vassilios / savgol

Implements Savitzky-Golay filters in ruby (and eventually in NMatrix)

savgol

Provides implementations of Savitzky-Golay smoothing (filtering).

The gem is based on the scipy implementation (gives exactly the same result). A good explanation of the process may be found here on stackexchange.

Examples

Evenly spaced data

Array implementation (object oriented)

require 'savgol/array'
data = [1, 2, 3, 4, 3.5, 5, 3, 2.2, 3, 0, -1, 2, 0, -2, -5, -8, -7, -2, 0, 1, 1]
# window size = 5, polynomial order = 3
data.savgol(5,3)

Module implementation

require 'savgol'
data = [1, 2, 3, 4, 3.5, 5, 3, 2.2, 3, 0, -1, 2, 0, -2, -5, -8, -7, -2, 0, 1, 1]
# window size = 5, polynomial order = 3
Savgol.savgol(data, 5,3)

Uneven data

The speed gain of the Savitzky-Golay filter is lost when interpolating unevenly spaced data and devolves into simple polynomial linear regression [At least I believe they are equivalent in complexity since both require a matrix pseudo-inverse calculation as the most complex operation]. Even though it may be much slower, a filter that handles unevenly spaced data may be useful in some cases.

require 'savgol'
xvals = %w(-1 0 2 3 4 7 8 10 11 12 13 14 17 18).map &:to_f
yvals = %w(-2 1 0 1 1 3 4 7  8  9  7  4  1   2).map {|v| v.to_f + 30 }

Interpolate at the given x-values

Savgol.savgol_uneven(xvals, yvals, 5, 2)

Interpolate at a new set of x values

new_xvals = xvals.map {|v| v + 0.5 }
Savgol.savgol_uneven(xvals, yvals, 5, 2, new_xvals: new_xvals)

Installation

gem install savgol

TODO

• Implement for Scriruby's Nmatrix and NArray.
• Implement smoothing for unevenly sampled data.

Copyright

MIT license. See LICENSE.txt.