Quasi Monte Carlo method gives zero for the following example

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
2
down vote

favorite












Consider the example



NIntegrate[UnitStep[9-x^2-y^2],x,0,xmax,y,0,ymax,Method->"QuasiMonteCarlo"]


If xmax = ymax = 3, the answer is meaningful. If xmax = ymax = 100, the answer is slightly smaller, while for xmax = ymax = 1000, the answer is zero. This means that QuasiMonteCarlo method evaluates the integral to zero if in most part of the integration domain the integrand is zero.



Could you please tell me whether there is some way to fix this problem?






numerical-integration







share|improve this question

















  • 1




    The chance that a random point thrown into a square of size $1000 times 1000$ to land in the quarter of the disk of radius 3 is about 7.06858*10^-6. So if it comes to Monte Carlo methods, that just does never happen.
    – Henrik Schumacher
    4 hours ago














up vote
2
down vote

favorite












Consider the example



NIntegrate[UnitStep[9-x^2-y^2],x,0,xmax,y,0,ymax,Method->"QuasiMonteCarlo"]


If xmax = ymax = 3, the answer is meaningful. If xmax = ymax = 100, the answer is slightly smaller, while for xmax = ymax = 1000, the answer is zero. This means that QuasiMonteCarlo method evaluates the integral to zero if in most part of the integration domain the integrand is zero.



Could you please tell me whether there is some way to fix this problem?






numerical-integration







share|improve this question

















  • 1




    The chance that a random point thrown into a square of size $1000 times 1000$ to land in the quarter of the disk of radius 3 is about 7.06858*10^-6. So if it comes to Monte Carlo methods, that just does never happen.
    – Henrik Schumacher
    4 hours ago












up vote
2
down vote

favorite









up vote
2
down vote

favorite











Consider the example



NIntegrate[UnitStep[9-x^2-y^2],x,0,xmax,y,0,ymax,Method->"QuasiMonteCarlo"]


If xmax = ymax = 3, the answer is meaningful. If xmax = ymax = 100, the answer is slightly smaller, while for xmax = ymax = 1000, the answer is zero. This means that QuasiMonteCarlo method evaluates the integral to zero if in most part of the integration domain the integrand is zero.



Could you please tell me whether there is some way to fix this problem?






numerical-integration







share|improve this question













Consider the example



NIntegrate[UnitStep[9-x^2-y^2],x,0,xmax,y,0,ymax,Method->"QuasiMonteCarlo"]


If xmax = ymax = 3, the answer is meaningful. If xmax = ymax = 100, the answer is slightly smaller, while for xmax = ymax = 1000, the answer is zero. This means that QuasiMonteCarlo method evaluates the integral to zero if in most part of the integration domain the integrand is zero.



Could you please tell me whether there is some way to fix this problem?






numerical-integration




numerical-integration






share|improve this question













share|improve this question











share|improve this question




share|improve this question










asked 4 hours ago









John Taylor

600211




600211







  • 1




    The chance that a random point thrown into a square of size $1000 times 1000$ to land in the quarter of the disk of radius 3 is about 7.06858*10^-6. So if it comes to Monte Carlo methods, that just does never happen.
    – Henrik Schumacher
    4 hours ago












  • 1




    The chance that a random point thrown into a square of size $1000 times 1000$ to land in the quarter of the disk of radius 3 is about 7.06858*10^-6. So if it comes to Monte Carlo methods, that just does never happen.
    – Henrik Schumacher
    4 hours ago







1




1




The chance that a random point thrown into a square of size $1000 times 1000$ to land in the quarter of the disk of radius 3 is about 7.06858*10^-6. So if it comes to Monte Carlo methods, that just does never happen.
– Henrik Schumacher
4 hours ago




The chance that a random point thrown into a square of size $1000 times 1000$ to land in the quarter of the disk of radius 3 is about 7.06858*10^-6. So if it comes to Monte Carlo methods, that just does never happen.
– Henrik Schumacher
4 hours ago










1 Answer
1






active

oldest

votes

















up vote
3
down vote



accepted










xmax = ymax = 1000;
NIntegrate[UnitStep[9 - x^2 - y^2], x, 0, xmax, y, 0, ymax, 
 Method -> "QuasiMonteCarlo", "SymbolicProcessing" -> True]



7.06875







share|improve this answer




















    Your Answer




    StackExchange.ifUsing("editor", function ()
    return StackExchange.using("mathjaxEditing", function ()
    StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
    StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
    );
    );
    , "mathjax-editing");

    StackExchange.ready(function()
    var channelOptions =
    tags: "".split(" "),
    id: "387"
    ;
    initTagRenderer("".split(" "), "".split(" "), channelOptions);

    StackExchange.using("externalEditor", function()
    // Have to fire editor after snippets, if snippets enabled
    if (StackExchange.settings.snippets.snippetsEnabled)
    StackExchange.using("snippets", function()
    createEditor();
    );

    else
    createEditor();

    );

    function createEditor()
    StackExchange.prepareEditor(
    heartbeatType: 'answer',
    convertImagesToLinks: false,
    noModals: false,
    showLowRepImageUploadWarning: true,
    reputationToPostImages: null,
    bindNavPrevention: true,
    postfix: "",
    onDemand: true,
    discardSelector: ".discard-answer"
    ,immediatelyShowMarkdownHelp:true
    );



    );













     

    draft saved


    draft discarded


















    StackExchange.ready(
    function ()
    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f183217%2fquasi-monte-carlo-method-gives-zero-for-the-following-example%23new-answer', 'question_page');

    );

    Post as a guest

















    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    3
    down vote



    accepted










    xmax = ymax = 1000;
    NIntegrate[UnitStep[9 - x^2 - y^2], x, 0, xmax, y, 0, ymax, 
     Method -> "QuasiMonteCarlo", "SymbolicProcessing" -> True]



    7.06875







    share|improve this answer
























      up vote
      3
      down vote



      accepted










      xmax = ymax = 1000;
      NIntegrate[UnitStep[9 - x^2 - y^2], x, 0, xmax, y, 0, ymax, 
       Method -> "QuasiMonteCarlo", "SymbolicProcessing" -> True]



      7.06875







      share|improve this answer






















        up vote
        3
        down vote



        accepted







        up vote
        3
        down vote



        accepted






        xmax = ymax = 1000;
        NIntegrate[UnitStep[9 - x^2 - y^2], x, 0, xmax, y, 0, ymax, 
         Method -> "QuasiMonteCarlo", "SymbolicProcessing" -> True]



        7.06875







        share|improve this answer












        xmax = ymax = 1000;
        NIntegrate[UnitStep[9 - x^2 - y^2], x, 0, xmax, y, 0, ymax, 
         Method -> "QuasiMonteCarlo", "SymbolicProcessing" -> True]



        7.06875








        share|improve this answer












        share|improve this answer



        share|improve this answer










        answered 4 hours ago









        kglr

        163k8188387




        163k8188387



























             

            draft saved


            draft discarded















































             


            draft saved


            draft discarded














            StackExchange.ready(
            function ()
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f183217%2fquasi-monte-carlo-method-gives-zero-for-the-following-example%23new-answer', 'question_page');

            );

            Post as a guest
































































            Comments

            Post a Comment

            Popular posts from this blog

            Long meetings (6-7 hours a day): Being “babysat” by supervisor

            Image
            Clash Royale CLAN TAG #URR8PPP .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty margin-bottom:0; up vote 31 down vote favorite 4 I hold a PhD in mechanical engineering with a 7 year background in self-guided, self-paced research including 2 years as a graduate level course instructor and a subject matter expert for various engineering projects in a university setting in the United States. For the last 10-11 months, I am working in a research industry in France where my task is to debug C++ spaghetti code written over a period of several years by my current supervisor. It is a team of 2: just I and my supervisor. Diurnally, I am posed with a "bug of the day" to get out of this C++ code. My supervisor generally gives me about 15-30 minutes to solve it and then accosts me about whether or not the task is completed and then rinses and repeats this until the end of the day. Off-late, my supervisor has been holding 6-7 hour long "meetin
            Read more

            What does second last employer means? [closed]

            Image
            Clash Royale CLAN TAG #URR8PPP .everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty margin-bottom:0; up vote -3 down vote favorite Say, for example I have worked in the following companies, Company A => 2010 - 2011 Company B => 2011 - 2012 Company C => 2012 - Till Date Company D => Have offer Now assume Company D is asking to submit documents from my second last employer. So from the list of companies given, which company would be qualified as second last employer? software-industry employer share | improve this question asked Aug 10 '14 at 5:16 Rajaprabhu Aravindasamy 559 1 6 13 closed as off-topic by Jim G., jmort253 ♦ Aug 11 '14 at 1:58 This question appears to be off-topic. The users who voted to close gave this specific reason: "Questions seeking advice on company-specific regulations, agreements, or policies should be directed to your manager or HR department. Questions that address only
            Read more

            One-line joke

            A one-liner is a joke that is delivered in a single line. A good one-liner is said to be pithy - concise and meaningful. [1] Comedians and actors use this comedic method as part of their act, e.g. Jimmy Carr, Tommy Cooper, Rodney Dangerfield, Norm Macdonald, Ken Dodd, Stewart Francis, Zach Galifianakis, Mitch Hedberg, Anthony Jeselnik, Milton Jones, Shappi Khorsandi, Jay London, Mark Linn-Baker, Demetri Martin, Groucho Marx, Dan Mintz, Emo Philips, Tim Vine, Steven Wright and Henny Youngman and Arnold Schwarzenegger. [ citation needed ] Many fictional characters are also known to deliver one-liners, including James Bond, who usually includes pithy and laconic quips after disposing of a villain. [ citation needed ] Examples "A baby seal walks into a club." "A dyslexic man walks into a bra." (Anonymous) "There are three types of people, those who can count and those who can't." "Venison's dear, isn't it?" (Jimmy Carr) "An escala
            Read more