Description Usage Arguments Details Value Author(s) See Also Examples

After polar transformation of Cartesian intensity values, the estimated standard errors are no longer useful. This function normalizes the standard errors depending on the polar “intensity” value

1 | ```
findSeTheta(pooledSE.raw, R, dist = "manhattan", pNorm = NULL)
``` |

`pooledSE.raw` |
Matrix of pooled standard errors of the Cartesian intensities
“A” and “B” (see |

`R` |
Matrix of polar coordinates intensities |

`dist` |
Distance measure. See |

`pNorm` |
Minkowski norm. See |

Usually called from within `createAlleleSet`

. The standard
errors of the Cartesian intensities “A” and “B” are not
meaningful when the polar coordinates “theta” and
“intensity” are plotted on Cartesian axes. In a plot of
homoscedastic “B” vs. “A” (see
`transformChannels`

), the standard error of each bead-type
is independent of the signal intensities. In a Cartesian plot of
“intensity” vs. “theta”, however, bead-types with low
intensity will have a large uncertainty, and the precision of the
points will increase with increasing intensity. This is beacause the
arc-length of the first quadrant semi-circle, which increases with the
distance from origin, gets a constant value of unity as the polar
coordinates are plotted on Cartesian axes. The pooled standard errors
are therefore scaled with the intensity dependent arc-length of the
semi-circle between 0 and 90 degrees.

The arc-lengths by which the standard errors are scaled also depend on
`dist`

and `pNorm`

. The circumference of a circle in
Manhattan geometry, using a Euclidean metric, is
`4*sqrt(2)*R`

, and the circumference of a Euclidean circle is
`2*pi*R`

. It follows that the arc-lengths in the first quadrant
only are `sqrt(2)*R`

and `pi*R/2`

, respectively. The more
general arc-length of a Minkowski geometry circle is estimated by
numerical integration along the the curve of the super-ellipse between
0 to 90 degrees.

Matrix of transformed standard errors

Lars Gidskehaug

1 2 3 4 5 | ```
#A single standard error value for points of increasing intensity
R <- .1:10
pooledSE.raw <- 1
pooledSE.theta <- findSeTheta(pooledSE.raw=pooledSE.raw,R=R)
print(pooledSE.theta)
``` |

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