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## Detailed Description

The Mersenne Twister is a twisted generalized feedback shift-register generator of Matsumoto and Nishimura. The period of this generator is and it is equi-distributed in 623 dimensions for 32-bit numbers. The time performance of this generator is comparable to the commonly used generators.

This implementation is specialized for both 32-bit and 64-bit architectures. The generators differ sligthly in the initialization and generation phase so they produce two completly different sequences.

The generator gives back random numbers of serveral types. To get a random number from a range of a floating point type you can use one form of the `operator()` or the `real()` member function. If you want to get random number from the {0, 1, ..., n-1} integer range use the `operator`[] or the `integer()` method. And to get random number from the whole range of an integer type you can use the argumentless `integer()` or `uinteger()` functions. After all you can get random bool with equal chance of true and false or given probability of true result with the `boolean()` member functions.

* // The commented code is identical to the other
* double a = rnd(); // [0.0, 1.0)
* // double a = rnd.real(); // [0.0, 1.0)
* double b = rnd(100.0); // [0.0, 100.0)
* // double b = rnd.real(100.0); // [0.0, 100.0)
* double c = rnd(1.0, 2.0); // [1.0, 2.0)
* // double c = rnd.real(1.0, 2.0); // [1.0, 2.0)
* int d = rnd[100000]; // 0..99999
* // int d = rnd.integer(100000); // 0..99999
* int e = rnd[6] + 1; // 1..6
* // int e = rnd.integer(1, 1 + 6); // 1..6
* int b = rnd.uinteger<int>(); // 0 .. 2^31 - 1
* int c = rnd.integer<int>(); // - 2^31 .. 2^31 - 1
* bool g = rnd.boolean(); // P(g = true) = 0.5
* bool h = rnd.boolean(0.8); // P(h = true) = 0.8
*

LEMON provides a global instance of the random number generator which name is rnd. Usually it is a good programming convenience to use this global generator to get random numbers.

`#include <lemon/random.h>`

## Public Member Functions
Initialization
| Random ()
| Default constructor. More...
template<typename Number >
| Random (Number seed)
| Constructor with seed. More...
template<typename Iterator >
| Random (Iterator begin, Iterator end)
| Constructor with array seeding. More...
| Random (const Random &other)
| Copy constructor. More...
Random & | operator= (const Random &other)
| Assign operator. More...
template<typename Number >
void | seed (Number seed)
| Seeding random sequence. More...
template<typename Iterator >
void | seed (Iterator begin, Iterator end)
| Seeding random sequence. More...
bool | seed ()
| Seeding from file or from process id and time. More...
bool | seedFromFile (const std::string &file="/dev/urandom", int offset=0)
| Seeding from file. More...
bool | seedFromTime ()
| Seding from process id and time. More...
Uniform Distributions
template<typename Number >
Number | real ()
| Returns a random real number from the range [0, 1) More...
double | real ()
double | operator() ()
| Returns a random real number from the range [0, 1) More...
double | operator() (double b)
| Returns a random real number from the range [0, b) More...
double | operator() (double a, double b)
| Returns a random real number from the range [a, b) More...
template<typename Number >
Number | integer (Number b)
| Returns a random integer from a range. More...
template<typename Number >
Number | integer (Number a, Number b)
| Returns a random integer from a range. More...
template<typename Number >
Number | operator[] (Number b)
| Returns a random integer from a range. More...
template<typename Number >
Number | uinteger ()
| Returns a random non-negative integer. More...
unsigned int | uinteger ()
template<typename Number >
Number | integer ()
| Returns a random integer. More...
int | integer ()
bool | boolean ()
| Returns a random bool. More...
Non-uniform Distributions
bool | boolean (double p)
| Returns a random bool with given probability of true result. More...
double | gauss ()
| Standard normal (Gauss) distribution. More...
double | gauss (double mean, double std_dev)
| Normal (Gauss) distribution with given mean and standard deviation. More...
double | lognormal (double n_mean, double n_std_dev)
| Lognormal distribution. More...
double | lognormal (const std::pair< double, double > &params)
| Lognormal distribution. More...
std::pair< double, double > | lognormalParamsFromMD (double mean, double std_dev)
| Compute the lognormal parameters from mean and standard deviation. More...
double | lognormalMD (double mean, double std_dev)
| Lognormal distribution with given mean and standard deviation. More...
double | exponential (double lambda=1.0)
| Exponential distribution with given mean. More...
double | gamma (int k)
| Gamma distribution with given integer shape. More...
double | gamma (double k, double theta=1.0)
| Gamma distribution with given shape and scale parameter. More...
double | weibull (double k, double lambda)
| Weibull distribution. More...
double | pareto (double k, double x_min)
| Pareto distribution. More...
int | poisson (double lambda)
| Poisson distribution. More...
Two Dimensional Distributions
dim2::Point< double > | disc ()
| Uniform distribution on the full unit circle. More...
dim2::Point< double > | gauss2 ()
| A kind of two dimensional normal (Gauss) distribution. More...
dim2::Point< double > | exponential2 ()
| A kind of two dimensional exponential distribution. More...

## Constructor & Destructor Documentation

Random | ( |  | ) |
| inline

Constructor with constant seeding.

Random | ( | Number | seed | ) |
| inline

Constructor with seed. The current number type will be converted to the architecture word type.

Random | ( | Iterator | begin,
|  | Iterator | end
| ) |  |
| inline

Constructor with array seeding. The given range should contain any number type and the numbers will be converted to the architecture word type.

Random | ( | const Random & | other | ) |
| inline

Copy constructor. The generated sequence will be identical to the other sequence. It can be used to save the current state of the generator and later use it to generate the same sequence.

## Member Function Documentation

Random& operator= | ( | const Random & | other | ) |
| inline

Assign operator. The generated sequence will be identical to the other sequence. It can be used to save the current state of the generator and later use it to generate the same sequence.

void seed | ( | Number | seed | ) |
| inline

Seeding the random sequence. The current number type will be converted to the architecture word type.

void seed | ( | Iterator | begin,
|  | Iterator | end
| ) |  |
| inline

Seeding the random sequence. The given range should contain any number type and the numbers will be converted to the architecture word type.

bool seed | ( |  | ) |
| inline

By default, this function calls the `seedFromFile()` member function with the `/dev/urandom` file. If it does not success, it uses the `seedFromTime()`.

Returns
  Currently always `true`.

bool seedFromFile | ( | const std::string & | file = `"/dev/urandom"`,
|  | int | offset = `0`
| ) |  |
| inline

Seeding the random sequence from file. The linux kernel has two devices, `/dev/random` and `/dev/urandom` which could give good seed values for pseudo random generators (The difference between two devices is that the `random` may block the reading operation while the kernel can give good source of randomness, while the `urandom` does not block the input, but it could give back bytes with worse entropy).

Parameters

  file | The source file
  offset | The offset, from the file read.

Returns
  `true` when the seeding successes.

bool seedFromTime | ( |  | ) |
| inline

Seding from process id and time. This function uses the current process id and the current time for initialize the random sequence.

Returns
  Currently always `true`.

Number real | ( |  | ) |
| inline

It returns a random real number from the range [0, 1). The default Number type is `double`.

double operator() | ( |  | ) |
| inline

It returns a random double from the range [0, 1).

double operator() | ( | double | b | ) |
| inline

It returns a random real number from the range [0, b).

double operator() | ( | double | a,
|  | double | b
| ) |  |
| inline

It returns a random real number from the range [a, b).

Number integer | ( | Number | b | ) |
| inline

It returns a random integer from the range {0, 1, ..., b - 1}.

Number integer | ( | Number | a,
|  | Number | b
| ) |  |
| inline

It returns a random integer from the range {a, a + 1, ..., b - 1}.

Number operator[] | ( | Number | b | ) |
| inline

It returns a random integer from the range {0, 1, ..., b - 1}.

Number uinteger | ( |  | ) |
| inline

It returns a random non-negative integer uniformly from the whole range of the current `Number` type. The default result type of this function is `unsigned int`.

Number integer | ( |  | ) |
| inline

It returns a random integer uniformly from the whole range of the current `Number` type. The default result type of this function is `int`.

bool boolean | ( |  | ) |
| inline

It returns a random bool. The generator holds a buffer for random bits. Every time when it become empty the generator makes a new random word and fill the buffer up.

bool boolean | ( | double | p | ) |
| inline

It returns a random bool with given probability of true result.

double gauss | ( |  | ) |
| inline

Standard normal (Gauss) distribution.

Note
  The Cartesian form of the Box-Muller transformation is used to generate a random normal distribution.

double gauss | ( | double | mean,
|  | double | std_dev
| ) |  |
| inline

Normal (Gauss) distribution with given mean and standard deviation.

See Also
  gauss()

double lognormal | ( | double | n_mean,
|  | double | n_std_dev
| ) |  |
| inline

Lognormal distribution. The parameters are the mean and the standard deviation of `exp(X)`.

double lognormal | ( | const std::pair< double, double > & | params | ) |
| inline

Lognormal distribution. The parameter is an `std::pair` of the mean and the standard deviation of `exp(X)`.

std::pair<double,double> lognormalParamsFromMD | ( | double | mean,
|  | double | std_dev
| ) |  |
| inline

This function computes the lognormal parameters from mean and standard deviation. The return value can direcly be passed to lognormal().

double lognormalMD | ( | double | mean,
|  | double | std_dev
| ) |  |
| inline

Lognormal distribution with given mean and standard deviation.

double exponential | ( | double | lambda = `1.0` | ) |
| inline

This function generates an exponential distribution random number with mean `1/lambda`.

double gamma | ( | int | k | ) |
| inline

This function generates a gamma distribution random number.

Parameters

  k | shape parameter (`k>0` integer)

double gamma | ( | double | k,
|  | double | theta = `1.0`
| ) |  |
| inline

This function generates a gamma distribution random number.

Parameters

  k | shape parameter (`k>0`)
  theta | scale parameter

double weibull | ( | double | k,
|  | double | lambda
| ) |  |
| inline

This function generates a Weibull distribution random number.

Parameters

  k | shape parameter (`k>0`)
  lambda | scale parameter (`lambda>0`)

double pareto | ( | double | k,
|  | double | x_min
| ) |  |
| inline

This function generates a Pareto distribution random number.

Parameters

  k | shape parameter (`k>0`)
  x_min | location parameter (`x_min>0`)

int poisson | ( | double | lambda | ) |
| inline

This function generates a Poisson distribution random number with parameter `lambda`.

The probability mass function of this distribusion is

Note
  The algorithm is taken from the book of Donald E. Knuth titled ''Seminumerical Algorithms'' (1969). Its running time is linear in the return value.

dim2::Point<double> disc | ( |  | ) |
| inline

Uniform distribution on the full unit circle.

dim2::Point<double> gauss2 | ( |  | ) |
| inline

This function provides a turning symmetric two-dimensional distribution. Both coordinates are of standard normal distribution, but they are not independent.

Note
  The coordinates are the two random variables provided by the Box-Muller method.

dim2::Point<double> exponential2 | ( |  | ) |
| inline

This function provides a turning symmetric two-dimensional distribution. The x-coordinate is of conditionally exponential distribution with the condition that x is positive and y=0. If x is negative and y=0 then, -x is of exponential distribution. The same is true for the y-coordinate.