Hi everyone, Apologies to the group. In retrospect, despite the disclaimer in my first email, better to have error checked before sending (as Mike noted, I wrote acos not cos, and I borrowed from old code that assumed the vectors were already unit length; I also made mistakes in how the loop was set up; overall, a mess).

I might as well provide the corrected, checked code. Afterward, I explain why the function to compute the angle between vectors (vec.angle) requires a test for whether the vectors being compared are duplicates of one another ("any(duplicated(.))")... # matrix where each vector is a row vec.mat <- rbind(...) # empty square matrix for pairwise angles angle.mat <- matrix(NA,nrow=nrow(vec.mat),ncol=nrow(vec.mat)) # angle between vectors function, in degrees vec.angle <- function(v1,v2){ ifelse(any(duplicated(rbind(v1, v2))),0, acos((t(v1)%*%v2)/(sqrt(sum(v1^2))*sqrt(sum(v2^2))))*180/pi)} # fill the all pairwise angles matrix for(i in 1:nrow(vec.mat)){for(j in 1:nrow(vec.mat)){ angle.mat[i, j] <- vec.angle(v1=vec.mat[i,], v2=vec.mat[j,])}} The cosine of the angle between two *identical* vectors (call it CTI) is 1. But R will *occasionally* compute a value greater than one. This is not immediately apparent: If CTI is called, the value displayed in the console will be 1; however, use of the logical operator CTI*==*1 returns FALSE, and the logical CTI* > *1 returns TRUE. I think it's a machine precision issue. Because cosine ranges from -1 to 1, there's no such thing as an arccosine for a value greater than 1. R will return Nan for acos(CTI) . Incorporating any(duplicated(.)) into the vec.angle function assures that identical vectors will have an angle between them of 0. This will be so whether a vector is being compared to itself (*i = j, *hence deposited along the diagonal of the matrix of angles), or to an identical vector in another row (*i != j, *hence deposited in an off-diagonal cell). I think the line diag(vc) = 0 in Mike's vec.angle.matrix code is meant to do the same thing for his diagonal values. Again, sorry for any confusion I caused. Thanks again to Mike. Best, David On Fri, Nov 3, 2017 at 10:46 AM, Mike Collyer <mlcoll...@gmail.com> wrote: > Dear David, and others, > > Be careful with the code you just introduced here. There are a couple of > mistakes. First, vectors need to be unit length. You code does not > transform the vectors to unit length. Second, it’s the arccosine, the > cosine of the vector inner product that finds the angle. Third, though > less of an error but more of a precision issue, there is no need to round > 180/pi, as you have done. This is what R will return if you ask it to > divide 180 by pi, but the four decimal places are for your visual benefit. > By using 180/pi instead of 57.2958, the results will be more precise. This > last part is not much issue but the first two are big problems. > > Here is a demo using two x,y vectors - 0,1 and 1,1 - which we know has an > angle of 45 degrees between them in a plane. I calculate the angles using > your method and one with unit length vectors and arccosine of their inner > products, which is what we use in geomorph. > > > v1 <- c(1,0) > > v2 <- c(1,1) > > V <- rbind(v1, v2) > > > > # Katz method > > vec.mat <- V > > angle.mat <- matrix(NA,nrow=nrow(vec.mat),ncol=nrow(vec.mat)) > > vec.angle <- function(v1,v2){cos(t(v1)%*%v2)*57.2958} > > for(i in 1:nrow(vec.mat)) { > + for(j in 1:nrow(vec.mat)) { > + angle.mat[i, j] <- vec.angle(vec.mat[i,], vec.mat[j,]) > + } > + } > > > > angle.mat > [,1] [,2] > [1,] 30.95705 30.95705 > [2,] 30.95705 -23.84347 > > > > geomorph:::vec.ang.matrix(V, type = "deg") > v1 v2 > v1 0 45 > v2 45 0 > > As you can see, using the cosine and not transforming the vectors to unit > length finds results that suggest there is some non-0 degree angle between > a vector and itself, in addition to the incorrect angle between vectors. > > You indicated that you were patching together code, so it might be an > oversight, but it is an important distinction for others who might use the > code. Here are the “guts” of the geomorph functions in case somebody wants > to reconcile the points I just made with the set-up in your code, which is > similar. > > > geomorph:::vec.cor.matrix > function(M) { > M <- as.matrix(M) > w <- 1/sqrt(diag(tcrossprod(M))) # weights used to make vectors unit > length > vc = tcrossprod(M*w)# outer-product matrix finds inner-products between > vectors for all elements > options(warn = -1) # turn off warnings for diagonal elements > vc # vector correlations returned > } > > > geomorph:::vec.ang.matrix > function(M, type = c("rad", "deg", "r")){ > M <- as.matrix(M) > type <- match.arg(type) > if(type == "r") { > vc <- vec.cor.matrix(M) # as above > } else { > vc <- vec.cor.matrix(M) > vc <- acos(vc) # finds angles for vector correlations > diag(vc) = 0 # Make sure computational 0s are true 0s > } > if(type == "deg") vc <- vc*180/pi # turns radians into degrees > vc > } > > These functions have some extras that would not pertain to the general > solution but are meant to trap warnings and round 0s for users, but they > should not get in the way of understanding. > > Cheers! > Mike > > On Nov 3, 2017, at 11:33 AM, David Katz <dck...@ucdavis.edu> wrote: > > I think this does it (but please check; I quickly stuck together two > different pieces of code)... > > # matrix where each vector is a row > vec.mat <- ... > #Compute group*loci matrix of mean microsatellite lengths > angle.mat <- matrix(NA,nrow=nrow(vec.mat),ncol=nrow(vec.mat)) > # angle function (radians converted to degrees) > vec.angle <- function(v1,v2){cos(t(v1)%*%v2)*57.2958} > # angles-to-matrix loop > for(i in 1:nrow(vec.mat)) > { > for(j in 1:nrow(vec.mat)) > { > # angle bw vec1 and vec2 > angle.mat[i, j] <- vec.angle(vec.mat[i,], vec.mat[j,])} > } > return(angle.mat) > } > > On Fri, Nov 3, 2017 at 2:38 AM, andrea cardini <alcard...@gmail.com> > wrote: > >> Dear All, >> please, does anyone know if there's an R package that, using a matrix >> with several vectors (e.g., coefficients for allometric regressions in >> different taxa), will compute the pairwise (all possible pairs of taxa) >> matrix of vector angles? >> >> Thanks in advance for any suggestion. >> Cheers >> >> Andrea >> >> >> -- >> >> Dr. Andrea Cardini >> Researcher, Dipartimento di Scienze Chimiche e Geologiche, Università di >> Modena e Reggio Emilia, Via Campi, 103 - 41125 Modena - Italy >> <https://maps.google.com/?q=Emilia,+Via+Campi,+103+-+41125+Modena+-+Italy&entry=gmail&source=g> >> tel. 0039 059 2058472 >> >> Adjunct Associate Professor, School of Anatomy, Physiology and Human >> Biology, The University of Western Australia, 35 Stirling Highway, >> Crawley WA 6009, Australia >> <https://maps.google.com/?q=35+Stirling+Highway,+Crawley+WA+6009,+Australia&entry=gmail&source=g> >> >> E-mail address: alcard...@gmail.com, andrea.card...@unimore.it >> WEBPAGE: https://sites.google.com/site/alcardini/home/main >> >> FREE Yellow BOOK on Geometric Morphometrics: >> http://www.italian-journal-of-mammalogy.it/public/journals/3 >> /issue_241_complete_100.pdf >> >> ESTIMATE YOUR GLOBAL FOOTPRINT: http://www.footprintnetwork.or >> g/en/index.php/GFN/page/calculators/ >> >> -- >> MORPHMET may be accessed via its webpage at http://www.morphometrics.org >> --- You received this message because you are subscribed to the Google >> Groups "MORPHMET" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to morphmet+unsubscr...@morphometrics.org. >> >> > > > -- > David C. Katz, Ph.D. > Postdoctoral Fellow > Benedikt Hallgrimsson Lab > University of Calgary > > Research Associate > Department of Anthropology > University of California, Davis > > ResearchGate profile <https://www.researchgate.net/profile/David_Katz29> > Personal webpage > <https://davidckatz.wordpress.com/> > > -- > MORPHMET may be accessed via its webpage at http://www.morphometrics.org > --- > You received this message because you are subscribed to the Google Groups > "MORPHMET" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to morphmet+unsubscr...@morphometrics.org. > > > -- David C. Katz, Ph.D. Postdoctoral Fellow Benedikt Hallgrimsson Lab University of Calgary Research Associate Department of Anthropology University of California, Davis ResearchGate profile <https://www.researchgate.net/profile/David_Katz29> Personal webpage <https://davidckatz.wordpress.com/> -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. To unsubscribe from this group and stop receiving emails from it, send an email to morphmet+unsubscr...@morphometrics.org.