| MATLAB Function Reference | |
Syntax
Definition
If the matrix U is regarded as a function 
evaluated at the point on a square grid, then 4*del2(U) is a finite difference approximation of Laplace's differential operator applied to 
, that is:
in the interior. On the edges, the same formula is applied to a cubic extrapolation.
For functions of more variables 
, del2(U) is an approximation,
where 
is the number of variables in 
.
Description
L = del2(U)
where U is a rectangular array is a discrete approximation of
The matrix L is the same size as U with each element equal to the difference between an element of U and the average of its four neighbors.
-L = del2(U)
when U is an multidimensional array, returns an approximation of
L = del2(U,h)
where H is a scalar uses H as the spacing between points in each direction (h=1 by default).
L = del2(U,hx,hy)
when U is a rectangular array, uses the spacing specified by hx and hy. If hx is a scalar, it gives the spacing between points in the x-direction. If hx is a vector, it must be of length size(u,2) and specifies the x-coordinates of the points. Similarly, if hy is a scalar, it gives the spacing between points in the y-direction. If hy is a vector, it must be of length size(u,1) and specifies the y-coordinates of the points.
L = del2(U,hx,hy,hz,...)
where U is multidimensional uses the spacing given by hx, hy, hz, ...
Examples
For this function, 4*del2(U) is also 4.
[x,y] = meshgrid(-4:4,-3:3); U = x.*x+y.*y U = 25 18 13 10 9 10 13 18 25 20 13 8 5 4 5 8 13 20 17 10 5 2 1 2 5 10 17 16 9 4 1 0 1 4 9 16 17 10 5 2 1 2 5 10 17 20 13 8 5 4 5 8 13 20 25 18 13 10 9 10 13 18 25
V = 4*del2(U) V = 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
See Also
| | deconv | delaunay | |
is