soerp 0.9

Overview

soerp is the Python implementation of the original Fortran code SOERP by N. D. Cox to apply a second-order analysis to error propagation (or uncertainty analysis). The soerp package allows you to easily and transparently track the effects of uncertainty through mathematical calculations. Advanced mathematical functions, similar to those in the standard math module can also be evaluated directly.

In order to correctly use soerp, the first eight statistical moments of the underlying distribution are required. These are the mean, variance, and then the standardized third through eighth moments. These can be input manually in the form of an array, but they can also be conveniently generated using either the nice constructors or directly by using the distributions from the scipy.stats sub-module. See the examples below for usage examples of both input methods. The result of all calculations generates a mean, variance, and standardized skewness and kurtosis coefficients.

Required Packages

• ad : For automatic differentiation (install this first).

Suggested Packages

• NumPy : Numeric Python

• SciPy : Scientific Python (the nice distribution constructors require this)

• Matplotlib : Python plotting library

Basic examples

>>> from soerp import *   # the constructors for uncertain variables

# these are equivalent ways to specify the distribution
>>> x = uv([10, 1, 0, 3, 0, 15, 0, 105])  # manually input moments
>>> x = uv(rv=ss.norm(loc=10, scale=1))  # directly using the scipy.stats distributions
>>> x = N(10, 1)  # a nice constructor (still requires scipy)

>>> x1 = N(24, 1)  # normally distributed
>>> x2 = N(37, 4)  # normally distributed
>>> x3 = Exp(2)  # exponentially distributed

>>> Z = (x1*x2**2)/(15*(1.5 + x3))
>>> Z  # output compactly shows the mean, variance, and standardized skewness and kurtosis
uv(1176.45, 99699.6822917, 0.708013052944, 6.16324345127)

>>> Z.describe()  # use for more detailed output
SOERP Uncertain Value:
 > Mean...................  1176.45
 > Variance...............  99699.6822917
 > Skewness Coefficient...  0.708013052944
 > Kurtosis Coefficient...  6.16324345127

>>> x1.moments()  # the eight moments can be accessed at any time
[24.0, 1.0, 0.0, 3.0000000000000053, 0.0, 15.000000000000004, 0.0, 105.0]

>>> x1-x1  # correlations are correctly handled
0.0

# convenient access to derivatives
>>> Z.d(x1)  # first derivative wrt x1 (returns all if no input, 0 if derivative doesn't exist)
45.63333333333333

>>> Z.d2(x2)  # second derivative wrt x2
1.6

>>> Z.d2c(x1, x3)  # second cross-derivative wrt x1 and x3 (order doesn't matter)
-22.816666666666666

>>> Z.gradient([x1, x2, x3])  # convenience function, useful for optimization
[45.63333333333333, 59.199999999999996, -547.6]

>>> Z.hessian([x1, x2, x3])   # another convenience function
[[0.0, 2.466666666666667, -22.816666666666666], [2.466666666666667, 1.6, -29.6], [-22.816666666666666, -29.6, 547.6]]

>>> Z.error_components(pprint=True)  # show how each variable is contributing errors
COMPOSITE VARIABLE ERROR COMPONENTS
uv(37.0, 16.0, 0.0, 3.0) = 58202.9155556 or 58.378236%
uv(24.0, 1.0, 0.0, 3.0) = 2196.15170139 or 2.202767%
uv(0.5, 0.25, 2.0, 9.0) = -35665.8249653 or 35.773258%

# a more advanced example (volumetric gas flow through orifice meter)
>>> from soerp.umath import *  # sin, exp, sqrt, etc.
>>> H = N(64, 0.5)
>>> M = N(16, 0.1)
>>> P = N(361, 2)
>>> t = N(165, 0.5)
>>> C = 38.4
>>> Q = C*umath.sqrt((520*H*P)/(M*(t + 460)))

>>> Q.describe()
SOERP Uncertain Value:
 > Mean...................  1330.99973939
 > Variance...............  58.210762839
 > Skewness Coefficient...  0.0109422068056
 > Kurtosis Coefficient...  3.00032693502

Main Features

1. Transparent calculations with derivatives automatically calculated. No or little modification to existing code required.

2. Basic NumPy support without modification. Vectorized calculations built-in to the ad package.

3. Nearly all standard math module functions supported through the soerp.umath sub-module. If you think a function is in there, it probably is.

4. Nearly all derivatives calculated analytically using ad functionality.

5. Easy continuous distribution constructors:

   • N(mu, sigma) : Normal distribution

   • U(a, b) : Uniform distribution

   • Exp(lamda, [mu]) : Exponential distribution

   • Gamma(k, theta) : Gamma distribution

   • Beta(alpha, beta, [a, b]) : Beta distribution

   • LogN(mu, sigma) : Log-normal distribution

   • X2(k) : Chi-squared distribution

   • F(d1, d2) : F-distribution

   • Tri(a, b, c) : Triangular distribution

   • T(v) : T-distribution

   • Weib(lamda, k) : Weibull distribution

   The location, scale, and shape parameters follow the notation in the respective Wikipedia articles.

Installation

Make sure you install the ad package first!

You have several easy, convenient options to install the soerp package (administrative privileges may be required)

1. Download the package files below, unzip to any directory, and run python setup.py install from the command-line.

2. Simply copy the unzipped soerp-XYZ directory to any other location that python can find it and rename it soerp.

3. If setuptools is installed, run easy_install --upgrade soerp from the command-line.

4. If pip is installed, run pip --upgrade soerp from the command-line

Python 3

To use this package with Python 3.x, you will need to run the 2to3 conversion tool at the command-line using the following syntax while in the unzipped soerp directory:

$ 2to3 -w -f all *.py

This should take care of the main changes required. Then, run python3 setup.py install. If bugs continue to pop up, please email the author.

See Also

• uncertainties : First order error propagation

• mcerp : Real-time Monte Carlo, Latin-Hypercube Sampling-based, Error Propagation

Contact

Please send feature requests, bug reports, or feedback to Abraham Lee.

Acknowledgements

A lot of the credit goes to Eric O. LEBIGOT who first developed uncertainties, a very nice first-order package for error propagation, from which many inspiring ideas (like correlating variables, etc.) are re-used or slightly evolved. If you don’t need second order functionality, I recommend using his package.

References

• N.D. Cox, 1979, Tolerance Analysis by Computer, Journal of Quality Technology, Vol. 11, No. 2, pp. 80-87