Hi folks, given that I received many requests for R functions associated to Varano, V., Gabriele, S., Teresi, L., Dryden, I., Puddu, P., Torromeo, C., & Piras, P. 2015. Comparing shape trajectories of biological soft tissues in the size-and-shape space. In Biomat 2014: International Symposium on Mathematical and Computational Biology (pp. 351-365), I decided to share them here with some fully working examples. I invite those to which I already sent the functions to re-download this updated material. I then attach R functions (including ancyllaries), the main function help, a workspace and the R script for running the examples. These examples are very easy and more complex designs could be set. As wrote at the begin of the R script, I stress that, in order to recover perfectly deformations, there is the need to go beyond Levi Civita connection. I hope to update you soon on this issue. Best paolo
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The arguments of the pt2dvar() function are : array = an input array of n shapes represented by k landmarks in 2-dimensions, i.e. k x 2 x n; these are the input data subjected to the entire procedure; If you want to use this for studying allometry your input data should be predictions coming from separate regressions between size+shape and size or shape and size. This because estimating hierarchically the deformations within each group relatively to a local reference assumes that a reasonably "clean deformational direction" exists. Using real data there is too much noise. It is also *mandatory* that these shapes are ordered, within each group, according to the direction of deformation. For example, in the case of allometry, when using predictions, be sure that these predictions are ordered by group and, within each group, by size at which predictions were calculated. The best should be to do such ordination before running regression and claculating predictions to be inputted here. Scale them at unit size if the analysis in the shape space is desired. group = a factor corresponding to group affiliation of each shape in the array doopa= F leave this default tol=0.000001 the value to manage possible reflections in deformation vector differences; leave it as is if you do not have reflections in the output. CR=NULL a kx2 matrix; this is the shape towards which you transport deformations hierarchically estimated within each group; if NULL the GRAND mean of the entire sample is used. In case of allometry-oriented investigations CR should be the consensus of smallest per-group predictions. Scale it at unit size if the analysis in the shape space is desired. locs=NULL an array k x 2 x n追evels(group) these are the local references, one for each group, relatively to which you will estimate the within-group deformations. If NULL per-group means are used. In case of allometry-oriented investigations locs should be smallest (in terms of size at which predictions were calculated) per-group predictions. Scale them at unit size if the analysis in the shape space is desired. sss=T Data are assumed to be analyzed in the Size and Shape Space. The Shape Space is now implemented (sss=F). In this case array, CR and locs should be scaled at unit size. Rotation is not mandatory in input as all objects are properly aligned internally at the various steps. OUTPUT is a list that includes: final=the data that have been transported. epsilons= error relative to an euclidean approximattion in the size and shape space epsilons2= error relative to an euclidean approximattion in the shape space THESE RESULTS ARE ROTATION DIAGNOSTICS FOR INNER STEPS useful TO DETECT POSSIBLE REFLECTIONS. HOPEFULLY YOU SHOULD IGNORE THEM trasprotsmua= vectors deriving from the Parallel Transport. For diagnostics only. trasprotsva= rotations deriving from the Parallel Transport. For diagnostics only. locsop= locs rotated on CR via OPA locsrot= rotation matrices corresponding to locsop specop= input specimens rotated on their proper loc via OPA specrots= rotation matrices corresponding to specop
R script with examples.R
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Data example for running pt2dvar.RData
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pt2dvar and necessary ancillaries.r
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