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Section: 29.6.8.6.2 [rand.dist.samp.pconst] Status: Resolved Submitter: P.J. Plauger Opened: 2008-02-09 Last modified: 2017-02-03
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) 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, 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
In 29.6.8.6.2 [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);
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:
- fw shall be callable with one argument of type RealType, and shall return values of a type convertible to double;
- For all sample values x_{k} defined below, fw(x_{k}) shall return a weight value w_{k} that is non-negative, non-NaN, and non-infinity;
- The following relations shall hold: x_{min} < x_{max}, and 0 < S = w_{0}+. . .+w_{n-1}.
[p5_3] Effects:
If nf == 0,
- sets deltax = x_{max} - x_{min}, and
- lets the sequence w have length n = 1 and consist of the single value w_{0} = 1, and
- lets the sequence b have length n+1 with b_{0} = x_{min} and b_{1} = x_{max}
Otherwise,
- sets n = nf, deltax = (x_{max} - x_{min})/n, x_{cent} = x_{min} + 0.5 * deltax, and
lets the sequences w and b have length n and n+1, resp. and
for each k = 0, . . . ,n-1, calculates:
dx_{k} = k * deltax b_{k} = x_{min} + dx_{k} x_{k} = x_{cent} + dx_{k} w_{k} = fw(x_{k}),
and
- sets b_{n} = x_{max}
Constructs a piecewise_constant_distribution object with the above computed sequence b as the interval boundaries and with the probability densities:
ρ_{k} = w_{k}/(S * deltax) for k = 0, . . . , n-1.
[p5_4] [Note: In this context, the subintervals [b_{k}, b_{k+1}) are commonly known as the bins of a histogram. -- end note]
Concept version of the proposed resolution
In 29.6.8.6.2 [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);
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:
- For all sample values x_{k} defined below, fw(x_{k}) shall return a weight value w_{k} that is non-negative, non-NaN, and non-infinity;
- The following relations shall hold: x_{min} < x_{max}, and 0 < S = w_{0}+. . .+w_{n-1}.
[p5_3] Effects:
If nf == 0,
- sets deltax = x_{max} - x_{min}, and
- lets the sequence w have length n = 1 and consist of the single value w_{0} = 1, and
- lets the sequence b have length n+1 with b_{0} = x_{min} and b_{1} = x_{max}
Otherwise,
- sets n = nf, deltax = (x_{max} - x_{min})/n, x_{cent} = x_{min} + 0.5 * deltax, and
lets the sequences w and b have length n and n+1, resp. and
for each k = 0, . . . ,n-1, calculates: dx_{k} = k * deltax b_{k} = x_{min} + dx_{k} x_{k} = x_{cent} + dx_{k} w_{k} = fw(x_{k}),
and
- sets b_{n} = x_{max}
Constructs a piecewise_constant_distribution object with the above computed sequence b as the interval boundaries and with the probability densities:
ρ_{k} = w_{k}/(S * deltax) for k = 0, . . . , n-1.
[p5_4] [Note: In this context, the subintervals [b_{k}, b_{k+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".