Crate argmin_testfunctions

A collection of two- and multidimensional test functions (and their derivatives and Hessians) for optimization algorithms. For two-dimensional test functions, the derivate and Hessian calculation does not allocate. For multi-dimensional tes functions, the derivative and Hessian calculation comes in two variants. One variant returns Vecs and hence does allocate. This is needed for cases, where the number of parameters is only known at run time. In case the number of parameters are known at compile-time, the _const variants can be used, which return fixed size arrays and hence do not allocate.

The derivative and Hessian calculation is always named <test function name>_derivative and <test function name>_hessian, respectively. The const generics variants are defined as <test function name>_derivative_const and <test function name>_hessian_const.

Some functions, such as ackley, rosenbrock and rastrigin come with additional optional parameters which change the shape of the functions. These additional parameters are exposed in ackley_abc, rosenbrock_ab and rastrigin_a.

All functions are generic over their inputs and work with [f64] and [f32].

Python wrapper

Thanks to the python module argmin-testfunctions-py, it is possible to use the functions in Python as well. Note that the derivative and Hessian calculation used in the wrapper will always allocate.

Running the tests and benchmarks

The tests can be run with

cargo test

The test functions derivatives and Hessians are tested against finitediff using proptest to sample the functions at various points.

All functions are benchmarked using criterion.rs. Run the benchmarks with

cargo bench

The report is available in target/criterion/report/index.html.

Contributing

This library is the most useful the more test functions it contains, therefore any contributions are highly welcome. For inspiration on what to implement and how to proceed, feel free to have a look at this issue.

While most of the implemented functions are probably already quite efficient, there are probably a few which may profit from performance improvements.

License

Licensed under either of

• Apache License, Version 2.0, (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)
• MIT License (LICENSE-MIT or http://opensource.org/licenses/MIT)

at your option.

Contribution

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.

Functions

• ackley
  Ackley test function
• ackley_abc
  Ackley test function
• ackley_abc_derivative
  Derivative of Ackley test function
• ackley_abc_derivative_const
  Derivative of Ackley test function
• ackley_abc_hessian
  Hessian of Ackley test function
• ackley_abc_hessian_const
  Hessian of Ackley test function
• ackley_derivative
  Derivative of Ackley test function
• ackley_derivative_const
  Derivative of Ackley test function
• ackley_hessian
  Hessian of Ackley test function
• ackley_hessian_const
  Hessian of Ackley test function
• beale
  Beale test function
• beale_derivative
  Derivative of Beale test function
• beale_hessian
  Derivative of Beale test function
• booth
  Booth test function
• booth_derivative
  Derivative of Booth test function
• booth_hessian
  Hessian of Booth test function
• bukin_n6
  Bukin test function No. 6
• bukin_n6_derivative
  Derivative of Bukin test function No. 6
• bukin_n6_hessian
  Hessian of Bukin test function No. 6
• cross_in_tray
  Cross-in-tray test function
• cross_in_tray_derivative
  Derivative of Cross-in-tray test function
• cross_in_tray_hessian
  Hessian of Cross-in-tray test function
• easom
  Easom test function
• easom_derivative
  Derivative of Easom test function
• easom_hessian
  Hessian of Easom test function
• eggholder
  Eggholder test function
• eggholder_derivative
  Derivative of Eggholder test function
• eggholder_hessian
  Hessian of Eggholder test function
• goldsteinprice
  Goldstein-Price test function
• goldsteinprice_derivative
  Derivative of Goldstein-Price test function
• goldsteinprice_hessian
  Hessian of Goldstein-Price test function
• himmelblau
  Himmelblau test function
• himmelblau_derivative
  Derivative of Himmelblau test function
• himmelblau_hessian
  Hessian of Himmelblau test function
• holder_table
  Holder table test function
• holder_table_derivative
  Derivative of the Holder table test function
• holder_table_hessian
  Hessian of the Holder table test function
• levy
  Levy test function
• levy_derivative
  Derivative of Levy test function
• levy_derivative_const
  Derivative of Levy test function
• levy_hessian
  Hessian of Levy test function
• levy_hessian_const
  Hessian of Levy test function
• levy_n13
  Levy test function No. 13
• levy_n13_derivative
  Derivative of Levy test function No. 13
• levy_n13_hessian
  Hessian of Levy test function No. 13
• matyas
  Matyas test function
• matyas_derivative
  Derivative of Matyas test function
• matyas_hessian
  Hessian of Matyas test function
• mccorminck
  McCorminck test function
• mccorminck_derivative
  Derivative of McCorminck test function
• mccorminck_hessian
  Hessian of McCorminck test function
• picheny
  Picheny test function
• picheny_derivative
  Derivative of Picheny test function
• picheny_hessian
  Hessian of Picheny test function
• rastrigin
  Rastrigin test function
• rastrigin_a
  Rastrigin test function
• rastrigin_a_derivative
  Derivative of Rastrigin test function where a can be chosen freely
• rastrigin_a_derivative_const
  Derivative of Rastrigin test function where a can be chosen freely
• rastrigin_a_hessian
  Hessian of Rastrigin test function where a can be chosen freely
• rastrigin_a_hessian_const
  Hessian of Rastrigin test function where a can be chosen freely
• rastrigin_derivative
  Derivative of Rastrigin test function
• rastrigin_derivative_const
  Derivative of Rastrigin test function
• rastrigin_hessian
  Hessian of Rastrigin test function
• rastrigin_hessian_const
  Hessian of Rastrigin test function
• rosenbrock
  Multidimensional Rosenbrock test function
• rosenbrock_ab
  Multidimensional Rosenbrock test function
• rosenbrock_ab_derivative
  Derivative of the multidimensional Rosenbrock test function
• rosenbrock_ab_derivative_const
  Derivative of the multidimensional Rosenbrock test function
• rosenbrock_ab_hessian
  Hessian of the multidimensional Rosenbrock test function
• rosenbrock_ab_hessian_const
  Hessian of the multidimensional Rosenbrock test function
• rosenbrock_derivative
  Derivative of the multidimensional Rosenbrock test function
• rosenbrock_derivative_const
  Derivative of the multidimensional Rosenbrock test function
• rosenbrock_hessian
  Hessian of the multidimensional Rosenbrock test function
• rosenbrock_hessian_const
  Hessian of the multidimensional Rosenbrock test function
• schaffer_n2
  Schaffer test function No. 2
• schaffer_n4
  Schaffer test function No. 4
• schaffer_n2_derivative
  Derivative of Schaffer test function No. 2
• schaffer_n2_hessian
  Hessian of Schaffer test function No. 2
• schaffer_n4_derivative
  Derivative of Schaffer test function No. 4
• schaffer_n4_hessian
  Hessian of Schaffer test function No. 4
• sphere
  Sphere test function
• sphere_derivative
  Derivative of sphere test function
• sphere_derivative_const
  Derivative of sphere test function
• sphere_hessian
  Hessian of sphere test function
• sphere_hessian_const
  Hessian of sphere test function
• styblinski_tang
  Styblinski-Tang test function
• styblinski_tang_derivative
  Derivative of Styblinski-Tang test function
• styblinski_tang_derivative_const
  Derivative of Styblinski-Tang test function
• styblinski_tang_hessian
  Hessian of Styblinski-Tang test function
• styblinski_tang_hessian_const
  Hessian of Styblinski-Tang test function
• threehumpcamel
  Three-hump camel test function
• threehumpcamel_derivative
  Derivative of Three-hump camel test function
• threehumpcamel_hessian
  Hessian of Three-hump camel test function
• zero
  Zero test function
• zero_derivative
  Derivative of zero test function
• zero_derivative_const
  Derivative of zero test function (const version)
• zero_hessian
  Hessian of zero test function
• zero_hessian_const
  Hessian of zero test function (const version)