Fix computation of trend according to #167 (#168)

* Fix computation of trend according to #167

* fix test result of trend

* fix test results of trend

* Update CHANGELOG.md

* Update docstring of `trend`

* Update CHANGELOG.md

---------

Co-authored-by: George Datseris <[email protected]>

Author: heliosdrm

CHANGELOG.md

@@ -2,6 +2,9 @@
 
 ## v2.1.0
 
+- Bugfix: computation of `trend` is changed to use balanced distance from diagonal [(#167)](https://github.com/JuliaDynamics/RecurrenceAnalysis.jl/issues/167)
+
+
 Updated to StateSpaceSets.jl v2.
 
 ## v2.0.0

Project.toml

@@ -1,7 +1,7 @@
 name = "RecurrenceAnalysis"
 uuid = "639c3291-70d9-5ea2-8c5b-839eba1ee399"
 repo = "https://github.com/JuliaDynamics/RecurrenceAnalysis.jl.git"
-version = "2.1.0"
+version = "2.1.1"
 
 [deps]
 DelimitedFiles = "8bb1440f-4735-579b-a4ab-409b98df4dab"

src/rqa/rqa.jl

@@ -220,13 +220,14 @@ the trend will have a negative value.
 It is calculated as:
 
 ```math
-TREND = 10^3\\frac{\\sum_{d=\\tau}^{\\tilde{N}}\\delta[d]\\left(RR[d]-\\langle RR[d]\\rangle\\right)}{\\sum_{d=\\tau}^{\\tilde{N}}\\delta[d]^2}
+TREND = 10^3\\frac{\\sum_{d=1+\\tau}^{\\tilde{N}}\\delta[d]\\left(RR[d]-\\langle RR[d]\\rangle\\right)}{\\sum_{d=1+\\tau}^{\\tilde{N}}\\delta[d]^2}
 ```
 
 where ``RR[d]`` is the local recurrence rate of the diagonal ``d``,
-``\\delta[d]`` is a balanced measure of the distance between that diagonal and the LOI,
-``\\tau`` is the Theiler window (number of central diagonals that are excluded), and
-``\\tilde{N}`` is the number of the outmost diagonal that is included.
+``\\tau`` is the Theiler window (number of central diagonals that are excluded),
+``\\tilde{N}`` is the number of the outmost diagonal that is included, and
+``\\delta[d]`` is a balanced measure of the distance between that diagonal and the LOI
+equal to ``d-(\\tilde{N}+\\tau)/2``.
 
 This parameter is expressed in units of variation recurrence rate every
 1000 data points, hence the factor ``10^3`` in the formula [1].
@@ -282,7 +283,7 @@ function _trend(rr_τ::Vector; theiler=1, border=10, kwargs...)::Float64
     numerator = denominator = 0.0
     mean_rr = mean(@view rr_τ[a:b])
     for d in a:b
-        δ = d - b/2
+        δ = d - (b+theiler)/2
         numerator += δ*(rr_τ[d] - mean_rr)
         denominator += δ*δ
     end

test/rqa_rna_analytic.jl

@@ -68,7 +68,7 @@ rmat = CrossRecurrenceMatrix(sparse(i,j,trues(length(i))), RecurrenceThreshold(0
         @test rqa_params[:Lmax] == 5
         @test rqa_params[:DIV] == 0.2
         @test rqa_params[:ENTR] ≈ 0.830 atol=0.001
-        @test rqa_params[:TREND] ≈ -12.2 atol=0.1
+        @test rqa_params[:TREND] ≈ -17.9 atol=0.1
         @test rqa_params[:LAM] == 1.0
         @test rqa_params[:TT] == 22/15
         @test rqa_params[:Vmax] == 3
@@ -114,7 +114,7 @@ rmat = CrossRecurrenceMatrix(sparse(i,j,trues(length(i))), RecurrenceThreshold(0
         @test rqa_params[:Lmax] == 5
         @test rqa_params[:DIV] == 0.2
         @test rqa_params[:ENTR] ≈ 0.500 atol=0.001
-        @test rqa_params[:TREND] ≈ -12.2 atol=0.1
+        @test rqa_params[:TREND] ≈ -17.9 atol=0.1
         @test rqa_params[:LAM] == 12/22
         @test rqa_params[:TT] == 12/5
         @test rqa_params[:Vmax] == 3