220 11603 <8c420393-c2ac-45a1-8b3b-4b0029894bc0@isocpp.org> article Path: news.gmane.org!not-for-mail From: Mikhail Semenov Newsgroups: gmane.comp.lang.c++.isocpp.proposals Subject: Re: Proposal. Generators of numeric sequences: the steps class template Date: Sat, 28 Jun 2014 13:06:28 -0700 (PDT) Lines: 157 Approved: news@gmane.org Message-ID: <8c420393-c2ac-45a1-8b3b-4b0029894bc0@isocpp.org> References: <8aec4acb-2eea-4288-b215-81e828cd0b42@isocpp.org> Reply-To: std-proposals@isocpp.org NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: multipart/alternative; boundary="----=_Part_1353_24319980.1403985989215" X-Trace: ger.gmane.org 1403985998 25552 80.91.229.3 (28 Jun 2014 20:06:38 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 28 Jun 2014 20:06:38 +0000 (UTC) To: std-proposals@isocpp.org Original-X-From: std-proposals+bncBDC55PNFRYGRBRWAXSOQKGQEIHANWLI@isocpp.org Sat Jun 28 22:06:33 2014 Return-path: Envelope-to: gclcip-std-proposals@m.gmane.org Original-Received: from mail-ob0-f200.google.com ([209.85.214.200]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1X0ytL-0000fV-Lh for gclcip-std-proposals@m.gmane.org; Sat, 28 Jun 2014 22:06:31 +0200 Original-Received: by mail-ob0-f200.google.com with SMTP id wm4sf38496706obc.7 for ; Sat, 28 Jun 2014 13:06:30 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=date:from:to:message-id:in-reply-to:references:subject:mime-version :x-original-sender:reply-to:precedence:mailing-list:list-id :list-post:list-help:list-archive:list-subscribe:list-unsubscribe :content-type; bh=QsX2BEx5JhRLZiSkxHouhfPz32NPHB2GRA25WKsMrbU=; b=EEASuEUT876FDynlEy8wOxXNV+XCe99tXisOCNxKBVoUgCsh0mARH5TitXxBnpksED zZIFLjqWAI4dKVfTFEHdBBoWeZdFeHYLOUip72PJ4/DxzrRAj69uClFUiw4L0Z0qcKYc bYYFqCydRRGchW8IM/XwOP6R4wpdoDW9Mm+7NrwhiCQ1hD1ZkMup4FTHJ7L50iHaC3kl YnPj/GA/NYTN/rcK6TsOBMU1ynspek9h9ZCBEO91cSJtTKPnuHzBwj1xC8vUxLzHGhR8 gnmpLAHhodzEEC2VQmoL8ZRU97srPT6zdr8zVpKrDSQgg8RFGhBhiHA5VMEA3ZnMs70t aPsQ== X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20130820; h=x-gm-message-state:date:from:to:message-id:in-reply-to:references :subject:mime-version:x-original-sender:reply-to:precedence :mailing-list:list-id:list-post:list-help:list-archive :list-subscribe:list-unsubscribe:content-type; bh=QsX2BEx5JhRLZiSkxHouhfPz32NPHB2GRA25WKsMrbU=; b=HDtYIriOZJkqoqm44Vi9VYaI5bHNI1HeU0OJjKktkqASAjDhgJisgflM2cVkLjIrS/ EVyiJj5c6Yx3jCaN+pJsHpPz9fgSikWFAQYlZgrSkNC45lYOxM5Zy+sXt5D14iQ9yKNs 7n1phezWxnLXv1PFo8gKPHlWkCVQwcz3CWfwBX95eD1ATXyrIper9asbh2q7Z+/fX5l1 k+O82+gyvGDiRFPbf27PMhPH0hWsx5C18MXogwrup0MLTSE5sBLFye0/rv6I8g1QjZX2 apbAhhpxi2K1c9qS/vPWhxaBPdUESo7n1VwtYmkHryQW0yi4hFQHxV23m+VGn/YMjqWR mB7g== X-Gm-Message-State: ALoCoQksS0mEEHBgy4a83BvWpDcMvebwkRklooAu3k3rMy+7af50ETAOzigci8pwkkade8b5ZOs2 X-Received: by 10.182.209.37 with SMTP id mj5mr17391598obc.7.1403985990733; Sat, 28 Jun 2014 13:06:30 -0700 (PDT) X-BeenThere: std-proposals@isocpp.org Original-Received: by 10.140.50.80 with SMTP id r74ls980822qga.71.gmail; Sat, 28 Jun 2014 13:06:30 -0700 (PDT) X-Received: by 10.140.94.38 with SMTP id f35mr678qge.9.1403985990034; Sat, 28 Jun 2014 13:06:30 -0700 (PDT) In-Reply-To: X-Original-Sender: mikhailsemenov1957@gmail.com Precedence: list Mailing-list: list std-proposals@isocpp.org; contact std-proposals+owners@isocpp.org List-ID: X-Google-Group-Id: 399137483710 List-Post: , List-Help: , List-Archive: List-Subscribe: , List-Unsubscribe: , Xref: news.gmane.org gmane.comp.lang.c++.isocpp.proposals:11603 Archived-At: ------=_Part_1353_24319980.1403985989215 Content-Type: text/plain; charset=UTF-8 Jim. I was thinking about something like that: make_table(a,b,N, upper_bound_included) make_table(f,a,b,N, upper_bound_included) I probably should add them to the proposal. On Saturday, June 28, 2014 8:15:13 PM UTC+1, Jim Porter wrote: > On 6/28/2014 10:50 AM, Mikhail Semenov wrote: > > https://dl.dropboxusercontent.com/u/35715999/steps_template.htm > > In this, you describe ways to use std::steps with floating point values, > which requires some special handling to stop the iteration if you're > within epsilon of the endpoint. However, for the floating point case, > I'd really recommend using something more like NumPy's linspace, which > takes, a start, a stop, and a *number of samples*. > > Supposing we had a function like template std::linspace(T > start, T stop, size_t num, include_endpoint = true) and a corresponding > std::make_linspace, this is how you could write your integrate function: > > double integrate( > std::function f, double a, double b, int N > ) { > double h = (b - a) / N; > double h2 = h * 0.5; > double sum = 0.0; > > for(auto x : std::make_linspace(a + h2, b - h2, N)) { > sum += f(x); > } > > return sum * h; > } > > This allows you to avoid worrying about how to define epsilon so that > you're guaranteed to get the number of steps you expect. The extra > complexity for the user is minimal, and makes it clearer that you expect > N steps. If you cared less about efficiency, you could make the loop > look even simpler: > > for(auto x : std::make_linspace(a, b, N, false)) { > sum += f(x + h2); > } > > Even with the epsilon calculation for std::steps, I'd still be worried > about using it if I expected a particular number of iteration steps, and > if that number were quite large. std::linspace would have no such trouble. > > - Jim > > -- --- You received this message because you are subscribed to the Google Groups "ISO C++ Standard - Future Proposals" group. To unsubscribe from this group and stop receiving emails from it, send an email to std-proposals+unsubscribe@isocpp.org. To post to this group, send email to std-proposals@isocpp.org. Visit this group at http://groups.google.com/a/isocpp.org/group/std-proposals/. ------=_Part_1353_24319980.1403985989215 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
Jim. I was thinking about something like that:
<= div>make_table(a,b,N, upper_bound_included)
make_table(f,a,b,N, u= pper_bound_included)
I probably should add them to the proposal.<= br>
On Saturday, June 28, 2014 8:15:13 PM UTC+1, Jim Porter wrote:
=
On 6/28/2014 10:50 AM, Mikhail Semenov wrote:
> https://dl.dropboxusercontent.com/u/35715999/steps_template.htm=

In this, you describe ways to use std::steps with floating point values= ,=20
which requires some special handling to stop the iteration if you're=20
within epsilon of the endpoint. However, for the floating point case,= =20
I'd really recommend using something more like NumPy's linspace, which= =20
takes, a start, a stop, and a *number of samples*.

Supposing we had a function like template <typename T> std::linsp= ace(T=20
start, T stop, size_t num, include_endpoint =3D true) and a correspondi= ng=20
std::make_linspace, this is how you could write your integrate function= :

   double integrate(
     std::function<double(double)> f, double a, do= uble b, int N
   ) {
     double h =3D (b - a) / N;
     double h2 =3D h * 0.5;
     double sum =3D 0.0;

     for(auto x : std::make_linspace(a + h2, b - h2, N))= {
       sum +=3D f(x);
     }

     return sum * h;
   }

This allows you to avoid worrying about how to define epsilon so that= =20
you're guaranteed to get the number of steps you expect. The extra=20
complexity for the user is minimal, and makes it clearer that you expec= t=20
N steps. If you cared less about efficiency, you could make the loop=20
look even simpler:

     for(auto x : std::make_linspace(a, b, N, false)) {
       sum +=3D f(x + h2);
     }

Even with the epsilon calculation for std::steps, I'd still be worried= =20
about using it if I expected a particular number of iteration steps, an= d=20
if that number were quite large. std::linspace would have no such troub= le.

- Jim

--

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