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Operators and Keywords

Function List:

C++ API

: d = del2 (M)
: d = del2 (M, h)
: d = del2 (M, dx, dy, …)

Calculate the discrete Laplace operator.

For a 2-dimensional matrix M this is defined as 

      1    / d^2            d^2         \
D  = --- * |---  M(x,y) +  ---  M(x,y) |
      4    \ dx^2           dy^2        /

For N-dimensional arrays the sum in parentheses is expanded to include second derivatives over the additional higher dimensions.

The spacing between evaluation points may be defined by h, which is a scalar defining the equidistant spacing in all dimensions. Alternatively, the spacing in each dimension may be defined separately by dx, dy, etc. A scalar spacing argument defines equidistant spacing, whereas a vector argument can be used to specify variable spacing. The length of the spacing vectors must match the respective dimension of M. The default spacing value is 1.

At least 3 data points are needed for each dimension. Boundary points are calculated from the linear extrapolation of interior points.

See also: gradient, diff.

Package: octave