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:

$\begin{array}{l} \frac{3}{4} e^{- ({(9 x - 2)}^{2} + {(9 y - 2)}^{2}) / 4} + \frac{3}{4} e^{- ({(9 x + 1)}^{2} / 49 + (9 y + 1) / 10)} \\ + \frac{1}{2} e^{- ({(9 x - 7)}^{2} + {(9 y - 3)}^{2}) / 4} - \frac{1}{5} e^{- ({(9 x - 4)}^{2} + {(9 y - 7)}^{2})} \end{array}$

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)

The plot shows a surface with two peaks.

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.