Welcome to the numdifftools’ documentation!

This is the documentation of Numdifftools version 0.9.41 released Dec 10, 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

• Contributors
• License
• Acknowledgments
• Indices and tables
• Bibliography