# logicletGml2-class: Class logicletGml2 In flowCore: flowCore: Basic structures for flow cytometry data

## Details

logicletGml2 is defined by the following function:

bound(logicle, boundMin, boundMax) = max(min(logicle,boundMax),boundMin))

where

logicle(x, T, W, M, A) = root(B(y, T, W, M, A) - x)

and B is a modified biexponential function:

B(y, T, W, M, A) = ae^{by} - ce^{-dy} - f

where

• x is the value that is being transformed (an FCS dimension value). Typically, x is less than or equal to T, although the transformation function is also defined for x greater than T.

• y is the result of the transformation.

• T is greater than zero and represents the top of scale value.

• M is greater than zero and represents the number of decades that the true logarithmic scale approached at the high end of the Logicle scale would cover in the plot range.

• W is non-negative and not greater than half of M and represents the number of such decades in the approximately linear region. The choice of W = M/2 specifies a scale that is essentially linear over the whole range except for a small region of large data values. For situations in which values of W approaching M/2 might be chosen, ordinary linear display scales will usually be more appropriate. The choice of W = 0 gives essentially the hyperbolic sine function.

• A is the number of additional decades of negative data values to be included. A shall be greater than or equal to -W, and less than or equal to M - 2W

• root is a standard root finding algorithm (e.g., Newton's method) that finds y such as B(y, T, W, M, A) = x.

and a, b, c, d and f are defined by means of T, W, M, A, w, x0, x1, x2, ca and fa as:

w = W/(M+A)

x2 = A/(M+A)

x1 = x2 + w

x0 = x2 + 2*w

b = (M + A)*ln(10)

and d is a constant so that

2*(ln(d) - ln(b)) + w*(d + b) = 0

given b and w, and

ca = e^{x0*(b+d)}

fa = e^{b*x1} - (ca/(e^{d*x1}))

a = T / (e^b - fa - (ca/e^d))

c = ca * a

f = fa * a

The Logicle scale is the inverse of a modified biexponential function. It provides a Logicle display that maps scale values onto the [0,1] interval such that the data value T is mapped to 1, large data values are mapped to locations similar to an (M + A)-decade logarithmic scale, and A decades of negative data are brought on scale. For implementation purposes, it is recommended to follow guidance in Moore and Parks publication.

In addition, if a boundary is defined by the boundMin and/or boundMax parameters, then the result of this transformation is restricted to the [boundMin,boundMax] interval. Specifically, should the result of the logicle function be less than boundMin, then let the result of this transformation be boundMin. Analogically, should the result of the logicle function be more than boundMax, then let the result of this transformation be boundMax. The boundMin parameter shall not be greater than the boundMax parameter.

## Slots

`.Data`

Object of class `function`.

`T`

Object of class `numeric` – positive constant (top of scale value).

`M`

Object of class `numeric` – positive constant (desired number of decades).

`W`

Object of class `numeric` – non-negative constant that is not greater than half of M (the number of such decades in the approximately linear region).

`A`

Object of class `numeric` – a constant that is greater than or equal to -W, and also less than or equal to M-2W. (A represents the number of additional decades of negative data values to be included.)

`parameters`

Object of class `"transformation"` – flow parameter to be transformed.

`transformationId`

Object of class `"character"` – unique ID to reference the transformation.

`boundMin`

Object of class `numeric` – lower bound of the transformation, default -Inf.

`boundMax`

Object of class `numeric` – upper bound of the transformation, default Inf.

## Objects from the Class

Objects can be created by calls to the constructor

```logicletGml2(parameter, T, M, W, A, transformationId, boundMin, boundMax)```

## Extends

Class `singleParameterTransform`, directly.

Class `transform`, by class singleParameterTransform, distance 2.

Class `transformation`, by class singleParameterTransform, distance 3.

Class `characterOrTransformation`, by class singleParameterTransform, distance 4.

## Note

Please note that `logicletGml2` and `logicleTransform` are similar transformations; however, the Gating-ML 2.0 compliant `logicletGml2` brings "reasonable" data values to the scale of [0,1] while the `logicleTransform` scales these values to [0,M].

The logicle transformation object can be evaluated using the eval method by passing the data frame as an argument. The transformed parameters are returned as a matrix with a single column. (See example below)

## Author(s)

Spidlen, J., Moore, W.

## References

Gating-ML 2.0: International Society for Advancement of Cytometry (ISAC) standard for representing gating descriptions in flow cytometry. http://flowcyt.sourceforge.net/gating/20141009.pdf

Moore, WA and Parks, DR. Update for the logicle data scale including operational code implementations. Cytometry A., 2012:81A(4):273-277.

Parks, DR and Roederer, M and Moore, WA. A new "Logicle" display method avoids deceptive effects of logarithmic scaling for low signals and compensated data. Cytometry A., 2006:69(6):541-551.

`logicleTransform`, `transform-class`, `transform`
Other mathematical transform classes: `EHtrans-class`, `asinht-class`, `asinhtGml2-class`, `dg1polynomial-class`, `exponential-class`, `hyperlog-class`, `hyperlogtGml2-class`, `invsplitscale-class`, `lintGml2-class`, `logarithm-class`, `logtGml2-class`, `quadratic-class`, `ratio-class`, `ratiotGml2-class`, `sinht-class`, `splitscale-class`, `squareroot-class`, `unitytransform-class`
 ```1 2 3 4 5``` ```myDataIn <- read.FCS(system.file("extdata", "0877408774.B08", package="flowCore")) myLogicle <- logicletGml2(parameters = "FSC-H", T = 1023, M = 4.5, W = 0.5, A = 0, transformationId="myLogicle") transOut <- eval(myLogicle)(exprs(myDataIn)) ```