Provides an implementation of the Logicle data scale and its inverse. The Logicle data scale is a generalization of the inverse hyperbolic sine function or arcsinh. Like arcsinh it is logarithmic for large data values, linear in the neighborhood of zero, symmetric around zero and changes smoothly between the log and linear regions. It is more general because the width of the linear region can be independently controlled. The scale is parameterized by the choice of a number of decades of data range to cover, the maximum data value on scale and the width of the linear region. It is used in flow cytometry where a large dynamic range of data, most suitable for a logarithmic scale, is present along with other data distributed near zero and including negative values, for which an ordinary logarithmic scale is not suitable.

Related Documentation

The Logicle methods was originally described in the publication:

A new "Logicle" display method avoids deceptive effects of logarithmic scaling for low signals and compensated data
David R. Parks, Mario Roederer, Wayne A. Moore,
Cytometry Part A, Volume 69A, Issue 6, Pages 541-551
available online as PDF or HTML .

The method is included in the Gating-ML proposed standard of the International Society for the Advancement of Cytometry. The specifications for Gating-ML are available here.

Copyright, License and Patent

Copyright (c) 2009, 2011, The Board of Trustees of The Leland Stanford Junior University. All rights reserved.

Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

The Logicle method is patented under United States Patent 6,954,722. However, Stanford University does not enforce the patent for non-profit academic purposes or for commercial use in the field of flow cytometry.

@author Wayne A. Moore @version 1.0