Module ImportFrom alias alias alias ImportFrom alias alias alias alias alias alias alias alias alias ImportFrom alias ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults Num body Expr Call AttributeLoad NameLoad attr NameLoad NameLoad Assign AttributeStore NameLoad attr Call NameLoad BinOpMult ListLoad Num AttributeLoad NameLoad attr BinOpMult ListLoad Num AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr ListLoad ListComp Num comprehension NameStore Call NameLoad AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr ListLoad TupleLoad Num Num TupleLoad Num Num Assign AttributeStore NameLoad attr Num Assign AttributeStore NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults vararg body AugAssignAdd AttributeStore NameLoad attr Num Assign NameStore Num Assign NameStore AttributeLoad Call NameLoad Call NameLoad Num BinOpAdd NameLoad Num attr Assign NameStore Call NameLoad Num BinOpMult AttributeLoad NameLoad attr Num Assign NameStore BinOpMult Call NameLoad BinOpMult BinOpPow Num NameLoad NameLoad BinOpPow Num UnaryOpUSub NameLoad Return Call NameLoad BinOpAdd BinOpMult Call NameLoad NameLoad keyword Num BinOpAdd NameLoad Num Num decorator_list decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults Num body Expr Call AttributeLoad NameLoad attr NameLoad NameLoad Assign AttributeStore NameLoad attr Call NameLoad BinOpMult ListLoad Num AttributeLoad NameLoad attr BinOpMult ListLoad Num AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr ListLoad ListLoad Num Num Assign AttributeStore NameLoad attr ListLoad TupleLoad Num Num TupleLoad Num Num Assign AttributeStore NameLoad attr Num decorator_list FunctionDef arguments args NameParam NameParam defaults vararg body AugAssignAdd AttributeStore NameLoad attr Num Assign NameStore BinOpMult BinOpPow Call NameLoad BinOpSub SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num Num BinOpPow Call NameLoad BinOpAdd SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num Num Return BinOpDiv NameLoad Call NameLoad BinOpAdd BinOpPow SubscriptLoad NameLoad Index Num Num BinOpPow SubscriptLoad NameLoad Index Num Num decorator_list decorator_list ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam defaults Num body Expr Call AttributeLoad NameLoad attr NameLoad NameLoad Assign AttributeStore NameLoad attr Call NameLoad BinOpMult ListLoad Num AttributeLoad NameLoad attr BinOpMult ListLoad Num AttributeLoad NameLoad attr Assign AttributeStore NameLoad attr ListLoad ListLoad Num Num Num Num Assign AttributeStore NameLoad attr Num Assign AttributeStore NameLoad attr Call NameLoad ListLoad Num Num Num BinOpDiv Num Num BinOpDiv Num Num BinOpDiv Num Num BinOpDiv Num Num BinOpDiv Num Num BinOpDiv Num Num BinOpDiv Num Num BinOpDiv Num Num Assign AttributeStore NameLoad attr Call NameLoad ListLoad Num Num Num Num Num Num Num Num Num Num Num decorator_list FunctionDef arguments args NameParam NameParam defaults vararg body AugAssignAdd AttributeStore NameLoad attr Num Assign NameStore BinOpSub AttributeLoad NameLoad attr BinOpDiv BinOpMult SubscriptLoad NameLoad Index Num BinOpAdd BinOpPow AttributeLoad NameLoad attr Num BinOpMult AttributeLoad NameLoad attr SubscriptLoad NameLoad Index Num BinOpAdd BinOpAdd BinOpPow AttributeLoad NameLoad attr Num BinOpMult AttributeLoad NameLoad attr SubscriptLoad NameLoad Index Num SubscriptLoad NameLoad Index Num Return Call NameLoad BinOpPow NameLoad Num decorator_list decorator_list
N/A __future__ division print_function absolute_import numpy asarray atleast_2d floor arange sin sqrt prod sum round go_benchmark Benchmark Katsuura N/A Benchmark N/A N/A 
    Katsuura objective function.

    This class defines the Katsuura [1]_ global optimization problem. This is a
    multimodal minimization problem defined as follows:

    .. math::

        f_{\text{Katsuura}}(x) = \prod_{i=0}^{n-1} \left [ 1 +
        (i+1) \sum_{k=1}^{d} \lfloor (2^k x_i) \rfloor 2^{-k} \right ]


    Where, in this exercise, :math:`d = 32`.

    Here, :math:`n` represents the number of dimensions and 
    :math:`x_i \in [0, 100]` for :math:`i = 1, ..., n`.

    *Global optimum*: :math:`f(x) = 1` for :math:`x_i = 0` for
    :math:`i = 1, ..., n`.

    .. [1] Adorio, E. MVF - "Multivariate Test Functions Library in C for
    Unconstrained Global Optimization", 2005
    .. [2] Gavana, A. Global Optimization Benchmarks and AMPGO retrieved 2015

    TODO: Adorio has wrong global minimum.  Adorio uses round, Gavana docstring
    uses floor, but Gavana code uses round.  We'll use round...
     __init__ N/A N/A self dimensions N/A 2 N/A N/A N/A N/A Benchmark __init__ self dimensions N/A N/A self _bounds N/A zip N/A N/A 0.0 N/A self N N/A N/A 100.0 N/A self N N/A N/A self global_optimum N/A N/A 0.0 N/A _ N/A range N/A self N N/A N/A self custom_bounds N/A N/A 0 1 N/A 0 1 N/A N/A self fglob 1.0 N/A N/A self change_dimensionality True N/A fun N/A N/A self x N/A args N/A N/A N/A self nfev 1 N/A d 32 N/A k N/A N/A atleast_2d N/A arange 1 N/A d 1 T N/A i N/A arange 0.0 N/A N/A self N 1.0 N/A inner N/A N/A round N/A N/A 2 k x N/A 2.0 N/A k N/A N/A prod N/A N/A N/A sum inner axis 0 N/A i 1 1 N/A N/A Keane N/A Benchmark N/A N/A 
    Keane objective function.

    This class defines the Keane [1]_ global optimization problem. This
    is a multimodal minimization problem defined as follows:

    .. math::

        f_{\text{Keane}}(x) = \frac{\sin^2(x_1 - x_2)\sin^2(x_1 + x_2)}
        {\sqrt{x_1^2 + x_2^2}}


    with :math:`x_i \in [0, 10]` for :math:`i = 1, 2`.

    *Global optimum*: :math:`f(x) = 0.0` for 
    :math:`x = [7.85396153, 7.85396135]`.

    .. [1] Jamil, M. & Yang, X.-S. A Literature Survey of Benchmark Functions
    For Global Optimization Problems Int. Journal of Mathematical Modelling
    and Numerical Optimisation, 2013, 4, 150-194.

    TODO: Jamil #69, there is no way that the function can have a negative
    value.  Everything is squared.  I think that they have the wrong solution.
     __init__ N/A N/A self dimensions N/A 2 N/A N/A N/A N/A Benchmark __init__ self dimensions N/A N/A self _bounds N/A zip N/A N/A 0.0 N/A self N N/A N/A 10.0 N/A self N N/A N/A self global_optimum N/A N/A 7.85396153 7.85396135 N/A N/A self custom_bounds N/A N/A -1 0.34 N/A -1 0.34 N/A N/A self fglob 0.0 N/A fun N/A N/A self x N/A args N/A N/A N/A self nfev 1 N/A val N/A N/A N/A sin N/A N/A x N/A 0 N/A x N/A 1 2 N/A N/A sin N/A N/A x N/A 0 N/A x N/A 1 2 N/A N/A val N/A sqrt N/A N/A N/A x N/A 0 2 N/A N/A x N/A 1 2 N/A N/A Kowalik N/A Benchmark N/A N/A 
    Kowalik objective function.

    This class defines the Kowalik [1]_ global optimization problem. This
    is a multimodal minimization problem defined as follows:

    .. math::

        f_{\text{Kowalik}}(x) = \sum_{i=0}^{10} \left [ a_i
        - \frac{x_1 (b_i^2 + b_i x_2)} {b_i^2 + b_i x_3 + x_4} \right ]^2

    Where:

    .. math::

        \begin{matrix}
        a = [4, 2, 1, 1/2, 1/4 1/8, 1/10, 1/12, 1/14, 1/16] \\
        b = [0.1957, 0.1947, 0.1735, 0.1600, 0.0844, 0.0627,
             0.0456, 0.0342, 0.0323, 0.0235, 0.0246]\\
        \end{matrix}


    Here, :math:`n` represents the number of dimensions and :math:`x_i \in 
    [-5, 5]` for :math:`i = 1, ..., 4`.

    *Global optimum*: :math:`f(x) = 0.00030748610` for :math:`x = 
    [0.192833, 0.190836, 0.123117, 0.135766]`.

    ..[1] http://www.itl.nist.gov/div898/strd/nls/data/mgh09.shtml
     __init__ N/A N/A self dimensions N/A 4 N/A N/A N/A N/A Benchmark __init__ self dimensions N/A N/A self _bounds N/A zip N/A N/A -5.0 N/A self N N/A N/A 5.0 N/A self N N/A N/A self global_optimum N/A N/A 0.192833 0.190836 0.123117 0.135766 N/A N/A self fglob 0.0003074861 N/A N/A self a N/A asarray N/A 4.0 2.0 1.0 N/A 1 2.0 N/A 1 4.0 N/A 1 6.0 N/A 1 8.0 N/A 1 10.0 N/A 1 12.0 N/A 1 14.0 N/A 1 16.0 N/A N/A self b N/A asarray N/A 0.1957 0.1947 0.1735 0.16 0.0844 0.0627 0.0456 0.0342 0.0323 0.0235 0.0246 N/A fun N/A N/A self x N/A args N/A N/A N/A self nfev 1 N/A vec N/A N/A self b N/A N/A N/A x N/A 0 N/A N/A N/A self a 2 N/A N/A self a N/A x N/A 1 N/A N/A N/A N/A self a 2 N/A N/A self a N/A x N/A 2 N/A x N/A 3 N/A N/A sum N/A vec 2 N/A N/A