Logicle transformation creates a subset of `biexponentialTransform`

hyperbolic sine transformation functions that provides several advantages over linear/log
transformations for display of flow cytometry data. (The logicleTransform method
makes use of the C++ implementation of the logicle transform contributed
by Wayne Moore et al.)

1 2 3 | ```
logicleTransform(transformationId="defaultLogicleTransform", w = 0.5, t = 262144,
m = 4.5, a = 0)
estimateLogicle(x, channels,...)
``` |

`transformationId` |
A name to assign to the transformation. Used by the transform/filter routines. |

`w` |
w is the linearization width in asymptotic decades. w should be > 0 and determines the slope of transformation at zero. w can be estimated using the equation w=(m-log10(t/abs(r)))/2, where r is the most negative value to be included in the display |

`t` |
Top of the scale data value, e.g, 10000 for common 4 decade data or 262144 for a 18 bit data range. t should be greater than zero |

`m` |
m is the full width of the transformed display in asymptotic decades. m should be greater than zero |

`a` |
Additional negative range to be included in the display in asymptotic decades. Positive values of the argument brings additional negative input values into the transformed display viewing area. Default value is zero corresponding to a Standard logicle function. |

`x` |
Input flow frame for which the logicle transformations are to be estimated. |

`channels` |
channels or markers for which the logicle transformation is to be estimated. |

`...` |
other arguments: q: a numeric type specifying quantile value, default is 0.05 |

Wayne Moore, N Gopalakrishnan

Parks D.R., Roederer M., Moore W.A.(2006) A new "logicle" display method avoids deceptive effects of logarithmic scaling for low signals and compensated data. CytometryA, 96(6):541-51.

`inverseLogicleTransform`

,
`estimateLogicle `

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
data(GvHD)
samp <- GvHD[[1]]
## User defined logicle function
lgcl <- logicleTransform( w = 0.5, t= 10000, m =4.5)
trans <- transformList(c("FL1-H", "FL2-H"), lgcl)
after <- transform(samp, trans)
invLgcl <- inverseLogicleTransform(trans = lgcl)
trans <- transformList(c("FL1-H", "FL2-H"), invLgcl)
before <- transform (after, trans)
## Automatically estimate the logicle transformation based on the data
lgcl <- estimateLogicle(samp, channels = c("FL1-H", "FL2-H", "FL3-H", "FL2-A", "FL4-H"))
## transform parameters using the estimated logicle transformation
after <- transform(samp, lgcl)
``` |

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