Welcome to the numdifftools’ documentation!

This is the documentation of Numdifftools version 0.9.42 released Dec 11, 2025.

Bleeding edge available at: https://github.com/pbrod/numdifftools.

Official releases are available at: http://pypi.python.org/pypi/Numdifftools.

Contents:

• 1. Introduction
  • 1.1. What is numdifftools?
  • 1.2. How the documentation is organized
• 2. Tutorials
  • 2.1. Install guide
    • 2.1.1. Install Python
    • 2.1.2. Dependencies
    • 2.1.3. Install numdifftools
    • 2.1.4. Verifying installation
    • 2.1.5. That’s it!
  • 2.2. Getting started
    • 2.2.1. The derivative
    • 2.2.2. Gradient and Hessian estimation
  • 2.3. Conclusion
  • 2.4. What to read next
    • 2.4.1. Finding documentation
    • 2.4.2. How the documentation is organized
    • 2.4.3. How documentation is updated
• 3. How-to guides
  • 3.1. How to create virtual environments for python with conda
    • 3.1.1. Check conda is installed and in your PATH.
    • 3.1.2. Check conda is up to date.
    • 3.1.3. Create a virtual environment for your project.
    • 3.1.4. Activate your virtual environment.
    • 3.1.5. Install additional Python packages to a virtual environment.
    • 3.1.6. Deactivate your virtual environment.
    • 3.1.7. Delete a no longer needed virtual environment.
    • 3.1.8. Related info.
  • 3.2. Contributing
    • 3.2.1. Contribute a patch
• 4. Topics guides
  • 4.1. Introduction derivative estimation
  • 4.2. Numerical differentiation of a general function of one variable
  • 4.3. Unequally spaced finite difference rules
  • 4.4. Odd and even transformations of a function
  • 4.5. Complex step derivative
  • 4.6. High order derivative
  • 4.7. Richardson extrapolation methodology applied to derivative estimation
  • 4.8. Multiple term Richardson extrapolants
  • 4.9. Uncertainty estimates for Derivative
• 5. Reference
  • 5.1. Numdifftools summary
    • 5.1.1. numdifftools.core module
    • 5.1.2. Step generators
    • 5.1.3. numdifftools.extrapolation module
    • 5.1.4. numdifftools.limits module
    • 5.1.5. numdifftools.multicomplex module
    • 5.1.6. numdifftools.nd_algopy module
    • 5.1.7. numdifftools.nd_scipy module
    • 5.1.8. numdifftools.nd_statsmodels module
  • 5.2. Numdifftools package details
    • 5.2.1. numdifftools.tests package
    • 5.2.2. numdifftools.core module
    • 5.2.3. numdifftools.extrapolation module
    • 5.2.4. numdifftools.finite_difference module
    • 5.2.5. numdifftools.fornberg module
    • 5.2.6. numdifftools.limits module
    • 5.2.7. numdifftools.multicomplex module
    • 5.2.8. numdifftools.nd_algopy module
    • 5.2.9. numdifftools.nd_scipy module
    • 5.2.10. numdifftools.nd_statsmodels module
    • 5.2.11. numdifftools.step_generators module

• Changelog
  • [0.9.42]
    • 🐛 Bug Fixes
    • 📚 Documentation
    • ⚙️ Miscellaneous Tasks
  • [0.9.41] - 2022-11-10
  • [0.9.40] - 2021-06-02
  • [0.9.39] - 2019-06-10
  • [0.9.38] - 2019-06-10
  • [0.9.20] - 2017-01-11
  • [0.9.19] - 2017-01-11
  • [0.9.18] - 2017-01-11
  • [0.9.17] - 2016-09-08
  • [0.9.15] - 2016-05-10
  • [0.9.14] - 2015-11-10
  • [0.9.13] - 2015-10-30
  • [0.9.12] - 2015-08-28
  • [0.9.11] - 2015-08-27
  • [0.9.10] - 2015-08-26
  • [0.9.4] - 2015-08-26
  • [0.9.3] - 2015-08-23
  • [0.9.2] - 2015-08-20
  • [0.9.1] - 2015-08-20
  • [0.7.7] - 2014-12-18
  • [0.7.3] - 2014-12-17
  • [0.6.0] - 2014-02-08
  • [0.5.0] - 2014-01-10
  • [0.4.0] - 2012-05-05
  • [0.3.5] - 2011-05-19
  • [0.3.4] - 2011-02-24
  • [0.3.1] - 2009-05-20
• Contributors
• License
• Acknowledgments
• Indices and tables
• Bibliography