Metadata-Version: 1.1
Name: soerp
Version: 0.9.5
Summary: Second Order Error Propagation
Home-page: https://github.com/tisimst/soerp
Author: Abraham Lee
Author-email: tisimst@gmail.com
License: BSD License
Description: ===============================
        ``soerp`` Package Documentation
        ===============================
        
        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 first- and second-order automatic differentiation (install this first).
        
        - NumPy_ : Numeric Python
        
        - SciPy_ : Scientific Python (the nice distribution constructors require this)
        
        - Matplotlib_ : Python plotting library
        
        Basic examples
        ==============
        
        Let's begin by importing all the available constructors::
        
            >>> from soerp import *   # uv, N, U, Exp, etc.
        
        Now, 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:
        
        - Manually input the first 8 moments (mean, variance, and 3rd-8th standardized central moments)::
        
            >>> x = uv([10, 1, 0, 3, 0, 15, 0, 105])
        
        - Use the ``rv`` kwarg to input a distribution from the ``scipy.stats`` module::
        
            >>> x = uv(rv=ss.norm(loc=10, scale=1))
        
        - Use a built-in convenience constructor (typically the easiest if you can)::
        
            >>> x = N(10, 1)
        
        A Simple Example
        ----------------
        
        Now let's walk through an example of a three-part assembly stack-up::
        
            >>> 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))
        
        We can now see the results of the calculations in two ways:
        
        #. The usual ``print`` statement (or simply the object if in a terminal)::
        
            >>> Z  # "print" is optional at the command-line
            uv(1176.45, 99699.6822917, 0.708013052944, 6.16324345127)
        
        #. The ``describe`` class method that explains briefly what the values are::
        
            >>> Z.describe()
            SOERP Uncertain Value:
             > Mean...................  1176.45
             > Variance...............  99699.6822917
             > Skewness Coefficient...  0.708013052944
             > Kurtosis Coefficient...  6.16324345127
        
        Distribution Moments
        --------------------
        
        The eight moments of any input variable (and four of any output variable) can be accessed using the ``moments`` class method, as in::
        
            >>> x1.moments()
            [24.0, 1.0, 0.0, 3.0000000000000053, 0.0, 15.000000000000004, 0.0, 105.0]
            >>> Z.moments()
            [1176.45, 99699.6822917, 0.708013052944, 6.16324345127]
        
        Correlations
        ------------
        
        Statistical correlations are correctly handled, even after calculations have taken place::
        
            >>> x1 - x1
            0.0
            >>> square = x1**2
            >>> square - x1*x1
            0.0
        
        Derivatives
        -----------
        
        Derivatives with respect to original variables are calculated via the ad_ package and are accessed using the **intuitive class methods**::
        
            >>> Z.d(x1)  # dZ/dx1
            45.63333333333333
        
            >>> Z.d2(x2)  # d^2Z/dx2^2
            1.6
        
            >>> Z.d2c(x1, x3)  # d^2Z/dx1dx3 (order doesn't matter)
            -22.816666666666666
            
        When we need multiple derivatives at a time, we can use the ``gradient`` and ``hessian`` class methods::
        
            >>> Z.gradient([x1, x2, x3])
            [45.63333333333333, 59.199999999999996, -547.6]
        
            >>> Z.hessian([x1, x2, x3])
            [[0.0, 2.466666666666667, -22.816666666666666], [2.466666666666667, 1.6, -29.6], [-22.816666666666666, -29.6, 547.6]]
        
        Error Components/Variance Contributions
        ---------------------------------------
        
        Another useful feature is available through the ``error_components`` class method that has various ways of representing the first- and second-order variance components::
        
            >>> Z.error_components(pprint=True)
            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%
        
        Advanced Example
        ----------------
        
        Here's a *slightly* more advanced example, estimating the statistical properties of volumetric gas flow through an 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
         
        This 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).
        
        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`_
        
           - ``Chi2(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. *Discrete distributions are not recommended 
           for use at this time. If you need discrete distributions, try the* mcerp_ 
           *python package instead.*
        
        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::
        
            $ [sudo] python setup.py install
           
        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
           
        4. If ``pip`` is installed, run::
        
            $ pip install --upgrade soerp
        
        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 latin-hypercube sampling-based Monte Carlo error propagation
        
        Contact
        =======
        
        Please send **feature requests, bug reports, or feedback** to 
        `Abraham Lee`_.
        
        Acknowledgements
        ================
        
        The author wishes to thank `Eric O. LEBIGOT`_ who first developed the
        `uncertainties`_ python package (for first-order error propagation), 
        from which many inspiring ideas (like maintaining object correlations, etc.) 
        are re-used and/or have been slightly evolved. *If you don't need second
        order functionality, his package is an excellent alternative since it is
        optimized for first-order uncertainty analysis.*
        
        References
        ==========
        
        - N.D. Cox, 1979, *Tolerance Analysis by Computer*, Journal of Quality Technology, Vol. 11, No. 2, pp. 80-87
        
        
        
        .. _error propagation: http://en.wikipedia.org/wiki/Propagation_of_uncertainty
        .. _math: http://docs.python.org/library/math.html
        .. _ad: http://pypi.python.org/pypi/ad
        .. _mcerp: http://pypi.python.org/pypi/mcerp
        .. _NumPy: http://www.numpy.org/
        .. _SciPy: http://scipy.org
        .. _Matplotlib: http://matplotlib.org/
        .. _uncertainties: http://pypi.python.org/pypi/uncertainties
        .. _Abraham Lee: mailto: tisimst@gmail.com
        .. _Eric O. LEBIGOT: http://www.linkedin.com/pub/eric-lebigot/22/293/277
        .. _PEP8: http://www.python.org/dev/peps/pep-0008
        .. _Normal distribution: http://en.wikipedia.org/wiki/Normal_distribution
        .. _Uniform distribution: http://en.wikipedia.org/wiki/Uniform_distribution_(continuous)
        .. _Exponential distribution: http://en.wikipedia.org/wiki/Exponential_distribution
        .. _Gamma distribution: http://en.wikipedia.org/wiki/Gamma_distribution
        .. _Beta distribution: http://en.wikipedia.org/wiki/Beta_distribution
        .. _Log-normal distribution: http://en.wikipedia.org/wiki/Log-normal_distribution
        .. _Chi-squared distribution: http://en.wikipedia.org/wiki/Chi-squared_distribution
        .. _F-distribution: http://en.wikipedia.org/wiki/F-distribution
        .. _Triangular distribution: http://en.wikipedia.org/wiki/Triangular_distribution
        .. _T-distribution: http://en.wikipedia.org/wiki/Student's_t-distribution
        .. _Weibull distribution: http://en.wikipedia.org/wiki/Weibull_distribution
        
Keywords: uncertainty analysis,uncertainties,error propagation,second order,derivative,statistics,method of moments,distribution
Platform: UNKNOWN
Classifier: Development Status :: 5 - Production/Stable
Classifier: Intended Audience :: Education
Classifier: Intended Audience :: Science/Research
Classifier: License :: OSI Approved :: BSD License
Classifier: Operating System :: OS Independent
Classifier: Programming Language :: Python
Classifier: Programming Language :: Python :: 2.6
Classifier: Programming Language :: Python :: 2.7
Classifier: Programming Language :: Python :: 3.0
Classifier: Programming Language :: Python :: 3.1
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Classifier: Topic :: Software Development :: Libraries :: Python Modules
Classifier: Topic :: Utilities
