R users may want to note that there are some extensions in packages for symbolic derivatives.

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In particular, Duncan Murdoch added some "all in R" tools in the package nlsr that I maintain. This is a substitute for the nls() function that uses a fairly unsatisfactory forward difference derivative approximation. Moreover, the solver in nlsr is a variant of the Marquardt stabilized Gauss-Newton approach, rather than the straight Gauss-Newton that often gives a "singular gradient" error. Nothing is free, of course, and the Marquardt approach often uses more iterations when the problem is uncomplicated. On the other hand, it is rather like a pit bull in trying to find a solution. There is also the Deriv package, also "all in R". Both it and nlsr allow extensions to the derivatives table, though I think most users will need to do some homework to become comfortable with doing that. There is also a Google Summer of Code proposal this year to wrap the Julia Automatic Differentiation tools to R. This would allow derivatives of coded functions to be computed avoiding approximations. I believe it will be at least partly successful in achieving its goals. Unfortunately (and I would rather hope that someone can say eventually that I am wrong), I believe no tool is universally applicable. JN On 2018-04-07 02:19 AM, Jeff Newmiller wrote: > I have never found the R symbolic differentiation helpful because my > functions are typically quite complicated, but was > prompted by Steve Ellison's suggestion to try it out in this case: > > ################# reprex (see reprex package) > graphdta <- read.csv( text = > "t,c > 0,100 > 40,78 > 80,59 > 120,38 > 160,25 > 200,21 > 240,16 > 280,12 > 320,10 > 360,9 > 400,7 > ", header = TRUE ) > > nd <- c( 100, 250, 300 ) > graphmodeld <- lm( log(c) ~ t, data = graphdta ) > graphmodelplin <- predict( graphmodeld > , newdata = data.frame( t = nd ) > ) > graphmodelp <- exp(graphmodelplin) > graphmodelp > #> 1 2 3 > #> 46.13085 16.58317 11.79125 > # derivative of exp( a + b*t ) is b * exp( a + b*t ) > graphmodeldpdt <- coef( graphmodeld )[ 2 ] * graphmodelp > graphmodeldpdt > #> 1 2 3 > #> -0.31464113 -0.11310757 -0.08042364 > > # Ellison suggestion - fancy, only works for simple functions > dc <- deriv( expression( exp( a + b * t ) ) > , namevec = "t" > ) > dcf <- function( t ) { > cgm <- coef( graphmodeld ) > a <- cgm[ 1 ] > b <- cgm[ 2 ] > eval(dc) > } > result <- dcf( nd ) > result > #> [1] 46.13085 16.58317 11.79125 > #> attr(,"gradient") > #> t > #> [1,] -0.31464113 > #> [2,] -0.11310757 > #> [3,] -0.08042364 > attr( result, "gradient" )[ , 1 ] > #> [1] -0.31464113 -0.11310757 -0.08042364 > ################# > > On Fri, 6 Apr 2018, David Winsemius wrote: > >> >>> On Apr 6, 2018, at 8:03 AM, David Winsemius <dwinsem...@comcast.net> wrote: >>> >>> >>>> On Apr 6, 2018, at 3:43 AM, g l <gnuli...@gmx.com> wrote: >>>> >>>>> Sent: Friday, April 06, 2018 at 5:55 AM >>>>> From: "David Winsemius" <dwinsem...@comcast.net> >>>>> >>>>> >>>>> Not correct. You already have `predict`. It is capale of using the >>>>> `newdata` values to do interpolation with the >>>>> values of the coefficients in the model. See: >>>>> >>>>> ?predict >>>>> >>>> >>>> The ? details did not mention interpolation explicity; thanks. >>>> >>>>> The original question asked for a derivative (i.e. a "gradient"), but so >>>>> far it's not clear that you understand the >>>>> mathematical definiton of that term. We also remain unclear whether this >>>>> is homework. >>>>> >>>> >>>> The motivation of this post was simple differentiation of a tangent point >>>> (dy/dx) manually, then wondering how to >>>> re-think in modern-day computing terms. Hence the original question about >>>> asking the appropriate functions/syntax to >>>> read further ("curiosity"), not the answer (indeed, "homework"). :) >>>> >>>> Personal curiosity should be considered "homework". >>> >>> Besides symbolic differentiation, there is also the option of numeric >>> differentiation. Here's an amateurish attempt: >>> >>> myNumDeriv <- function(x){ (exp( predict (graphmodeld, >>> newdata=data.frame(t=x+.0001))) - >>> exp( predict (graphmodeld, >>> newdata=data.frame(t=x) )))/ >>> .0001 } >>> myNumDeriv(c(100, 250, 350)) >> >> I realized that this would not work in the context of your construction. I >> had earlier made a more symbolic version >> using R formulae: >> >> graphdata<-read.csv(text='t,c >> 0,100 >> 40,78 >> 80,59 >> 120,38 >> 160,25 >> 200,21 >> 240,16 >> 280,12 >> 320,10 >> 360,9 >> 400,7') >> graphmodeld<-lm(log(c)~t, graphdata) >> graphmodelp<-exp(predict(graphmodeld)) >> plot(c~t, graphdata) >> lines(graphdata[,1],graphmodelp) >> myNumDeriv(c(100, 250, 350), graphmodeld ) >> #---------------------------------------------- >> 1 2 3 >> -0.31464102 -0.11310753 -0.05718414 >> >> >>> >>> >>> >>> David Winsemius >>> Alameda, CA, USA >>> >>> 'Any technology distinguishable from magic is insufficiently advanced.' >>> -Gehm's Corollary to Clarke's Third Law >>> >>> ______________________________________________ >>> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see >>> https://stat.ethz.ch/mailman/listinfo/r-help >>> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html >>> and provide commented, minimal, self-contained, reproducible code. >> >> David Winsemius >> Alameda, CA, USA >> >> 'Any technology distinguishable from magic is insufficiently advanced.' >> -Gehm's Corollary to Clarke's Third Law >> >> ______________________________________________ >> R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. >> > > --------------------------------------------------------------------------- > Jeff Newmiller The ..... ..... Go Live... > DCN:<jdnew...@dcn.davis.ca.us> Basics: ##.#. ##.#. Live Go... > Live: OO#.. Dead: OO#.. Playing > Research Engineer (Solar/Batteries O.O#. #.O#. with > /Software/Embedded Controllers) .OO#. .OO#. rocks...1k > > ______________________________________________ > R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list -- To UNSUBSCRIBE and more, see https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.