9.3.45: `smooth'

`smooth {x [.n.]} \ | {y [.n.]} \ | {grid data [.f.|{along x|y}]}'

The `smooth x' command does smoothing by the following formula

x[i-1] x[i] x[i+1] ------ + ---- + ------ 4 2 4

The `smooth x .n.' command does boxcar smoothing with centred boxcars `.n.' points wide. The `smooth y' command does the same as `smooth x', but on the `y' column.

There are several methods of smoothing grid data. Note that isolated missing values are filled in by each method. (Let the author know if you'd like that `feature' to be an option.)

The `smooth grid data' command smooths gridded data, by weighted average in a plus-shaped window about each gridpoint. The smoothing algorithm replaces each interior gridpoint value `z[i][j]' by

z[i][j] z[i-1][j] + z[i+1][j] + z[i][j-1] + z[i][j+1] ------- + --------------------------------------------- 2 8

Points along the edges are smoothed by the same formula, after inventing image points outside the domain by planar extrapolation.

The `smooth grid data .f.' command performs partial smoothing. A temporary fully-smoothed grid `zSMOOTH[i][h]' is constructed as above, and a linear combination of this grid and the original grid is used as the replacement grid:

z[i][j] = (1-f) * z[i][j] + f * zSMOOTH[i][j]

where `f' is the value indicated on the command line. Thus, `smooth grid data 0' performs no smoothing at all, while `smooth grid data 1' is equivalent to `smooth grid data'.

The `smooth grid data along x' command smooths the grid data across `x' (i.e., horizontally), by replacing each value `z[i][j]' with the value

z[i][j] z[i-1][j] + z[i+1][j] ------- + --------------------- 2 4

Points along the edges are smoothed by the same formula, after inventing image points outside the domain by linear extrapolation.

The `smooth grid data along y' command does the same thing as `smooth grid data along x', but the smoothing is along `y'.

See also see Filter, a generalization of `smooth x|y' which allows for more sophisticated filters.