# Getting Started¶

You can wrap any Python callable using unc_wrapper() or unc_wrapper_args(), that does the following:

• looks for __covariance__ as a keyword argument

• calculates the Jacobian and covariance matrices

• appends the Jacobian and covariance matrices to the return values.

However you may need to manipulate the input arguments to match the expected API.

## Simple Example¶

This simple example using two input arguments and two return values is from Uncertainty Benchmarks:

from uncertainty_wrapper import unc_wrapper
# unc_wrapper expects input args to be 2-D NumPy arrays
import numpy as np

# simple test functions with multiple input arguments and return
# values and whose derivatives are easily derived.
NARGS = 2  # number of input arguments
F = lambda x: np.array([(x[0] + x[1]) ** 2, x[1] ** 2 - x[0] ** 2])
G = lambda x: np.array([(2 * (x[0] + x[1]), 2 * (x[1] + x[0])),
(-2 * x[0], 2 * x[1])])
AVG = np.random.rand(NARGS) * 10.  # some test input arguments
# randomly generated symmetrical covariance matrix
COV = np.random.rand(NARGS, NARGS) / 10.
COV = (COV + COV.T) / 2.0  # must be symmetrical

@unc_wrapper
def example(avg=AVG, f=F):
"""Example of unc_wrapper usage"""
avg = f(avg)
return avg

# uses @wraps from functools so docstrings should work
print example.__doc__
# Example of unc_wrapper usage

# reshape args as row stack since there is only one observation and
# unc_wrapper expects there to be multiple observations
AVG = AVG.reshape((NARGS, 1))
print AVG
# [[ 1.80222955]
#  [ 5.62897685]]

# the wrapped example now takes a second argument called
# __covariance__
print COV
# [[ 0.06798386  0.05971218]
#  [ 0.05971218  0.09359305]]

retval = example(AVG, F, __covariance__=COV)
# and appends covariance and Jacobian matrices to the return values
avg, cov, jac = retval

# squeeze out extra dimension we added since there's only one
# observation and display results
avg = avg.squeeze()
print avg
# [ 55.22282851  28.43734901]

print cov
# [[ 1164.60425675   790.5452895 ]
#  [  415.45944116   294.07938566]]

print jac
# [[ 14.86241279  14.86241279]
#  [ -3.6044591   11.2579537 ]]

# compare to analytical derivatives
print G(AVG).squeeze()
# [[ 14.86241279  14.86241279]
#  [ -3.6044591   11.2579537 ]]


## More Examples¶

The next sections contain more examples cover more advanced usage. Uncertanty Wrapper can consider multiple inputs arguments and return values. It can also be used with Python extensions written in c/c++. Finally unc_wrapper_args() can be used to specify which args are indepndent to include in the covariance and Jaconbian.

## Announcement¶

Previous versions of Uncertainty Wrapper have worked with Pint’s units wrapper to automatically check units, but unfortunately this is no longer supported.