Metadata-Version: 1.1
Name: numdifftools
Version: 0.9.17
Summary: 'Solves automatic numerical differentiation problems in one or more variables.'
Home-page: "https://github.com/pbrod/numdifftools/"
Author: pbrod
Author-email: per.andreas.brodtkorb(at)gmail.com
License: new BSD
Description: Numdifftools
        ============
        
        |pkg_img| |tests_img| |tests2_img| |docs_img| |health_img| |coverage_img| |versions_img| |depsy_img|
        
        
        Numdifftools is a suite of tools written in `_Python <http://www.python.org/>`_
        to solve automatic numerical differentiation problems in one or more variables.
        Finite differences are used in an adaptive manner, coupled with a Richardson
        extrapolation methodology to provide a maximally accurate result.
        The user can configure many options like; changing the order of the method or
        the extrapolation, even allowing the user to specify whether complex-step, central,
        forward or backward differences are used.
        
        The methods provided are:
        
        - **Derivative**: Compute the derivatives of order 1 through 10 on any scalar function.
        
        - **directionaldiff**: Compute directional derivative of a function of n variables
        
        - **Gradient**: Compute the gradient vector of a scalar function of one or more variables.
        
        - **Jacobian**: Compute the Jacobian matrix of a vector valued function of one or more variables.
        
        - **Hessian**: Compute the Hessian matrix of all 2nd partial derivatives of a scalar function of one or more variables.
        
        - **Hessdiag**: Compute only the diagonal elements of the Hessian matrix
        
        All of these methods also produce error estimates on the result.
        
        Numdifftools also provide an easy to use interface to derivatives calculated
        with in `_AlgoPy <https://pythonhosted.org/algopy/>`_. Algopy stands for Algorithmic
        Differentiation in Python.
        The purpose of AlgoPy is the evaluation of higher-order derivatives in the
        `forward` and `reverse` mode of Algorithmic Differentiation (AD) of functions
        that are implemented as Python programs.
        
        
        Getting Started
        ---------------
        
        Visualize high order derivatives of the tanh function
        
            >>> import numpy as np
            >>> import numdifftools as nd
            >>> import matplotlib.pyplot as plt
            >>> x = np.linspace(-2, 2, 100)
            >>> for i in range(10):
            ...    df = nd.Derivative(np.tanh, n=i)
            ...    y = df(x)
            ...    h = plt.plot(x, y/np.abs(y).max())
        
            >>> plt.show()
        
        .. image:: https://raw.githubusercontent.com/pbrod/numdifftools/master/examples/fun.png
            :target: https://github.com/pbrod/numdifftools/blob/master/examples/fun.py
        
        
        
        Compute 1'st and 2'nd derivative of exp(x), at x == 1::
        
            >>> fd = nd.Derivative(np.exp)        # 1'st derivative
            >>> fdd = nd.Derivative(np.exp, n=2)  # 2'nd derivative
            >>> np.allclose(fd(1), 2.7182818284590424)
            True
            >>> np.allclose(fdd(1), 2.7182818284590424)
            True
        
        Nonlinear least squares::
        
            >>> xdata = np.reshape(np.arange(0,1,0.1),(-1,1))
            >>> ydata = 1+2*np.exp(0.75*xdata)
            >>> fun = lambda c: (c[0]+c[1]*np.exp(c[2]*xdata) - ydata)**2
            >>> Jfun = nd.Jacobian(fun)
            >>> np.allclose(np.abs(Jfun([1,2,0.75])), 0) # should be numerically zero
            True
        
        Compute gradient of sum(x**2)::
        
            >>> fun = lambda x: np.sum(x**2)
            >>> dfun = nd.Gradient(fun)
            >>> dfun([1,2,3])
            array([ 2.,  4.,  6.])
        
        Compute the same with the easy to use interface to AlgoPy::
        
            >>> import numdifftools.nd_algopy as nda
            >>> import numpy as np
            >>> fd = nda.Derivative(np.exp)        # 1'st derivative
            >>> fdd = nda.Derivative(np.exp, n=2)  # 2'nd derivative
            >>> np.allclose(fd(1), 2.7182818284590424)
            True
            >>> np.allclose(fdd(1), 2.7182818284590424)
            True
        
        Nonlinear least squares::
        
            >>> xdata = np.reshape(np.arange(0,1,0.1),(-1,1))
            >>> ydata = 1+2*np.exp(0.75*xdata)
            >>> fun = lambda c: (c[0]+c[1]*np.exp(c[2]*xdata) - ydata)**2
            >>> Jfun = nda.Jacobian(fun, method='reverse')
            >>> np.allclose(np.abs(Jfun([1,2,0.75])), 0) # should be numerically zero
            True
        
        Compute gradient of sum(x**2)::
        
            >>> fun = lambda x: np.sum(x**2)
            >>> dfun = nda.Gradient(fun)
            >>> dfun([1,2,3])
            array([ 2.,  4.,  6.])
        
        
        See also
        --------
        scipy.misc.derivative
        
        
        Documentation and code
        ======================
        
        Numdifftools works on Python 2.7+ and Python 3.0+.
        
        Official releases available at: http://pypi.python.org/pypi/numdifftools |pkg_img|
        
        Official documentation available at: http://numdifftools.readthedocs.io/en/latest/ |docs_img|
        
        Bleeding edge: https://github.com/pbrod/numdifftools.
        
        
        Installation
        ============
        
        If you have pip installed, then simply type:
        
            $ pip install numdifftools
        
        to get the lastest stable version. Using pip also has the advantage that all
        requirements are automatically installed.
        
        
        Unit tests
        ==========
        To test if the toolbox is working paste the following in an interactive
        python session::
        
           import numdifftools as nd
           nd.test(coverage=True, doctests=True)
        
        
        Acknowledgement
        ===============
        The `numdifftools package <http://pypi.python.org/pypi/numdifftools/>`_ for
        `Python <https://www.python.org/>`_ was written by Per A. Brodtkorb
        based on the adaptive numerical differentiation toolbox written in `Matlab <http://www.mathworks.com>`_  by John D'Errico [DErrico2006]_.
        
        Numdifftools has as of version 0.9 been extended with some of the functionality
        found in the statsmodels.tools.numdiff module written by Josef Perktold [Perktold2014]_.
        
        
        References
        ===========
        
        .. [DErrico2006] D'Errico, J. R.  (2006), Adaptive Robust Numerical Differentiation
            http://www.mathworks.com/matlabcentral/fileexchange/13490-adaptive-robust-numerical-differentiation
        
        .. [Perktold2014] Perktold, J (2014), numdiff package
            http://statsmodels.sourceforge.net/0.6.0/_modules/statsmodels/tools/numdiff.html
        
        
        
        .. |pkg_img| image:: https://badge.fury.io/py/numdifftools.png
            :target: https://pypi.python.org/pypi/Numdifftools/
        
        .. |tests_img| image:: https://travis-ci.org/pbrod/numdifftools.svg?branch=master
            :target: https://travis-ci.org/pbrod/numdifftools
        
        .. |tests2_img| image:: https://ci.appveyor.com/api/projects/status/qeoegaocw41lkarv/branch/master?svg=true
            :target: https://ci.appveyor.com/project/pbrod/numdifftools
        
        
        .. |docs_img| image:: https://readthedocs.org/projects/pip/badge/?version=latest
            :target: http://numdifftools.readthedocs.org/en/latest/
        
        .. |health_img| image:: https://landscape.io/github/pbrod/numdifftools/master/landscape.svg?style=flat
           :target: https://landscape.io/github/pbrod/numdifftools/master
           :alt: Code Health
        
        .. |coverage_img| image:: https://coveralls.io/repos/pbrod/numdifftools/badge.svg?branch=master
           :target: https://coveralls.io/github/pbrod/numdifftools?branch=master
        
        .. |versions_img| image:: https://img.shields.io/pypi/pyversions/numdifftools.svg
           :target: https://github.com/pbrod/numdifftools
        
        .. |depsy_img| image:: http://depsy.org/api/package/pypi/Numdifftools/badge.svg
           :target: http://depsy.org/package/python/Numdifftools
        
        
Platform: UNKNOWN
Classifier: Development Status :: 4 - Beta
Classifier: Programming Language :: Python
Classifier: Programming Language :: Python :: 2.7
Classifier: Programming Language :: Python :: 3
Classifier: Programming Language :: Python :: 3.3
Classifier: Programming Language :: Python :: 3.4
Classifier: Programming Language :: Python :: 3.5
Classifier: Environment :: Console
Classifier: Intended Audience :: Education
Classifier: Intended Audience :: Science/Research
Classifier: License :: OSI Approved :: BSD License
Classifier: Operating System :: OS Independent
Classifier: Operating System :: POSIX :: Linux
Classifier: Operating System :: Unix
Classifier: Operating System :: MacOS
Classifier: Operating System :: Microsoft :: Windows
Classifier: Topic :: Scientific/Engineering :: Mathematics
