29 Numerics library [numerics]

29.6 Random number generation [rand]

29.6.8 Random number distribution class templates [rand.dist]

29.6.8.6 Sampling distributions [rand.dist.samp]

29.6.8.6.1 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

$P (i | p_{0}, \dots, p_{n - 1}) = p_{i} .$

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}

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();

    // 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;
  };

🔗

discrete_distribution();

Effects: Constructs a discrete_distribution object with

n = 1

and

p_{0} = 1

[ Note

Such an object will always deliver the value 0.

— end note

]

🔗

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

Requires: InputIterator shall satisfy the requirements of an input iterator ([input.iterators]).

Moreover, iterator_traits<InputIterator>::value_type shall denote a type that is convertible to double.

If firstW == lastW, let

n = 1

and

w_{0} = 1

Otherwise,

[firstW, lastW)

shall form a sequence w of length

n > 0

Effects: Constructs a discrete_distribution object with probabilities given by the formula above.

🔗

discrete_distribution(initializer_list<double> wl);

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

🔗

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

Requires: Each instance of type UnaryOperation shall be a function object ([function.objects]) whose return type shall be convertible to double.

Moreover, double shall be convertible to the type of UnaryOperation's sole parameter.

nw = 0

, let

n = 1

, otherwise let

n = nw

The relation

0 < δ = (xmax - xmin) / n

shall hold.

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 shall not exceed n.

🔗

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

29 Numerics library [numerics]

29.6 Random number generation [rand]

29.6.8 Random number distribution class templates [rand.dist]

29.6.8.6 Sampling distributions [rand.dist.samp]

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

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