29 Numerics library [numerics]

29.5 Random number generation [rand]

29.5.9 Random number distribution class templates [rand.dist]

29.5.9.6 Sampling distributions [rand.dist.samp]

29.5.9.6.1 Class template discrete_distribution [rand.dist.samp.discrete]

A discrete_distribution random number distribution produces random integers i,

0 \leq i < n

, distributed according to the discrete probability function in Formula 29.19 .

\begin{matrix} P (i | p_{0}, \dots, p_{n - 1}) = p_{i} \\ (29.19) \end{matrix}

Unless specified otherwise, the distribution parameters are calculated as:

p_{k} = w_{k} / S

for

k = 0, \dots, n - 1

, in which the values

w_{k}

, commonly known as the weights, shall be non-negative, non-NaN, and non-infinity.

Moreover, the following relation shall hold:

0 < S = w_{0} + \dots + w_{n - 1}

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namespace std { template<class IntType = int> class discrete_distribution { public: // types using result_type = IntType; using param_type = unspecified; // constructor and reset functions discrete_distribution(); template<class InputIterator> discrete_distribution(InputIterator firstW, InputIterator lastW); discrete_distribution(initializer_list<double> wl); template<class UnaryOperation> discrete_distribution(size_t nw, double xmin, double xmax, UnaryOperation fw); explicit discrete_distribution(const param_type& parm); void reset(); // equality operators friend bool operator==(const discrete_distribution& x, const discrete_distribution& y); // generating functions template<class URBG> result_type operator()(URBG& g); template<class URBG> result_type operator()(URBG& g, const param_type& parm); // property functions vector<double> probabilities() const; param_type param() const; void param(const param_type& parm); result_type min() const; result_type max() const; // inserters and extractors template<class charT, class traits> friend basic_ostream<charT, traits>& operator<<(basic_ostream<charT, traits>& os, const discrete_distribution& x); template<class charT, class traits> friend basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, discrete_distribution& x); }; }

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discrete_distribution();

Effects: Constructs a discrete_distribution object with

n = 1

and

p_{0} = 1

[Note 1:

Such an object will always deliver the value 0.

— end note]

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template<class InputIterator>
  discrete_distribution(InputIterator firstW, InputIterator lastW);

Mandates: is_convertible_v<iterator_traits<InputIterator>::value_type, double> is true.

Preconditions: InputIterator meets the Cpp17InputIterator requirements ([input.iterators]).

If firstW == lastW, let

n = 1

and

w_{0} = 1

Otherwise, [firstW, lastW) forms a sequence w of length

n > 0

Effects: Constructs a discrete_distribution object with probabilities given by the Formula 29.19 .

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discrete_distribution(initializer_list<double> wl);

Effects: Same as discrete_distribution(wl.begin(), wl.end()).

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template<class UnaryOperation>
  discrete_distribution(size_t nw, double xmin, double xmax, UnaryOperation fw);

Mandates: is_invocable_r_v<double, UnaryOperation&, double> is true.

Preconditions: If

nw = 0

, let

n = 1

, otherwise let

n = nw

The relation

0 < δ = (xmax - xmin) / n

holds.

Effects: Constructs a discrete_distribution object with probabilities given by the formula above, using the following values: If

nw = 0

, let

w_{0} = 1

Otherwise, let

w_{k} = fw (xmin + k \cdot δ + δ / 2)

for

k = 0, \dots, n - 1

Complexity: The number of invocations of fw does not exceed n.

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vector<double> probabilities() const;

Returns: A vector<double> whose size member returns n and whose operator[] member returns

p_{k}

when invoked with argument k for

k = 0, \dots, n - 1