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        "author": "Abraham Lee",
        "author_email": "tisimst@gmail.com",
        "bugtrack_url": null,
        "classifiers": [
            "Development Status :: 5 - Production/Stable",
            "Intended Audience :: Education",
            "Intended Audience :: Science/Research",
            "License :: OSI Approved :: BSD License",
            "Operating System :: OS Independent",
            "Programming Language :: Python",
            "Programming Language :: Python :: 2.6",
            "Programming Language :: Python :: 2.7",
            "Programming Language :: Python :: 3.0",
            "Programming Language :: Python :: 3.1",
            "Programming Language :: Python :: 3.2",
            "Programming Language :: Python :: 3.3",
            "Topic :: Education",
            "Topic :: Scientific/Engineering",
            "Topic :: Scientific/Engineering :: Mathematics",
            "Topic :: Scientific/Engineering :: Physics",
            "Topic :: Software Development",
            "Topic :: Software Development :: Libraries",
            "Topic :: Software Development :: Libraries :: Python Modules",
            "Topic :: Utilities"
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        "description": "===============================\n``soerp`` Package Documentation\n===============================\n\nOverview\n========\n\n``soerp`` is the Python implementation of the original Fortran code `SOERP` \nby N. D. Cox to apply a second-order analysis to `error propagation`_ (or \nuncertainty analysis). The ``soerp`` package allows you to **easily** and \n**transparently** track the effects of uncertainty through mathematical \ncalculations. Advanced mathematical functions, similar to those in the standard \nmath_ module can also be evaluated directly.\n\nIn order to correctly use ``soerp``, the **first eight statistical moments** \nof the underlying distribution are required. These are the *mean*, *variance*, \nand then the *standardized third through eighth moments*. These can be input \nmanually in the form of an array, but they can also be **conveniently \ngenerated** using either the **nice constructors** or directly by using the \ndistributions from the ``scipy.stats`` sub-module. See the examples below for \nusage examples of both input methods. The result of all calculations generates a \n*mean*, *variance*, and *standardized skewness and kurtosis* coefficients.\n\n\nRequired Packages\n=================\n\n- ad_ : For first- and second-order automatic differentiation (install this first).\n\n- NumPy_ : Numeric Python\n\n- SciPy_ : Scientific Python (the nice distribution constructors require this)\n\n- Matplotlib_ : Python plotting library\n\nBasic examples\n==============\n\nLet's begin by importing all the available constructors::\n\n    >>> from soerp import *   # uv, N, U, Exp, etc.\n\nNow, we can see that there are several equivalent ways to specify a statistical distribution, say a Normal distribution with a mean value of 10 and a standard deviation of 1:\n\n- Manually input the first 8 moments (mean, variance, and 3rd-8th standardized central moments)::\n\n    >>> x = uv([10, 1, 0, 3, 0, 15, 0, 105])\n\n- Use the ``rv`` kwarg to input a distribution from the ``scipy.stats`` module::\n\n    >>> x = uv(rv=ss.norm(loc=10, scale=1))\n\n- Use a built-in convenience constructor (typically the easiest if you can)::\n\n    >>> x = N(10, 1)\n\nA Simple Example\n----------------\n\nNow let's walk through an example of a three-part assembly stack-up::\n\n    >>> x1 = N(24, 1)  # normally distributed\n    >>> x2 = N(37, 4)  # normally distributed\n    >>> x3 = Exp(2)  # exponentially distributed\n    >>> Z = (x1*x2**2)/(15*(1.5 + x3))\n\nWe can now see the results of the calculations in two ways:\n\n#. The usual ``print`` statement (or simply the object if in a terminal)::\n\n    >>> Z  # \"print\" is optional at the command-line\n    uv(1176.45, 99699.6822917, 0.708013052944, 6.16324345127)\n\n#. The ``describe`` class method that explains briefly what the values are::\n\n    >>> Z.describe()\n    SOERP Uncertain Value:\n     > Mean...................  1176.45\n     > Variance...............  99699.6822917\n     > Skewness Coefficient...  0.708013052944\n     > Kurtosis Coefficient...  6.16324345127\n\nDistribution Moments\n--------------------\n\nThe eight moments of any input variable (and four of any output variable) can be accessed using the ``moments`` class method, as in::\n\n    >>> x1.moments()\n    [24.0, 1.0, 0.0, 3.0000000000000053, 0.0, 15.000000000000004, 0.0, 105.0]\n    >>> Z.moments()\n    [1176.45, 99699.6822917, 0.708013052944, 6.16324345127]\n\nCorrelations\n------------\n\nStatistical correlations are correctly handled, even after calculations have taken place::\n\n    >>> x1 - x1\n    0.0\n    >>> square = x1**2\n    >>> square - x1*x1\n    0.0\n\nDerivatives\n-----------\n\nDerivatives with respect to original variables are calculated via the ad_ package and are accessed using the **intuitive class methods**::\n\n    >>> Z.d(x1)  # dZ/dx1\n    45.63333333333333\n\n    >>> Z.d2(x2)  # d^2Z/dx2^2\n    1.6\n\n    >>> Z.d2c(x1, x3)  # d^2Z/dx1dx3 (order doesn't matter)\n    -22.816666666666666\n    \nWhen we need multiple derivatives at a time, we can use the ``gradient`` and ``hessian`` class methods::\n\n    >>> Z.gradient([x1, x2, x3])\n    [45.63333333333333, 59.199999999999996, -547.6]\n\n    >>> Z.hessian([x1, x2, x3])\n    [[0.0, 2.466666666666667, -22.816666666666666], [2.466666666666667, 1.6, -29.6], [-22.816666666666666, -29.6, 547.6]]\n\nError Components/Variance Contributions\n---------------------------------------\n\nAnother useful feature is available through the ``error_components`` class method that has various ways of representing the first- and second-order variance components::\n\n    >>> Z.error_components(pprint=True)\n    COMPOSITE VARIABLE ERROR COMPONENTS\n    uv(37.0, 16.0, 0.0, 3.0) = 58202.9155556 or 58.378236%\n    uv(24.0, 1.0, 0.0, 3.0) = 2196.15170139 or 2.202767%\n    uv(0.5, 0.25, 2.0, 9.0) = -35665.8249653 or 35.773258%\n\nAdvanced Example\n----------------\n\nHere's a *slightly* more advanced example, estimating the statistical properties of volumetric gas flow through an orifice meter::\n\n    >>> from soerp.umath import *  # sin, exp, sqrt, etc.\n    >>> H = N(64, 0.5)\n    >>> M = N(16, 0.1)\n    >>> P = N(361, 2)\n    >>> t = N(165, 0.5)\n    >>> C = 38.4\n    >>> Q = C*umath.sqrt((520*H*P)/(M*(t + 460)))\n    >>> Q.describe()\n    SOERP Uncertain Value:\n     > Mean...................  1330.99973939\n     > Variance...............  58.210762839\n     > Skewness Coefficient...  0.0109422068056\n     > Kurtosis Coefficient...  3.00032693502\n \nThis seems to indicate that even though there are products, divisions, and the usage of ``sqrt``, the result resembles a normal distribution (i.e., Q ~ N(1331, 7.63), where the standard deviation = sqrt(58.2) = 7.63).\n\nMain Features\n=============\n\n1. **Transparent calculations** with derivatives automatically calculated. \n   **No or little modification** to existing code required.\n\n2. Basic `NumPy` support without modification. Vectorized calculations built-in  \n   to the ``ad`` package.\n\n3. Nearly all standard `math`_ module functions supported through the \n   ``soerp.umath`` sub-module. If you think a function is in there, it probably \n   is.\n\n4. Nearly all derivatives calculated analytically using ``ad`` functionality.\n\n5. **Easy continuous distribution constructors**: \n\n   - ``N(mu, sigma)`` : `Normal distribution`_\n\n   - ``U(a, b)`` : `Uniform distribution`_\n\n   - ``Exp(lamda, [mu])`` : `Exponential distribution`_\n\n   - ``Gamma(k, theta)`` : `Gamma distribution`_\n\n   - ``Beta(alpha, beta, [a, b])`` : `Beta distribution`_\n\n   - ``LogN(mu, sigma)`` : `Log-normal distribution`_\n\n   - ``Chi2(k)`` : `Chi-squared distribution`_\n\n   - ``F(d1, d2)`` : `F-distribution`_\n\n   - ``Tri(a, b, c)`` : `Triangular distribution`_\n\n   - ``T(v)`` : `T-distribution`_\n\n   - ``Weib(lamda, k)`` : `Weibull distribution`_\n\n   The location, scale, and shape parameters follow the notation in the \n   respective Wikipedia articles. *Discrete distributions are not recommended \n   for use at this time. If you need discrete distributions, try the* mcerp_ \n   *python package instead.*\n\nInstallation\n============\n\n**Make sure you install the** `ad`_ **package first!** (If you use options \n3 or 4 below, this should be done automatically.)\n\nYou have several easy, convenient options to install the ``soerp`` package \n(administrative privileges may be required)\n\n1. Download the package files below, unzip to any directory, and run::\n\n    $ [sudo] python setup.py install\n   \n2. Simply copy the unzipped ``soerp-XYZ`` directory to any other location that \n   python can find it and rename it ``soerp``.\n   \n3. If ``setuptools`` is installed, run::\n\n    $ [sudo] easy_install [--upgrade] soerp\n   \n4. If ``pip`` is installed, run::\n\n    $ [sudo] pip install [--upgrade] soerp\n    \nUninstallation\n==============\n\nTo remove the package, there are really two good ways to do this:\n\n1. Go to the folder ``site-packages`` or ``dist-packages`` and simply delete\n   the folder ``soerp`` and ``soerp-XYZ-egg-info``.\n\n2. If ``pip`` is installed, run::\n\n    $ [sudo] pip uninstall soerp\n\nSee Also\n========\n\n- uncertainties_ : First-order error propagation\n\n- mcerp_ : Real-time latin-hypercube sampling-based Monte Carlo error \n  propagation\n\nContact\n=======\n\nPlease send **feature requests, bug reports, or feedback** to \n`Abraham Lee`_.\n\nAcknowledgements\n================\n\nThe author wishes to thank `Eric O. LEBIGOT`_ who first developed the\n`uncertainties`_ python package (for first-order error propagation), \nfrom which many inspiring ideas (like maintaining object correlations, etc.) \nare re-used and/or have been slightly evolved. *If you don't need second\norder functionality, his package is an excellent alternative since it is\noptimized for first-order uncertainty analysis.*\n\nReferences\n==========\n\n- N.D. Cox, 1979, *Tolerance Analysis by Computer*, Journal of Quality Technology, Vol. 11, No. 2, pp. 80-87\n\n\n\n.. _error propagation: http://en.wikipedia.org/wiki/Propagation_of_uncertainty\n.. _math: http://docs.python.org/library/math.html\n.. _ad: http://pypi.python.org/pypi/ad\n.. _mcerp: http://pypi.python.org/pypi/mcerp\n.. _NumPy: http://www.numpy.org/\n.. _SciPy: http://scipy.org\n.. _Matplotlib: http://matplotlib.org/\n.. _uncertainties: http://pypi.python.org/pypi/uncertainties\n.. _Abraham Lee: mailto: tisimst@gmail.com\n.. _Eric O. LEBIGOT: http://www.linkedin.com/pub/eric-lebigot/22/293/277\n.. _PEP8: http://www.python.org/dev/peps/pep-0008\n.. _Normal distribution: http://en.wikipedia.org/wiki/Normal_distribution\n.. _Uniform distribution: http://en.wikipedia.org/wiki/Uniform_distribution_(continuous)\n.. _Exponential distribution: http://en.wikipedia.org/wiki/Exponential_distribution\n.. _Gamma distribution: http://en.wikipedia.org/wiki/Gamma_distribution\n.. _Beta distribution: http://en.wikipedia.org/wiki/Beta_distribution\n.. _Log-normal distribution: http://en.wikipedia.org/wiki/Log-normal_distribution\n.. _Chi-squared distribution: http://en.wikipedia.org/wiki/Chi-squared_distribution\n.. _F-distribution: http://en.wikipedia.org/wiki/F-distribution\n.. _Triangular distribution: http://en.wikipedia.org/wiki/Triangular_distribution\n.. _T-distribution: http://en.wikipedia.org/wiki/Student's_t-distribution\n.. _Weibull distribution: http://en.wikipedia.org/wiki/Weibull_distribution",
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