libitpp-dev 4.3.1-2 / usr / include / itpp / base / random.h

/*!
 * \file
 * \brief Definition of classes for random number generators
 * \author Tony Ottosson and Adam Piatyszek
 *
 * -------------------------------------------------------------------------
 *
 * Copyright (C) 1995-2010  (see AUTHORS file for a list of contributors)
 *
 * This file is part of IT++ - a C++ library of mathematical, signal
 * processing, speech processing, and communications classes and functions.
 *
 * IT++ is free software: you can redistribute it and/or modify it under the
 * terms of the GNU General Public License as published by the Free Software
 * Foundation, either version 3 of the License, or (at your option) any
 * later version.
 *
 * IT++ is distributed in the hope that it will be useful, but WITHOUT ANY
 * WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
 * FOR A PARTICULAR PURPOSE.  See the GNU General Public License for more
 * details.
 *
 * You should have received a copy of the GNU General Public License along
 * with IT++.  If not, see <http://www.gnu.org/licenses/>.
 *
 * -------------------------------------------------------------------------
 */

#ifndef RANDOM_H
#define RANDOM_H

#include <itpp/base/random_dsfmt.h>
#include <itpp/base/operators.h>
#include <itpp/itexports.h>

namespace itpp
{

/*! \addtogroup randgen

Set of functions to work with global seed provider:
\code
void GlobalRNG_reset(unsigned int seed);
void GlobalRNG_reset();
unsigned int GlobalRNG_get_local_seed();
void GlobalRNG_randomize();
void GlobalRNG_get_state(ivec &state);
void GlobalRNG_set_state(const ivec &state);
\endcode

Global seed provider generate default seeds to initialize per-thread generators
of pseudo-random numbers. Functions implement mutually exclusive access to the
global seed provider instance.

Be carefull,

Mutual exclusion serializes access to the global seed provider
context and protects its integrity. It does not guarantee the expected results
if global seed provider is accessed simultaneously from several threads.

For example,
\code
ivec st_before,st_after;
GlobalRNG_get_state(st_before);
GlobalRNG_set_state(st_before);
GlobalRNG_get_state(st_after);
assert(st_before==st_after);
\endcode

last assert can fail in multithreaded environment.

Be aware,

Global seed provider generates seeds to initialize non-initialized per-thread RNG contexts.
Global seed provider is just a random numbers generator starting with default seed equal to
4257U. When RNGs are created in some thread, global seed provider is queried for the new seed to
initialize random number generation in the current thread.
The first seed returned by the global seed provider is also 4257U by default. Other
seeds are taken from the rng output directly. It is implemented this way because some ITPP tests
implicitly rely on this value. Global seed provider internals are defined in random.cpp and can be changed
easily if such a behaviour is not desirable.
Global initialization can be overriden by the explicit call of the local context initialization function.
Global seed provider changes will not affect already initialized contexts in running or parked threads, since
global seeds are used during the local context initialization only.
Local contexts get initialized upon creation of first RandomGenerator object in each thread. RNG_reset() without
arguments can also query a global seed if local context is not initialized when the function is called.
For example, if you want the main thread context to be affected by global settings,
GlobalRNG_reset(seed) shall be called BEFORE the construction of first RandomGenerator object.
The best place to do it is the very beginning of your main() function.
If you create itpp library objects, encapsulating RNGs, statically, the main thread context will not be
affected by any call to GlobalRNG_reset(s)/GlobalRNG_set_state(s). If you still want to
have main-thread state be derived from the global context, you should do the following trick
at the beginning of main():
\code
unsigned int my_global_seed = 0xAAAAAAAA;
GlobalRNG_reset(my_global_seed);
unsigned int s = GlobalRNG_get_local_seed(); //query new local seed
RNG_reset(s); //set it maually for the main thread
//you can call your main-thread RNGs here
\endcode

@{ */

//! Set the internal seed of the Global Seed Provider
ITPP_EXPORT void GlobalRNG_reset(unsigned int seed);

//! Reset the internal seed of the Global Seed Provider to the previously set value
ITPP_EXPORT void GlobalRNG_reset();

//! Get new seed to initialize thread-local generators
ITPP_EXPORT unsigned int GlobalRNG_get_local_seed();

//! Set a random seed for the Global Seed Provider seed
ITPP_EXPORT void GlobalRNG_randomize();

//! Save current full state of global seed provider in memory
ITPP_EXPORT void GlobalRNG_get_state(ivec &state);

//! Resume the global seed provider state saved in memory
ITPP_EXPORT void GlobalRNG_set_state(const ivec &state);

//!@}


/*! \addtogroup randgen

Local (per-thread) RNG context management.
\code
void RNG_reset(unsigned int seed);
void RNG_reset();
void RNG_get_state(ivec &state);
void RNG_set_state(const ivec &state);
\endcode

This set of functions allow to override seed value set from global seed provider and
use custom seeds/initialization vectors for each thread (including main thread).

@{ */

//! Set the seed for all Random Number Generators in the current thread
ITPP_EXPORT void RNG_reset(unsigned int seed);

/*!
\brief Reset the seed to the previously set value for all Random Number Generators in the current thread.

Seed will be queried from the global
seed provider if Random Number generation context is not initialized
*/
ITPP_EXPORT void RNG_reset();

//! Set a random seed for all Random Number Generators in the current thread
ITPP_EXPORT void RNG_randomize();

//! Save Random Number generation context used in the current thread
ITPP_EXPORT void RNG_get_state(ivec &state);

//! Resume Random Number generation in the current thread with previously stored context
ITPP_EXPORT void RNG_set_state(const ivec &state);

//!@}


/*!
 *\ingroup randgen
 *\brief Base class for random (stochastic) sources.
 *
 * Random_Generator provides thread-safe generation of pseudo-random numbers
 *
 * \sa DSFMT
 */
class ITPP_EXPORT Random_Generator
{
  typedef random_details::ActiveDSFMT DSFMT;
public:
  //! Default constructor
  Random_Generator(): _dsfmt(random_details::lc_get()) {
    if(!random_details::lc_is_initialized()) {
      _dsfmt.init_gen_rand(GlobalRNG_get_local_seed());
      random_details::lc_mark_initialized();
    }
  }

  //Constructor using a certain seed - do not want to provide it. Use free-standing functions to change per-thread local seed
  //Random_Generator(unsigned int seed) { init_gen_rand(seed); random_details::lc_mark_initialized();}

  //provide wrappers for DSFMT algorithm functions

  //Set the seed to a semi-random value (based on hashed time and clock)  - do not want to provide it. Use free-standing functions to change per-thread local seed
  //void randomize(){RNG_randomize();}

  //Reset the generator with the same seed as used last time  - do not want to provide it. Use free-standing functions to change per-thread local seed
  //void reset() {RNG_reset();}

  //Initialise the generator with a new seed (\sa init_gen_rand())  - do not want to provide it. Use free-standing functions to change per-thread local seed
  //void reset(unsigned int seed) { RNG_reset(seed); }

  //Resume the state of the generator from a previously saved ivec  - do not want to provide it. Use free-standing functions to change per-thread local seed
  //void set_state(const ivec &state) {RNG_set_state(state);}

  //Return current state of generator in the form of ivec  - do not want to provide it. Use free-standing functions to change per-thread local seed
  //ivec get_state() const {ivec ret; RNG_get_state(ret); return ret; }

  //! Return a uniformly distributed (0,1) value.
  double random_01() { return genrand_open_open(); }
  //! Return a uniformly distributed [0,1) value.
  double random_01_lclosed() { return genrand_close_open(); }
  //! Return a uniformly distributed (0,1] value.
  double random_01_rclosed() { return genrand_open_close(); }
  //! Return a uniformly distributed [0, UINT_MAX) value.
  uint32_t random_int() { return genrand_uint32(); }

  //! Generate uniform [0, UINT_MAX) integer pseudorandom number.
  uint32_t genrand_uint32() { return _dsfmt.genrand_uint32(); }

  /*!
   * \brief Generate uniform [1, 2) double pseudorandom number.
   *
   * This function generates and returns double precision pseudorandom
   * number which distributes uniformly in the range [1, 2).  This is
   * the primitive and faster than generating numbers in other ranges.
   * \c init_gen_rand() must be called before this function.
   * \return double precision floating point pseudorandom number
   */
  double genrand_close1_open2() { return _dsfmt.genrand_close1_open2(); }

  /*!
   * \brief Generate uniform [0, 1) double pseudorandom number.
   *
   * This function generates and returns double precision pseudorandom
   * number which distributes uniformly in the range [0, 1).
   * \c init_gen_rand() must be called before this function.
   * \return double precision floating point pseudorandom number
   */
  double genrand_close_open() { return genrand_close1_open2() - 1.0; }

  /*!
   * \brief Generate uniform (0, 1] double pseudorandom number.
   *
   * This function generates and returns double precision pseudorandom
   * number which distributes uniformly in the range (0, 1].
   * \c init_gen_rand() must be called before this function.
   * \return double precision floating point pseudorandom number
   */
  double genrand_open_close() { return 2.0 - genrand_close1_open2(); }

  /*!
   * \brief Generate uniform (0, 1) double pseudorandom number.
   *
   * This function generates and returns double precision pseudorandom
   * number which distributes uniformly in the range (0, 1).
   * \c init_gen_rand() must be called before this function.
   * \return double precision floating point pseudorandom number
   */
  double genrand_open_open() { return _dsfmt.genrand_open_open();}

private:
  DSFMT _dsfmt;
};

/*!
  \brief Bernoulli distribution
  \ingroup randgen
*/
class ITPP_EXPORT Bernoulli_RNG
{
public:
  //! Binary source with probability prob for a 1
  Bernoulli_RNG(double prob) { setup(prob); }
  //! Binary source with probability prob for a 1
  Bernoulli_RNG() { p = 0.5; }
  //! set the probability
  void setup(double prob) {
    it_assert(prob >= 0.0 && prob <= 1.0, "The Bernoulli source probability "
              "must be between 0 and 1");
    p = prob;
  }
  //! return the probability
  double get_setup() const { return p; }
  //! Get one sample.
  bin operator()() { return sample(); }
  //! Get a sample vector.
  bvec operator()(int n) { bvec temp(n); sample_vector(n, temp); return temp; }
  //! Get a sample matrix.
  bmat operator()(int h, int w) { bmat temp(h, w); sample_matrix(h, w, temp); return temp; }
  //! Get a sample
  bin sample() { return RNG.genrand_close_open() < p ? bin(1) : bin(0); }
  //! Get a sample vector.
  void sample_vector(int size, bvec &out) {
    out.set_size(size, false);
    for(int i = 0; i < size; i++) out(i) = sample();
  }
  //! Get a sample matrix.
  void sample_matrix(int rows, int cols, bmat &out) {
    out.set_size(rows, cols, false);
    for(int i = 0; i < rows * cols; i++) out(i) = sample();
  }
protected:
private:
  //!
  double p;
  //!
  Random_Generator RNG;
};

/*!
  \brief Integer uniform distribution
  \ingroup randgen

  Example: Generation of random uniformly distributed integers in the interval [0,10].
  \code
  #include "itpp/sigproc.h"

  int main() {

  I_Uniform_RNG gen(0, 10);

  cout << gen() << endl; // prints a random integer
  cout << gen(10) << endl; // prints 10 random integers
  }
  \endcode
*/
class ITPP_EXPORT I_Uniform_RNG
{
public:
  //! constructor. Sets min and max values.
  I_Uniform_RNG(int min = 0, int max = 1);
  //! set min and max values
  void setup(int min, int max);
  //! get the parameters
  void get_setup(int &min, int &max) const;
  //! Get one sample.
  int operator()() { return sample(); }
  //! Get a sample vector.
  ivec operator()(int n);
  //! Get a sample matrix.
  imat operator()(int h, int w);
  //! Return a single value from this random generator
  int sample() {
    return floor_i(RNG.genrand_close_open() * (hi - lo + 1)) + lo;
  }
private:
  //!
  int lo;
  //!
  int hi;
  //!
  Random_Generator RNG;
};

/*!
  \brief Uniform distribution
  \ingroup randgen
*/
class ITPP_EXPORT Uniform_RNG
{
public:
  //! Constructor. Set min, max and seed.
  Uniform_RNG(double min = 0, double max = 1.0);
  //! set min and max
  void setup(double min, double max);
  //! get parameters
  void get_setup(double &min, double &max) const;
  //! Get one sample.
  double operator()() { return (sample() * (hi_bound - lo_bound) + lo_bound); }
  //! Get a sample vector.
  vec operator()(int n) {
    vec temp(n);
    sample_vector(n, temp);
    temp *= hi_bound - lo_bound;
    temp += lo_bound;
    return temp;
  }
  //! Get a sample matrix.
  mat operator()(int h, int w) {
    mat temp(h, w);
    sample_matrix(h, w, temp);
    temp *= hi_bound - lo_bound;
    temp += lo_bound;
    return temp;
  }
  //! Get a Uniformly distributed [0,1) sample
  double sample() {  return RNG.genrand_close_open(); }
  //! Get a Uniformly distributed [0,1) vector
  void sample_vector(int size, vec &out) {
    out.set_size(size, false);
    for(int i = 0; i < size; i++) out(i) = sample();
  }
  //! Get a Uniformly distributed [0,1) matrix
  void sample_matrix(int rows, int cols, mat &out) {
    out.set_size(rows, cols, false);
    for(int i = 0; i < rows * cols; i++) out(i) = sample();
  }
protected:
private:
  //!
  double lo_bound, hi_bound;
  //!
  Random_Generator RNG;
};

/*!
  \brief Exponential distribution
  \ingroup randgen
*/
class ITPP_EXPORT Exponential_RNG
{
public:
  //! constructor. Set lambda.
  Exponential_RNG(double lambda = 1.0);
  //! Set lambda
  void setup(double lambda) { l = lambda; }
  //! get lambda
  double get_setup() const;
  //! Get one sample.
  double operator()() { return sample(); }
  //! Get a sample vector.
  vec operator()(int n);
  //! Get a sample matrix.
  mat operator()(int h, int w);
private:
  double sample() { return (-std::log(RNG.genrand_open_close()) / l); }
  double l;
  Random_Generator RNG;
};

/*!
 * \brief Normal distribution
 * \ingroup randgen
 *
 * Normal (Gaussian) random variables, using a simplified Ziggurat method.
 *
 * For details see the following arcticle: George Marsaglia, Wai Wan
 * Tsang, "The Ziggurat Method for Generating Random Variables", Journal
 * of Statistical Software, vol. 5 (2000), no. 8
 *
 * This implementation is based on the generator written by Jochen Voss
 * found at http://seehuhn.de/comp/ziggurat/, which is also included in
 * the GSL library (randlist/gauss.c).
 */
class ITPP_EXPORT Normal_RNG
{
public:
  //! Constructor. Set mean and variance.
  Normal_RNG(double meanval, double variance):
    mean(meanval), sigma(std::sqrt(variance)) {}
  //! Constructor. Set mean and variance.
  Normal_RNG(): mean(0.0), sigma(1.0) {}
  //! Set mean, and variance
  void setup(double meanval, double variance)
  { mean = meanval; sigma = std::sqrt(variance); }
  //! Get mean and variance
  void get_setup(double &meanval, double &variance) const;
  //! Get one sample.
  double operator()() { return (sigma * sample() + mean); }
  //! Get a sample vector.
  vec operator()(int n) {
    vec temp(n);
    sample_vector(n, temp);
    temp *= sigma;
    temp += mean;
    return temp;
  }
  //! Get a sample matrix.
  mat operator()(int h, int w) {
    mat temp(h, w);
    sample_matrix(h, w, temp);
    temp *= sigma;
    temp += mean;
    return temp;
  }
  //! Get a Normal distributed (0,1) sample
  double sample();

  //! Get a Normal distributed (0,1) vector
  void sample_vector(int size, vec &out) {
    out.set_size(size, false);
    for(int i = 0; i < size; i++) out(i) = sample();
  }

  //! Get a Normal distributed (0,1) matrix
  void sample_matrix(int rows, int cols, mat &out) {
    out.set_size(rows, cols, false);
    for(int i = 0; i < rows * cols; i++) out(i) = sample();
  }
private:
  double mean, sigma;
  static const double ytab[128];
  static const unsigned int ktab[128];
  static const double wtab[128];
  static const double PARAM_R;
  Random_Generator RNG;
};

/*!
 * \brief Gamma distribution
 * \ingroup randgen
 *
 * Generate samples from Gamma(alpha,beta) density, according to the
 * following equation:
 * \f[ x \sim \Gamma(\alpha,\beta) =
 * \frac{\beta^\alpha}{\Gamma(\alpha)}x^{\alpha-1} \exp(-\beta x) \f]
 *
 * For \f$\alpha=1\f$ the Gamma distribution is equivalent to the
 * Exponential distribution.
 *
 * \note The implementation of the sample() function was adapted from the
 * R statistical language.
 * \author Vasek Smidl
 */
class ITPP_EXPORT Gamma_RNG
{
public:
  //! Constructor, which sets alpha (a) and beta (b)
  Gamma_RNG(double a = 1.0, double b = 1.0): alpha(a), beta(b) {init_state();}
  //! Set alpha and beta
  void setup(double a, double b) { alpha = a; beta = b; }
  //! Get one sample
  double operator()() { return sample(); }
  //! Get a sample vector
  vec operator()(int n);
  //! Get a sample matrix
  mat operator()(int r, int c);
  //! Get a sample
  double sample();
private:
  //! Initializer of state variables
  void init_state();
  //! shape parameter of Gamma distribution
  double alpha;
  //! inverse scale parameter of Gamma distribution
  double beta;

  Random_Generator RNG;
  Normal_RNG NRNG;

  /* State variables - used in Gamma_Rng::sample()*/
  double _s, _s2, _d, _scale;
  double _q0, _b, _si, _c;
};

/*!
  \brief Laplacian distribution
  \ingroup randgen
*/
class ITPP_EXPORT Laplace_RNG
{
public:
  //! Constructor. Set mean and variance.
  Laplace_RNG(double meanval = 0.0, double variance = 1.0);
  //! Set mean and variance
  void setup(double meanval, double variance);
  //! Get mean and variance
  void get_setup(double &meanval, double &variance) const;
  //! Get one sample.
  double operator()() { return sample(); }
  //! Get a sample vector.
  vec operator()(int n);
  //! Get a sample matrix.
  mat operator()(int h, int w);
  //! Returns a single sample
  double sample() {
    double u = RNG.genrand_open_open();
    double l = sqrt_12var;
    if(u < 0.5)
      l *= std::log(2.0 * u);
    else
      l *= -std::log(2.0 * (1 - u));
    return (l + mean);
  }
private:
  double mean, var, sqrt_12var;
  Random_Generator RNG;
};

/*!
  \brief A Complex Normal Source
  \ingroup randgen
*/
class ITPP_EXPORT Complex_Normal_RNG
{
public:
  //! Constructor. Set mean and variance.
  Complex_Normal_RNG(std::complex<double> mean, double variance):
    norm_factor(1.0 / std::sqrt(2.0)) {
    setup(mean, variance);
  }
  //! Default constructor
  Complex_Normal_RNG(): m_re(0.0), m_im(0.0), sigma(1.0), norm_factor(1.0 / std::sqrt(2.0)) {}
  //! Set mean and variance
  void setup(std::complex<double> mean, double variance) {
    m_re = mean.real();
    m_im = mean.imag();
    sigma = std::sqrt(variance);
  }
  //! Get mean and variance
  void get_setup(std::complex<double> &mean, double &variance) {
    mean = std::complex<double>(m_re, m_im);
    variance = sigma * sigma;
  }
  //! Get one sample.
  std::complex<double> operator()() { return sigma * sample() + std::complex<double>(m_re, m_im); }
  //! Get a sample vector.
  cvec operator()(int n) {
    cvec temp(n);
    sample_vector(n, temp);
    temp *= sigma;
    temp += std::complex<double>(m_re, m_im);
    return temp;
  }
  //! Get a sample matrix.
  cmat operator()(int h, int w) {
    cmat temp(h, w);
    sample_matrix(h, w, temp);
    temp *= sigma;
    temp += std::complex<double>(m_re, m_im);
    return temp;
  }
  //! Get a Complex Normal (0,1) distributed sample
  std::complex<double> sample() {
    double a = nRNG.sample() * norm_factor;
    double b = nRNG.sample() * norm_factor;
    return std::complex<double>(a, b);
  }

  //! Get a Complex Normal (0,1) distributed vector
  void sample_vector(int size, cvec &out) {
    out.set_size(size, false);
    for(int i = 0; i < size; i++) out(i) = sample();
  }

  //! Get a Complex Normal (0,1) distributed matrix
  void sample_matrix(int rows, int cols, cmat &out) {
    out.set_size(rows, cols, false);
    for(int i = 0; i < rows * cols; i++) out(i) = sample();
  }

  //! Dummy assignment operator - MSVC++ warning C4512
  Complex_Normal_RNG & operator=(const Complex_Normal_RNG&) { return *this; }

private:
  double m_re;
  double m_im;
  double sigma;
  const double norm_factor;
  Normal_RNG nRNG;
};

/*!
  \brief Filtered normal distribution
  \ingroup randgen
*/
class ITPP_EXPORT AR1_Normal_RNG
{
public:
  //! Constructor. Set mean, variance, and correlation.
  AR1_Normal_RNG(double meanval = 0.0, double variance = 1.0,
                 double rho = 0.0);
  //! Set mean, variance, and correlation
  void setup(double meanval, double variance, double rho);
  //! Get mean, variance and correlation
  void get_setup(double &meanval, double &variance, double &rho) const;
  //! Set memory contents to zero
  void reset();
  //! Get a single random sample
  double operator()() { return sample(); }
  //! Get a sample vector.
  vec operator()(int n);
  //! Get a sample matrix.
  mat operator()(int h, int w);
private:
  double sample() {
    mem *= r;
    if(odd) {
      r1 = m_2pi * RNG.genrand_open_close();
      r2 = std::sqrt(factr * std::log(RNG.genrand_open_close()));
      mem += r2 * std::cos(r1);
    }
    else {
      mem += r2 * std::sin(r1);
    }
    odd = !odd;
    return (mem + mean);
  }
  double mem, r, factr, mean, var, r1, r2;
  bool odd;
  Random_Generator RNG;
};

/*!
  \brief Gauss_RNG is the same as Normal Source
  \ingroup randgen
*/
typedef Normal_RNG Gauss_RNG;

/*!
  \brief AR1_Gauss_RNG is the same as AR1_Normal_RNG
  \ingroup randgen
*/
typedef AR1_Normal_RNG AR1_Gauss_RNG;

/*!
  \brief Weibull distribution
  \ingroup randgen
*/
class ITPP_EXPORT Weibull_RNG
{
public:
  //! Constructor. Set lambda and beta.
  Weibull_RNG(double lambda = 1.0, double beta = 1.0);
  //! Set lambda, and beta
  void setup(double lambda, double beta);
  //! Get lambda and beta
  void get_setup(double &lambda, double &beta) { lambda = l; beta = b; }
  //! Get one sample.
  double operator()() { return sample(); }
  //! Get a sample vector.
  vec operator()(int n);
  //! Get a sample matrix.
  mat operator()(int h, int w);
private:
  double sample() {
    return (std::pow(-std::log(RNG.genrand_open_close()), 1.0 / b) / l);
  }
  double l, b;
  double mean, var;
  Random_Generator RNG;
};

/*!
  \brief Rayleigh distribution
  \ingroup randgen
*/
class ITPP_EXPORT Rayleigh_RNG
{
public:
  //! Constructor. Set sigma.
  Rayleigh_RNG(double sigma = 1.0);
  //! Set sigma
  void setup(double sigma) { sig = sigma; }
  //! Get sigma
  double get_setup() { return sig; }
  //! Get one sample.
  double operator()() { return sample(); }
  //! Get a sample vector.
  vec operator()(int n);
  //! Get a sample matrix.
  mat operator()(int h, int w);
private:
  double sample() {
    double s1 = nRNG.sample();
    double s2 = nRNG.sample();
    // s1 and s2 are N(0,1) and independent
    return (sig * std::sqrt(s1 * s1 + s2 * s2));
  }
  double sig;
  Normal_RNG nRNG;
};

/*!
  \brief Rice distribution
  \ingroup randgen
*/
class ITPP_EXPORT Rice_RNG
{
public:
  //! Constructor. Set sigma, and v (if v = 0, Rice -> Rayleigh).
  Rice_RNG(double sigma = 1.0, double v = 1.0);
  //! Set sigma, and v (if v = 0, Rice -> Rayleigh).
  void setup(double sigma, double v) { sig = sigma; s = v; }
  //! Get parameters
  void get_setup(double &sigma, double &v) { sigma = sig; v = s; }
  //! Get one sample
  double operator()() { return sample(); }
  //! Get a sample vector
  vec operator()(int n);
  //! Get a sample matrix
  mat operator()(int h, int w);
private:
  double sample() {
    double s1 = nRNG.sample() + s;
    double s2 = nRNG.sample();
    // s1 and s2 are N(0,1) and independent
    return (sig * std::sqrt(s1 * s1 + s2 * s2));
  }
  double sig, s;
  Normal_RNG nRNG;
};

//! \addtogroup randgen
//!@{

//! Generates a random bit (equally likely 0s and 1s)
inline bin randb(void) { Bernoulli_RNG src; return src.sample(); }
//! Generates a random bit vector (equally likely 0s and 1s)
inline void randb(int size, bvec &out) { Bernoulli_RNG src; src.sample_vector(size, out); }
//! Generates a random bit vector (equally likely 0s and 1s)
inline bvec randb(int size) { bvec temp; randb(size, temp); return temp; }
//! Generates a random bit matrix (equally likely 0s and 1s)
inline void randb(int rows, int cols, bmat &out) { Bernoulli_RNG src; src.sample_matrix(rows, cols, out); }
//! Generates a random bit matrix (equally likely 0s and 1s)
inline bmat randb(int rows, int cols) { bmat temp; randb(rows, cols, temp); return temp; }

//! Generates a random uniform (0,1) number
inline double randu(void) { Uniform_RNG src; return src.sample(); }
//! Generates a random uniform (0,1) vector
inline void randu(int size, vec &out) { Uniform_RNG src; src.sample_vector(size, out); }
//! Generates a random uniform (0,1) vector
inline vec randu(int size) { vec temp; randu(size, temp); return temp; }
//! Generates a random uniform (0,1) matrix
inline void randu(int rows, int cols, mat &out) { Uniform_RNG src; src.sample_matrix(rows, cols, out); }
//! Generates a random uniform (0,1) matrix
inline mat randu(int rows, int cols) { mat temp; randu(rows, cols, temp); return temp; }

//! Generates a random integer in the interval [low,high]
inline int randi(int low, int high) { I_Uniform_RNG src; src.setup(low, high); return src(); }
//! Generates a random ivec with elements in the interval [low,high]
inline ivec randi(int size, int low, int high) { I_Uniform_RNG src; src.setup(low, high); return src(size); }
//! Generates a random imat with elements in the interval [low,high]
inline imat randi(int rows, int cols, int low, int high) { I_Uniform_RNG src; src.setup(low, high); return src(rows, cols); }

//! Generates a random Rayleigh vector
inline vec randray(int size, double sigma = 1.0) { Rayleigh_RNG src; src.setup(sigma); return src(size); }

//! Generates a random Rice vector (See J.G. Poakis, "Digital Communications, 3rd ed." p.47)
inline vec randrice(int size, double sigma = 1.0, double s = 1.0) { Rice_RNG src; src.setup(sigma, s); return src(size); }

//! Generates a random complex Gaussian vector
inline vec randexp(int size, double lambda = 1.0) { Exponential_RNG src; src.setup(lambda); return src(size); }

//! Generates a random Gaussian (0,1) variable
inline double randn(void) { Normal_RNG src; return src.sample(); }
//! Generates a random Gaussian (0,1) vector
inline void randn(int size, vec &out) { Normal_RNG src; src.sample_vector(size, out); }
//! Generates a random Gaussian (0,1) vector
inline vec randn(int size) { vec temp; randn(size, temp); return temp; }
//! Generates a random Gaussian (0,1) matrix
inline void randn(int rows, int cols, mat &out)  { Normal_RNG src; src.sample_matrix(rows, cols, out); }
//! Generates a random Gaussian (0,1) matrix
inline mat randn(int rows, int cols) { mat temp; randn(rows, cols, temp); return temp; }

/*! \brief Generates a random complex Gaussian (0,1) variable

The real and imaginary parts are independent and have variances equal to 0.5
*/
inline std::complex<double> randn_c(void) { Complex_Normal_RNG src; return src.sample(); }
//! Generates a random complex Gaussian (0,1) vector
inline void randn_c(int size, cvec &out)  { Complex_Normal_RNG src; src.sample_vector(size, out); }
//! Generates a random complex Gaussian (0,1) vector
inline cvec randn_c(int size) { cvec temp; randn_c(size, temp); return temp; }
//! Generates a random complex Gaussian (0,1) matrix
inline void randn_c(int rows, int cols, cmat &out) { Complex_Normal_RNG src; src.sample_matrix(rows, cols, out); }
//! Generates a random complex Gaussian (0,1) matrix
inline cmat randn_c(int rows, int cols) { cmat temp; randn_c(rows, cols, temp); return temp; }

//!@}

} // namespace itpp

#endif // #ifndef RANDOM_H