.. include:: headings.inc

.. currentmodule:: go_benchmark

.. _scipy test functions index:

|test_functions| SciPy Test Functions Index
===========================================

This page contains the general index of the benchmark problems used to test different
Global Optimization algorithms. It also shows some statistics on the "difficulty" of a multi-modal test problem, based
on the average successful minimization across all the Global Optimizers tested in this benchmark exercise. The *SciPy
Extended* test suite is based on the current SciPy Global Optimization benchmarks.

The test suite currently contains:

1. 18 one-dimensional test functions with multiple local/global minima;
2. 235 multivariate problems (where the number of independent variables ranges from 2 to 17),
   again with multiple local/global minima. I have added about 40 new functions to the standard
   `SciPy benchmarks <https://github.com/scipy/scipy/tree/master/benchmarks/benchmarks/go_benchmark_functions>`_.


Some of the multivariate problems are well known in the mathematical literature; for the less well-known
functions, I have taken their definitions mostly from the following references:

- A Literature Survey of Benchmark Functions For Global Optimization Problems (http://arxiv.org/pdf/1308.4008v1.pdf)
- Test functions for optimization needs (http://www.zsd.ict.pwr.wroc.pl/files/docs/functions.pdf)
- A Numerical Evaluation of Several Stochastic Algorithms on Selected Continuous Global 
  Optimization Test Problems (http://folk.uib.no/ssu029/Pdf_file/Ali05.pdf)
- NIST standard regression dataset (http://www.itl.nist.gov/div898/strd/nls/data/eckerle4.shtml)


  
Test Functions "Hardness"
-------------------------

The test suite contains a variety of Global Optimization problems, some of them are harder to solve than others,
irrespectively of the algorithm chosen to minimize the test function. The following table has been obtained by
running all the Global Optimizers available against all the N-D test functions for a collection of 100 random starting
points, and then averaging the successful minimizations across all the optimizers.

It can be easily seen that the :class:`~go_benchmark.DeVilliersGlasser02`, :class:`~go_benchmark.Meyer` and
:class:`~go_benchmark.CrownedCross` were always hard problems for all the algorithms, while others like
:class:`~go_benchmark.SchmidtVetters` and :class:`~go_benchmark.PenHolder` are amongst the easiest ones.

.. cssclass:: pretty-table

.. table:: Benchmark test functions "hardness"

    +------------------------------+----+---------------------+
    | Optimization Method          | N  | Overall Success (%) |
    +==============================+====+=====================+
    | DeVilliersGlasser02          | 5  | 0.00                |
    +------------------------------+----+---------------------+
    | Meyer                        | 3  | 0.00                |
    +------------------------------+----+---------------------+
    | Thurber                      | 7  | 0.00                |
    +------------------------------+----+---------------------+
    | CrownedCross                 | 2  | 0.08                |
    +------------------------------+----+---------------------+
    | XinSheYang03                 | 2  | 0.77                |
    +------------------------------+----+---------------------+
    | CrossLegTable                | 2  | 1.31                |
    +------------------------------+----+---------------------+
    | Trefethen                    | 2  | 1.85                |
    +------------------------------+----+---------------------+
    | Damavandi                    | 2  | 2.00                |
    +------------------------------+----+---------------------+
    | SineEnvelope                 | 2  | 2.31                |
    +------------------------------+----+---------------------+
    | Whitley                      | 2  | 3.69                |
    +------------------------------+----+---------------------+
    | Cola                         | 17 | 5.15                |
    +------------------------------+----+---------------------+
    | PowerSum                     | 4  | 5.46                |
    +------------------------------+----+---------------------+
    | BiggsExp05                   | 5  | 6.85                |
    +------------------------------+----+---------------------+
    | NewFunction02                | 2  | 7.15                |
    +------------------------------+----+---------------------+
    | Bukin06                      | 2  | 7.23                |
    +------------------------------+----+---------------------+
    | RosenbrockModified           | 2  | 8.15                |
    +------------------------------+----+---------------------+
    | Griewank                     | 2  | 8.46                |
    +------------------------------+----+---------------------+
    | Mishra03                     | 2  | 9.08                |
    +------------------------------+----+---------------------+
    | Salomon                      | 2  | 9.92                |
    +------------------------------+----+---------------------+
    | Stochastic                   | 2  | 11.23               |
    +------------------------------+----+---------------------+
    | Schaffer03                   | 2  | 11.38               |
    +------------------------------+----+---------------------+
    | XinSheYang01                 | 2  | 11.38               |
    +------------------------------+----+---------------------+
    | Zimmerman                    | 2  | 11.54               |
    +------------------------------+----+---------------------+
    | OddSquare                    | 2  | 12.46               |
    +------------------------------+----+---------------------+
    | Schaffer04                   | 2  | 12.62               |
    +------------------------------+----+---------------------+
    | NewFunction01                | 2  | 13.15               |
    +------------------------------+----+---------------------+
    | Kowalik                      | 4  | 14.31               |
    +------------------------------+----+---------------------+
    | Schaffer01                   | 2  | 14.77               |
    +------------------------------+----+---------------------+
    | Mishra04                     | 2  | 15.54               |
    +------------------------------+----+---------------------+
    | EggHolder                    | 2  | 16.00               |
    +------------------------------+----+---------------------+
    | DeVilliersGlasser01          | 4  | 16.15               |
    +------------------------------+----+---------------------+
    | Ripple01                     | 2  | 17.38               |
    +------------------------------+----+---------------------+
    | Watson                       | 6  | 17.54               |
    +------------------------------+----+---------------------+
    | Easom                        | 2  | 18.46               |
    +------------------------------+----+---------------------+
    | Price02                      | 2  | 18.62               |
    +------------------------------+----+---------------------+
    | DropWave                     | 2  | 19.31               |
    +------------------------------+----+---------------------+
    | Deb03                        | 2  | 19.69               |
    +------------------------------+----+---------------------+
    | Corana                       | 4  | 20.08               |
    +------------------------------+----+---------------------+
    | Ratkowsky01                  | 4  | 20.23               |
    +------------------------------+----+---------------------+
    | XinSheYang04                 | 2  | 20.38               |
    +------------------------------+----+---------------------+
    | Eckerle4                     | 3  | 21.85               |
    +------------------------------+----+---------------------+
    | BiggsExp04                   | 4  | 22.00               |
    +------------------------------+----+---------------------+
    | Deceptive                    | 2  | 23.54               |
    +------------------------------+----+---------------------+
    | ZeroSum                      | 2  | 23.77               |
    +------------------------------+----+---------------------+
    | Weierstrass                  | 2  | 23.92               |
    +------------------------------+----+---------------------+
    | Branin02                     | 2  | 24.08               |
    +------------------------------+----+---------------------+
    | Dolan                        | 5  | 24.54               |
    +------------------------------+----+---------------------+
    | Shubert03                    | 2  | 25.77               |
    +------------------------------+----+---------------------+
    | Pathological                 | 2  | 26.69               |
    +------------------------------+----+---------------------+
    | Colville                     | 4  | 26.85               |
    +------------------------------+----+---------------------+
    | XinSheYang02                 | 2  | 26.92               |
    +------------------------------+----+---------------------+
    | Schaffer02                   | 2  | 27.23               |
    +------------------------------+----+---------------------+
    | Powell                       | 4  | 27.54               |
    +------------------------------+----+---------------------+
    | UrsemWaves                   | 2  | 27.77               |
    +------------------------------+----+---------------------+
    | Gulf                         | 3  | 28.08               |
    +------------------------------+----+---------------------+
    | Shekel05                     | 4  | 29.15               |
    +------------------------------+----+---------------------+
    | Ratkowsky02                  | 3  | 29.31               |
    +------------------------------+----+---------------------+
    | WayburnSeader02              | 2  | 29.38               |
    +------------------------------+----+---------------------+
    | Tripod                       | 2  | 29.46               |
    +------------------------------+----+---------------------+
    | Wavy                         | 2  | 29.77               |
    +------------------------------+----+---------------------+
    | Paviani                      | 10 | 29.92               |
    +------------------------------+----+---------------------+
    | Trid                         | 6  | 31.00               |
    +------------------------------+----+---------------------+
    | Penalty02                    | 2  | 31.85               |
    +------------------------------+----+---------------------+
    | Chichinadze                  | 2  | 32.15               |
    +------------------------------+----+---------------------+
    | Shekel10                     | 4  | 33.38               |
    +------------------------------+----+---------------------+
    | Rastrigin                    | 2  | 34.15               |
    +------------------------------+----+---------------------+
    | Shekel07                     | 4  | 34.54               |
    +------------------------------+----+---------------------+
    | Hansen                       | 2  | 34.69               |
    +------------------------------+----+---------------------+
    | Leon                         | 2  | 35.15               |
    +------------------------------+----+---------------------+
    | Trigonometric02              | 2  | 35.15               |
    +------------------------------+----+---------------------+
    | TestTubeHolder               | 2  | 35.38               |
    +------------------------------+----+---------------------+
    | YaoLiu09                     | 2  | 35.54               |
    +------------------------------+----+---------------------+
    | Xor                          | 9  | 35.92               |
    +------------------------------+----+---------------------+
    | Ackley01                     | 2  | 36.00               |
    +------------------------------+----+---------------------+
    | Schwefel06                   | 2  | 36.00               |
    +------------------------------+----+---------------------+
    | Hartmann6                    | 6  | 37.77               |
    +------------------------------+----+---------------------+
    | Rosenbrock                   | 2  | 37.85               |
    +------------------------------+----+---------------------+
    | Levy05                       | 2  | 38.15               |
    +------------------------------+----+---------------------+
    | Ursem03                      | 2  | 38.31               |
    +------------------------------+----+---------------------+
    | Shubert01                    | 2  | 38.46               |
    +------------------------------+----+---------------------+
    | BartelsConn                  | 2  | 39.31               |
    +------------------------------+----+---------------------+
    | DeflectedCorrugatedSpring    | 2  | 39.54               |
    +------------------------------+----+---------------------+
    | Cube                         | 2  | 40.08               |
    +------------------------------+----+---------------------+
    | Ripple25                     | 2  | 40.15               |
    +------------------------------+----+---------------------+
    | Decanomial                   | 2  | 41.62               |
    +------------------------------+----+---------------------+
    | Trigonometric01              | 2  | 42.38               |
    +------------------------------+----+---------------------+
    | JennrichSampson              | 2  | 43.08               |
    +------------------------------+----+---------------------+
    | VenterSobiezcczanskiSobieski | 2  | 43.08               |
    +------------------------------+----+---------------------+
    | Shubert04                    | 2  | 43.62               |
    +------------------------------+----+---------------------+
    | Schwefel21                   | 2  | 43.77               |
    +------------------------------+----+---------------------+
    | BiggsExp03                   | 3  | 43.92               |
    +------------------------------+----+---------------------+
    | ElAttarVidyasagarDutta       | 2  | 44.00               |
    +------------------------------+----+---------------------+
    | BoxBetts                     | 3  | 44.15               |
    +------------------------------+----+---------------------+
    | Mishra09                     | 3  | 44.38               |
    +------------------------------+----+---------------------+
    | Cigar                        | 2  | 44.77               |
    +------------------------------+----+---------------------+
    | FreudensteinRoth             | 2  | 45.23               |
    +------------------------------+----+---------------------+
    | Step01                       | 2  | 45.62               |
    +------------------------------+----+---------------------+
    | Step02                       | 2  | 45.92               |
    +------------------------------+----+---------------------+
    | Wolfe                        | 3  | 46.15               |
    +------------------------------+----+---------------------+
    | Price03                      | 2  | 46.77               |
    +------------------------------+----+---------------------+
    | Hartmann3                    | 3  | 46.85               |
    +------------------------------+----+---------------------+
    | Bohachevsky03                | 2  | 47.00               |
    +------------------------------+----+---------------------+
    | Mishra08                     | 2  | 47.08               |
    +------------------------------+----+---------------------+
    | MieleCantrell                | 4  | 47.46               |
    +------------------------------+----+---------------------+
    | Schwefel20                   | 2  | 47.46               |
    +------------------------------+----+---------------------+
    | Langermann                   | 2  | 47.54               |
    +------------------------------+----+---------------------+
    | HelicalValley                | 3  | 47.69               |
    +------------------------------+----+---------------------+
    | Ackley02                     | 2  | 48.23               |
    +------------------------------+----+---------------------+
    | Mishra06                     | 2  | 48.38               |
    +------------------------------+----+---------------------+
    | NeedleEye                    | 2  | 48.62               |
    +------------------------------+----+---------------------+
    | LennardJones                 | 6  | 48.92               |
    +------------------------------+----+---------------------+
    | WayburnSeader01              | 2  | 48.92               |
    +------------------------------+----+---------------------+
    | YaoLiu04                     | 2  | 48.92               |
    +------------------------------+----+---------------------+
    | Ursem04                      | 2  | 49.77               |
    +------------------------------+----+---------------------+
    | Price04                      | 2  | 50.92               |
    +------------------------------+----+---------------------+
    | Schwefel22                   | 2  | 51.62               |
    +------------------------------+----+---------------------+
    | Mishra10                     | 2  | 51.77               |
    +------------------------------+----+---------------------+
    | Alpine01                     | 2  | 52.54               |
    +------------------------------+----+---------------------+
    | CrossInTray                  | 2  | 52.54               |
    +------------------------------+----+---------------------+
    | Beale                        | 2  | 52.92               |
    +------------------------------+----+---------------------+
    | Parsopoulos                  | 2  | 53.69               |
    +------------------------------+----+---------------------+
    | Judge                        | 2  | 54.31               |
    +------------------------------+----+---------------------+
    | Quintic                      | 2  | 54.38               |
    +------------------------------+----+---------------------+
    | Schwefel36                   | 2  | 55.38               |
    +------------------------------+----+---------------------+
    | Bohachevsky02                | 2  | 55.46               |
    +------------------------------+----+---------------------+
    | Gear                         | 4  | 55.77               |
    +------------------------------+----+---------------------+
    | StretchedV                   | 2  | 56.31               |
    +------------------------------+----+---------------------+
    | StyblinskiTang               | 2  | 56.92               |
    +------------------------------+----+---------------------+
    | Qing                         | 2  | 57.85               |
    +------------------------------+----+---------------------+
    | Bohachevsky01                | 2  | 58.77               |
    +------------------------------+----+---------------------+
    | BiggsExp02                   | 2  | 59.08               |
    +------------------------------+----+---------------------+
    | Schwefel26                   | 2  | 59.15               |
    +------------------------------+----+---------------------+
    | Mishra05                     | 2  | 59.54               |
    +------------------------------+----+---------------------+
    | RotatedEllipse01             | 2  | 59.62               |
    +------------------------------+----+---------------------+
    | Penalty01                    | 2  | 59.85               |
    +------------------------------+----+---------------------+
    | EggCrate                     | 2  | 59.92               |
    +------------------------------+----+---------------------+
    | Pinter                       | 2  | 60.38               |
    +------------------------------+----+---------------------+
    | Deb01                        | 2  | 60.62               |
    +------------------------------+----+---------------------+
    | Vincent                      | 2  | 60.85               |
    +------------------------------+----+---------------------+
    | RotatedEllipse02             | 2  | 61.38               |
    +------------------------------+----+---------------------+
    | Bird                         | 2  | 61.62               |
    +------------------------------+----+---------------------+
    | Price01                      | 2  | 61.77               |
    +------------------------------+----+---------------------+
    | Mishra01                     | 2  | 61.85               |
    +------------------------------+----+---------------------+
    | PermFunction01               | 2  | 62.15               |
    +------------------------------+----+---------------------+
    | McCormick                    | 2  | 62.92               |
    +------------------------------+----+---------------------+
    | Giunta                       | 2  | 63.00               |
    +------------------------------+----+---------------------+
    | Csendes                      | 2  | 63.15               |
    +------------------------------+----+---------------------+
    | Levy13                       | 2  | 63.38               |
    +------------------------------+----+---------------------+
    | Brent                        | 2  | 63.46               |
    +------------------------------+----+---------------------+
    | DeckkersAarts                | 2  | 63.62               |
    +------------------------------+----+---------------------+
    | Ackley03                     | 2  | 63.77               |
    +------------------------------+----+---------------------+
    | GoldsteinPrice               | 2  | 64.38               |
    +------------------------------+----+---------------------+
    | Branin01                     | 2  | 64.69               |
    +------------------------------+----+---------------------+
    | Sargan                       | 2  | 64.77               |
    +------------------------------+----+---------------------+
    | Bukin04                      | 2  | 65.38               |
    +------------------------------+----+---------------------+
    | CarromTable                  | 2  | 65.69               |
    +------------------------------+----+---------------------+
    | ThreeHumpCamel               | 2  | 65.92               |
    +------------------------------+----+---------------------+
    | Exp2                         | 2  | 66.15               |
    +------------------------------+----+---------------------+
    | Matyas                       | 2  | 66.15               |
    +------------------------------+----+---------------------+
    | Plateau                      | 2  | 66.92               |
    +------------------------------+----+---------------------+
    | PermFunction02               | 2  | 67.69               |
    +------------------------------+----+---------------------+
    | Rana                         | 2  | 67.77               |
    +------------------------------+----+---------------------+
    | Zacharov                     | 2  | 67.85               |
    +------------------------------+----+---------------------+
    | Brown                        | 2  | 67.92               |
    +------------------------------+----+---------------------+
    | Keane                        | 2  | 67.92               |
    +------------------------------+----+---------------------+
    | MultiModal                   | 2  | 68.08               |
    +------------------------------+----+---------------------+
    | Alpine02                     | 2  | 68.08               |
    +------------------------------+----+---------------------+
    | DixonPrice                   | 2  | 68.38               |
    +------------------------------+----+---------------------+
    | Levy03                       | 2  | 68.46               |
    +------------------------------+----+---------------------+
    | Zettl                        | 2  | 68.62               |
    +------------------------------+----+---------------------+
    | Katsuura                     | 2  | 68.69               |
    +------------------------------+----+---------------------+
    | Schwefel01                   | 2  | 68.69               |
    +------------------------------+----+---------------------+
    | Adjiman                      | 2  | 69.00               |
    +------------------------------+----+---------------------+
    | Sodp                         | 2  | 69.08               |
    +------------------------------+----+---------------------+
    | Bukin02                      | 2  | 69.23               |
    +------------------------------+----+---------------------+
    | Mishra02                     | 2  | 69.23               |
    +------------------------------+----+---------------------+
    | AMGM                         | 2  | 69.31               |
    +------------------------------+----+---------------------+
    | Mishra11                     | 2  | 69.46               |
    +------------------------------+----+---------------------+
    | Schwefel02                   | 2  | 69.54               |
    +------------------------------+----+---------------------+
    | Ursem01                      | 2  | 70.08               |
    +------------------------------+----+---------------------+
    | Infinity                     | 2  | 70.23               |
    +------------------------------+----+---------------------+
    | HimmelBlau                   | 2  | 71.85               |
    +------------------------------+----+---------------------+
    | Sphere                       | 2  | 72.15               |
    +------------------------------+----+---------------------+
    | Exponential                  | 2  | 72.77               |
    +------------------------------+----+---------------------+
    | HolderTable                  | 2  | 72.92               |
    +------------------------------+----+---------------------+
    | Michalewicz                  | 2  | 73.38               |
    +------------------------------+----+---------------------+
    | Hosaki                       | 2  | 74.23               |
    +------------------------------+----+---------------------+
    | Schwefel04                   | 2  | 74.46               |
    +------------------------------+----+---------------------+
    | Zirilli                      | 2  | 74.62               |
    +------------------------------+----+---------------------+
    | Mishra07                     | 2  | 74.92               |
    +------------------------------+----+---------------------+
    | Treccani                     | 2  | 75.23               |
    +------------------------------+----+---------------------+
    | SixHumpCamel                 | 2  | 75.62               |
    +------------------------------+----+---------------------+
    | Quadratic                    | 2  | 76.38               |
    +------------------------------+----+---------------------+
    | CosineMixture                | 2  | 76.92               |
    +------------------------------+----+---------------------+
    | PenHolder                    | 2  | 79.00               |
    +------------------------------+----+---------------------+
    | SchmidtVetters               | 3  | 82.15               |
    +------------------------------+----+---------------------+
	
|


Multidimensional Test Functions Index
-------------------------------------
 
- :ref:`SciPy N-D Test Functions A`

  1. :class:`~go_benchmark.Ackley01`
  2. :class:`~go_benchmark.Ackley02`
  3. :class:`~go_benchmark.Ackley03`
  4. :class:`~go_benchmark.Ackley04`
  5. :class:`~go_benchmark.Adjiman`
  6. :class:`~go_benchmark.Alpine01`
  7. :class:`~go_benchmark.Alpine02`
  8. :class:`~go_benchmark.AMGM`

-----

- :ref:`SciPy N-D Test Functions B`

  1. :class:`~go_benchmark.BartelsConn`
  2. :class:`~go_benchmark.Beale`
  3. :class:`~go_benchmark.BiggsExp02`
  4. :class:`~go_benchmark.BiggsExp03`
  5. :class:`~go_benchmark.BiggsExp04`
  6. :class:`~go_benchmark.BiggsExp05`
  7. :class:`~go_benchmark.BiggsExp06`
  8. :class:`~go_benchmark.Bird`
  9. :class:`~go_benchmark.Bohachevsky01`
  10. :class:`~go_benchmark.Bohachevsky02`
  11. :class:`~go_benchmark.Bohachevsky03`
  12. :class:`~go_benchmark.Booth`
  13. :class:`~go_benchmark.BoxBetts`
  14. :class:`~go_benchmark.Brad`
  15. :class:`~go_benchmark.Branin01`
  16. :class:`~go_benchmark.Branin02`
  17. :class:`~go_benchmark.Brent`
  18. :class:`~go_benchmark.Brown`
  19. :class:`~go_benchmark.BuecheRastrigin`
  20. :class:`~go_benchmark.Bukin02`
  21. :class:`~go_benchmark.Bukin04`
  22. :class:`~go_benchmark.Bukin06`

-----

- :ref:`SciPy N-D Test Functions C`

  1. :class:`~go_benchmark.CarromTable`
  2. :class:`~go_benchmark.Chichinadze`
  3. :class:`~go_benchmark.Cigar`
  4. :class:`~go_benchmark.Cola`
  5. :class:`~go_benchmark.Colville`
  6. :class:`~go_benchmark.Corana`
  7. :class:`~go_benchmark.CosineMixture`
  8. :class:`~go_benchmark.Crescent`
  9. :class:`~go_benchmark.CrossInTray`
  10. :class:`~go_benchmark.CrossLegTable`
  11. :class:`~go_benchmark.CrownedCross`
  12. :class:`~go_benchmark.Csendes`
  13. :class:`~go_benchmark.Cube`

-----

- :ref:`SciPy N-D Test Functions D`

  1. :class:`~go_benchmark.Damavandi`
  2. :class:`~go_benchmark.Deb01`
  3. :class:`~go_benchmark.Deb03`
  4. :class:`~go_benchmark.Decanomial`
  5. :class:`~go_benchmark.Deceptive`
  6. :class:`~go_benchmark.DeckkersAarts`
  7. :class:`~go_benchmark.DeflectedCorrugatedSpring`
  8. :class:`~go_benchmark.DeJong5`
  9. :class:`~go_benchmark.DeVilliersGlasser01`
  10. :class:`~go_benchmark.DeVilliersGlasser02`
  11. :class:`~go_benchmark.DixonPrice`
  12. :class:`~go_benchmark.Dolan`
  13. :class:`~go_benchmark.DropWave`

-----

- :ref:`SciPy N-D Test Functions E`

  1. :class:`~go_benchmark.Easom`
  2. :class:`~go_benchmark.Eckerle4`
  3. :class:`~go_benchmark.EggCrate`
  4. :class:`~go_benchmark.EggHolder`
  5. :class:`~go_benchmark.ElAttarVidyasagarDutta`
  6. :class:`~go_benchmark.Engvall`
  7. :class:`~go_benchmark.Exp2`
  8. :class:`~go_benchmark.Exponential`

-----

- :ref:`SciPy N-D Test Functions F`

  1. :class:`~go_benchmark.F2`
  2. :class:`~go_benchmark.FreudensteinRoth`
  3. :class:`~go_benchmark.Friedman`

-----

- :ref:`SciPy N-D Test Functions G`

  1. :class:`~go_benchmark.Gear`
  2. :class:`~go_benchmark.Giunta`
  3. :class:`~go_benchmark.GoldsteinPrice`
  4. :class:`~go_benchmark.GramacyLee02`
  5. :class:`~go_benchmark.GramacyLee03`
  6. :class:`~go_benchmark.Griewank`
  7. :class:`~go_benchmark.Gulf`

-----

- :ref:`SciPy N-D Test Functions H`

  1. :class:`~go_benchmark.Hansen`
  2. :class:`~go_benchmark.HappyCat`
  3. :class:`~go_benchmark.Hartmann3`
  4. :class:`~go_benchmark.Hartmann6`
  5. :class:`~go_benchmark.HelicalValley`
  6. :class:`~go_benchmark.HimmelBlau`
  7. :class:`~go_benchmark.HolderTable01`
  8. :class:`~go_benchmark.HolderTable02`
  9. :class:`~go_benchmark.Hosaki`
  10. :class:`~go_benchmark.Hougen`
  11. :class:`~go_benchmark.HyperGrid`

-----

- :ref:`SciPy N-D Test Functions I`

  1. :class:`~go_benchmark.Infinity`
  2. :class:`~go_benchmark.InvertedCosine`

-----

- :ref:`SciPy N-D Test Functions J`

  1. :class:`~go_benchmark.JennrichSampson`
  2. :class:`~go_benchmark.Judge`

-----

- :ref:`SciPy N-D Test Functions K`

  1. :class:`~go_benchmark.Katsuura`
  2. :class:`~go_benchmark.Keane`
  3. :class:`~go_benchmark.Kearfott`
  4. :class:`~go_benchmark.Kowalik`

-----

- :ref:`SciPy N-D Test Functions L`

  1. :class:`~go_benchmark.Langermann`
  2. :class:`~go_benchmark.LennardJones`
  3. :class:`~go_benchmark.Leon`
  4. :class:`~go_benchmark.Levy03`
  5. :class:`~go_benchmark.Levy05`
  6. :class:`~go_benchmark.Levy13`
  7. :class:`~go_benchmark.LunacekBiRastrigin`
  8. :class:`~go_benchmark.LunacekBiSphere`

-----

- :ref:`SciPy N-D Test Functions M`

  1. :class:`~go_benchmark.Matyas`
  2. :class:`~go_benchmark.McCormick`
  3. :class:`~go_benchmark.Meyer`
  4. :class:`~go_benchmark.MeyerRoth`
  5. :class:`~go_benchmark.Michalewicz`
  6. :class:`~go_benchmark.MieleCantrell`
  7. :class:`~go_benchmark.Mishra01`
  8. :class:`~go_benchmark.Mishra02`
  9. :class:`~go_benchmark.Mishra03`
  10. :class:`~go_benchmark.Mishra04`
  11. :class:`~go_benchmark.Mishra05`
  12. :class:`~go_benchmark.Mishra06`
  13. :class:`~go_benchmark.Mishra07`
  14. :class:`~go_benchmark.Mishra08`
  15. :class:`~go_benchmark.Mishra09`
  16. :class:`~go_benchmark.Mishra10`
  17. :class:`~go_benchmark.Mishra10b`
  18. :class:`~go_benchmark.Mishra11`
  19. :class:`~go_benchmark.MullerBrown`
  20. :class:`~go_benchmark.MultiGaussian`
  21. :class:`~go_benchmark.MultiModal`

-----

- :ref:`SciPy N-D Test Functions N`

  1. :class:`~go_benchmark.NeedleEye`
  2. :class:`~go_benchmark.NewFunction01`
  3. :class:`~go_benchmark.NewFunction02`

-----

- :ref:`SciPy N-D Test Functions O`

  1. :class:`~go_benchmark.OddSquare`
  2. :class:`~go_benchmark.Osborne`

-----

- :ref:`SciPy N-D Test Functions P`

  1. :class:`~go_benchmark.Parsopoulos`
  2. :class:`~go_benchmark.Pathological`
  3. :class:`~go_benchmark.Paviani`
  4. :class:`~go_benchmark.Peaks`
  5. :class:`~go_benchmark.Penalty01`
  6. :class:`~go_benchmark.Penalty02`
  7. :class:`~go_benchmark.PenHolder`
  8. :class:`~go_benchmark.PermFunction01`
  9. :class:`~go_benchmark.PermFunction02`
  10. :class:`~go_benchmark.Picheny`
  11. :class:`~go_benchmark.Pinter`
  12. :class:`~go_benchmark.Plateau`
  13. :class:`~go_benchmark.Powell`
  14. :class:`~go_benchmark.PowerSum`
  15. :class:`~go_benchmark.Price01`
  16. :class:`~go_benchmark.Price02`
  17. :class:`~go_benchmark.Price03`
  18. :class:`~go_benchmark.Price04`

-----

- :ref:`SciPy N-D Test Functions Q`

  1. :class:`~go_benchmark.Qing`
  2. :class:`~go_benchmark.Quadratic`
  3. :class:`~go_benchmark.Quintic`

-----

- :ref:`SciPy N-D Test Functions R`

  1. :class:`~go_benchmark.Rana`
  2. :class:`~go_benchmark.Rastrigin`
  3. :class:`~go_benchmark.Ratkowsky01`
  4. :class:`~go_benchmark.Ratkowsky02`
  5. :class:`~go_benchmark.ReduxSum`
  6. :class:`~go_benchmark.Ripple01`
  7. :class:`~go_benchmark.Ripple25`
  8. :class:`~go_benchmark.Rosenbrock`
  9. :class:`~go_benchmark.RosenbrockDisc`
  10. :class:`~go_benchmark.RosenbrockModified`
  11. :class:`~go_benchmark.RotatedEllipse01`
  12. :class:`~go_benchmark.RotatedEllipse02`

-----

- :ref:`SciPy N-D Test Functions S`

  1. :class:`~go_benchmark.Salomon`
  2. :class:`~go_benchmark.Sargan`
  3. :class:`~go_benchmark.SawtoothXY`
  4. :class:`~go_benchmark.Schaffer01`
  5. :class:`~go_benchmark.Schaffer02`
  6. :class:`~go_benchmark.Schaffer03`
  7. :class:`~go_benchmark.Schaffer04`
  8. :class:`~go_benchmark.SchmidtVetters`
  9. :class:`~go_benchmark.Schwefel01`
  10. :class:`~go_benchmark.Schwefel02`
  11. :class:`~go_benchmark.Schwefel04`
  12. :class:`~go_benchmark.Schwefel06`
  13. :class:`~go_benchmark.Schwefel20`
  14. :class:`~go_benchmark.Schwefel21`
  15. :class:`~go_benchmark.Schwefel22`
  16. :class:`~go_benchmark.Schwefel26`
  17. :class:`~go_benchmark.Schwefel36`
  18. :class:`~go_benchmark.Shekel05`
  19. :class:`~go_benchmark.Shekel07`
  20. :class:`~go_benchmark.Shekel10`
  21. :class:`~go_benchmark.Shubert01`
  22. :class:`~go_benchmark.Shubert03`
  23. :class:`~go_benchmark.Shubert04`
  24. :class:`~go_benchmark.Simpleton`
  25. :class:`~go_benchmark.SineEnvelope`
  26. :class:`~go_benchmark.Sinusoidal`
  27. :class:`~go_benchmark.SixHumpCamel`
  28. :class:`~go_benchmark.Sodp`
  29. :class:`~go_benchmark.Sphere`
  30. :class:`~go_benchmark.SphericalSinc`
  31. :class:`~go_benchmark.Spike`
  32. :class:`~go_benchmark.Step01`
  33. :class:`~go_benchmark.Step02`
  34. :class:`~go_benchmark.Step03`
  35. :class:`~go_benchmark.Stochastic`
  36. :class:`~go_benchmark.StretchedV`
  37. :class:`~go_benchmark.StyblinskiTang`

-----

- :ref:`SciPy N-D Test Functions T`

  1. :class:`~go_benchmark.TestTubeHolder`
  2. :class:`~go_benchmark.ThreeHumpCamel`
  3. :class:`~go_benchmark.Thurber`
  4. :class:`~go_benchmark.Treccani`
  5. :class:`~go_benchmark.Trefethen`
  6. :class:`~go_benchmark.Trid`
  7. :class:`~go_benchmark.TridiagonalMatrix`
  8. :class:`~go_benchmark.Trigonometric01`
  9. :class:`~go_benchmark.Trigonometric02`
  10. :class:`~go_benchmark.Tripod`
  11. :class:`~go_benchmark.Tsoulos`

-----

- :ref:`SciPy N-D Test Functions U`

  1. :class:`~go_benchmark.Ursem01`
  2. :class:`~go_benchmark.Ursem03`
  3. :class:`~go_benchmark.Ursem04`
  4. :class:`~go_benchmark.UrsemWaves`

-----

- :ref:`SciPy N-D Test Functions V`

  1. :class:`~go_benchmark.VenterSobiezcczanskiSobieski`
  2. :class:`~go_benchmark.Vincent`

-----

- :ref:`SciPy N-D Test Functions W`

  1. :class:`~go_benchmark.Watson`
  2. :class:`~go_benchmark.Wavy`
  3. :class:`~go_benchmark.WayburnSeader01`
  4. :class:`~go_benchmark.WayburnSeader02`
  5. :class:`~go_benchmark.WayburnSeader03`
  6. :class:`~go_benchmark.Weierstrass`
  7. :class:`~go_benchmark.Whitley`
  8. :class:`~go_benchmark.Wolfe`

-----

- :ref:`SciPy N-D Test Functions X`

  1. :class:`~go_benchmark.XinSheYang01`
  2. :class:`~go_benchmark.XinSheYang02`
  3. :class:`~go_benchmark.XinSheYang03`
  4. :class:`~go_benchmark.XinSheYang04`
  5. :class:`~go_benchmark.Xor`

-----

- :ref:`SciPy N-D Test Functions Y`

  1. :class:`~go_benchmark.YaoLiu04`
  2. :class:`~go_benchmark.YaoLiu09`

-----

- :ref:`SciPy N-D Test Functions Z`

  1. :class:`~go_benchmark.Zacharov`
  2. :class:`~go_benchmark.Zagros`
  3. :class:`~go_benchmark.ZeroSum`
  4. :class:`~go_benchmark.Zettl`
  5. :class:`~go_benchmark.Zimmerman`
  6. :class:`~go_benchmark.Zirilli`


.. toctree::
   :maxdepth: 2
   :hidden:

   scipy_test_functions_nd_A
   scipy_test_functions_nd_B
   scipy_test_functions_nd_C
   scipy_test_functions_nd_D
   scipy_test_functions_nd_E
   scipy_test_functions_nd_F
   scipy_test_functions_nd_G
   scipy_test_functions_nd_H
   scipy_test_functions_nd_I
   scipy_test_functions_nd_J
   scipy_test_functions_nd_K
   scipy_test_functions_nd_L
   scipy_test_functions_nd_M
   scipy_test_functions_nd_N
   scipy_test_functions_nd_O
   scipy_test_functions_nd_P
   scipy_test_functions_nd_Q
   scipy_test_functions_nd_R
   scipy_test_functions_nd_S
   scipy_test_functions_nd_T
   scipy_test_functions_nd_U
   scipy_test_functions_nd_V
   scipy_test_functions_nd_W
   scipy_test_functions_nd_X
   scipy_test_functions_nd_Y
   scipy_test_functions_nd_Z