franke

Franke's bivariate test function

Syntax

z = franke(x,y)

Description

z = franke(x,y) returns the value z(i) of Franke's function at the site (x(i),y(i)), i=1:numel(x), with z of the same size as x and y (which must be of the same size).

Franke's function is the following weighted sum of four exponentials:

34e−((9x−2)2+(9y−2)2)/4+34e−((9x+1)2/49−(9y+1)/10)    +12e−((9x−7)2+(9y−3)2)/4−15e−((9x−4)2+(9y−7)2)

Examples

The following commands provide a plot of Franke's function:

pts = (0:50)/50; [x,y] = ndgrid(pts,pts); z = franke(x,y);
surf(x,y,z), view(145,-2), set(gca,'Fontsize',16)

References

[1] Richard Franke. “A critical comparison of some methods for interpolation of scattered data.” Naval Postgraduate School Tech.Rep. NPS-53-79-003, March 1979.

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