Revision f4cf173371c068e77677d0572d5698a110633aaf authored by Toni Giorgino on 28 September 2020, 12:40:07 UTC, committed by cran-robot on 28 September 2020, 12:40:07 UTC
1 parent 532d219
warpArea.R
##
## Copyright (c) 2006-2019 of Toni Giorgino
##
## This file is part of the DTW package.
##
## DTW is free software: you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or
## (at your option) any later version.
##
## DTW is distributed in the hope that it will be useful, but WITHOUT
## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
## or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public
## License for more details.
##
## You should have received a copy of the GNU General Public License
## along with DTW. If not, see <http://www.gnu.org/licenses/>.
##
## Compute the (approximate) area between the warping function and the
## diagonal (in unit steps).
#' Compute Warping Path Area
#'
#' Compute the area between the warping function and the diagonal (no-warping)
#' path, in unit steps.
#'
#'
#' Above- and below- diagonal unit areas all count *plus* one (they do not
#' cancel with each other). The "diagonal" goes from one corner to the other
#' of the possibly rectangular cost matrix, therefore having a slope of
#' `M/N`, not 1, as in [slantedBandWindow()].
#'
#' The computation is approximate: points having multiple correspondences are
#' averaged, and points without a match are interpolated. Therefore, the area
#' can be fractionary.
#'
#' @param d an object of class `dtw`
#' @return The area, not normalized by path length or else.
#' @note There could be alternative definitions to the area, including
#' considering the envelope of the path.
#' @author Toni Giorgino
#' @keywords ts
#' @examples
#'
#' ds<-dtw(1:4,1:8);
#'
#' plot(ds);lines(seq(1,8,len=4),col="red");
#'
#' warpArea(ds)
#'
#' ## Result: 6
#' ## index 2 is 2 while diag is 3.3 (+1.3)
#' ## 3 3 5.7 (+2.7)
#' ## 4 4:8 (avg to 6) 8 (+2 )
#' ## --------
#' ## 6
#'
#' @export warpArea
warpArea <- function(d) {
if(!is.dtw(d))
stop("dtw object required");
## rebuild query->templ map, interpolating holes
ii<-stats::approx(x=d$index1,y=d$index2,1:d$N);
dg<-seq(from=1,to=d$M,len=d$N);
ad<-abs(ii$y-dg);
sum(ad);
}
## Exmp:
## t <- localWarpingStretch(alignment)
##
## # local warping amount, based on the warping function
## plot(t)
##
## # lwa, based on the input position
## plot(t~alignment$index1)
##
## # or its pointwise approximation
## plot(approx(alignment$index1,t,1:alignemnt$N)$y)
##
## diff(localWarpingStretch) contains +1 for each "insertion" and -1
## for each "deletion". Since we have max N deletions + M
## insertions, a reasonable normalization would be to divide
## sum(abs(diff())) by 2N
##
## localWarpingCost is the amount of mismatch
## at each point ("local substitution cost")
## Return how far from the diagonal is each point on the warping
## function. A good normalization factor can be 2 * N, so that maximum
## stretch is 1.
.localWarpingStretch <- function(d) {
## The diagonal line
# dg <- seq(from = 1, to = d$M, len = d$N)
## get local copies
id1 <- d$index1;
id2 <- d$index2;
## remap reference indices to a square alignment
id2 <- id2*d$N/d$M;
## return the local distance from the diagonal
id1-id2;
}
## Return the local costs along the warping path i.e. d[i[t],j[t]] . A
## reasonable normalization could be to d$distance, so that each
## element would be the fraction of cost accumulated at that step.
.localWarpingCost <- function(d) {
if(is.null(d$localCostMatrix))
stop("A dtw object with keep.internals=TRUE is required");
diag(d$localCostMatrix[d$index1,d$index2]);
}
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