Package: numdifftools
numdifftoolsThe numdifftools library is a suite of tools written in_Pythonto 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 variablesGradient: 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 matrixAll of these methods also produce error estimates on the result.Numdifftools also provide an easy to use interface to derivatives calculated
with in_AlgoPy. Algopy stands for Algorithmic
Differentiation in Python.
The purpose of AlgoPy is the evaluation of higher-order derivatives in theforwardandreversemode of Algorithmic Differentiation (AD) of functions
that are implemented as Python programs.Getting StartedVisualize 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() # doctest: +SKIPCompute 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)
TrueNonlinear 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
TrueCompute gradient of sum(x**2):>>> fun = lambda x: np.sum(x**2)
>>> dfun = nd.Gradient(fun)
>>> np.allclose(dfun([1,2,3]), [ 2.,  4.,  6.])
TrueCompute 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)
TrueNonlinear 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
TrueCompute gradient of sum(x**2):>>> fun = lambda x: np.sum(x**2)
>>> dfun = nda.Gradient(fun)
>>> np.allclose(dfun([1,2,3]), [ 2.,  4.,  6.])
TrueSee alsoscipy.misc.derivativeDocumentation and codeNumdifftools works on Python 2.7+ and Python 3.0+.Official releases available at:http://pypi.python.org/pypi/numdifftoolsOfficial documentation available at:http://numdifftools.readthedocs.io/en/latest/Bleeding edge:https://github.com/pbrod/numdifftools.InstallationIf you have pip installed, then simply type:$ pip install numdifftoolsto get the lastest stable version. Using pip also has the advantage that all
requirements are automatically installed.Unit testsTo test if the toolbox is working paste the following in an interactive
python session:import numdifftools as nd
nd.test('--doctest-modules', '--disable-warnings')AcknowledgementThenumdifftools packageforPythonwas written by Per A. Brodtkorb
based on the adaptive numerical differentiation toolbox written inMatlabby John D’Errico[DErrico06].Later the package was extended with some of the functionality
found in the statsmodels.tools.numdiff module written by Josef Perktold[JPerktold14]which is based on[Rid09].
The implementation of bicomplex numbers is based on the matlab implementation
described in the project report of[Ver14]which is based on [GLD12].
For completeness the[For98]method for computing the weights and points in general
finite difference formulas as well as the[For81]method for cumputing the
taylor coefficients of complex analytic function using FFT, was added.References[JPerktold14]Perktold, J (2014), numdiff packagehttp://statsmodels.sourceforge.net/0.6.0/_modules/statsmodels/tools/numdiff.html[Ver14]Adriaen Verheyleweghen, (2014)
“Computation of higher-order derivatives using the multi-complex step method”,
Project report, NTNU[GLD12]Gregory Lantoine, R.P. Russell, and T. Dargent (2012)
“Using multicomplex variables for automatic computation of high-order derivatives”,
ACM Transactions on Mathematical Software,
Vol. 38, No. 3, Article 16, April 2012, 21 pages,http://doi.acm.org/10.1145/2168773.2168774[MELEV12]M.E. Luna-Elizarraras, M. Shapiro, D.C. Struppa1, A. Vajiac (2012),
“Bicomplex Numbers and Their Elementary Functions”,
CUBO A Mathematical Journal,
Vol. 14, No 2, (61-80). June 2012.[Lan10]Gregory Lantoine (2010),
“A methodology for robust optimization of low-thrust trajectories in multi-body environments”,
Phd thesis, Georgia Institute of Technology[Rid09]Ridout, M.S. (2009)
“Statistical applications of the complex-step method of numerical differentiation”,The American Statistician, 63, 66-74[DErrico06]D’Errico, J. R.  (2006),
“Adaptive Robust Numerical Differentiation”,http://www.mathworks.com/matlabcentral/fileexchange/13490-adaptive-robust-numerical-differentiation[KLLK05]K.-L. Lai, J.L. Crassidis, Y. Cheng, J. Kim (2005),
“New complex step derivative approximations with application to second-order kalman filtering”,
AIAA Guidance,Navigation and Control Conference,
San Francisco, California, August 2005, AIAA-2005-5944.[For98]B. Fornberg (1998)
“Calculation of weights_and_points in finite difference formulas”,
SIAM Review 40, pp. 685-691.[For81]Fornberg, B. (1981).
“Numerical Differentiation of Analytic Functions”,
ACM Transactions on Mathematical Software (TOMS),
7(4), 512-526.http://doi.org/10.1145/355972.355979[JML69]Lyness, J. M., Moler, C. B. (1969).
“Generalized Romberg Methods for Integrals of Derivatives”,Numerische Mathematik.[JML66]Lyness, J. M., Moler, C. B. (1966).
“Vandermonde Systems and Numerical Differentiation”,Numerische Mathematik.[NAG]NAG Library. NAG Fortran Library Document: D04AAFChangelogVersion 0.9.41 Nov 10, 2022Fabian Joswig (5):ci: execute test action only on push to master and on pull requests.ci: test requirements added to ci workflow.ci: first version of github actions ci added.fix: import from from scipy.ndimage.filters replaced by from scipy.ndimagefix: np.info(float).machar.tiny replaced by np.info(float).tinyJonas Eschle (6):Drop Python 3.6Remove Python 2.7, 3.6 from appveyor CIUpdate .travis.ymlUpdate setup.cfgUpdate .travis.ymlUpdate to Python310Per A Brodtkorb (19):Commented out deprecated pep8ignore and pep8maxlinelength in setup.cfgFixed issue #59: numpy deprecation warning on machar.tinyDeleted obsolete travis_install.shReplaced deprecatednp.MachAr().eps(NumPy 1.22) with np.finfo(float).eps in test_multicomplex.pyAdded requirements.tests.txtUpdated .github/workflows/test.yml to use requirements.tests.txtRemoved obsolete .travis.yml and appveyor.yml.Github-actions are now used instead.Replaced appveyor badge and travis badge with github-actions badge in README.rst, info.py and index.rstRemoved python 2.7 from classifiers in setup.cfgUpdated .travis.ymlFixed doctest so they don’t crash on travis: Replaced “# doctest + SKIP” with “# doctest: +SKIP” in docstrings.Updated download badge in README.rst and info.pyUpdated test_img in README.rstUpdated tests_img path for travis.Added “# doctest + SKIP” to doctest string in info.pyReplaced “version|” with “release|” in docs/index.rstAdded matplotlib to requirements.txt Removed failing python 3.8 from appveyor.ymlPer A. Brodtkorb (4):Merge pull request #65 from fjosw/feat/github_actions_ciMerge pull request #66 from jonas-eschle/patch-1Merge pull request #60 from peendebak/performance/percentileMerge pull request #63 from fjosw/feat/numpy_deprecationPieter Eendebak (2):workaround for known issue with np.nanpercentileimprove performance by combining percentile calculationsVersion 0.9.40 Jun 2, 2021Per A Brodtkorb (109):Replaced python 3.5 with 3.9 in .travis.ymlRemoved python 3.5 from appveyor.ymlAdded bibtex_bibfiles = … to docs/conf.pyFixed doctest failures indocs/src/numerical/derivest.rstdocs/tutorials/getting_started.rstnumdifftools.core.pynumdifftools.limits.pynumdifftools.nd_algopy.pynumdifftools.nd_scipy.pynumdifftools.nd_statsmodels.pyInsulated import of click in a if __name__ ==’__main__’ clause.Added activate to appveyor.ymlAddedhttps://mathworld.wolfram.com/WynnsEpsilonMethod.htmlreference for the Epsilon algorithm in extrapolation.py.Disabled the restriction that n must be one in LogJacobianRuleAdded complex_even and central_even methods to the JacobianDifferenceFunctionsUpdated documentation of Derivative in core.pyUpdated documentation of Richardson.Removed obsolete tests from test_nd_scipy.pyFixed a bug in TestJacobian.test_scalar_to_vector in test_nd_scipy.py for method=”complex’Refactored code from core.py to finite_difference.pyAdded LogJacobianRule, LogHessdiagRule, LogHessianRule to finite_difference.pyFixed a bug in Richardson._estimate_error: Complex rule resulted wrongly in complex error values.Added netlib.org/quadpack reference.Updated Dea to conform with QuadpackReplaced reference to Brezinski with refs to Quadpack.Reduced cyclomatic complexity in Dea in extrapolation.pyRemoved commented out code in profile_numdifftools.pyUpdated pycodestyle ignore section in setup.cfgRemoved commented out code in run_benchmark.py Made get_nominal_step continous as function of xMade datetime call python 2.7 compatible in run_benchmark.pySimplified the Derivative._step_generator function in core.py.Made plots generated from run_benchmark.py prettier.step_ratio in the step generators by default 2 for n=1 and 1.6 otherwise in step_generators.pyFixed failing doctests in core.py and nd_statsmodels.pyAdded doctests to setup.cfg.Reordered imports in test_example_functions.pyFixed .travis.yml so that he file paths in coverage.xml is discoverable
under the sonar.sources folder. The problem is that SonarQube is
analysing the checked-out source code (in src/numdifftools) but the
actual unit tests and coverage.py is run against the installed code (in
build/lib/numdifftools). Thus the absolute files paths to the installedRemoved commented code from test_numdifftools.pyRun only coverage xml when python version is 3.7Updated .travis.yml Removed commented out code from extrapolation.py and nd_statsmodels.pyFinalized the moved of XXXDifferencdFunctions from core.py to finite_difference.pyAdded missing docstring for default_scale function in step_generators.py.Removed unused import of itertools in _find_default_scale.py.Changed default scale from 1.35 to 1.06 for complex/multicomplex methods when n=1Added richardson_demo to extrapolation.py Simplified EpsAlg class in extrapolation.pyCorrected a small error for dea3: Now dea3 and Dea(limexp=3) gives the same result!Added python 3.8 to appveyor.yml Added python 3.9 to setup.cfgFixed reference to how-to/indexAdded doctest configuration to docs.conf.pyFixes issue #50 by adding function value f(x) to the info.f_value.Updated README.rstAdded @UnusedVariable here and there.Silence warnings in Hessian by adding __init__ that set the correct order given the method.Updated the Richardson._r_matrix method to generate complex matrix when step_ratio is complex.Fixed profile_hessian in profile_numdifftools.py so it works again.Added with np.errstate(all=’ignore’) to test_derivative_on_sinh and test_scalar_to_vector in test_nd_algopy.py to silence warnings.Changed citation style to alpha.Replaced bibliography.rst with refs1.bib and zreferences.rstRemoved badges for latexChanged sonar addon tokenAdded CC_TEST_REPORTER_IDFixed a typo in docs/numdifftools.rstAdded docs/make.batRemoved python 2.7 from .travis.ymlMoved test_requires from setup.cfg to setup.pyAdded Latex to setup.pyChanged default radius to 0.0059 which appears to cause less failures in Taylor in fornberg.py.Updated MANIFEST.inFixes issue #49 : Dimension of Jacobian of vector valued function (length n) with scalar input should be n X 1Updated build_package.pyAttempt to silence divide by zero and invalid warnings.Fix issue#52: Gradient tries to apply squeeze to the output tuple containing both the result and the full_output object.Made docstring a rawdocstring since it contains slashes.Added “# pylint: disable=unused-argument” in appropriate places.API change: replaced “python setup.py doctests” with “python setup.py doctest”Removed unused importsFixed a bug in test_low_order_derivative_on_example_functions:  Same variable (i) was used both in the outer and inner loop.Updated badge for pypi and documentation of fornberg.pyFixed failing tests.Updated docs + added a testAdded  “python -m pip install –upgrade pytest” to appveyor.yml due to a package conflict on python2.7 32 bitAdded - “python -m pip install –upgrade setuptools” in appveyor.yml to avoid build error.Try  “python setup.py bdist_wheel” and “pip install numdifftools –find-links=dist” in appveyor.ymlPut qoutes on “python -m pip install –upgrade pip” in appveyor.ymlChanged “python setup.py install” topython setup.py bdist_wheel”pip install numdifftools –find-links=distAdded “pip install –upgrade pip” to appveyor.ymlUpdated the detailed package documentation.Added missing pytest-pep8 to installUpdated badge + appveyor.ymlongoing work to harmonize the the output from approx_fprime and approx_fprime_csAdded Taylor class to nd_algopy.py Fixed a bug in _get_best_taylor_coefficient in fornberg.pyUpdated references Added test_mod_c function to test_multicomplex.pyFixed a typo.Removed –strict-markersFixed issue #39 TypeError: unsupported operand type(s) for /: ‘float’ and ‘Bicomplex’Fixed a typo in the documentation. Closing issue #51Added separate test for nd_scipy.added skip on tests if LineProfiler is not installed.Removed obsolete centered argument from call to approx_hess1 + pep8Move Jacobian._increment method to _JacobianDifferenceFunctionsstep_nom was unused in CStepGenerator.__init__ Added pytest.markers.slow in to setup.cfgMade two tests more forgiving in order to avoid failure on travis.Renamed nominal_step and base_step to get_nominal_step and get_base_step, respectively.Removed obsolete import of example from hypothesisUpdated testingUpdated coverage call: coverage run -m py.test src/numdifftools/testsDelete obsolete conftest.pyVersion 0.9.39 Jun 10, 2019Robert Parini (1):Fix issue #43: numpy future warningVersion 0.9.38 Jun 10, 2019Andrew Nelson (1):MAINT: special.factorial instead of misc.factorialDougal J. Sutherland (1):include LICENSE.txt in distributionsPer A Brodtkorb (140):Adjusted runtime for hypothesis tests to avoid failure and fixed pep8 failures.Fixed a bug in setup.cfgReplaced valarray function with numpy.full in step_generators.pyAdded try except on import of algopyUpdated the badges used in the README.rstReplaced numpy.testing.Tester with pytest.Removed dependence on pyscaffold.Simplified setup.py and setup.cfgUpdated .travis.yml configuration.Reorganized the documentation.Ongoing work to simplify the classes.Replaced unittest with pytest.Added finite_difference.pyreplaced , with .Reverted to coverage=4.3.4New attemptFixed conflicting importMissing import of EPSAdded missing FD_RULES = {}Removed pinned coverage, removed dependence on pyscaffoldUpdated .travis.yml and .appveyor.ymlReplaced conda channel omnia with conda-forgeRemoved commented out code. Set pyqt=5 in appveyor.ymlUpdated codeclimate checksDropped support for python 3.3 and 3.4. Added support for python 3.6, 3.7Simplified code.Pinned IPython==5.0 in order to make the testserver not crash.Added line_profiler to appveyor.ymlRemoved line_profiler from requirements.txtFix issue #37: Unable to install on Python 2.7Added method=’backward’ to nd_statsmodels.pySkip test_profile_numdifftools_profile_hessian and TestDoProfileAdded missing import of warningsAdded tests for the scripts from profile_numdifftools.py, _find_default_scale.py and run_benchmark.py.Added reason to unittest.skipIfAdded line_profiler to requirements.misssing import of warnings fixed.Renamed test so it comes last, because I suspect this test mess up the coverage stats.Reordered the tests.Added more tests.Cleaned up _find_default_scale.pyRemoved link to depsyReverted: install of cython and pip install setuptoolsDisabled sonar-scanner -X for python 3.5 because it crashes.Reverted [options.packages.find] to exclude tests againAdded cython and reverted to pip install setuptoolsUpdated sphinx to 1.6.7Try to install setuptools with conda instead.Added hypothesis and pytest to requirements.readthedocs.txtSet version of setuptools==37.0Added algopy, statsmodels and numpy to requirements.readthedocs.txtRestricted sphinx in the hope that the docs will be generated.Removed exclusion of tests/ directory from test coverage.Added dependencies into setup.cfgReadded six as dependencyRefactored and removed commented out code.Fixed a bug in the docstring example: Made sure the shape passed on to zeros is an integer.Fixed c_abs so it works with algopy on python 3.6.Fixed flaky test and made it more robust.Fixed bug in .travis.ymlRefactored the taylor function into the Taylor class in order to simplify the code.Fixed issue #35 and added testsAttempt to simplify complexityMade doctests more robustUpdated project pathChanged install of algopyFixed small bugsUpdated docstringsChanged Example and Reference to Examples and References in docstrings to comply with numpydoc-style.Renamed CHANGES.rst to CHANGELOG.rstRenamed source pathHack due to a bug in algopy or changed behaviour.Small fix.Try to reduce complexityReduced cognitive complexity of min_num_stepsSimplified  code in JacobianMerge branch ‘master’ ofhttps://github.com/pbrod/numdifftoolsFixed issue #34 Licence clarification.Locked coverage=4.3.4 due to a bug in coverage that cause code-climate test-reporter to fail.Added script for finding default scaleupdated from sonarcube to sonarcloudMade sure shape is an integer.Refactored make_step_generator into a step propertyIssue warning message to the user when setting the order to something different than 1 or 2 in Hessian.Updated example in Gradient.Reverted –timid option to coverage because it took too long time to run.Reverted –pep8 optionpep8 + added –timid in .travis.yml coverage run in order to to increase missed coverage.Refactored taylor to reduce complexityNo support for python 3.3. Added python 3.6Fixed a small bug and updated test.Removed unneccasarry perenthesis. Reduced the complexity of do_profileMade python3 compatibleRemoved assert FalseMade unittests more forgiving.updated doctest in nd_scipy.py and profiletools.py install line_profiler on travisMade python 3 compatibleUpdated testsAdded test_profiletools.py and capture_stdout_and_stderr in testing.pyOptimized numdifftools.core.py for speed: fd_rules are now only computed once.Only keeping html docs in the distribution.Added doctest and updated .pylintrc and requirements.txtReduced time footprint on tests in the hope that it will pass on Travis CI.Prefer static methods over instance methodsBetter memory handling: This fixes issue #27Added statsmodels to requirements.txtAdded nd_statsmodels.pySimplified inputMerge branch ‘master’ ofhttps://github.com/pbrod/numdifftoolsUpdated link to the documentation.Robert Parini (4):Avoid RuntimeWarning in _get_lognAllow fd_derivative to take complex valued functionssolarjoe (1):doc: added nd.directionaldiff exampleVersion 0.9.20, Jan 11, 2017Per A Brodtkorb (1):Updated the author email address in order for twine to be able to upload to pypi.Version 0.9.19, Jan 11, 2017Per A Brodtkorb (1):Updated setup.py in a attempt to get upload to pypi working again.Version 0.9.18, Jan 11, 2017Per A Brodtkorb (38):Updated setupAdded import statements in help header examples.Added more rigorous tests using hypothesis.Forced to use wxagg backendMoved import of matplotlib.pyplot to main in order to avoid import error on travis.Added fd_derivative functionUpdated references.Attempt to automate sonarcube analysisAdded testcoverage to sonarqube and codeclimateSimplified codeAdded .pylintrc + pep8Major change in api: class member variable self.f changed to self.funFixes issue #25 (Jacobian broken since 0.9.15)Version 0.9.17, Sep 8, 2016Andrew Fowlie (1):Fix ReadTheDocs link as mentioned in #21Per A Brodtkorb (79):Added test for MinMaxStepgeneratorRemoved obsolete docs from core.pyUpdated appveyor.ymlFixed sign in inverse matrixSimplified codeAdded appveyor badge + synchronised info.py with README.rst.Removed plot in help headerAdded Programming Language :: Python :: 3.5Simplified codeRenamed bicomplex to BicomplexSimplified example_functions.pyMoved MinStepGenerator, MaxStepGeneretor and MinMaxStepGenerator to step_generators.pyUnified the step generatorsMoved step_generator tests to test_step_generators.pyMajor simplification of step_generators.pyRemoved duplicated code + pep8Moved fornberg_weights to fornberg.py + added taylor and derivativeFixed print statementReplace xrange with rangeAdded examples + made computation more robust.Made ‘backward’ and alias for ‘reverse’ in nd_algopy.pyExpanded the tests + added test_docstrings to testing.pyReplace string interpolation with format()Removed obsolete parameterSmaller start radius for Fornberg methodSimplified “n” and “order” propertiesSimplified default_scaleRemoved unecessary parenthesis and code.Fixed a bug in Dea + small refactorings.Added test for EpsAlgAvoid mutable default args and prefer static methods over instance-meth.Refactored to reduce cyclomatic complexityChanged some instance methods to static methodsRenamed non-pythonic variable namesTurned on xvfb (X Virtual Framebuffer) to imitate a display.Added extra test for JacobianReplace lambda function with a defRemoved unused importAdded test for epsalgFixed test_scalar_to_vectorUpdated test_docstringsVersion 0.9.15, May 10, 2016Cody (2):Migrated%string formatingMigrated%string formatingPer A Brodtkorb (28):Updated README.rst + setup.cfgReplaced instance methods with static methods +pep8Merge branch ‘master’ ofhttps://github.com/pbrod/numdifftoolsFixed a bug: replaced missing triple quoteAdded depsy badgeadded .checkignore for quantificodeAdded .codeclimate.ymlFixed failing testsChanged instance methods to static methodsMade untyped exception handlers specificReplaced local function with a static methodSimplified testsRemoved duplicated code Simplified _Derivative._get_function_nameexclude tests from testclimateRenamed test_functions.py to example_functions.py Added test_example_functions.pyPer A. Brodtkorb (2):Merge pull request #17 from pbrod/autofix/wrapped2_to3_fixMerge pull request #18 from pbrod/autofix/wrapped2_to3_fix-0pbrod (17):updated conf.pyadded numpydoc>=0.5, sphinx_rtd_theme>=0.1.7 to setup_requires if sphinxupdated setup.pyadded requirements.readthedocs.txtUpdated README.rst with info about how to install it using conda in an anaconda package.updated conda install descriptionFixed number of arguments so it does not differs from overridden ‘_default_base_step’ methodAdded codecov to .travis.ymlAttempt to remove coverage of test-filesAdded directionaldiff function in order to calculate directional derivatives. Fixes issue #16. Also added supporting tests and examples to the documentation.Fixed isssue #19 multiple observations mishandled in JacobianMoved rosen function into numdifftools.testing.pyupdated import of rosen function from numdifftools.testingSimplified code + pep8 + added TestResidueUpdated readme.rst and replaced string interpolation with format()Cleaned Dea class + pep8Updated references for Wynn extrapolation method.Version 0.9.14, November 10, 2015pbrod (53):Updated documentation of setup.pyUpdated README.rstupdated versionAdded more documentationUpdated exampleAdded .landscape.yml     updated .coveragerc, .travis.ymlAdded coverageall to README.rst.updated docs/index.rstRemoved unused code and added tests/test_extrapolation.pyupdated testsAdded more testsReadded c_abs c_atan2Removed dependence on wheel, numpydoc>=0.5 and sphinx_rtd_theme>=0.1.7 (only needed for building documentation)updated conda path in .travis.ymladded omnia channel to .travis.ymlAdded conda_recipe files     Filtered out warnings in limits.pyVersion 0.9.13, October 30, 2015pbrod (21):Updated README.rst and CHANGES.rst.updated Limits.Made it possible to differentiate complex functions and allow zero’th order derivative.BUG: added missing derivative order, n to Gradient, Hessian, Jacobian.Made test more robust.Updated structure in setup according to pyscaffold version 2.4.2.Updated setup.cfg and deleted duplicate tests folder.removed unused code.Added appveyor.yml.Added required appveyor install scriptsFixed bug in appveyor.yml.added wheel to requirements.txt.updated appveyor.yml.Removed import matplotlib.Justin Lecher (1):Fix min version for numpy.kikocorreoso (1):fix some prints on run_benchmark.py to make it work with py3Version 0.9.12, August 28, 2015pbrod (12):Updated documentation.Updated version in conf.py.Updated CHANGES.rst.Reimplemented outlier detection and made it more robust.Added limits.py with tests.Updated main tests folder.Moved Richardson and dea3 to extrapolation.py.Making a new release in order to upload to pypi.Version 0.9.11, August 27, 2015pbrod (2):Fixed sphinx-build and updated docs.Fixed issue #9 Backward differentiation method fails with additional parameters.Version 0.9.10, August 26, 2015pbrod (7):Fixed sphinx-build and updated docs.Added more tests to nd_algopy.Dropped support for Python 2.6.Version 0.9.4, August 26, 2015pbrod (7):Fixed sphinx-build and updated docs.Version 0.9.3, August 23, 2015Paul Kienzle (1):more useful benchmark plots.pbrod (7):Fixed bugs and updated docs.Major rewrite of the easy to use interface to Algopy.Added possibility to calculate n’th order derivative not just for n=1 in nd_algopy.Added tests to the easy to use interface to algopy.Version 0.9.2, August 20, 2015pbrod (3):Updated documentationAdded parenthesis to a call to the print functionMade the test less strict in order to pass the tests on Travis for python 2.6 and 3.2.Version 0.9.1, August 20,2015Christoph Deil (1):Fix Sphinx buildpbrod (47):Total remake of numdifftools with slightly different call syntax.Can compute derivatives of order up to 10-14 depending on function and method used.Updated documentation and tests accordingly.Fixed a bug in dea3.Added StepsGenerator as an replacement for the adaptive option.Added bicomplex class for testing the complex step second derivative.Added fornberg_weights_all for computing optimal finite difference rules in a stable way.Added higher order complex step derivative methods.Version 0.7.7, December 18, 2014pbrod (35):Got travis-ci working in order to run the tests automatically.Fixed bugs in Dea class.Fixed better error estimate for the Hessian.Fixed tests for python 2.6.Adding tests as subpackage.Restructerd folders of numdifftools.Version 0.7.3, December 17, 2014pbrod (5):Small cosmetic fixes.pep8 + some refactorings.Simplified code by refactoring.Version 0.6.0, February 8, 2014pbrod (20):Update and rename README.md to README.rst.Simplified call to Derivative: removed step_fix.Deleted unused code.Simplified and Refactored. Now possible to choose step_num=1.Changed default step_nom from max(abs(x0), 0.2) to max(log2(abs(x0)), 0.2).pep8ified code and made sure that all tests pass.Version 0.5.0, January 10, 2014pbrod (9):Updated the examples in Gradient class and in info.py.Added test for vec2mat and docstrings + cosmetic fixes.Refactored code into private methods.Fixed issue #7: Derivative(fun)(numpy.ones((10,5)) * 2) failed.Made print statements compatible with python 3.Version 0.4.0, May 5, 2012pbrod (1)Fixed a bug for inf and nan values.Version 0.3.5, May 19, 2011pbrod (1)Fixed a bug for inf and nan values.Version 0.3.4, Feb 24, 2011pbrod (11)Made automatic choice for the stepsize more robust.Added easy to use interface to the algopy and scientificpython modules.Version 0.3.1, May 20, 2009pbrod (4)First version of numdifftools published on google.codeCopyright (c) 2009-2022, Per A. Brodtkorb, John D’Errico
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