Python package for stochastic dimension reduction based on nonlinearity of a quantity of interest. This package uses stochastic collocation to estimate statistical moments of a quantity of interest (QoI).

Besides Numpy and SciPy, this package depends on another python package called chaospy, which can be installed using

pip install chaospy==2.3.5

The documentation of chaospy can be found at the following link

http://chaospy.readthedocs.io/en/master/

Using pyStatReduce for approximating statistics involves working with objects of the following major classes and their subclasses

• QuantityOfInterest : Base class for creating subclasses for a specific quantity of interest. examples of subclasses of QuantityOfInterest can be found in src/examples directory
• StochasticCollocation : Base class that handles uncertainty propagation using stochastic collocation. This is designed to handle multivariate uniform or normal distributions.
• Dist : Base class in chaospy upon different distributions have been defined. see here for a complete list of available distributions.
• DimensionReduction : Base class that identifies the directions with highest nonlinearity in the QoI. This is done by computing the dominant eigenmodes of the Hessian of the QoI in the isoprobabilistic space.

A sample script for using the package has been provided below. However, the user is recommended to look in the test to see the latest API for the package

systemsize = 4
eigen_decayrate = 2.0

# Create Hadmard Quadratic object
QoI = examples.HadamardQuadratic(systemsize, eigen_decayrate)

# Create stochastic collocation object
collocation = StochasticCollocation(3, "Normal")

# Create dimension reduction object
threshold_factor = 0.9
dominant_space = DimensionReduction(threshold_factor)

# Initialize chaospy distribution
std_dev = 0.2*np.ones(QoI.systemsize)
x = np.ones(QoI.systemsize)
jdist = cp.MvNormal(x, np.diag(std_dev))

# Get the eigenmodes of the Hessian product and the dominant indices
dominant_space.getDominantDirections(QoI, jdist)

mu_j = collocation.normalReduced(QoI, jdist, dominant_space)