"""
The ``clearsky`` module contains several methods
to calculate clear sky GHI, DNI, and DHI.
"""
from __future__ import division
import logging
logger = logging.getLogger('pvlib')
import os
import numpy as np
import pandas as pd
from pvlib import tools
from pvlib import irradiance
from pvlib import atmosphere
from pvlib import solarposition
[docs]def ineichen(time, location, linke_turbidity=None,
solarposition_method='pyephem', zenith_data=None,
airmass_model='young1994', airmass_data=None,
interp_turbidity=True):
'''
Determine clear sky GHI, DNI, and DHI from Ineichen/Perez model
Implements the Ineichen and Perez clear sky model for global horizontal
irradiance (GHI), direct normal irradiance (DNI), and calculates
the clear-sky diffuse horizontal (DHI) component as the difference
between GHI and DNI*cos(zenith) as presented in [1, 2]. A report on clear
sky models found the Ineichen/Perez model to have excellent performance
with a minimal input data set [3].
Default values for montly Linke turbidity provided by SoDa [4, 5].
Parameters
-----------
time : pandas.DatetimeIndex
location : pvlib.Location
linke_turbidity : None or float
If None, uses ``LinkeTurbidities.mat`` lookup table.
solarposition_method : string
Sets the solar position algorithm.
See solarposition.get_solarposition()
zenith_data : None or pandas.Series
If None, ephemeris data will be calculated using ``solarposition_method``.
airmass_model : string
See pvlib.airmass.relativeairmass().
airmass_data : None or pandas.Series
If None, absolute air mass data will be calculated using
``airmass_model`` and location.alitude.
interp_turbidity : bool
If ``True``, interpolates the monthly Linke turbidity values
found in ``LinkeTurbidities.mat`` to daily values.
Returns
--------
DataFrame with the following columns: ``GHI, DNI, DHI``.
Notes
-----
If you are using this function
in a loop, it may be faster to load LinkeTurbidities.mat outside of
the loop and feed it in as a variable, rather than
having the function open the file each time it is called.
References
----------
[1] P. Ineichen and R. Perez, "A New airmass independent formulation for
the Linke turbidity coefficient", Solar Energy, vol 73, pp. 151-157, 2002.
[2] R. Perez et. al., "A New Operational Model for Satellite-Derived
Irradiances: Description and Validation", Solar Energy, vol 73, pp.
307-317, 2002.
[3] M. Reno, C. Hansen, and J. Stein, "Global Horizontal Irradiance Clear
Sky Models: Implementation and Analysis", Sandia National
Laboratories, SAND2012-2389, 2012.
[4] http://www.soda-is.com/eng/services/climat_free_eng.php#c5 (obtained
July 17, 2012).
[5] J. Remund, et. al., "Worldwide Linke Turbidity Information", Proc.
ISES Solar World Congress, June 2003. Goteborg, Sweden.
'''
# Initial implementation of this algorithm by Matthew Reno.
# Ported to python by Rob Andrews
# Added functionality by Will Holmgren
I0 = irradiance.extraradiation(time.dayofyear)
if zenith_data is None:
ephem_data = solarposition.get_solarposition(time, location,
method=solarposition_method)
time = ephem_data.index # fixes issue with time possibly not being tz-aware
try:
ApparentZenith = ephem_data['apparent_zenith']
except KeyError:
ApparentZenith = ephem_data['zenith']
logger.warning('could not find apparent_zenith. using zenith')
else:
ApparentZenith = zenith_data
#ApparentZenith[ApparentZenith >= 90] = 90 # can cause problems in edge cases
if linke_turbidity is None:
# The .mat file 'LinkeTurbidities.mat' contains a single 2160 x 4320 x 12
# matrix of type uint8 called 'LinkeTurbidity'. The rows represent global
# latitudes from 90 to -90 degrees; the columns represent global longitudes
# from -180 to 180; and the depth (third dimension) represents months of
# the year from January (1) to December (12). To determine the Linke
# turbidity for a position on the Earth's surface for a given month do the
# following: LT = LinkeTurbidity(LatitudeIndex, LongitudeIndex, month).
# Note that the numbers within the matrix are 20 * Linke Turbidity,
# so divide the number from the file by 20 to get the
# turbidity.
try:
import scipy.io
except ImportError:
raise ImportError('The Linke turbidity lookup table requires scipy. ' +
'You can still use clearsky.ineichen if you ' +
'supply your own turbidities.')
# consider putting this code at module level
this_path = os.path.dirname(os.path.abspath(__file__))
logger.debug('this_path={}'.format(this_path))
mat = scipy.io.loadmat(os.path.join(this_path, 'data', 'LinkeTurbidities.mat'))
linke_turbidity = mat['LinkeTurbidity']
LatitudeIndex = np.round_(_linearly_scale(location.latitude,90,- 90,1,2160))
LongitudeIndex = np.round_(_linearly_scale(location.longitude,- 180,180,1,4320))
g = linke_turbidity[LatitudeIndex][LongitudeIndex]
if interp_turbidity:
logger.info('interpolating turbidity to the day')
g2 = np.concatenate([[g[-1]], g, [g[0]]]) # wrap ends around
days = np.linspace(-15, 380, num=14) # map day of year onto month (approximate)
LT = pd.Series(np.interp(time.dayofyear, days, g2), index=time)
else:
logger.info('using monthly turbidity')
ApplyMonth = lambda x:g[x[0]-1]
LT = pd.DataFrame(time.month, index=time)
LT = LT.apply(ApplyMonth, axis=1)
TL = LT / 20.
logger.info('using TL=\n{}'.format(TL))
else:
TL = linke_turbidity
# Get the absolute airmass assuming standard local pressure (per
# alt2pres) using Kasten and Young's 1989 formula for airmass.
if airmass_data is None:
AMabsolute = atmosphere.absoluteairmass(AMrelative=atmosphere.relativeairmass(ApparentZenith, airmass_model),
pressure=atmosphere.alt2pres(location.altitude))
else:
AMabsolute = airmass_data
fh1 = np.exp(-location.altitude/8000.)
fh2 = np.exp(-location.altitude/1250.)
cg1 = 5.09e-05 * location.altitude + 0.868
cg2 = 3.92e-05 * location.altitude + 0.0387
logger.debug('fh1={}, fh2={}, cg1={}, cg2={}'.format(fh1, fh2, cg1, cg2))
# Dan's note on the TL correction: By my reading of the publication on
# pages 151-157, Ineichen and Perez introduce (among other things) three
# things. 1) Beam model in eqn. 8, 2) new turbidity factor in eqn 9 and
# appendix A, and 3) Global horizontal model in eqn. 11. They do NOT appear
# to use the new turbidity factor (item 2 above) in either the beam or GHI
# models. The phrasing of appendix A seems as if there are two separate
# corrections, the first correction is used to correct the beam/GHI models,
# and the second correction is used to correct the revised turibidity
# factor. In my estimation, there is no need to correct the turbidity
# factor used in the beam/GHI models.
# Create the corrected TL for TL < 2
# TLcorr = TL;
# TLcorr(TL < 2) = TLcorr(TL < 2) - 0.25 .* (2-TLcorr(TL < 2)) .^ (0.5);
# This equation is found in Solar Energy 73, pg 311.
# Full ref: Perez et. al., Vol. 73, pp. 307-317 (2002).
# It is slightly different than the equation given in Solar Energy 73, pg 156.
# We used the equation from pg 311 because of the existence of known typos
# in the pg 156 publication (notably the fh2-(TL-1) should be fh2 * (TL-1)).
cos_zenith = tools.cosd(ApparentZenith)
clearsky_GHI = cg1 * I0 * cos_zenith * np.exp(-cg2*AMabsolute*(fh1 + fh2*(TL - 1))) * np.exp(0.01*AMabsolute**1.8)
clearsky_GHI[clearsky_GHI < 0] = 0
# BncI == "normal beam clear sky radiation"
b = 0.664 + 0.163/fh1
BncI = b * I0 * np.exp( -0.09 * AMabsolute * (TL - 1) )
logger.debug('b={}'.format(b))
# "empirical correction" SE 73, 157 & SE 73, 312.
BncI_2 = clearsky_GHI * ( 1 - (0.1 - 0.2*np.exp(-TL))/(0.1 + 0.882/fh1) ) / cos_zenith
#return BncI, BncI_2
clearsky_DNI = np.minimum(BncI, BncI_2) # Will H: use np.minimum explicitly
clearsky_DHI = clearsky_GHI - clearsky_DNI*cos_zenith
df_out = pd.DataFrame({'GHI':clearsky_GHI, 'DNI':clearsky_DNI,
'DHI':clearsky_DHI})
df_out.fillna(0, inplace=True)
#df_out['BncI'] = BncI
#df_out['BncI_2'] = BncI
return df_out
[docs]def haurwitz(ApparentZenith):
'''
Determine clear sky GHI from Haurwitz model
Implements the Haurwitz clear sky model for global horizontal
irradiance (GHI) as presented in [1, 2]. A report on clear
sky models found the Haurwitz model to have the best performance of
models which require only zenith angle [3]. Extreme care should
be taken in the interpretation of this result!
Parameters
----------
ApparentZenith : DataFrame
The apparent (refraction corrected) sun zenith angle
in degrees.
Returns
-------
pd.Series
The modeled global horizonal irradiance in W/m^2 provided
by the Haurwitz clear-sky model.
Initial implementation of this algorithm by Matthew Reno.
References
----------
[1] B. Haurwitz, "Insolation in Relation to Cloudiness and Cloud
Density," Journal of Meteorology, vol. 2, pp. 154-166, 1945.
[2] B. Haurwitz, "Insolation in Relation to Cloud Type," Journal of
Meteorology, vol. 3, pp. 123-124, 1946.
[3] M. Reno, C. Hansen, and J. Stein, "Global Horizontal Irradiance Clear
Sky Models: Implementation and Analysis", Sandia National
Laboratories, SAND2012-2389, 2012.
'''
cos_zenith = tools.cosd(ApparentZenith)
clearsky_GHI = 1098.0 * cos_zenith * np.exp(-0.059/cos_zenith)
clearsky_GHI[clearsky_GHI < 0] = 0
df_out = pd.DataFrame({'GHI':clearsky_GHI})
return df_out
def _linearly_scale(inputmatrix, inputmin, inputmax, outputmin, outputmax):
""" used by linke turbidity lookup function """
inputrange = inputmax - inputmin
outputrange = outputmax - outputmin
OutputMatrix = (inputmatrix - inputmin) * outputrange / inputrange + outputmin
return OutputMatrix
[docs]def disc(GHI, zenith, times, pressure=101325):
'''
Estimate Direct Normal Irradiance from Global Horizontal Irradiance
using the DISC model.
The DISC algorithm converts global horizontal irradiance to direct
normal irradiance through empirical relationships between the global
and direct clearness indices.
Parameters
----------
GHI : Series
Global horizontal irradiance in W/m^2.
zenith : Series
True (not refraction - corrected) solar zenith
angles in decimal degrees.
times : DatetimeIndex
pressure : float or Series
Site pressure in Pascal.
Returns
-------
DataFrame with the following keys:
* ``DNI_gen_DISC``: The modeled direct normal irradiance
in W/m^2 provided by the
Direct Insolation Simulation Code (DISC) model.
* ``Kt_gen_DISC``: Ratio of global to extraterrestrial
irradiance on a horizontal plane.
* ``AM``: Airmass
References
----------
[1] Maxwell, E. L., "A Quasi-Physical Model for Converting Hourly
Global Horizontal to Direct Normal Insolation", Technical
Report No. SERI/TR-215-3087, Golden, CO: Solar Energy Research
Institute, 1987.
[2] J.W. "Fourier series representation of the position of the sun".
Found at:
http://www.mail-archive.com/sundial@uni-koeln.de/msg01050.html on
January 12, 2012
See Also
--------
atmosphere.alt2pres
dirint
'''
logger.debug('clearsky.disc')
temp = pd.DataFrame(index=times, columns=['A','B','C'], dtype=float)
doy = times.dayofyear
DayAngle = 2. * np.pi*(doy - 1) / 365
re = (1.00011 + 0.034221*np.cos(DayAngle) + 0.00128*np.sin(DayAngle)
+ 0.000719*np.cos(2.*DayAngle) + 7.7e-05*np.sin(2.*DayAngle) )
I0 = re * 1370.
I0h = I0 * np.cos(np.radians(zenith))
Ztemp = zenith.copy()
Ztemp[zenith > 87] = np.NaN
AM = 1.0 / ( np.cos(np.radians(Ztemp)) + 0.15*( (93.885 - Ztemp)**(-1.253) ) ) * (pressure / 101325)
Kt = GHI / I0h
Kt[Kt < 0] = 0
Kt[Kt > 2] = np.NaN
temp.A[Kt > 0.6] = -5.743 + 21.77*(Kt[Kt > 0.6]) - 27.49*(Kt[Kt > 0.6] ** 2) + 11.56*(Kt[Kt > 0.6] ** 3)
temp.B[Kt > 0.6] = 41.4 - 118.5*(Kt[Kt > 0.6]) + 66.05*(Kt[Kt > 0.6] ** 2) + 31.9*(Kt[Kt > 0.6] ** 3)
temp.C[Kt > 0.6] = -47.01 + 184.2*(Kt[Kt > 0.6]) - 222.0 * Kt[Kt > 0.6] ** 2 + 73.81*(Kt[Kt > 0.6] ** 3)
temp.A[Kt <= 0.6] = 0.512 - 1.56*(Kt[Kt <= 0.6]) + 2.286*(Kt[Kt <= 0.6] ** 2) - 2.222*(Kt[Kt <= 0.6] ** 3)
temp.B[Kt <= 0.6] = 0.37 + 0.962*(Kt[Kt <= 0.6])
temp.C[Kt <= 0.6] = -0.28 + 0.932*(Kt[Kt <= 0.6]) - 2.048*(Kt[Kt <= 0.6] ** 2)
delKn = temp.A + temp.B * np.exp(temp.C*AM)
Knc = 0.866 - 0.122*(AM) + 0.0121*(AM ** 2) - 0.000653*(AM ** 3) + 1.4e-05*(AM ** 4)
Kn = Knc - delKn
DNI = Kn * I0
DNI[zenith > 87] = np.NaN
DNI[(GHI < 0) | (DNI < 0)] = 0
DFOut = pd.DataFrame({'DNI_gen_DISC':DNI})
DFOut['Kt_gen_DISC'] = Kt
DFOut['AM'] = AM
return DFOut
[docs]def dirint(ghi, zenith, times, pressure=101325, use_delta_kt_prime=True,
temp_dew=None):
"""
Determine DNI from GHI using the DIRINT modification
of the DISC model.
Implements the modified DISC model known as "DIRINT" introduced in [1].
DIRINT predicts direct normal irradiance (DNI) from measured global
horizontal irradiance (GHI). DIRINT improves upon the DISC model by
using time-series GHI data and dew point temperature information. The
effectiveness of the DIRINT model improves with each piece of
information provided.
Parameters
----------
ghi : pd.Series
Global horizontal irradiance in W/m^2.
zenith : pd.Series
True (not refraction-corrected) zenith
angles in decimal degrees. If Z is a vector it must be of the
same size as all other vector inputs. Z must be >=0 and <=180.
times : DatetimeIndex
pressure : float or pd.Series
The site pressure in Pascal.
Pressure may be measured or an average pressure may be
calculated from site altitude.
use_delta_kt_prime : bool
Indicates if the user would like to
utilize the time-series nature of the GHI measurements. A value of ``False``
will not use the time-series improvements, any other numeric value
will use time-series improvements. It is recommended that time-series
data only be used if the time between measured data points is less
than 1.5 hours. If none of the input arguments are
vectors, then time-series improvements are not used (because it's not
a time-series).
temp_dew : None, float, or pd.Series
Surface dew point temperatures, in degrees C.
Values of temp_dew may be numeric or NaN. Any
single time period point with a DewPtTemp=NaN does not have dew point
improvements applied. If DewPtTemp is not provided, then dew point
improvements are not applied.
Returns
-------
pd.Series. The modeled direct normal irradiance in W/m^2 provided by the
DIRINT model.
References
----------
[1] Perez, R., P. Ineichen, E. Maxwell, R. Seals and A. Zelenka, (1992).
"Dynamic Global-to-Direct Irradiance Conversion Models". ASHRAE
Transactions-Research Series, pp. 354-369
[2] Maxwell, E. L., "A Quasi-Physical Model for Converting Hourly
Global Horizontal to Direct Normal Insolation", Technical
Report No. SERI/TR-215-3087, Golden, CO: Solar Energy Research
Institute, 1987.
DIRINT model requires time series data (ie. one of the inputs must be a
vector of length >2.
"""
logger.debug('clearsky.dirint')
disc_out = disc(ghi, zenith, times)
kt = disc_out['Kt_gen_DISC']
# Absolute Airmass, per the DISC model
# Note that we calculate the AM pressure correction slightly differently
# than Perez. He uses altitude, we use pressure (which we calculate
# slightly differently)
airmass = (1./(tools.cosd(zenith) + 0.15*((93.885-zenith)**(-1.253))) *
pressure/101325)
coeffs = _get_dirint_coeffs()
kt_prime = kt / (1.031 * np.exp(-1.4/(0.9+9.4/airmass)) + 0.1)
kt_prime[kt_prime > 0.82] = 0.82 # From SRRL code. consider np.NaN
kt_prime.fillna(0, inplace=True)
logger.debug('kt_prime:\n{}'.format(kt_prime))
# wholmgren:
# the use_delta_kt_prime statement is a port of the MATLAB code.
# I am confused by the abs() in the delta_kt_prime calculation.
# It is not the absolute value of the central difference.
if use_delta_kt_prime:
delta_kt_prime = 0.5*( (kt_prime - kt_prime.shift(1)).abs()
.add(
(kt_prime - kt_prime.shift(-1)).abs(),
fill_value=0))
else:
delta_kt_prime = pd.Series(-1, index=times)
if temp_dew is not None:
w = pd.Series(np.exp(0.07 * temp_dew - 0.075), index=times)
else:
w = pd.Series(-1, index=times)
# @wholmgren: the following bin assignments use MATLAB's 1-indexing.
# Later, we'll subtract 1 to conform to Python's 0-indexing.
# Create kt_prime bins
kt_prime_bin = pd.Series(index=times)
kt_prime_bin[(kt_prime>=0) & (kt_prime<0.24)] = 1
kt_prime_bin[(kt_prime>=0.24) & (kt_prime<0.4)] = 2
kt_prime_bin[(kt_prime>=0.4) & (kt_prime<0.56)] = 3
kt_prime_bin[(kt_prime>=0.56) & (kt_prime<0.7)] = 4
kt_prime_bin[(kt_prime>=0.7) & (kt_prime<0.8)] = 5
kt_prime_bin[(kt_prime>=0.8) & (kt_prime<=1)] = 6
logger.debug('kt_prime_bin:\n{}'.format(kt_prime_bin))
# Create zenith angle bins
zenith_bin = pd.Series(index=times)
zenith_bin[(zenith>=0) & (zenith<25)] = 1
zenith_bin[(zenith>=25) & (zenith<40)] = 2
zenith_bin[(zenith>=40) & (zenith<55)] = 3
zenith_bin[(zenith>=55) & (zenith<70)] = 4
zenith_bin[(zenith>=70) & (zenith<80)] = 5
zenith_bin[(zenith>=80)] = 6
logger.debug('zenith_bin:\n{}'.format(zenith_bin))
# Create the bins for w based on dew point temperature
w_bin = pd.Series(index=times)
w_bin[(w>=0) & (w<1)] = 1
w_bin[(w>=1) & (w<2)] = 2
w_bin[(w>=2) & (w<3)] = 3
w_bin[(w>=3)] = 4
w_bin[(w == -1)] = 5
logger.debug('w_bin:\n{}'.format(w_bin))
# Create delta_kt_prime binning.
delta_kt_prime_bin = pd.Series(index=times)
delta_kt_prime_bin[(delta_kt_prime>=0) & (delta_kt_prime<0.015)] = 1
delta_kt_prime_bin[(delta_kt_prime>=0.015) & (delta_kt_prime<0.035)] = 2
delta_kt_prime_bin[(delta_kt_prime>=0.035) & (delta_kt_prime<0.07)] = 3
delta_kt_prime_bin[(delta_kt_prime>=0.07) & (delta_kt_prime<0.15)] = 4
delta_kt_prime_bin[(delta_kt_prime>=0.15) & (delta_kt_prime<0.3)] = 5
delta_kt_prime_bin[(delta_kt_prime>=0.3) & (delta_kt_prime<=1)] = 6
delta_kt_prime_bin[delta_kt_prime == -1] = 7
logger.debug('delta_kt_prime_bin:\n{}'.format(delta_kt_prime_bin))
# subtract 1 to account for difference between MATLAB-style bin
# assignment and Python-style array lookup.
dirint_coeffs = coeffs[kt_prime_bin-1, zenith_bin-1,
delta_kt_prime_bin-1, w_bin-1]
dni = disc_out['DNI_gen_DISC'] * dirint_coeffs
dni.name = 'DNI_DIRINT'
return dni
def _get_dirint_coeffs():
"""
A place to stash the dirint coefficients.
Returns
-------
np.array with shape ``(6, 6, 7, 5)``.
Ordering is ``[kt_prime_bin, zenith_bin, delta_kt_prime_bin, w_bin]``
"""
# To allow for maximum copy/paste from the MATLAB 1-indexed code,
# we create and assign values to an oversized array.
# Then, we return the [1:, 1:, :, :] slice.
coeffs = np.zeros((7,7,7,5))
coeffs[1,1,:,:] = [
[0.385230, 0.385230, 0.385230, 0.462880, 0.317440],
[0.338390, 0.338390, 0.221270, 0.316730, 0.503650],
[0.235680, 0.235680, 0.241280, 0.157830, 0.269440],
[0.830130, 0.830130, 0.171970, 0.841070, 0.457370],
[0.548010, 0.548010, 0.478000, 0.966880, 1.036370],
[0.548010, 0.548010, 1.000000, 3.012370, 1.976540],
[0.582690, 0.582690, 0.229720, 0.892710, 0.569950 ]]
coeffs[1,2,:,:] = [
[0.131280, 0.131280, 0.385460, 0.511070, 0.127940],
[0.223710, 0.223710, 0.193560, 0.304560, 0.193940],
[0.229970, 0.229970, 0.275020, 0.312730, 0.244610],
[0.090100, 0.184580, 0.260500, 0.687480, 0.579440],
[0.131530, 0.131530, 0.370190, 1.380350, 1.052270],
[1.116250, 1.116250, 0.928030, 3.525490, 2.316920],
[0.090100, 0.237000, 0.300040, 0.812470, 0.664970 ]]
coeffs[1,3,:,:] = [
[0.587510, 0.130000, 0.400000, 0.537210, 0.832490],
[0.306210, 0.129830, 0.204460, 0.500000, 0.681640],
[0.224020, 0.260620, 0.334080, 0.501040, 0.350470],
[0.421540, 0.753970, 0.750660, 3.706840, 0.983790],
[0.706680, 0.373530, 1.245670, 0.864860, 1.992630],
[4.864400, 0.117390, 0.265180, 0.359180, 3.310820],
[0.392080, 0.493290, 0.651560, 1.932780, 0.898730 ]]
coeffs[1,4,:,:] = [
[0.126970, 0.126970, 0.126970, 0.126970, 0.126970],
[0.810820, 0.810820, 0.810820, 0.810820, 0.810820],
[3.241680, 2.500000, 2.291440, 2.291440, 2.291440],
[4.000000, 3.000000, 2.000000, 0.975430, 1.965570],
[12.494170, 12.494170, 8.000000, 5.083520, 8.792390],
[21.744240, 21.744240, 21.744240, 21.744240, 21.744240],
[3.241680, 12.494170, 1.620760, 1.375250, 2.331620 ]]
coeffs[1,5,:,:] = [
[0.126970, 0.126970, 0.126970, 0.126970, 0.126970],
[0.810820, 0.810820, 0.810820, 0.810820, 0.810820],
[3.241680, 2.500000, 2.291440, 2.291440, 2.291440],
[4.000000, 3.000000, 2.000000, 0.975430, 1.965570],
[12.494170, 12.494170, 8.000000, 5.083520, 8.792390],
[21.744240, 21.744240, 21.744240, 21.744240, 21.744240],
[3.241680, 12.494170, 1.620760, 1.375250, 2.331620 ]]
coeffs[1,6,:,:] = [
[0.126970, 0.126970, 0.126970, 0.126970, 0.126970],
[0.810820, 0.810820, 0.810820, 0.810820, 0.810820],
[3.241680, 2.500000, 2.291440, 2.291440, 2.291440],
[4.000000, 3.000000, 2.000000, 0.975430, 1.965570],
[12.494170, 12.494170, 8.000000, 5.083520, 8.792390],
[21.744240, 21.744240, 21.744240, 21.744240, 21.744240],
[3.241680, 12.494170, 1.620760, 1.375250, 2.331620 ]]
coeffs[2,1,:,:] = [
[0.337440, 0.337440, 0.969110, 1.097190, 1.116080],
[0.337440, 0.337440, 0.969110, 1.116030, 0.623900],
[0.337440, 0.337440, 1.530590, 1.024420, 0.908480],
[0.584040, 0.584040, 0.847250, 0.914940, 1.289300],
[0.337440, 0.337440, 0.310240, 1.435020, 1.852830],
[0.337440, 0.337440, 1.015010, 1.097190, 2.117230],
[0.337440, 0.337440, 0.969110, 1.145730, 1.476400 ]]
coeffs[2,2,:,:] = [
[0.300000, 0.300000, 0.700000, 1.100000, 0.796940],
[0.219870, 0.219870, 0.526530, 0.809610, 0.649300],
[0.386650, 0.386650, 0.119320, 0.576120, 0.685460],
[0.746730, 0.399830, 0.470970, 0.986530, 0.785370],
[0.575420, 0.936700, 1.649200, 1.495840, 1.335590],
[1.319670, 4.002570, 1.276390, 2.644550, 2.518670],
[0.665190, 0.678910, 1.012360, 1.199940, 0.986580 ]]
coeffs[2,3,:,:] = [
[0.378870, 0.974060, 0.500000, 0.491880, 0.665290],
[0.105210, 0.263470, 0.407040, 0.553460, 0.582590],
[0.312900, 0.345240, 1.144180, 0.854790, 0.612280],
[0.119070, 0.365120, 0.560520, 0.793720, 0.802600],
[0.781610, 0.837390, 1.270420, 1.537980, 1.292950],
[1.152290, 1.152290, 1.492080, 1.245370, 2.177100],
[0.424660, 0.529550, 0.966910, 1.033460, 0.958730 ]]
coeffs[2,4,:,:] = [
[0.310590, 0.714410, 0.252450, 0.500000, 0.607600],
[0.975190, 0.363420, 0.500000, 0.400000, 0.502800],
[0.175580, 0.196250, 0.476360, 1.072470, 0.490510],
[0.719280, 0.698620, 0.657770, 1.190840, 0.681110],
[0.426240, 1.464840, 0.678550, 1.157730, 0.978430],
[2.501120, 1.789130, 1.387090, 2.394180, 2.394180],
[0.491640, 0.677610, 0.685610, 1.082400, 0.735410 ]]
coeffs[2,5,:,:] = [
[0.597000, 0.500000, 0.300000, 0.310050, 0.413510],
[0.314790, 0.336310, 0.400000, 0.400000, 0.442460],
[0.166510, 0.460440, 0.552570, 1.000000, 0.461610],
[0.401020, 0.559110, 0.403630, 1.016710, 0.671490],
[0.400360, 0.750830, 0.842640, 1.802600, 1.023830],
[3.315300, 1.510380, 2.443650, 1.638820, 2.133990],
[0.530790, 0.745850, 0.693050, 1.458040, 0.804500 ]]
coeffs[2,6,:,:] = [
[0.597000, 0.500000, 0.300000, 0.310050, 0.800920],
[0.314790, 0.336310, 0.400000, 0.400000, 0.237040],
[0.166510, 0.460440, 0.552570, 1.000000, 0.581990],
[0.401020, 0.559110, 0.403630, 1.016710, 0.898570],
[0.400360, 0.750830, 0.842640, 1.802600, 3.400390],
[3.315300, 1.510380, 2.443650, 1.638820, 2.508780],
[0.204340, 1.157740, 2.003080, 2.622080, 1.409380 ]]
coeffs[3,1,:,:] = [
[1.242210, 1.242210, 1.242210, 1.242210, 1.242210],
[0.056980, 0.056980, 0.656990, 0.656990, 0.925160],
[0.089090, 0.089090, 1.040430, 1.232480, 1.205300],
[1.053850, 1.053850, 1.399690, 1.084640, 1.233340],
[1.151540, 1.151540, 1.118290, 1.531640, 1.411840],
[1.494980, 1.494980, 1.700000, 1.800810, 1.671600],
[1.018450, 1.018450, 1.153600, 1.321890, 1.294670 ]]
coeffs[3,2,:,:] = [
[0.700000, 0.700000, 1.023460, 0.700000, 0.945830],
[0.886300, 0.886300, 1.333620, 0.800000, 1.066620],
[0.902180, 0.902180, 0.954330, 1.126690, 1.097310],
[1.095300, 1.075060, 1.176490, 1.139470, 1.096110],
[1.201660, 1.201660, 1.438200, 1.256280, 1.198060],
[1.525850, 1.525850, 1.869160, 1.985410, 1.911590],
[1.288220, 1.082810, 1.286370, 1.166170, 1.119330 ]]
coeffs[3,3,:,:] = [
[0.600000, 1.029910, 0.859890, 0.550000, 0.813600],
[0.604450, 1.029910, 0.859890, 0.656700, 0.928840],
[0.455850, 0.750580, 0.804930, 0.823000, 0.911000],
[0.526580, 0.932310, 0.908620, 0.983520, 0.988090],
[1.036110, 1.100690, 0.848380, 1.035270, 1.042380],
[1.048440, 1.652720, 0.900000, 2.350410, 1.082950],
[0.817410, 0.976160, 0.861300, 0.974780, 1.004580 ]]
coeffs[3,4,:,:] = [
[0.782110, 0.564280, 0.600000, 0.600000, 0.665740],
[0.894480, 0.680730, 0.541990, 0.800000, 0.669140],
[0.487460, 0.818950, 0.841830, 0.872540, 0.709040],
[0.709310, 0.872780, 0.908480, 0.953290, 0.844350],
[0.863920, 0.947770, 0.876220, 1.078750, 0.936910],
[1.280350, 0.866720, 0.769790, 1.078750, 0.975130],
[0.725420, 0.869970, 0.868810, 0.951190, 0.829220 ]]
coeffs[3,5,:,:] = [
[0.791750, 0.654040, 0.483170, 0.409000, 0.597180],
[0.566140, 0.948990, 0.971820, 0.653570, 0.718550],
[0.648710, 0.637730, 0.870510, 0.860600, 0.694300],
[0.637630, 0.767610, 0.925670, 0.990310, 0.847670],
[0.736380, 0.946060, 1.117590, 1.029340, 0.947020],
[1.180970, 0.850000, 1.050000, 0.950000, 0.888580],
[0.700560, 0.801440, 0.961970, 0.906140, 0.823880 ]]
coeffs[3,6,:,:] = [
[0.500000, 0.500000, 0.586770, 0.470550, 0.629790],
[0.500000, 0.500000, 1.056220, 1.260140, 0.658140],
[0.500000, 0.500000, 0.631830, 0.842620, 0.582780],
[0.554710, 0.734730, 0.985820, 0.915640, 0.898260],
[0.712510, 1.205990, 0.909510, 1.078260, 0.885610],
[1.899260, 1.559710, 1.000000, 1.150000, 1.120390],
[0.653880, 0.793120, 0.903320, 0.944070, 0.796130 ]]
coeffs[4,1,:,:] = [
[1.000000, 1.000000, 1.050000, 1.170380, 1.178090],
[0.960580, 0.960580, 1.059530, 1.179030, 1.131690],
[0.871470, 0.871470, 0.995860, 1.141910, 1.114600],
[1.201590, 1.201590, 0.993610, 1.109380, 1.126320],
[1.065010, 1.065010, 0.828660, 0.939970, 1.017930],
[1.065010, 1.065010, 0.623690, 1.119620, 1.132260],
[1.071570, 1.071570, 0.958070, 1.114130, 1.127110 ]]
coeffs[4,2,:,:] = [
[0.950000, 0.973390, 0.852520, 1.092200, 1.096590],
[0.804120, 0.913870, 0.980990, 1.094580, 1.042420],
[0.737540, 0.935970, 0.999940, 1.056490, 1.050060],
[1.032980, 1.034540, 0.968460, 1.032080, 1.015780],
[0.900000, 0.977210, 0.945960, 1.008840, 0.969960],
[0.600000, 0.750000, 0.750000, 0.844710, 0.899100],
[0.926800, 0.965030, 0.968520, 1.044910, 1.032310 ]]
coeffs[4,3,:,:] = [
[0.850000, 1.029710, 0.961100, 1.055670, 1.009700],
[0.818530, 0.960010, 0.996450, 1.081970, 1.036470],
[0.765380, 0.953500, 0.948260, 1.052110, 1.000140],
[0.775610, 0.909610, 0.927800, 0.987800, 0.952100],
[1.000990, 0.881880, 0.875950, 0.949100, 0.893690],
[0.902370, 0.875960, 0.807990, 0.942410, 0.917920],
[0.856580, 0.928270, 0.946820, 1.032260, 0.972990 ]]
coeffs[4,4,:,:] = [
[0.750000, 0.857930, 0.983800, 1.056540, 0.980240],
[0.750000, 0.987010, 1.013730, 1.133780, 1.038250],
[0.800000, 0.947380, 1.012380, 1.091270, 0.999840],
[0.800000, 0.914550, 0.908570, 0.999190, 0.915230],
[0.778540, 0.800590, 0.799070, 0.902180, 0.851560],
[0.680190, 0.317410, 0.507680, 0.388910, 0.646710],
[0.794920, 0.912780, 0.960830, 1.057110, 0.947950 ]]
coeffs[4,5,:,:] = [
[0.750000, 0.833890, 0.867530, 1.059890, 0.932840],
[0.979700, 0.971470, 0.995510, 1.068490, 1.030150],
[0.858850, 0.987920, 1.043220, 1.108700, 1.044900],
[0.802400, 0.955110, 0.911660, 1.045070, 0.944470],
[0.884890, 0.766210, 0.885390, 0.859070, 0.818190],
[0.615680, 0.700000, 0.850000, 0.624620, 0.669300],
[0.835570, 0.946150, 0.977090, 1.049350, 0.979970 ]]
coeffs[4,6,:,:] = [
[0.689220, 0.809600, 0.900000, 0.789500, 0.853990],
[0.854660, 0.852840, 0.938200, 0.923110, 0.955010],
[0.938600, 0.932980, 1.010390, 1.043950, 1.041640],
[0.843620, 0.981300, 0.951590, 0.946100, 0.966330],
[0.694740, 0.814690, 0.572650, 0.400000, 0.726830],
[0.211370, 0.671780, 0.416340, 0.297290, 0.498050],
[0.843540, 0.882330, 0.911760, 0.898420, 0.960210 ]]
coeffs[5,1,:,:] = [
[1.054880, 1.075210, 1.068460, 1.153370, 1.069220],
[1.000000, 1.062220, 1.013470, 1.088170, 1.046200],
[0.885090, 0.993530, 0.942590, 1.054990, 1.012740],
[0.920000, 0.950000, 0.978720, 1.020280, 0.984440],
[0.850000, 0.908500, 0.839940, 0.985570, 0.962180],
[0.800000, 0.800000, 0.810080, 0.950000, 0.961550],
[1.038590, 1.063200, 1.034440, 1.112780, 1.037800 ]]
coeffs[5,2,:,:] = [
[1.017610, 1.028360, 1.058960, 1.133180, 1.045620],
[0.920000, 0.998970, 1.033590, 1.089030, 1.022060],
[0.912370, 0.949930, 0.979770, 1.020420, 0.981770],
[0.847160, 0.935300, 0.930540, 0.955050, 0.946560],
[0.880260, 0.867110, 0.874130, 0.972650, 0.883420],
[0.627150, 0.627150, 0.700000, 0.774070, 0.845130],
[0.973700, 1.006240, 1.026190, 1.071960, 1.017240 ]]
coeffs[5,3,:,:] = [
[1.028710, 1.017570, 1.025900, 1.081790, 1.024240],
[0.924980, 0.985500, 1.014100, 1.092210, 0.999610],
[0.828570, 0.934920, 0.994950, 1.024590, 0.949710],
[0.900810, 0.901330, 0.928830, 0.979570, 0.913100],
[0.761030, 0.845150, 0.805360, 0.936790, 0.853460],
[0.626400, 0.546750, 0.730500, 0.850000, 0.689050],
[0.957630, 0.985480, 0.991790, 1.050220, 0.987900 ]]
coeffs[5,4,:,:] = [
[0.992730, 0.993880, 1.017150, 1.059120, 1.017450],
[0.975610, 0.987160, 1.026820, 1.075440, 1.007250],
[0.871090, 0.933190, 0.974690, 0.979840, 0.952730],
[0.828750, 0.868090, 0.834920, 0.905510, 0.871530],
[0.781540, 0.782470, 0.767910, 0.764140, 0.795890],
[0.743460, 0.693390, 0.514870, 0.630150, 0.715660],
[0.934760, 0.957870, 0.959640, 0.972510, 0.981640 ]]
coeffs[5,5,:,:] = [
[0.965840, 0.941240, 0.987100, 1.022540, 1.011160],
[0.988630, 0.994770, 0.976590, 0.950000, 1.034840],
[0.958200, 1.018080, 0.974480, 0.920000, 0.989870],
[0.811720, 0.869090, 0.812020, 0.850000, 0.821050],
[0.682030, 0.679480, 0.632450, 0.746580, 0.738550],
[0.668290, 0.445860, 0.500000, 0.678920, 0.696510],
[0.926940, 0.953350, 0.959050, 0.876210, 0.991490 ]]
coeffs[5,6,:,:] = [
[0.948940, 0.997760, 0.850000, 0.826520, 0.998470],
[1.017860, 0.970000, 0.850000, 0.700000, 0.988560],
[1.000000, 0.950000, 0.850000, 0.606240, 0.947260],
[1.000000, 0.746140, 0.751740, 0.598390, 0.725230],
[0.922210, 0.500000, 0.376800, 0.517110, 0.548630],
[0.500000, 0.450000, 0.429970, 0.404490, 0.539940],
[0.960430, 0.881630, 0.775640, 0.596350, 0.937680 ]]
coeffs[6,1,:,:] = [
[1.030000, 1.040000, 1.000000, 1.000000, 1.049510],
[1.050000, 0.990000, 0.990000, 0.950000, 0.996530],
[1.050000, 0.990000, 0.990000, 0.820000, 0.971940],
[1.050000, 0.790000, 0.880000, 0.820000, 0.951840],
[1.000000, 0.530000, 0.440000, 0.710000, 0.928730],
[0.540000, 0.470000, 0.500000, 0.550000, 0.773950],
[1.038270, 0.920180, 0.910930, 0.821140, 1.034560 ]]
coeffs[6,2,:,:] = [
[1.041020, 0.997520, 0.961600, 1.000000, 1.035780],
[0.948030, 0.980000, 0.900000, 0.950360, 0.977460],
[0.950000, 0.977250, 0.869270, 0.800000, 0.951680],
[0.951870, 0.850000, 0.748770, 0.700000, 0.883850],
[0.900000, 0.823190, 0.727450, 0.600000, 0.839870],
[0.850000, 0.805020, 0.692310, 0.500000, 0.788410],
[1.010090, 0.895270, 0.773030, 0.816280, 1.011680 ]]
coeffs[6,3,:,:] = [
[1.022450, 1.004600, 0.983650, 1.000000, 1.032940],
[0.943960, 0.999240, 0.983920, 0.905990, 0.978150],
[0.936240, 0.946480, 0.850000, 0.850000, 0.930320],
[0.816420, 0.885000, 0.644950, 0.817650, 0.865310],
[0.742960, 0.765690, 0.561520, 0.700000, 0.827140],
[0.643870, 0.596710, 0.474460, 0.600000, 0.651200],
[0.971740, 0.940560, 0.714880, 0.864380, 1.001650 ]]
coeffs[6,4,:,:] = [
[0.995260, 0.977010, 1.000000, 1.000000, 1.035250],
[0.939810, 0.975250, 0.939980, 0.950000, 0.982550],
[0.876870, 0.879440, 0.850000, 0.900000, 0.917810],
[0.873480, 0.873450, 0.751470, 0.850000, 0.863040],
[0.761470, 0.702360, 0.638770, 0.750000, 0.783120],
[0.734080, 0.650000, 0.600000, 0.650000, 0.715660],
[0.942160, 0.919100, 0.770340, 0.731170, 0.995180 ]]
coeffs[6,5,:,:] = [
[0.952560, 0.916780, 0.920000, 0.900000, 1.005880],
[0.928620, 0.994420, 0.900000, 0.900000, 0.983720],
[0.913070, 0.850000, 0.850000, 0.800000, 0.924280],
[0.868090, 0.807170, 0.823550, 0.600000, 0.844520],
[0.769570, 0.719870, 0.650000, 0.550000, 0.733500],
[0.580250, 0.650000, 0.600000, 0.500000, 0.628850],
[0.904770, 0.852650, 0.708370, 0.493730, 0.949030 ]]
coeffs[6,6,:,:] = [
[0.911970, 0.800000, 0.800000, 0.800000, 0.956320],
[0.912620, 0.682610, 0.750000, 0.700000, 0.950110],
[0.653450, 0.659330, 0.700000, 0.600000, 0.856110],
[0.648440, 0.600000, 0.641120, 0.500000, 0.695780],
[0.570000, 0.550000, 0.598800, 0.400000, 0.560150],
[0.475230, 0.500000, 0.518640, 0.339970, 0.520230],
[0.743440, 0.592190, 0.603060, 0.316930, 0.794390 ]]
return coeffs[1:,1:,:,:]