Chapters: 1: Introduction 2: Simple example 3: Invocation 4: Finer Control 5: X-Y Plots 6: Contour Plots 7: Image Plots 8: Examples 9: Gri Commands 10: Programming 11: Environment 12: Emacs Mode 13: History 14: Installation 15: Gri Bugs 16: Test Suite 17: Gri in Press 18: Acknowledgments 19: License Indices: ConceptsCommandsVariables |
## 9.3.45: `
All these smoothing commands ignore the |

`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.