From jerry.lewis at biogen.com  Fri Feb 17 23:13:06 2017
From: jerry.lewis at biogen.com (Jerry Lewis)
Date: Fri, 17 Feb 2017 22:13:06 +0000
Subject: [Rd] Wish List: Extensions to the derivatives table
In-Reply-To: <CAL6gwnLONZ9HuARELKm0ODAGVopfOwMWftm2p3c1SDQZ-tw2RA@mail.gmail.com>
References: <SN1PR12MB03180780C156867FC3A0CB89815D0@SN1PR12MB0318.namprd12.prod.outlook.com>
	<CAL6gwnLONZ9HuARELKm0ODAGVopfOwMWftm2p3c1SDQZ-tw2RA@mail.gmail.com>
Message-ID: <SN1PR12MB0318832AA2C0706676EB730B815D0@SN1PR12MB0318.namprd12.prod.outlook.com>

The issue is that without an extensible derivative table or the proposed extensions, it is not possible to automatically produce (without manual modification of the deriv3 output) a function that avoids catastrophic cancellation regardless of the working range.

Manual modification is not onerous as a one-time exercise, but can be time consuming when it must be done numerous times, for example when evaluating the impact of different parameterizations on parameter effects curvature.  The alternative of more flexible differentiation does not seem to be a difficult addition to R.  In S+ (which does not have deriv3) it would simply involve adding the following lines to the switch statement in D

  expm1 = make.call("*", make.call("exp", expr[[2]]), D(expr[[2]], name)),
  log1p = make.call("/", D(expr[[2]], name), make.call("+", 1., expr[[2]])),
  log2 = make.call("/", make.call("/", D(expr[[2]], name), expr[[2]]), quote(log(2)) ),
  log10 = make.call("/", make.call("/", D(expr[[2]], name), expr[[2]]), quote(log(10)) ),
  cospi = make.call("*", make.call("*", make.call("sinpi", expr[[2]]), make.call("-", D(expr[[2]], name))), quote(pi)),
  sinpi = make.call("*", make.call("*", make.call("cospi", expr[[2]]), D(expr[[2]], name)), quote(pi)),
  tanpi = make.call("/", make.call("*", D(expr[[2]], name), quote(pi)), make.call("^", make.call("cospi", expr[[2]]), 2)),

Jerry

From: Avraham Adler [mailto:avraham.adler at gmail.com]
Sent: Friday, February 17, 2017 4:16 PM
To: Jerry Lewis; r-devel at r-project.org
Subject: Re: [Rd] Wish List: Extensions to the derivatives table

Hi.

Unless I'm misremembering, log, exp, sin, cos, and tan are all handled in deriv3. The functions listed are  specially coded slightly more accurate versions but can be substituted with native ones for which deriv/deriv3 will work automatically. I believe that if you  write your functions using log(a + 1) instead of log1p(a) or log(x) / log(2) instead of log2(x) deriv3 will work fine.

Thanks,

Avi

On Fri, Feb 17, 2017 at 2:02 PM Jerry Lewis <jerry.lewis at biogen.com<mailto:jerry.lewis at biogen.com>> wrote:
The derivative table resides in the function D.  In S+ that table is extensible because it is written in the S language.  R is faster but less flexible, since that table is programmed in C.  It would be useful if R provided a mechanism for extending the derivative table, or barring that, provided a broader table.  Currently unsupported mathematical functions of one argument include expm1, log1p, log2, log10, cospi, sinpi, and tanpi.

While manual differentiation of these proposed additions is straight-forward, their absence complicates what otherwise could be much simpler, such as using deriv() or deriv3() to generate functions, for example to use as an nls model.

Thanks,

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[Rd] Wish List: Extensions to the derivatives table
Jerry Lewis