e-3,500.)
+	16.621174077862747
     """
     Rd   = constants.dry_air_gas_constant
     Rv   = constants.water_vapor_gas_constant