def fitStat(xdata, ydata, p, cov, infodict):
"""
Function fitStat
================
Purpose:
Derive statistical data from least square fit of TUV data for MCM parameterisations.
Variables:
I/O:
xdata,ydata: x-,y-data for curve fit (sza and j values)
p: optimised parameters from least square fit
cov: covariance matrix from least square fit
infodict: further statistical data from least square fit
rsquared: correlation coefficient
ss_tot: standard deviation
rmse: root mean square error
el,em,en: confidence of parameters
internal:
ss_err: for calculation of R2 and RMSE
dof: degrees of freedom for calculation of RMSE
s_sq: for calculation of confidences of parameters
err: list of all confidences
Dependencies:
uses: residuals,datfcn.order,numpy
called from: datfcn.xydat
"""
# load functions
import numpy as np
from datfcn import order
# R2:
ss_err = (infodict['fvec']**2).sum()
ss_tot = ((ydata - ydata.mean())**2).sum()
rsquared = 1 - (ss_err / ss_tot)
# RMSE:
dof = len(xdata) - len(p)
rmse = np.sqrt(ss_err / dof)
# Confidence:
if (len(ydata) > len(p)) and cov is not None:
s_sq = (residuals(p, xdata, ydata)**2).sum() / (len(ydata) - len(p))
cov = cov * s_sq
else:
cov = inf
err = np.sqrt(np.diag(cov))
el = err[0] / order(p[0])[1]
em = err[1]
en = err[2]
return rsquared, ss_tot, rmse, el, em, en
#______________________________________________________________________________________________
def gpscat(gpfile, rxn, data):
"""
Function gnuinp
===============
Purpose:
Write gnuplot input file with data for scatter plots of TUV data.
Variables:
I/O:
gpfile: gnuplot file with data for scatter plots
rxn: matrix with indices and labels of available photoreactions
data: matrix with sza-dependent j values from TUV model
om: matrix with all orders of magnitudes (for sza column 0 dummy inserted)
internal:
h,x,y: counters/indices
o1,o2: order of magnitude of maximum value in each j data column
Dependencies:
uses: numpy, datfcn.order
called from: photMCM (main)
"""
# initilise data
import numpy as np
from datfcn import order
om = []
# open text file
with open(gpfile, 'w+') as gnu:
# write header
gnu.write("# sza / rad ")
for h in range(len(rxn)):
gnu.write("\t%s" % (rxn[h][1]))
gnu.write("\n")
# determine order of magnitude from maximum (first) value
# for nicer output
for y in range(len(rxn)):
o1, o2 = order(data[0][y + 1])
om = np.append(om, o2)
om = np.insert(om, 0, 1.)
# write data matrix
for x in range(len(data)):
for y in range(len(rxn) + 1):
if (y == 0):
data[x][0] = np.deg2rad(data[x][0])
gnu.write("\t%.3f" % (data[x][y] / om[y]))
gnu.write("\n")
return rxn, data, om
def fitTUV(xdata, ydata):
"""
Function fitTUV
===============
Purpose:
Curve fit of TUV data to parameterisation for photolysis in MCM.8///////////////////8=74
j = l*(cos(x))^m*exp(-n*sec(x))
Variables:
I/O:
xdata,ydata: x-,y-data for curve fit (sza and j values)
p: optimised parameters from least square fit
cov: covariance matrix from least square fit
infodict: further statistical data from least square fit
mesg, ier: not used (see description of leastsq function)
internal:
Param list with parameters for curve fitting
p_guess: initial parameters for curve fit
Dependencies:
uses: residuals,numpy,scipy.optimize.leastsq, collections.namedtuple
called from: datfcn.xydat
"""
# load functions
import numpy as np
import collections #
from scipy.optimize import leastsq # for curve fit
from datfcn import order
# curve fitting
Param = collections.namedtuple('Param', 'l m n')
p_guess = Param(l=ydata[0] * np.exp(-0.8), m=0.8, n=0.25)
p, cov, infodict, mesg, ier = leastsq(residuals,
p_guess,
args=(xdata, ydata),
full_output=True)
p = Param(*p)
l = p[0]
ol, ml = order(l)
l = l / ml
m = p[1]
n = p[2]
return p, l, ol, m, n, cov, infodict
def scatdat(rxn, data):
"""
Function scatdat
================
Purpose:
Derive matrix with plot data and vector with associated photoreactions.
Variables:
I/O
rxn: matrix with indices and labels of available photoreactions
data: matrix with sza-dependent j values from TUV model
om: matrix with all orders of magnitudes (for sza column 0 dummy inserted)
internal:
h,x,y: counters/indices
o1,o2: order of magnitude of maximum value in each j data column
Dependencies:
uses: numpy, datfcn.order
called from: photMCM (main)
"""
# initilise data
import numpy as np
from datfcn import order
om = []
# determine order of magnitude from maximum (first) value for nicer output
for y in range(len(rxn)):
o1, o2 = order(data[0][y + 1])
om = np.append(om, o2)
om = np.insert(om, 0, 1.)
# write data matrix
for x in range(len(data)):
for y in range(len(rxn) + 1):
if (y == 0):
data[x][0] = np.deg2rad(data[x][0])
return rxn, data, om