getFunc.m File Reference

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Functions
function	getFunc (in x, in y)
	Return the value of the 2-dimensional Himmelblau function at the specified input value. More...

Function Documentation

getFunc()

function getFunc	(	in	x,
		in	y
	)

Return the value of the 2-dimensional Himmelblau function at the specified input value.

Himmelblau's function is a multi-modal function, used to test the performance of optimization algorithms. The function is defined by:

\begin{equation} H(x, y) = (x^{2} + y - 11)^{2} + (x + y^{2} - 7)^{2} ~. \end{equation}

It has one local maximum at \(x = -0.270845\) and \(y = -0.923039\) where \(H(x, y) = 181.617\), and four identical local minima:

\begin{eqnarray} H(3.0,2.0) &=& 0.0 ~,\\ H(-2.805118, 3.131312) &=& 0.0 ~,\\ H(-3.779310, -3.283186) &=& 0.0 ~,\\ H(3.584428, -1.848126) &=& 0.0 ~. \end{eqnarray}

The function is named after David Mautner Himmelblau (1924–2011), who introduced it.
The locations of all the minima can be found analytically.

Parameters

[in]	x	: The input scalar or array of the same rank and shape as other input array-like arguments of type MATLAB double, representing the x-component of the state within the domain of Himmelblau function at which the function value must be computed.
[in]	y	: The input scalar or array of the same rank and shape as other input array-like arguments of type MATLAB double, representing the y-component of the state within the domain of Himmelblau function at which the function value must be computed.

Returns

func : The output scalar or array of the same rank and shape as the input array-like arguments representing the value of the Himmelblau function at the specified input x and y.

Possible calling interfaces ⛓

func = pm.stats.himmelblau.getFunc(x, y);

See also

pm.stats.himmelblau.getFunc
pm.stats.himmelblau.getLogUDF
pm.sampling.Paradram

Example usage ⛓

cd(fileparts(mfilename('fullpath'))); % Change working directory to source code directory.
addpath('../../../../../'); % Add the ParaMonte library root directory to the search path.
 
range = -6 : 0.01 : 6;
[x, y] = meshgrid(range, range);
z = pm.math.func.himmelblau.getFunc(x, y);
for dim = 2 : 3
    figure("color", "white");
    if  dim == 2
        contourf(x, y, z, 50);
    else
        surf(x, y, z, "EdgeColor", "none");
        zlabel("Z");
    end
    xlabel("X");
    ylabel("Y");
    cbar = colorbar();
    ylabel(cbar, "Function Value")
    pm.vis.figure.savefig("himmelblau.getFunc." + string(dim) + "d.png", "-m3");
end

Visualization of the example output ⛓

Final Remarks ⛓

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For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
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Copyright

Computational Data Science Lab

Author:

Amir Shahmoradi, May 16 2016, 9:03 AM, Oden Institute for Computational Engineering and Sciences (ICES), UT Austin