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794. piecewise_constant_distribution missing constructor

Section: 29.5.9.6.2 [rand.dist.samp.pconst] Status: Resolved Submitter: P.J. Plauger Opened: 2008-02-09 Last modified: 2016-01-28

Priority: Not Prioritized

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Discussion:

piecewise_constant_distribution should have a constructor like: 

template<class _Fn>
   piecewise_constant_distribution(size_t _Count,
            _Ty _Low, _Ty _High, _Fn& _Func);

(Makes it easier to fill a histogram with function values over a range. The two (reference 793(i)) make a sensible replacement for general_pdf_distribution.)

[ Sophia Antipolis: ]

Marc: uses variable width of bins and weight for each bin. This is not giving enough flexibility to control both variables.

Add a library issue to provide an constructor taking an initializer_list<double> and _Fn for piecewise_constant_distribution.

Daniel to draft wording.

[ Pre San Francisco, Daniel provided wording. ]

The here proposed changes of the WP refer to the current state of N2691. For reasons explained in 793(i), the author decided to propose a function argument that is provided by value. The issue proposes a c'tor signature, that does not take advantage of the full flexibility of piecewise_constant_distribution, because it restricts on a constant bin width, but the use-case seems to be popular enough to justify it's introduction.

Proposed resolution:

Non-concept version of the proposed resolution

  1. In 29.5.9.6.2 [rand.dist.samp.pconst]/1, class piecewise_constant_distribution, just before the member declaration 

    explicit piecewise_constant_distribution(const param_type& parm);

    insert: 

    template<typename Func>
piecewise_constant_distribution(size_t nf, RealType xmin, RealType xmax, Func fw);

  2. Between p.4 and p.5 insert a new sequence of paragraphs nominated below as [p5_1], [p5_2], [p5_3], and [p5_4] as part of the new member description: 

    template<typename Func>
piecewise_constant_distribution(size_t nf, RealType xmin, RealType xmax, Func fw);

    [p5_1] Complexity: Exactly nf invocations of fw.

    [p5_2] Requires:

    1. fw shall be callable with one argument of type RealType, and shall return values of a type convertible to double;
    2. For all sample values xk defined below, fw(xk) shall return a weight value wk that is non-negative, non-NaN, and non-infinity;
    3. The following relations shall hold: xmin < xmax, and 0 < S = w0+. . .+wn-1.

    [p5_3] Effects:

    1. If nf == 0,

      1. sets deltax = xmax - xmin, and
      2. lets the sequence w have length n = 1 and consist of the single value w0 = 1, and
      3. lets the sequence b have length n+1 with b0 = xmin and b1 = xmax

    2. Otherwise,

      1. sets n = nf, deltax = (xmax - xmin)/n, xcent = xmin + 0.5 * deltax, and

      2. lets the sequences w and b have length n and n+1, resp. and

        for each k = 0, . . . ,n-1, calculates:

        dxk = k * deltax bk = xmin + dxk xk = xcent + dxk wk = fw(xk),

        and

      3. sets bn = xmax

    3. Constructs a piecewise_constant_distribution object with the above computed sequence b as the interval boundaries and with the probability densities:

      ρk = wk/(S * deltax) for k = 0, . . . , n-1.

    [p5_4] [Note: In this context, the subintervals [bk, bk+1) are commonly known as the bins of a histogram. -- end note]

Concept version of the proposed resolution

  1. In 29.5.9.6.2 [rand.dist.samp.pconst]/1, class piecewise_constant_distribution, just before the member declaration 

    explicit piecewise_constant_distribution(const param_type& parm);

    insert: 

    template<Callable<auto, RealType> Func>
 requires Convertible<Func::result_type, double>
piecewise_constant_distribution(size_t nf, RealType xmin, RealType xmax, Func fw);

  2. Between p.4 and p.5 insert a new sequence of paragraphs nominated below as [p5_1], [p5_2], [p5_3], and [p5_4] as part of the new member description: 

    template<Callable<auto, RealType> Func>
 requires Convertible<Func::result_type, double>
piecewise_constant_distribution(size_t nf, RealType xmin, RealType xmax, Func fw);

    [p5_1] Complexity: Exactly nf invocations of fw.

    [p5_2] Requires:

    1. For all sample values xk defined below, fw(xk) shall return a weight value wk that is non-negative, non-NaN, and non-infinity;
    2. The following relations shall hold: xmin < xmax, and 0 < S = w0+. . .+wn-1.

    [p5_3] Effects:

    1. If nf == 0,

      1. sets deltax = xmax - xmin, and
      2. lets the sequence w have length n = 1 and consist of the single value w0 = 1, and
      3. lets the sequence b have length n+1 with b0 = xmin and b1 = xmax

    2. Otherwise,

      1. sets n = nf, deltax = (xmax - xmin)/n, xcent = xmin + 0.5 * deltax, and

      2. lets the sequences w and b have length n and n+1, resp. and

        for each k = 0, . . . ,n-1, calculates: dxk = k * deltax bk = xmin + dxk xk = xcent + dxk wk = fw(xk),

        and

      3. sets bn = xmax

    3. Constructs a piecewise_constant_distribution object with the above computed sequence b as the interval boundaries and with the probability densities:

      ρk = wk/(S * deltax) for k = 0, . . . , n-1.

    [p5_4] [Note: In this context, the subintervals [bk, bk+1) are commonly known as the bins of a histogram. -- end note]

Rationale:

Addressed by N2836 "Wording Tweaks for Concept-enabled Random Number Generation in C++0X".