Equality of symbolic derivatives in R

Question

I would like to use R to verify complicated derivative calculations. Here is my best attempt so far on a simple function:

f <- expression(a*log(x^2))
df.dx <- deriv(f, 'x')
(df.dx)
df.dx.byHand <- expression(2*a/x) # The derivative of f calculated by hand
(df.dx.byHand)
all.equal(df.dx, df.dx.byHand)

The output of the above is

> (df.dx)
 expression({
.expr1 <- x^2
.value <- a * log(.expr1)
.grad <- array(0, c(length(.value), 1L), list(NULL, c("x")))
.grad[, "x"] <- a * (2 * x/.expr1)
attr(.value, "gradient") <- .grad
.value

> (df.dx.byHand)
expression(2 * a/x)

[1] "Component 1: target, current do not match when deparsed"

I have already checked

Explicit formula versus symbolic derivatives in R,

http://stat.ethz.ch/R-manual/R-patched/library/stats/html/deriv.html

Symbolic derivatives and simplification in R

and also

http://stat.ethz.ch/R-manual/R-patched/library/base/html/expression.html

since the core issue seems to be that I don't know how to extract from 'df.dx' the 'grad[, 'x']' part of the expression.

Due to IT issues, neither Sage nor YACAS are available to me.

Many thanks for suggestions!

G. Grothendieck · Accepted Answer · 2014-05-13T12:41:07.770

2

The problem in the question is not just extracting the expression but also the fact that the expression needs to be simplified.

1) If the "IT issues" mean you had trouble installing Ryacas see the Ryacas home page for troubleshotting tips and try this:

library(Ryacas)
x <- Sym("x")
a <- Sym("a")
identical(Eval(Simplify(deriv(a*log(x^2), x))), 2 * a / x) # TRUE

If you get FALSE then they still might be the same if the simplification does not reduce it to the same form as the hand produced one so you might want to try the next method in any case.

2) If the "IT issues" mean you are not allowed to install packages then just compare them on a grid:

df.dx.byHand <- function(x) 2*a/x

df.dx <- function(x) {}
body(df.dx) <- D(f,'x')

a <- 3
all.equal(df.dx.byHand(1:100), df.dx(1:100)) # TRUE

UPDATED Provided Ryacas solution

edited May 13 '14 at 12:41

answered May 13 '14 at 10:19

G. Grothendieck

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Thanks! The 'IT issue' is the latter: I don't have the admin rights to install YACAS (but R packages alone I can install--which, as far as I understand, doesn't help if I don't also have YACAS) – Pavel L May 13 '14 at 10:43
What OS are you using? – G. Grothendieck May 13 '14 at 11:13
Windows 7. I had had trouble installing Yacas before, but now have managed it (following the advice on the Ryacas site). – Pavel L May 13 '14 at 12:31
In that case have added an Ryacas solution too. – G. Grothendieck May 13 '14 at 12:41
I still do get FALSE for the derivatives that interest me, so it looks like 2 is the better solution for my problem. Thank you very much! – Pavel L May 13 '14 at 14:38

Equality of symbolic derivatives in R

1 Answers1