[R] Obtain gradient at multiple values for exponential decay model

[Jeff Newmiller]

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 <dwinsemius using comcast.net> wrote:
>>
>>
>>> On Apr 6, 2018, at 3:43 AM, g l <gnulinux using gmx.com> wrote:
>>>
>>>> Sent: Friday, April 06, 2018 at 5:55 AM
>>>> From: "David Winsemius" <dwinsemius using 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 using 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 using 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.
>

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