Python Extension Example with UnitsΒΆ
Often Python packages contain extensions in C/C++ which can’t be tested using automatic differentiation. The Numdidfftools is an alternative package that can calculate derivatives more accurately than the central finite difference approximation.
An example of using unc_wrapper_args()
with a
Python extension written in C/C++ is in the tests called
test_solpos()
. This
test using C/C++ code from NREL that is called using Python ctypes
module.
This example also demonstrates using Pint’s units wrapper. When using the units
wrapper, you must use unc_wrapper_args()
and
specify the indices of the positional arguments which corresond to the covariance
matrix. Also, two additional None, None
should be appended to the units
wrapper return values because otherwise Pint uses zip(out_units, retvals)
and therefore the covariance and Jacobian matrices will get dropped.
@UREG.wraps(('deg', 'deg', None, None),
(None, 'deg', 'deg', 'Pa', 'm', 'degC'))
@unc_wrapper_args(1, 2, 3, 4, 5)
# indices specify positions of independent variables:
# 1: latitude, 2: longitude, 3: pressure, 4: altitude, 5: temperature
def spa(times, latitude, longitude, pressure, altitude, temperature):
dataframe = pvlib.solarposition.spa_c(times, latitude, longitude, pressure,
temperature)
retvals = dataframe.to_records()
zenith = retvals['apparent_zenith']
zenith = np.where(zenith < 90, zenith, np.nan)
azimuth = retvals['azimuth']
return zenith, azimuth
Then test it out.
times = pd.DatetimeIndex(start='2015/1/1', end='2015/1/2', freq='1h',
tz=PST).tz_convert(UTC)
latitude, longitude = 37.0 * UREG.deg, -122.0 * UREG.deg
pressure, temperature = 101325.0 * UREG.Pa, UREG.Quantity(22.0, UREG.degC)
altitude = 0.0 * UREG.m
# standard deviation of 1% assuming normal distribution
covariance = np.diag([0.0001] * 5)
ze, az, cov, jac = spa(times, latitude, longitude, pressure, altitude,
temperature, __covariance__=covariance)
The results are:
>>> ze
<Quantity([ nan nan nan nan nan
nan nan nan 84.10855021 74.98258957
67.47442104 62.27279883 60.00799371 61.01651321 65.14311785
71.83729124 80.41979434 89.92923993 nan nan
nan nan nan nan nan], 'deg')>
>>> az
<Quantity([ 349.29771499 40.21062767 66.71930375 80.93018543 90.85288686
99.21242575 107.18121735 115.45045069 124.56418347 135.02313717
147.24740279 161.37157806 176.92280365 192.74232655 207.51976817
220.49410796 231.60091006 241.18407504 249.7263611 257.75154961
265.87317048 275.01453439 287.07887655 307.28364551 348.92138471], 'deg')>
Note that Pint corrects the ambient temperature from Kelvin to Celsius and also converted Pascals to millibar. Finally Pint appends the specified units to the return values.
>>> idx = 8 # covariance at 8AM
>>> print times[idx]
Timestamp('2015-01-01 08:00:00-0800', tz='US/Pacific', offset='H')
>>> nf = 2 # number of dependent variables: [ze, az]
>>> print cov[(nf * idx):(nf * (idx + 1)), (nf * idx):(nf * (idx + 1))]
[[ 0.66082282, -0.61487518],
[-0.61487518, 0.62483904]]
>>> print np.sqrt(cov[(nf * idx), (nf * idx)]) / ze[idx] # standard deviation
0.0096710802029002577
This tells us that the standard deviation of the zenith is 1% if the input has a standard deviation of 1%. That’s reasonable.
>>> nargs = 5 # number of independent args
>>> print jac[nf*(idx-1):nf*idx, nargs*(idx-1):nargs*idx] # Jacobian at 8AM
[[ 5.56075143e-01, -6.44623321e-01, -1.42364184e-06, 0.00000000e+00, 1.06672083e-10],
[ 8.29163154e-02, 6.47436098e-01, 0.00000000e+00, 0.00000000e+00, 0.00000000e+00]]
This also tells that zenith is more sensitive to latitude and longitude than pressure or temperature and more sensitive to latitude than azimuth is.
Perhaps the most interesting outcome is the negative covariance between Zenith and Azimuth. From Wikipedia
... when the greater values of one variable mainly correspond to the lesser values of the other, the covariance is negative.
In other words when the error in Zenith increases, the error in Azimuth decreases. This is not uncommon but it’s not always intuitively obvious; we generally think that to get the largest error we should choose the largest errors for all independent variables.