Received: (at 58929) by debbugs.gnu.org; 5 Nov 2022 19:29:28 +0000 From debbugs-submit-bounces <at> debbugs.gnu.org Sat Nov 05 15:29:28 2022 Received: from localhost ([127.0.0.1]:58089 helo=debbugs.gnu.org) by debbugs.gnu.org with esmtp (Exim 4.84_2) (envelope-from <debbugs-submit-bounces <at> debbugs.gnu.org>) id 1orOr7-0005xV-I5 for submit <at> debbugs.gnu.org; Sat, 05 Nov 2022 15:29:28 -0400 Received: from relay7-d.mail.gandi.net ([217.70.183.200]:56631) by debbugs.gnu.org with esmtp (Exim 4.84_2) (envelope-from <matt@HIDDEN>) id 1orOr2-0005xE-E4 for 58929 <at> debbugs.gnu.org; Sat, 05 Nov 2022 15:29:23 -0400 Received: (Authenticated sender: matt@HIDDEN) by mail.gandi.net (Postfix) with ESMTPSA id 2168820004; Sat, 5 Nov 2022 19:29:12 +0000 (UTC) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=rfc20.org; s=gm1; t=1667676554; h=from:from:reply-to:subject:subject:date:date:message-id:message-id: to:to:cc:cc:mime-version:mime-version:content-type:content-type: content-transfer-encoding:content-transfer-encoding: in-reply-to:in-reply-to:references:references; bh=iN37Y3UB4CqKgDh04h4PIpLlwmKJsahGuqffc25ef0c=; b=il1Wj/JDPjIlBHsXKssXdMfpOAxtRAls+ld6WVUZHQSK8I09MdrxRD/CKgblckKiMSxc6Y 1Mzdaxmm3oUWGFRwiKVufpiyx4zXe4aYDrk33BlTZ/KUgBm35F2QRibacCNfGfKlJQTFZc OeNWygE9sGHkJSrHWUP7WTE/jqqbQHgOBk3+vMBQ2LZK6n5GBpLLTFW4Z5cwCgL7Z7w+gB V3YovRVipOvVXATZNSjkdjMOFWFVf0rAEMNjpEQ3APg4HnTcMjReZsLVX6n+RprPcw08at rb/5Z6IILWFuLwuy2Q2dWkfnTiUb3pc+s5xnC+1e+Y/Z6GsMGXnYDB2TUQofyA== Received: from matt by naz with local (Exim 4.96) (envelope-from <matt@HIDDEN>) id 1orOqs-000E9o-2t; Sat, 05 Nov 2022 12:29:10 -0700 From: Matt Armstrong <matt@HIDDEN> To: Eli Zaretskii <eliz@HIDDEN>, Mattias =?utf-8?Q?Engdeg=C3=A5rd?= <mattiase@HIDDEN> Subject: Re: bug#58929: 29.0.50; Calc: finding roots utpn doesn't work as advertised In-Reply-To: <83a6588kol.fsf@HIDDEN> References: <8773828B-3A5F-4B15-8786-91F6FCB6D2E2@HIDDEN> <87k04es5bt.fsf@HIDDEN> <EA909128-24C5-412B-B609-19C200D15E6D@HIDDEN> <83a6588kol.fsf@HIDDEN> Date: Sat, 05 Nov 2022 12:29:10 -0700 Message-ID: <878rkpci9l.fsf@HIDDEN> MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8 Content-Transfer-Encoding: quoted-printable X-Spam-Score: -0.7 (/) X-Debbugs-Envelope-To: 58929 Cc: 58929 <at> debbugs.gnu.org X-BeenThere: debbugs-submit <at> debbugs.gnu.org X-Mailman-Version: 2.1.18 Precedence: list List-Id: <debbugs-submit.debbugs.gnu.org> List-Unsubscribe: <https://debbugs.gnu.org/cgi-bin/mailman/options/debbugs-submit>, <mailto:debbugs-submit-request <at> debbugs.gnu.org?subject=unsubscribe> List-Archive: <https://debbugs.gnu.org/cgi-bin/mailman/private/debbugs-submit/> List-Post: <mailto:debbugs-submit <at> debbugs.gnu.org> List-Help: <mailto:debbugs-submit-request <at> debbugs.gnu.org?subject=help> List-Subscribe: <https://debbugs.gnu.org/cgi-bin/mailman/listinfo/debbugs-submit>, <mailto:debbugs-submit-request <at> debbugs.gnu.org?subject=subscribe> Errors-To: debbugs-submit-bounces <at> debbugs.gnu.org Sender: "Debbugs-submit" <debbugs-submit-bounces <at> debbugs.gnu.org> X-Spam-Score: -1.7 (-) Eli Zaretskii <eliz@HIDDEN> writes: >> Cc: 58929 <at> debbugs.gnu.org >> From: Mattias Engdeg=C3=A5rd <mattiase@HIDDEN> >> Date: Thu, 3 Nov 2022 09:53:02 +0100 >>=20 >> Of course an actual numerical analyst would know immediately what to do.= Is there one in the audience? > > I have good experience from using this technique: > > https://www.researchgate.net/publication/226830173_On_the_Structure_of_= Zero_Finders > > It employs a hybrid method that doesn't need derivatives (but is > almost as fast as Newton). However, its main advantage (which is a > huge one in some real-life situations) is that the structure of the > algorithm allows the caller to make arbitrary modifications to the > approximations that the algorithm produces, and in general have > complete control on the iterations' process. In particular, one can > easily deal with situations where the root approximation goes out of > the expected range, or lands in the area where the function doesn't > behave well enough. Interesting. I like how that algorithm attempts to "do its best" when given a single guess point, then adapts to bisection if it happens to find an opportunity and need. Calc's manual suggests that its "root" function attempts to do the same, opening a window to use this other approach. I'm not sure how to expose the root finding "loop" in calc's UI, but exposing it calc's lisp level interface would be a natural thing to do. https://en.wikipedia.org/wiki/ITP_method also looks like an interesting twist on the bisection/secant method. I have no personal experience with it, and on Wikipedia I always wonder if pages like this are reflective of a true utility or merely the ambitions of the paper's authors! This function needs function values that are opposite in sign before it is useful. It might be possible to incorporate it into the approach Eli linked to, but that method claims to be almost as fast as Newton's method in most cases so it may not need the improvement. I arrived here because I wanted to use calc to compute 95th and 99th percentile confidence intervals of some benchmarking results using the Student's t-distribution. I have figured this out now, but it has been more difficult than I anticipated, and the manual's over-promise with respect to "find the root, any guess works" sent me on a long tangent trying to figure out what I had done wrong. That said, my background in this area is weak, so I don't think I am the right person to improve Emacs' root finding implementation. The patch I sent previously, with my (hopefully) useful suggestions in the user manual, is probably the end of my useful contribution here.
bug-gnu-emacs@HIDDEN:bug#58929; Package emacs.
Full text available.Received: (at 58929) by debbugs.gnu.org; 3 Nov 2022 09:14:04 +0000 From debbugs-submit-bounces <at> debbugs.gnu.org Thu Nov 03 05:14:04 2022 Received: from localhost ([127.0.0.1]:47971 helo=debbugs.gnu.org) by debbugs.gnu.org with esmtp (Exim 4.84_2) (envelope-from <debbugs-submit-bounces <at> debbugs.gnu.org>) id 1oqWIW-0000eg-6N for submit <at> debbugs.gnu.org; Thu, 03 Nov 2022 05:14:04 -0400 Received: from eggs.gnu.org ([209.51.188.92]:48190) by debbugs.gnu.org with esmtp (Exim 4.84_2) (envelope-from <eliz@HIDDEN>) id 1oqWIU-0000e5-0j for 58929 <at> debbugs.gnu.org; Thu, 03 Nov 2022 05:14:02 -0400 Received: from fencepost.gnu.org ([2001:470:142:3::e]) by eggs.gnu.org with esmtps (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.90_1) (envelope-from <eliz@HIDDEN>) id 1oqWIO-0000kM-Dp; Thu, 03 Nov 2022 05:13:56 -0400 DKIM-Signature: v=1; a=rsa-sha256; q=dns/txt; c=relaxed/relaxed; d=gnu.org; s=fencepost-gnu-org; h=MIME-version:References:Subject:In-Reply-To:To:From: Date; bh=HmRX4UTcU6ZyhHcPxK4Ovk7boOJ74vw5QpUFOdXI+RY=; b=JuyfATZgfWr9FtF572k/ ihoJP5otF6LO5ZFJbbVvEn2zBIGQWLh35TKDpBugYZ6h1raAJOZat5mM7v4GSM6nCKhyMSE4J5z9i GxfWscxDe8dZsIzwrzuy1zhnPpEgwiZx7WY0UfAnFJFuzak+WW6JPY0QRB7h/imKqJMRXC6mX2s92 APznLosKFuF0R+z1TiiUh8yl7Qa/cTsmn5qaE2G73itFjFUwTuCKAAntVHczvyisUFptITlIdcSSP EMpdYJijitR/oRhOdYRkKAijoC72xaRVoKT3qu0TB7Zx3mTyl69jawpZPS8X3h7IaWc0t1XQIT49f 6tYqbBs2c0wOHg==; Received: from [87.69.77.57] (helo=home-c4e4a596f7) by fencepost.gnu.org with esmtpsa (TLS1.2:ECDHE_RSA_AES_256_GCM_SHA384:256) (Exim 4.90_1) (envelope-from <eliz@HIDDEN>) id 1oqWIN-0004me-Ln; Thu, 03 Nov 2022 05:13:56 -0400 Date: Thu, 03 Nov 2022 11:13:46 +0200 Message-Id: <83a6588kol.fsf@HIDDEN> From: Eli Zaretskii <eliz@HIDDEN> To: Mattias =?utf-8?Q?Engdeg=C3=A5rd?= <mattiase@HIDDEN> In-Reply-To: <EA909128-24C5-412B-B609-19C200D15E6D@HIDDEN> (message from Mattias =?utf-8?Q?Engdeg=C3=A5rd?= on Thu, 3 Nov 2022 09:53:02 +0100) Subject: Re: bug#58929: 29.0.50; Calc: finding roots utpn doesn't work as advertised References: <8773828B-3A5F-4B15-8786-91F6FCB6D2E2@HIDDEN> <87k04es5bt.fsf@HIDDEN> <EA909128-24C5-412B-B609-19C200D15E6D@HIDDEN> MIME-version: 1.0 Content-type: text/plain; charset=utf-8 Content-Transfer-Encoding: 8bit X-Spam-Score: -2.3 (--) X-Debbugs-Envelope-To: 58929 Cc: matt@HIDDEN, 58929 <at> debbugs.gnu.org X-BeenThere: debbugs-submit <at> debbugs.gnu.org X-Mailman-Version: 2.1.18 Precedence: list List-Id: <debbugs-submit.debbugs.gnu.org> List-Unsubscribe: <https://debbugs.gnu.org/cgi-bin/mailman/options/debbugs-submit>, <mailto:debbugs-submit-request <at> debbugs.gnu.org?subject=unsubscribe> List-Archive: <https://debbugs.gnu.org/cgi-bin/mailman/private/debbugs-submit/> List-Post: <mailto:debbugs-submit <at> debbugs.gnu.org> List-Help: <mailto:debbugs-submit-request <at> debbugs.gnu.org?subject=help> List-Subscribe: <https://debbugs.gnu.org/cgi-bin/mailman/listinfo/debbugs-submit>, <mailto:debbugs-submit-request <at> debbugs.gnu.org?subject=subscribe> Errors-To: debbugs-submit-bounces <at> debbugs.gnu.org Sender: "Debbugs-submit" <debbugs-submit-bounces <at> debbugs.gnu.org> X-Spam-Score: -3.3 (---) > Cc: 58929 <at> debbugs.gnu.org > From: Mattias Engdegård <mattiase@HIDDEN> > Date: Thu, 3 Nov 2022 09:53:02 +0100 > > Of course an actual numerical analyst would know immediately what to do. Is there one in the audience? I have good experience from using this technique: https://www.researchgate.net/publication/226830173_On_the_Structure_of_Zero_Finders It employs a hybrid method that doesn't need derivatives (but is almost as fast as Newton). However, its main advantage (which is a huge one in some real-life situations) is that the structure of the algorithm allows the caller to make arbitrary modifications to the approximations that the algorithm produces, and in general have complete control on the iterations' process. In particular, one can easily deal with situations where the root approximation goes out of the expected range, or lands in the area where the function doesn't behave well enough.
bug-gnu-emacs@HIDDEN:bug#58929; Package emacs.
Full text available.Received: (at 58929) by debbugs.gnu.org; 3 Nov 2022 08:53:15 +0000 From debbugs-submit-bounces <at> debbugs.gnu.org Thu Nov 03 04:53:15 2022 Received: from localhost ([127.0.0.1]:47814 helo=debbugs.gnu.org) by debbugs.gnu.org with esmtp (Exim 4.84_2) (envelope-from <debbugs-submit-bounces <at> debbugs.gnu.org>) id 1oqVyM-0008S9-Gd for submit <at> debbugs.gnu.org; Thu, 03 Nov 2022 04:53:14 -0400 Received: from mail1475c50.megamailservers.eu ([91.136.14.75]:53854 helo=mail118c50.megamailservers.eu) by debbugs.gnu.org with esmtp (Exim 4.84_2) (envelope-from <mattiase@HIDDEN>) id 1oqVyK-0008Rn-Qp for 58929 <at> debbugs.gnu.org; Thu, 03 Nov 2022 04:53:14 -0400 X-Authenticated-User: mattiase@HIDDEN DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/simple; d=megamailservers.eu; s=maildub; t=1667465585; bh=3H/TRIx62B1I2//tAhGCdpp1QYXDCtYh7SOzW7bKErQ=; h=Subject:From:In-Reply-To:Date:Cc:References:To:From; b=Wrv5K7DkIgDE8vUefniwhpK1jpaXtzo5i9mA9xsM1bjdVXxo9e12HUuJ5oDqC2r1N QFW7//euAd4hJVqLyNCxByVpVg6wm2yGYsC7OxsfaX3iMf+1JT6ArodLSP0SF3aTSa SyXwi4ZcxTtLEPh7dUzuqWqAXzTVFsWP/9L6++4A= Feedback-ID: mattiase@HIDDEN Received: from smtpclient.apple (c188-150-171-209.bredband.tele2.se [188.150.171.209]) (authenticated bits=0) by mail118c50.megamailservers.eu (8.14.9/8.13.1) with ESMTP id 2A38r3Bi059627; Thu, 3 Nov 2022 08:53:05 +0000 Content-Type: text/plain; charset=us-ascii Mime-Version: 1.0 (Mac OS X Mail 14.0 \(3654.120.0.1.13\)) Subject: Re: bug#58929: 29.0.50; Calc: finding roots utpn doesn't work as advertised From: =?utf-8?Q?Mattias_Engdeg=C3=A5rd?= <mattiase@HIDDEN> In-Reply-To: <87k04es5bt.fsf@HIDDEN> Date: Thu, 3 Nov 2022 09:53:02 +0100 Content-Transfer-Encoding: quoted-printable Message-Id: <EA909128-24C5-412B-B609-19C200D15E6D@HIDDEN> References: <8773828B-3A5F-4B15-8786-91F6FCB6D2E2@HIDDEN> <87k04es5bt.fsf@HIDDEN> To: Matt Armstrong <matt@HIDDEN> X-Mailer: Apple Mail (2.3654.120.0.1.13) X-CTCH-RefID: str=0001.0A782F18.63638171.006B, ss=1, re=0.000, recu=0.000, reip=0.000, cl=1, cld=1, fgs=0 X-CTCH-VOD: Unknown X-CTCH-Spam: Unknown X-CTCH-Score: 0.000 X-CTCH-Rules: X-CTCH-Flags: 0 X-CTCH-ScoreCust: 0.000 X-Origin-Country: SE X-Spam-Score: 0.3 (/) X-Debbugs-Envelope-To: 58929 Cc: 58929 <at> debbugs.gnu.org X-BeenThere: debbugs-submit <at> debbugs.gnu.org X-Mailman-Version: 2.1.18 Precedence: list List-Id: <debbugs-submit.debbugs.gnu.org> List-Unsubscribe: <https://debbugs.gnu.org/cgi-bin/mailman/options/debbugs-submit>, <mailto:debbugs-submit-request <at> debbugs.gnu.org?subject=unsubscribe> List-Archive: <https://debbugs.gnu.org/cgi-bin/mailman/private/debbugs-submit/> List-Post: <mailto:debbugs-submit <at> debbugs.gnu.org> List-Help: <mailto:debbugs-submit-request <at> debbugs.gnu.org?subject=help> List-Subscribe: <https://debbugs.gnu.org/cgi-bin/mailman/listinfo/debbugs-submit>, <mailto:debbugs-submit-request <at> debbugs.gnu.org?subject=subscribe> Errors-To: debbugs-submit-bounces <at> debbugs.gnu.org Sender: "Debbugs-submit" <debbugs-submit-bounces <at> debbugs.gnu.org> X-Spam-Score: -0.7 (/) 1 nov. 2022 kl. 23.00 skrev Matt Armstrong <matt@HIDDEN>: > See attached patch for what I wish the docs had said all along > (would have saved me a lot of time). Thank you, I have not worked through your table to confirm all the = details but it looks fine on the whole. One detail: it's not just that the functions are "flat" (ie, all = derivatives rapidly vanishing as we stray from the mean) but at least = for the normal distribution, Newton actively diverges with a bad = starting guess even if computed with infinite precision (draw the = graph). > I wonder if the implementation can be improved. > = https://www.gnu.org/software/emacs/manual/html_node/calc/Root-Finding.html= > suggests that there are some cases where calc will switch over to the > bisection method. Perhaps the heuristics can be tweaked? =46rom what I can tell, bisection is used if there is an interval = bracketing the root and either no derivative could be computed or Newton = fails to converge. Clearly Newton is preferable when it converges since = it's much faster than bisection. We could employ special tactics by pattern-matching the function = expression (perhaps according to your table); not sure if it would be = worth the trouble. Of course an actual numerical analyst would know immediately what to do. = Is there one in the audience?
bug-gnu-emacs@HIDDEN:bug#58929; Package emacs.
Full text available.Matt Armstrong <matt@HIDDEN>
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From: Matt Armstrong <matt@HIDDEN>
To: Mattias =?utf-8?Q?Engdeg=C3=A5rd?= <mattiase@HIDDEN>
Subject: Re: bug#58929: 29.0.50; Calc: finding roots utpn doesn't work as
advertised
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References: <8773828B-3A5F-4B15-8786-91F6FCB6D2E2@HIDDEN>
Date: Tue, 01 Nov 2022 15:00:38 -0700
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Mattias Engdeg=C3=A5rd <mattiase@HIDDEN> writes:
> Obviously the claim to guarantee a solution for "any initial guess" is
> fanciful.
Yes. See attached patch for what I wish the docs had said all along
(would have saved me a lot of time).
> Unfortunately straight Newton won't converge for this function (erf,
> essentially) if you stray too far from the origin (ie, the mean) so I
> suggest you always use that as a starting guess no matter what point
> you are trying to find the inverse for.
>
> Another way is to use an interval as starting guess instead of a
> single point; that seems to make Calc switch tactics and persevere.
I wonder if the implementation can be improved.
https://www.gnu.org/software/emacs/manual/html_node/calc/Root-Finding.html
suggests that there are some cases where calc will switch over to the
bisection method. Perhaps the heuristics can be tweaked?
> One thing that can happen is running out of stack, because many of the
> implementations like math-newton-root are recursive. This should be
> easy to remedy as they all seem to be tail calls.
Good to know.
--=-=-=
Content-Type: text/x-diff
Content-Disposition: inline;
filename=0002-In-calc.texi-provide-guidance-for-taking-the-inverse.patch
From ba68ca5671f9772994bc5c0b2b0b9216a750b692 Mon Sep 17 00:00:00 2001
From: Matt Armstrong <matt@HIDDEN>
Date: Tue, 1 Nov 2022 14:51:36 -0700
Subject: [PATCH 2/2] In calc.texi provide guidance for taking the inverse of
PDFs.
* doc/misc/calc.texi (Probability Distribution Functions): Stop
claiming that the 'a R' function will "always work" for any guess.
Explain the problem with the PDF functions being very flat. Provide
recommended guess values for each function. bug#58929
---
doc/misc/calc.texi | 36 +++++++++++++++++++++++++++++++++---
1 file changed, 33 insertions(+), 3 deletions(-)
diff --git a/doc/misc/calc.texi b/doc/misc/calc.texi
index 89a340e7343..e6b416a447a 100644
--- a/doc/misc/calc.texi
+++ b/doc/misc/calc.texi
@@ -19456,9 +19456,39 @@ Probability Distribution Functions
While Calc does not provide inverses of the probability distribution
functions, the @kbd{a R} command can be used to solve for the inverse.
-Since the distribution functions are monotonic, @kbd{a R} is guaranteed
-to be able to find a solution given any initial guess.
-@xref{Numerical Solutions}.
+@xref{Root Finding}.
+
+The distribution functions, while monotonic, are also be very flat,
+which can cause problems for the Newton's root-finding algorithm used
+by @kbd{a R}. The problem can be avoided by providing a good starting
+guess. Prefer guesses that occur where the slope of the plotted
+function is not flat. Alternatively, use an interval range for the
+guess. The table below provides a recommendation for each of the
+probability distribution functions.
+
+@multitable @columnfractions .25 .25 .25
+@headitem Function
+@tab When solving for
+@tab Recommended initial guess
+@item @samp{utpb(x,n,p)}
+@tab @expr{x}
+@tab @code{0.5}
+@item @samp{utpc(x,c)}
+@tab @expr{x}
+@tab @code{1.0}
+@item @samp{utpf(F,v1,v2)}
+@tab @expr{F}
+@tab @code{1.0}
+@item @samp{utpn(x,m,s)}
+@tab @expr{x}
+@tab @expr{m}
+@item @samp{utpp(n,x)}
+@tab @expr{n}
+@tab @expr{x}
+@item @samp{utpt(t,v)}
+@tab @expr{t}
+@tab @code{[0..1e4]}
+@end multitable
@node Matrix Functions
@chapter Vector/Matrix Functions
--
2.35.1
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From: Matt Armstrong <matt@HIDDEN>
To: bug-gnu-emacs@HIDDEN
Subject: 29.0.50; Calc: finding roots utpn doesn't work as advertised
Date: Mon, 31 Oct 2022 11:10:22 -0700
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Quick facts:
- all of these examples work with emacs -Q
- reproduces in Emacs 29, 27, 25
I think I have found that the calc package's "root" finding command does
not work as documented with calc's probability distribution functions.
Or, at least, not with "utpn", the probability distribution function for
the normal (gaussian) distribution. I have found similar issues with
"utpt" (the Student's t-distribution), but will focus on "utpn" here.
The Emacs Calc package info page for Probability Distribution Functions
(https://www.gnu.org/software/emacs/manual/html_node/calc/Probability-Distr=
ibution-Functions.html)
has this to say about the normal distribution function:
> The =E2=80=98utpn(x,m,s)=E2=80=99 function uses a normal (Gaussian) distr=
ibution with
> mean =E2=80=98m=E2=80=99 and standard deviation =E2=80=98s=E2=80=99. It i=
s the probability that such a
> normal-distributed random variable would exceed =E2=80=98x=E2=80=99.
I am interested in solving `utpn(x,m,s) =3D p` for `p` given a fixed `m`
and `s`. The same info page has this to say about that:
> While Calc does not provide inverses of the probability distribution
> functions, the a R command can be used to solve for the inverse. Since
> the distribution functions are monotonic, a R is guaranteed to be able
> to find a solution given any initial guess.
SUPPOSITION: the above is true, especially this: "a R is guaranteed to be
able to find a solution given any initial guess."
The Root Finding info page
(https://www.gnu.org/software/emacs/manual/html_node/calc/Root-Finding.html)
has this to say about the a R command:
> The a R (calc-find-root) [root] command finds a numerical solution (or
> root) of an equation. (This command treats inequalities the same as
> equations. If the input is any other kind of formula, it is interpreted
> as an equation of the form =E2=80=98X =3D 0=E2=80=99.)
>
> The a R command requires an initial guess on the top of the stack, and a
> formula in the second-to-top position. It prompts for a solution
> variable, which must appear in the formula. All other variables that
> appear in the formula must have assigned values, i.e., when a value is
> assigned to the solution variable and the formula is evaluated with =3D, =
it
> should evaluate to a number. Any assigned value for the solution variable
> itself is ignored and unaffected by this command.
>
> When the command completes, the initial guess is replaced on the stack by
> a vector of two numbers: The value of the solution variable that solves
> the equation, and the difference between the lefthand and righthand sides
> of the equation at that value. Ordinarily, the second number will be zero
> or very nearly zero. (Note that Calc uses a slightly higher precision
> while finding the root, and thus the second number may be slightly
> different from the value you would compute from the equation yourself.)
WHAT I HAVE TRIED
I have tried entering the formula `utpn(x, 10, 1) =3D 0.5` and invoking `a
R` with an initial guess of `10`. I then solve for `x`, expecting
`x =3D 10`.
Note that the correct answer of `x =3D 10` is "obviously" correct. I am
passing `m =3D 10` for the "mean" arg to `utpn`, and by definition a
random value from the normal distribution has an `0.5` chance of being
larger than the mean.
To do this I type "C-x * *" to enter the *Calculator* buffer and then
type:
` utpn(x, 10, 1) =3D 0.5 RET
10 RET <-- initial guess
a R RET <-- invoke "root" function
x RET <-- answer to prompt; solve for "x"
and I end up with this in the `*Calculator*` buffer:
2: utpn(x, 10, 1) =3D 0.5
1: [10., 0.]
This is correct. The 'a R' command has returned a vector whose first
element is `x` and the second is an error delta (not important here).
Alternatively, evaluate this lisp to do the same thing:
ELISP> (calc-eval '("root(utpn(x, 10, 1) =3D 0.5, x, 10)"))
"[10., 0.]"
While correct, here I have *given* the answer to calc in the initial
guess (the root function's third arg). The problem is that the function
doesn't do well when given other guesses.
```
` utpn(x,10,1)=3D0.5 RET
1.0 RET <---- a different guess
a R RET
x RET
```
results in this:
```
2: utpn(x, 10, 1) =3D 0.5
1: root(utpn(x, 10, 1) =3D 0.5, x, 1)
```
With this in the minibuffer:
> *Newton's method failed to converge: 4.8639203627839e17*
I'm finding that if the initial guess is close enough to the right answer,
in this case `10`, then `a R` works, otherwise not. E.g. guessing `8.6`
fails but `8.7` works.
This behavior makes `a R` much less useful. Also, documentation
suggests that any guess is expected to work (re-quoting from above with
my emphasis):
> Since the distribution functions are monotonic, 'a R' is guaranteed to
> be able to find a solution *given any initial guess*.
Have I found a bug here, or am I doing something wrong?
ADDENDUM
This shows the function failing to find a root for guesses not all that
far away from the actual answer:
ELISP> (cl-loop for x from 8.0 to 12.0 by 0.1 collect (list (format "%.1f" =
x) (calc-eval '("root(utpn(x,10,1)=3D0.5,x,$)") nil (prin1-to-string x))))
(("8.0" "root(utpn(x, 10, 1) =3D 0.5, x, 8.)")
("8.1" "root(utpn(x, 10, 1) =3D 0.5, x, 8.1)")
("8.2" "root(utpn(x, 10, 1) =3D 0.5, x, 8.2)")
("8.3" "root(utpn(x, 10, 1) =3D 0.5, x, 8.3)")
("8.4" "root(utpn(x, 10, 1) =3D 0.5, x, 8.4)")
("8.5" "root(utpn(x, 10, 1) =3D 0.5, x, 8.5)")
("8.6" "root(utpn(x, 10, 1) =3D 0.5, x, 8.6)")
("8.7" "[10., 0.]")
("8.8" "[10., 0.]")
("8.9" "[10., 0.]")
("9.0" "[10., 0.]")
("9.1" "[10., 0.]")
("9.2" "[10., 0.]")
("9.3" "[10., 0.]")
("9.4" "[10., 0.]")
("9.5" "[10., 0.]")
("9.6" "[10., 0.]")
("9.7" "[10., 0.]")
("9.8" "[10., 0.]")
("9.9" "[10., 0.]")
("10.0" "[10., 0.]")
("10.1" "[10., 0.]")
("10.2" "[10., 0.]")
("10.3" "[10., 0.]")
("10.4" "[10., 0.]")
("10.5" "[10., 0.]")
("10.6" "[10., 0.]")
("10.7" "[10., 0.]")
("10.8" "[10., 0.]")
("10.9" "[10., 0.]")
("11.0" "[10., 0.]")
("11.1" "[10., 0.]")
("11.2" "[10., 0.]")
("11.3" "[10., 0.]")
("11.4" "root(utpn(x, 10, 1) =3D 0.5, x, 11.4)")
("11.5" "root(utpn(x, 10, 1) =3D 0.5, x, 11.5)")
("11.6" "root(utpn(x, 10, 1) =3D 0.5, x, 11.6)")
("11.7" "root(utpn(x, 10, 1) =3D 0.5, x, 11.7)")
("11.8" "root(utpn(x, 10, 1) =3D 0.5, x, 11.8)")
("11.9" "root(utpn(x, 10, 1) =3D 0.5, x, 11.9)")
("12.0" "root(utpn(x, 10, 1) =3D 0.5, x, 12.)"))
In GNU Emacs 29.0.50 (build 3, x86_64-pc-linux-gnu, GTK+ Version
3.24.34, cairo version 1.16.0) of 2022-10-30 built on naz
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vertico-autoloads web-mode-autoloads which-key-autoloads
with-editor-autoloads compat-autoloads yaml-mode-autoloads
yasnippet-autoloads rmc iso-transl tooltip cconv eldoc paren electric
uniquify ediff-hook vc-hooks lisp-float-type elisp-mode mwheel
term/x-win x-win term/common-win x-dnd tool-bar dnd fontset image
regexp-opt fringe tabulated-list replace newcomment text-mode lisp-mode
prog-mode register page tab-bar menu-bar rfn-eshadow isearch easymenu
timer select scroll-bar mouse jit-lock font-lock syntax font-core
term/tty-colors frame minibuffer nadvice seq simple cl-generic
indonesian philippine cham georgian utf-8-lang misc-lang vietnamese
tibetan thai tai-viet lao korean japanese eucjp-ms cp51932 hebrew greek
romanian slovak czech european ethiopic indian cyrillic chinese
composite emoji-zwj charscript charprop case-table epa-hook
jka-cmpr-hook help abbrev obarray oclosure cl-preloaded button loaddefs
theme-loaddefs faces cus-face macroexp files window text-properties
overlay sha1 md5 base64 format env code-pages mule custom widget keymap
hashtable-print-readable backquote threads dbusbind inotify lcms2
dynamic-setting system-font-setting font-render-setting cairo
move-toolbar gtk x-toolkit xinput2 x multi-tty make-network-process
emacs)
Memory information:
((conses 16 977488 266858)
(symbols 48 43332 287)
(strings 32 225511 12569)
(string-bytes 1 5996788)
(vectors 16 103426)
(vector-slots 8 1994918 188498)
(floats 8 517 940)
(intervals 56 9190 882)
(buffers 984 38))
Matt Armstrong <matt@HIDDEN>:bug-gnu-emacs@HIDDEN.
Full text available.bug-gnu-emacs@HIDDEN:bug#58929; Package emacs.
Full text available.
GNU bug tracking system
Copyright (C) 1999 Darren O. Benham,
1997 nCipher Corporation Ltd,
1994-97 Ian Jackson.