#Tables and functions for doing polynomial fit to OLR(rh, CO2,T)

from ClimateUtilities import * # needed for polint and interpolation object
import math

#%-------------Table:Cubic fit to (T-275)----------------------------------------------------
#%**Layout: Make sure this table comes after the corresponding figure
#%Y = M0 + M1*x + ... M8*x\u8\n + M9*x\u9
#\begin{table}
#\begin{tabular}{lcccc}
#$CO_2$ , $a_o$   , $a_1$  , $a_2$      ,  $a_3$     \\
CO2Vals = [10.,100.,1000.,10000.,100000.]
logCO2Vals = [math.log(co2) for co2 in CO2Vals]
fitTcoeffs = []
#10ppmv
fitTcoeffs.append([ 258.56, 2.5876,-0.0059165,-0.00013402])
#100ppmv 
fitTcoeffs.append([246.13, 2.5056,-0.0034095,-0.00010672 ])
#1000ppmv
fitTcoeffs.append([232.51, 2.3815,-0.0015855 ,-8.3397e-05])
#10000ppmv
fitTcoeffs.append([ 215.74,2.1915,0.00056634,-5.0508e-05])
#100000ppmv
fitTcoeffs.append([189.06,1.8554,0.0044094,1.0735e-05])
#\end{tabular}
#\caption{Coefficients for polynomial fit $OLR = a_o + a_1 x + a_2 x^2 + a_3 x^3$,
#where $x = T_g - 275$. Calculation carried out with $rh = .5$.}
#\label{table:OLRvsTfit}
#\end{table}
#%---------------------------------------------------------------------------------------------

#%--------Table:Cubic fit to ln(co2/300)-------------------------------------------------------
#%**Layout: Make sure this table comes after the corresponding figure
#\begin{table}
#\begin{tabular}{lcccc}
#$rh$      , $a_o$   , $a_1$  , $a_2$    ,  $a_3$     \\
rhVals = [0.,.1,.5,1.]
fitCO2coeffs = []
#Dry
fitCO2coeffs.append([313.8,-6.275,-0.36107 ,-0.019467])
 #.1
fitCO2coeffs.append([277.28,-5.9416 ,-0.35596 ,-0.020237])
 #.5
fitCO2coeffs.append([259.52,-5.5332 ,-0.33915 ,-0.018932])
#Saturated
fitCO2coeffs.append([249.1,-5.183,-0.32187,-0.017367])
#\end{tabular}
#\caption{Coefficients for polynomial fit $OLR = a_o + a_1 x + a_2 x^2 + a_3 x^3$,
#where $x = \ln (CO_2/100)$, with $CO_2$ in $ppmv$. Calculation carried out with $T_g = 280K$ for
#the indicated moisture conditions.}
#\label{table:OLRvsCO2fit}
#\end{table}
#%------------------------------------------------------------

#Utility to evaluate polynomial
def evalPoly(coeffs,x):
    sum = coeffs[-1]
    for i in range(2,len(coeffs)+1):
        sum = x*sum + coeffs[-i]
    return sum

#CO2 in ppmv
def OLRT(CO2,T):
    x = T-275.
    y = math.log(CO2)
    #interpolate coefficients
    coeffs = []
    for i in range(len(fitTcoeffs[0])):
        a = [fitTcoeffs[j][i] for j in range(len(logCO2Vals))]
        coeffs.append(polint(logCO2Vals,a,y))
    #Evaluate the polynomial
    return evalPoly(coeffs,x)

#CO2 in ppmv
def OLRCO2(rh,CO2):
    x = math.log(CO2/100.)
    y = rh #Note, some kind of log-linear fit would be better
    #interpolate coefficients
    coeffs = []
    for i in range(len(fitCO2coeffs[0])):
        a = [fitCO2coeffs[j][i] for j in range(len(rhVals))]
        coeffs.append(polint(rhVals,a,y))
    #Evaluate the polynomial
    #print coeffs
    return evalPoly(coeffs,x)

co2List = [10.**(i/4.) for i in range(21)]
olr = [OLRT(co2,280.) for co2 in co2List]