A robust and very sensitive tester for analytic derivatives.

## Project description

Derivcheck provides a robust and very sensitive checker of analytic partial derivates. It is intended to be used in unit tests of other projects. See deriv_check/basic_example.py for a basic example.

## Installation

Derivcheck can be installed with pip (system wide or in a virtual environment):

```pip install derivcheck
```

Alternatively, you can install derivcheck in your home directory:

```pip install derivcheck --user
```

```conda install -c theochem derivcheck
```

## Testing

The tests can be executed as follows:

```nosetests derivcheck
```

## Background and usage

This module implements a function assert_deriv, which uses Ridders’ numerical finite difference scheme to test the implementation of analytic finite differences. Ridders’ method automatically finds the step size (given an initial upper estimate) and the polynomial order that result in the best approximation. In practice, this means that 14 digits of precision can be reached with 6 to 12 evaluations of the function of interest.

The implementation of Ridders’ method is based on the one from the book “Numerical Recipes” (http://numerical.recipes/), which is in turn a slight rendition of the original method as proposed by Ridders. (Ridders, C.J.F. 1982, Advances in Engineering Software, vol. 4, no. 2, pp. 75–76. https://doi.org/10.1016/S0141-1195(82)80057-0)

It is assumed that you have implemented two functions: f and its derivative or gradient g. The function f takes one argument: a scalar or array with shape shape_in. It returns a scalar or an array with shape shape_out. The function g has the same input but returns a scalar or an array with shape (shape_out + shape_in).

The consistency of f and g, can then be tested around a input value origin with the following code:

```assert_deriv(f, g, origin)
```

where origin is a scalar or array with shape shape_in, depending on what f and g expect as input. An AssertionError is raised when the gradient function g is not consistent with numerical derivatives of f. If Ridders’ method does not converge to sufficiently accurate estimates of a derivative, a FloatingPointError is raised.

The function assert_deriv takes several optional arguments to tune its behavior:

• widths : float or np.ndarray (default 1e-4)

The initial (maximal) step size for the finite difference method. Do not take a value that is too small. When an array is given, each matrix element of the input of the function gets a different step size. When a matrix element is set to zero, the derivative towards that element is not tested. The function will not be sampled beyond [origin-widths, origin+widths].

• output_mask : np.ndarray or None (default)

This option is useful when the function returns an array output: it allows the caller to select which components of the output need to be tested. When not given, all components are tested.

• rtol : float

The allowed relative error on the derivative.

• atol : float

The allowed absolute error on the derivative.

## Release history

• 2017-08-22 1.1.3

Switch to theochem channel on anaconda.

• 2017-08-01 1.1.2

Remove unused dependency on future.

• 2017-08-01 1.1.1

Fix dependencies to simplify testing.

• 2017-08-01 1.1.0

• Tests are now included with the installed module.
• Experimental: deployment to github, pypi and anaconda.
• 2017-07-30 1.0.2

Updated README and install recipe for Conda

• 2017-07-30 1.0.1

Fix some missing files and extend README

• 2017-07-28 1.0.0

• Ridders’ finite difference scheme for testing analytic derivatives.
• Fully deterministic procedure.
• More intuitive API
• 2017-07-27 0.1.0

Code is made Python 3 compatible and still works with 2.7. Some packaging improvements.

• 2017-07-27 0.0.0

Initial version: code taken from the Romin project (with contributions and ideas from Michael Richer and Paul W. Ayers). Some bugs were fixed through QA and CI (pylint, pycodestyle, pydocstyle, nosetests and coverage).

## How to make a release (Github, PyPI and anaconda.org)

Before you do this, make sure everything is OK. The PyPI releases cannot be undone. If you delete a file from PyPI (because of a mistake), you cannot upload the fixed file with the same filename! See https://github.com/pypa/packaging-problems/issues/74

1. Update the release history.
2. Commit the final changes to master and push to github.
3. Wait for the CI tests to pass. Check if the README looks ok, etc. If needed, fix things and repeat step 2.
4. Make a git version tag: git tag <some_new_version> Follow the semantic versioning guidelines: http://semver.org
5. Push the tag to github: git push origin master --tags