rand.cc

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/////////////////////////////////////////////////////////////////////////*
//
// Copyright (C) 1996-2024 The Octave Project Developers
//
// See the file COPYRIGHT.md in the top-level directory of this
// distribution or <https://octave.org/copyright/>.
//
// This file is part of Octave.
//
// Octave 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.
//
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// 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 Octave; see the file COPYING.  If not, see
// <https://www.gnu.org/licenses/>.
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////////////////////////////////////////////////////////////////////////
 
#if defined (HAVE_CONFIG_H)
#  include "config.h"
#endif
 
#include <unordered_map>
#include <string>
 
#include "f77-fcn.h"
#include "lo-mappers.h"
#include "oct-rand.h"
#include "quit.h"
 
#include "defun.h"
#include "error.h"
#include "errwarn.h"
#include "ovl.h"
#include "unwind-prot.h"
#include "utils.h"
#include "ov-re-mat.h"
 
OCTAVE_BEGIN_NAMESPACE(octave)
 
/*
%% Restore all rand* "seed" and "state" values in order, so that the
%% new "state" algorithm remains active after these tests complete.
%!function restore_rand_states (seed, state)
%!  rand ("seed", seed.rand);
%!  rande ("seed", seed.rande);
%!  randg ("seed", seed.randg);
%!  randn ("seed", seed.randn);
%!  randp ("seed", seed.randp);
%!  rand ("state", state.rand);
%!  rande ("state", state.rande);
%!  randg ("state", state.randg);
%!  randn ("state", state.randn);
%!  randp ("state", state.randp);
%!endfunction
 
%!shared __random_statistical_tests__, old_seed, old_state, restore_state
%! ## Flag whether the statistical tests should be run in "make check" or not
%! __random_statistical_tests__ = 0;
%! ## Save and restore the states of each of the random number generators
%! ## that are tested by the unit tests in this file.
%! old_seed.rand = rand ("seed");
%! old_seed.rande = rande ("seed");
%! old_seed.randg = randg ("seed");
%! old_seed.randn = randn ("seed");
%! old_seed.randp = randp ("seed");
%! old_state.rand = rand ("state");
%! old_state.rande = rande ("state");
%! old_state.randg = randg ("state");
%! old_state.randn = randn ("state");
%! old_state.randp = randp ("state");
%! restore_state = onCleanup (@() restore_rand_states (old_seed, old_state));
*/
 
static octave_value
do_rand (const octave_value_list& args, int nargin, const char *fcn,
         const std::string& distribution, bool additional_arg = false)
{
  NDArray a;
  int idx = 0;
  bool is_single = false;
 
  if (nargin > 0 && args(nargin-1).is_string ())
    {
      std::string s_arg = args(nargin-1).string_value ();
 
      if (s_arg == "single")
        {
          is_single = true;
          nargin--;
        }
      else if (s_arg == "double")
        nargin--;
    }
 
  if (additional_arg)
    {
      if (nargin == 0)
        error ("%s: at least one argument is required", fcn);
      else if (args(0).is_string ())
        additional_arg = false;
      else
        {
          a = args(0).xarray_value ("%s: dimension must be a scalar integer", fcn);
 
          idx++;
          nargin--;
        }
    }
 
  octave_value retval;
  dim_vector dims;
 
  // Restore current distribution on any exit.
  unwind_action restore_distribution
  ([] (const std::string& old_distribution)
  {
    rand::distribution (old_distribution);
  }, rand::distribution ());
 
  rand::distribution (distribution);
 
  switch (nargin)
    {
    case 0:
      {
        if (additional_arg)
          dims = a.dims ();
        else
          {
            dims.resize (2);
 
            dims(0) = 1;
            dims(1) = 1;
          }
 
        goto gen_matrix;
      }
      break;
 
    case 1:
      {
        octave_value tmp = args(idx);
 
        if (tmp.is_string ())
          {
            std::string s_arg = tmp.string_value ();
 
            if (s_arg == "dist")
              retval = rand::distribution ();
            else if (s_arg == "seed")
              retval = rand::seed ();
            else if (s_arg == "state" || s_arg == "twister")
              retval = rand::state (fcn);
            else if (s_arg == "uniform")
              rand::uniform_distribution ();
            else if (s_arg == "normal")
              rand::normal_distribution ();
            else if (s_arg == "exponential")
              rand::exponential_distribution ();
            else if (s_arg == "poisson")
              rand::poisson_distribution ();
            else if (s_arg == "gamma")
              rand::gamma_distribution ();
            else
              error ("%s: unrecognized string argument", fcn);
          }
        else if (tmp.is_scalar_type ())
          {
            octave_idx_type n = tmp.idx_type_value (true);
 
            dims.resize (2);
 
            dims(0) = dims(1) = n;
 
            goto gen_matrix;
          }
        else if (tmp.is_range ())
          {
            range<double> r = tmp.range_value ();
 
            if (! r.all_elements_are_ints ())
              error ("%s: all elements of range must be integers", fcn);
 
            octave_idx_type n = r.numel ();
 
            dims.resize (n);
 
            octave_idx_type base = math::nint_big (r.base ());
            octave_idx_type incr = math::nint_big (r.increment ());
 
            for (octave_idx_type i = 0; i < n; i++)
              {
                // Negative dimensions treated as zero for Matlab compatibility
                dims(i) = (base >= 0 ? base : 0);
                base += incr;
              }
 
            goto gen_matrix;
          }
        else if (tmp.is_matrix_type ())
          {
            Array<octave_idx_type> iv;
 
            try
              {
                iv = tmp.octave_idx_type_vector_value (true);
              }
            catch (execution_exception& ee)
              {
                error (ee, "%s: dimensions must be a scalar or array of integers", fcn);
              }
 
            octave_idx_type len = iv.numel ();
 
            dims.resize (len);
 
            for (octave_idx_type i = 0; i < len; i++)
              {
                // Negative dimensions treated as zero for Matlab compatibility
                octave_idx_type elt = iv(i);
                dims(i) = (elt >=0 ? elt : 0);
              }
 
            goto gen_matrix;
          }
        else
          err_wrong_type_arg ("rand", tmp);
      }
      break;
 
    default:
      {
        octave_value tmp = args(idx);
 
        if (nargin == 2 && tmp.is_string ())
          {
            std::string ts = tmp.string_value ();
 
            if (ts == "seed")
              {
                if (args(idx+1).is_real_scalar ())
                  {
                    double d = args(idx+1).double_value ();
 
                    rand::seed (d);
                  }
                else if (args(idx+1).is_string ()
                         && args(idx+1).string_value () == "reset")
                  rand::reset ();
                else
                  error ("%s: seed must be a real scalar", fcn);
              }
            else if (ts == "state" || ts == "twister")
              {
                if (args(idx+1).is_string ()
                    && args(idx+1).string_value () == "reset")
                  rand::reset (fcn);
                else
                  {
                    ColumnVector s
                      = ColumnVector (args(idx+1).vector_value (false, true));
 
                    // Backwards compatibility with previous versions of
                    // Octave which mapped Inf to 0.
                    for (octave_idx_type i = 0; i < s.numel (); i++)
                      if (math::isinf (s.xelem (i)))
                        s.xelem (i) = 0.0;
 
                    rand::state (s, fcn);
                  }
              }
            else
              error ("%s: unrecognized string argument", fcn);
          }
        else
          {
            dims.resize (nargin);
 
            for (int i = 0; i < nargin; i++)
              {
                octave_idx_type elt = args(idx+i).idx_type_value (true);
 
                // Negative dimensions treated as zero for Matlab compatibility
                dims(i) = (elt >= 0 ? elt : 0);
              }
 
            goto gen_matrix;
          }
      }
      break;
    }
 
  // No "goto gen_matrix" in code path.  Must be done processing.
  return retval;
 
gen_matrix:
 
  dims.chop_trailing_singletons ();
 
  if (is_single)
    {
      if (additional_arg)
        {
          if (a.numel () == 1)
            return rand::float_nd_array (dims, a(0));
          else
            {
              if (a.dims () != dims)
                error ("%s: mismatch in argument size", fcn);
 
              octave_idx_type len = a.numel ();
              FloatNDArray m (dims);
              float *v = m.fortran_vec ();
 
              for (octave_idx_type i = 0; i < len; i++)
                v[i] = rand::float_scalar (a(i));
 
              return m;
            }
        }
      else
        return rand::float_nd_array (dims);
    }
  else
    {
      if (additional_arg)
        {
          if (a.numel () == 1)
            return rand::nd_array (dims, a(0));
          else
            {
              if (a.dims () != dims)
                error ("%s: mismatch in argument size", fcn);
 
              octave_idx_type len = a.numel ();
              NDArray m (dims);
              double *v = m.fortran_vec ();
 
              for (octave_idx_type i = 0; i < len; i++)
                v[i] = rand::scalar (a(i));
 
              return m;
            }
        }
      else
        return rand::nd_array (dims);
    }
}
 
DEFUN (rand, args, ,
       doc: /* -*- texinfo -*-
@deftypefn  {} {@var{x} =} rand (@var{n})
@deftypefnx {} {@var{x} =} rand (@var{m}, @var{n}, @dots{})
@deftypefnx {} {@var{x} =} rand ([@var{m} @var{n} @dots{}])
@deftypefnx {} {@var{x} =} rand (@dots{}, "single")
@deftypefnx {} {@var{x} =} rand (@dots{}, "double")
@deftypefnx {} {@var{v} =} rand ("state")
@deftypefnx {} {} rand ("state", @var{v})
@deftypefnx {} {} rand ("state", "reset")
@deftypefnx {} {@var{v} =} rand ("seed")
@deftypefnx {} {} rand ("seed", @var{v})
@deftypefnx {} {} rand ("seed", "reset")
Return a matrix with random elements uniformly distributed on the
interval (0, 1).
 
The arguments are handled the same as the arguments for @code{eye}.
 
You can query the state of the random number generator using the form
 
@example
v = rand ("state")
@end example
 
This returns a column vector @var{v} of length 625.  Later, you can restore
the random number generator to the state @var{v} using the form
 
@example
rand ("state", v)
@end example
 
@noindent
You may also initialize the state vector from an arbitrary vector of length
@leq{} 625 for @var{v}.  This new state will be a hash based on the value of
@var{v}, not @var{v} itself.
 
By default, the generator is initialized by contributing entropy from the
wall clock time, the CPU time, the current fraction of a second, the process
ID and---if available---up to 1024 bits from the C++ random numbers source
@code{random_device}, which might be non-deterministic (implementation
specific).  Note that this differs from @sc{matlab}, which always initializes
the state to the same state at startup.  To obtain behavior comparable to
@sc{matlab}, initialize with a deterministic state vector in Octave's startup
files (@pxref{Startup Files}).
 
To compute the pseudo-random sequence, @code{rand} uses the Mersenne
Twister with a period of @math{2^{19937}-1}
(See @nospell{M. Matsumoto and T. Nishimura},
@cite{Mersenne Twister: A 623-dimensionally equidistributed uniform
pseudorandom number generator},
@nospell{ACM} Trans.@: on Modeling and Computer Simulation Vol.@: 8, No.@: 1,
pp.@: 3--30, January 1998,
@url{http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html}).
Do @strong{not} use for cryptography without securely hashing several
returned values together, otherwise the generator state can be learned after
reading 624 consecutive values.
 
Older versions of Octave used a different random number generator.
The new generator is used by default as it is significantly faster than the
old generator, and produces random numbers with a significantly longer cycle
time.  However, in some circumstances it might be desirable to obtain the
same random sequences as produced by the old generators.  To do this the
keyword @qcode{"seed"} is used to specify that the old generators should
be used, as in
 
@example
rand ("seed", val)
@end example
 
@noindent
which sets the seed of the generator to @var{val}.  The seed of the
generator can be queried with
 
@example
s = rand ("seed")
@end example
 
However, it should be noted that querying the seed will not cause
@code{rand} to use the old generators, only setting the seed will.  To cause
@code{rand} to once again use the new generators, the keyword
@qcode{"state"} should be used to reset the state of the @code{rand}.
 
The state or seed of the generator can be reset to a new random value using
the @qcode{"reset"} keyword.
 
The class of the value returned can be controlled by a trailing
@qcode{"double"} or @qcode{"single"} argument.  These are the only valid
classes.
@seealso{randn, rande, randg, randp}
@end deftypefn */)
{
  return do_rand (args, args.length (), "rand", "uniform");
}
 
// FIXME: The old generator (selected when "seed" is set) will not
// work properly if compiled to use 64-bit integers.
 
/*
%!test  # "state" can be a scalar
%! rand ("state", 12);  x = rand (1,4);
%! rand ("state", 12);  y = rand (1,4);
%! assert (x, y);
%!test  # "state" can be a vector
%! rand ("state", [12,13]);  x = rand (1,4);
%! rand ("state", [12;13]);  y = rand (1,4);
%! assert (x, y);
%!test  # querying "state" returns a value which can be used later
%! s = rand ("state");  x = rand (1,2);
%! rand ("state", s);   y = rand (1,2);
%! assert (x, y);
%!test  # querying "state" doesn't disturb sequence
%! rand ("state", 12);  rand (1,2);  x = rand (1,2);
%! rand ("state", 12);  rand (1,2);  s = rand ("state");  y = rand (1,2);
%! assert (x, y);
%! rand ("state", s);   z = rand (1,2);
%! assert (x, z);
%!test  # "seed" must be a scalar
%! rand ("seed", 12);  x = rand (1,4);
%! rand ("seed", 12);  y = rand (1,4);
%! assert (x, y);
%!error <seed must be a real scalar> rand ("seed", [12,13])
%!test  # querying "seed" returns a value which can be used later
%! s = rand ("seed");  x = rand (1,2);
%! rand ("seed", s);   y = rand (1,2);
%! assert (x, y);
%!test  # querying "seed" doesn't disturb sequence
%! rand ("seed", 12);  rand (1,2);  x = rand (1,2);
%! rand ("seed", 12);  rand (1,2);  s = rand ("seed");  y = rand (1,2);
%! assert (x, y);
%! rand ("seed", s);  z = rand (1,2);
%! assert (x, z);
*/
 
/*
%!test
%! ## Test a known fixed state
%! rand ("state", 1);
%! assert (rand (1,6), [0.1343642441124013 0.8474337369372327 0.763774618976614 0.2550690257394218 0.495435087091941 0.4494910647887382], eps);
%!test
%! ## Test a known fixed seed
%! rand ("seed", 1);
%! assert (rand (1,6), [0.8668024251237512 0.9126510815694928 0.09366085007786751 0.1664607301354408 0.7408077004365623 0.7615650338120759], 1e-6);
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   rand ("state", 12);
%!   x = rand (100_000, 1);
%!   assert (min (x) > 0);   #*** Please report this!!! ***
%!   assert (max (x) < 1);   #*** Please report this!!! ***
%!   assert (mean (x), 0.5, 0.0024);
%!   assert (var (x), 1/48, 0.0632);
%!   assert (skewness (x), 0, 0.012);
%!   assert (kurtosis (x), -6/5, 0.0094);
%! endif
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   rand ("seed", 12);
%!   x = rand (100_000, 1);
%!   assert (max (x) < 1);   #*** Please report this!!! ***
%!   assert (min (x) > 0);   #*** Please report this!!! ***
%!   assert (mean (x), 0.5, 0.0024);
%!   assert (var (x), 1/48, 0.0632);
%!   assert (skewness (x), 0, 0.012);
%!   assert (kurtosis (x), -6/5, 0.0094);
%! endif
*/
 
/*
## Test out-of-range values as rand() seeds.
%!function v = __rand_sample__ (initval)
%!  rand ("state", initval);
%!  v = rand (1, 6);
%!endfunction
%!
%!assert (__rand_sample__ (-1), __rand_sample__ (0))
%!assert (__rand_sample__ (-Inf), __rand_sample__ (0))
%!assert (__rand_sample__ (2^33), __rand_sample__ (intmax ("uint32")))
%!assert (__rand_sample__ (Inf), __rand_sample__ (0))
%!assert (__rand_sample__ (NaN), __rand_sample__ (0))
*/
 
/*
## Note: Matlab compatibility requires using 0 for negative dimensions.
%!assert (size (rand (1, -1, 2)), [1, 0, 2])
 
## Test input validation
%!error <conversion of 1.1 to.* failed> rand (1, 1.1)
%!error <dimensions must be .* array of integers> rand ([1, 1.1])
*/
 
static std::string current_distribution = rand::distribution ();
 
DEFUN (randn, args, ,
       doc: /* -*- texinfo -*-
@deftypefn  {} {@var{x} =} randn (@var{n})
@deftypefnx {} {@var{x} =} randn (@var{m}, @var{n}, @dots{})
@deftypefnx {} {@var{x} =} randn ([@var{m} @var{n} @dots{}])
@deftypefnx {} {@var{x} =} randn (@dots{}, "single")
@deftypefnx {} {@var{x} =} randn (@dots{}, "double")
@deftypefnx {} {@var{v} =} randn ("state")
@deftypefnx {} {} randn ("state", @var{v})
@deftypefnx {} {} randn ("state", "reset")
@deftypefnx {} {@var{v} =} randn ("seed")
@deftypefnx {} {} randn ("seed", @var{v})
@deftypefnx {} {} randn ("seed", "reset")
Return a matrix with normally distributed random elements having zero mean
and variance one.
 
The arguments are handled the same as the arguments for @code{rand}.
 
By default, @code{randn} uses the @nospell{Marsaglia and Tsang}
``Ziggurat technique'' to transform from a uniform to a normal distribution.
 
The class of the value returned can be controlled by a trailing
@qcode{"double"} or @qcode{"single"} argument.  These are the only valid
classes.
 
Reference: @nospell{G. Marsaglia and W.W. Tsang},
@cite{Ziggurat Method for Generating Random Variables},
J. Statistical Software, vol 5, 2000,
@url{https://www.jstatsoft.org/v05/i08/}
 
@seealso{rand, rande, randg, randp}
@end deftypefn */)
{
  return do_rand (args, args.length (), "randn", "normal");
}
 
/*
%!test
%! ## Test a known fixed state
%! randn ("state", 1);
%! assert (randn (1, 6), [-2.666521678978671 -0.7381719971724564 1.507903992673601 0.6019427189162239 -0.450661261143348 -0.7054431351574116], 14*eps);
%!test
%! ## Test a known fixed seed
%! randn ("seed", 1);
%! assert (randn (1, 6), [-1.039402365684509 -1.25938892364502 0.1968704611063004 0.3874166905879974 -0.5976632833480835 -0.6615074276924133], 1e-6);
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   randn ("state", 12);
%!   x = randn (100_000, 1);
%!   assert (mean (x), 0, 0.01);
%!   assert (var (x), 1, 0.02);
%!   assert (skewness (x), 0, 0.02);
%!   assert (kurtosis (x), 0, 0.04);
%! endif
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   randn ("seed", 12);
%!   x = randn (100_000, 1);
%!   assert (mean (x), 0, 0.01);
%!   assert (var (x), 1, 0.02);
%!   assert (skewness (x), 0, 0.02);
%!   assert (kurtosis (x), 0, 0.04);
%! endif
*/
 
DEFUN (rande, args, ,
       doc: /* -*- texinfo -*-
@deftypefn  {} {@var{x} =} rande (@var{n})
@deftypefnx {} {@var{x} =} rande (@var{m}, @var{n}, @dots{})
@deftypefnx {} {@var{x} =} rande ([@var{m} @var{n} @dots{}])
@deftypefnx {} {@var{x} =} rande (@dots{}, "single")
@deftypefnx {} {@var{x} =} rande (@dots{}, "double")
@deftypefnx {} {@var{v} =} rande ("state")
@deftypefnx {} {} rande ("state", @var{v})
@deftypefnx {} {} rande ("state", "reset")
@deftypefnx {} {@var{v} =} rande ("seed")
@deftypefnx {} {} rande ("seed", @var{v})
@deftypefnx {} {} rande ("seed", "reset")
Return a matrix with exponentially distributed random elements.
 
The arguments are handled the same as the arguments for @code{rand}.
 
By default, @code{rande} uses the @nospell{Marsaglia and Tsang}
``Ziggurat technique'' to transform from a uniform to an exponential
distribution.
 
The class of the value returned can be controlled by a trailing
@qcode{"double"} or @qcode{"single"} argument.  These are the only valid
classes.
 
Reference: @nospell{G. Marsaglia and W.W. Tsang},
@cite{Ziggurat Method for Generating Random Variables},
J. Statistical Software, vol 5, 2000,
@url{https://www.jstatsoft.org/v05/i08/}
 
@seealso{rand, randn, randg, randp}
@end deftypefn */)
{
  return do_rand (args, args.length (), "rande", "exponential");
}
 
/*
%!test
%! ## Test a known fixed state
%! rande ("state", 1);
%! assert (rande (1, 6), [3.602973885835625 0.1386190677555021 0.6743112889616958 0.4512830847258422 0.7255744741233175 0.3415969205292291], 2*eps);
%!test
%! ## Test a known fixed seed
%! rande ("seed", 1);
%! assert (rande (1, 6), [0.06492075175653866 1.717980206012726 0.4816154008731246 0.5231300676241517 0.103910739364359 1.668931916356087], 1e-6);
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally
%!   rande ("state", 1);
%!   x = rande (100_000, 1);
%!   assert (min (x) > 0);   # *** Please report this!!! ***
%!   assert (mean (x), 1, 0.01);
%!   assert (var (x), 1, 0.03);
%!   assert (skewness (x), 2, 0.06);
%!   assert (kurtosis (x), 6, 0.7);
%! endif
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally
%!   rande ("seed", 1);
%!   x = rande (100_000, 1);
%!   assert (min (x)>0);   # *** Please report this!!! ***
%!   assert (mean (x), 1, 0.01);
%!   assert (var (x), 1, 0.03);
%!   assert (skewness (x), 2, 0.06);
%!   assert (kurtosis (x), 6, 0.7);
%! endif
*/
 
DEFUN (randg, args, ,
       doc: /* -*- texinfo -*-
@deftypefn  {} {@var{x} =} randg (@var{a}, @var{n})
@deftypefnx {} {@var{x} =} randg (@var{a}, @var{m}, @var{n}, @dots{})
@deftypefnx {} {@var{x} =} randg (@var{a}, [@var{m} @var{n} @dots{}])
@deftypefnx {} {@var{x} =} randg (@dots{}, "single")
@deftypefnx {} {@var{x} =} randg (@dots{}, "double")
@deftypefnx {} {@var{v} =} randg ("state")
@deftypefnx {} {} randg ("state", @var{v})
@deftypefnx {} {} randg ("state", "reset")
@deftypefnx {} {@var{v} =} randg ("seed")
@deftypefnx {} {} randg ("seed", @var{v})
@deftypefnx {} {} randg ("seed", "reset")
 
Return a matrix with @code{gamma (@var{a},1)} distributed random elements.
 
The arguments are handled the same as the arguments for @code{rand}, except
for the argument @var{a}.
 
This can be used to generate many distributions:
 
@table @asis
@item @code{gamma (a, b)} for @code{a > -1}, @code{b > 0}
 
@example
r = b * randg (a)
@end example
 
@item @code{beta (a, b)} for @code{a > -1}, @code{b > -1}
 
@example
@group
r1 = randg (a, 1)
r = r1 / (r1 + randg (b, 1))
@end group
@end example
 
@item @code{Erlang (a, n)}
 
@example
r = a * randg (n)
@end example
 
@item @code{chisq (df)} for @code{df > 0}
 
@example
r = 2 * randg (df / 2)
@end example
 
@item @code{t (df)} for @code{0 < df < inf} (use randn if df is infinite)
 
@example
r = randn () / sqrt (2 * randg (df / 2) / df)
@end example
 
@item @code{F (n1, n2)} for @code{0 < n1}, @code{0 < n2}
 
@example
@group
## r1 equals 1 if n1 is infinite
r1 = 2 * randg (n1 / 2) / n1
## r2 equals 1 if n2 is infinite
r2 = 2 * randg (n2 / 2) / n2
r = r1 / r2
@end group
@end example
 
@item negative @code{binomial (n, p)} for @code{n > 0}, @code{0 < p <= 1}
 
@example
r = randp ((1 - p) / p * randg (n))
@end example
 
@item non-central @code{chisq (df, L)}, for @code{df >= 0} and @code{L > 0}
(use chisq if @code{L = 0})
 
@example
@group
r = randp (L / 2)
r(r > 0) = 2 * randg (r(r > 0))
r(df > 0) += 2 * randg (df(df > 0)/2)
@end group
@end example
 
@item @code{Dirichlet (a1, @dots{} ak)}
 
@example
@group
r = (randg (a1), @dots{}, randg (ak))
r = r / sum (r)
@end group
@end example
 
@end table
 
The class of the value returned can be controlled by a trailing
@qcode{"double"} or @qcode{"single"} argument.  These are the only valid
classes.
@seealso{rand, randn, rande, randp}
@end deftypefn */)
{
  int nargin = args.length ();
 
  if (nargin < 1)
    error ("randg: insufficient arguments");
 
  return do_rand (args, nargin, "randg", "gamma", true);
}
 
/*
%!test
%! randg ("state", 12);
%! assert (randg ([-inf, -1, 0, inf, nan]), [nan, nan, nan, nan, nan]);
 
%!test
%! ## Test a known fixed state
%! randg ("state", 1);
%! assert (randg (0.1, 1, 6), [0.0103951513331241 8.335671459898252e-05 0.00138691397249762 0.000587308416993855 0.495590518784736 2.3921917414795e-12], eps);
%!test
%! ## Test a known fixed state
%! randg ("state", 1);
%! assert (randg (0.95, 1, 6), [3.099382433255327 0.3974529788871218 0.644367450750855 1.143261091802246 1.964111762696822 0.04011915547957939], 12*eps);
%!test
%! ## Test a known fixed state
%! randg ("state", 1);
%! assert (randg (1, 1, 6), [0.2273389379645993 1.288822625058359 0.2406335209340746 1.218869553370733 1.024649860162554 0.09631230343599533], 40*eps);
%!test
%! ## Test a known fixed state
%! randg ("state", 1);
%! assert (randg (10, 1, 6), [3.520369644331133 15.15369864472106 8.332112081991205 8.406211067432674 11.81193475187611 10.88792728177059], 56*eps);
%!test
%! ## Test a known fixed state
%! randg ("state", 1);
%! assert (randg (100, 1, 6), [75.34570255262264 115.4911985594699 95.23493031356388 95.48926019250911 106.2397448229803 103.4813150404118], 256*eps);
%!test
%! ## Test a known fixed seed
%! randg ("seed", 1);
%! assert (randg (0.1, 1, 6), [0.07144210487604141 0.460641473531723 0.4749028384685516 0.06823389977216721 0.000293838675133884 1.802567535340305e-12], 1e-6);
%!test
%! ## Test a known fixed seed
%! randg ("seed", 1);
%! assert (randg (0.95, 1, 6), [1.664905071258545 1.879976987838745 1.905677795410156 0.9948706030845642 0.5606933236122131 0.0766092911362648], 1e-6);
%!test
%! ## Test a known fixed seed
%! randg ("seed", 1);
%! assert (randg (1, 1, 6), [0.03512085229158401 0.6488978862762451 0.8114678859710693 0.1666885763406754 1.60791552066803 1.90356981754303], 1e-6);
%!test
%! ## Test a known fixed seed
%! randg ("seed", 1);
%! assert (randg (10, 1, 6), [6.566435813903809 10.11648464202881 10.73162078857422 7.747178077697754 6.278522491455078 6.240195751190186], 1e-5);
%!test
%! ## Test a known fixed seed
%! randg ("seed", 1);
%! assert (randg (100, 1, 6), [89.40208435058594 101.4734725952148 103.4020004272461 93.62763214111328 88.33104705810547 88.1871337890625], 1e-4);
%!test
%! ## Test out-of-bounds values produce NaN w/old-style generators & floats
%! randg ("seed", 1);
%! result = randg ([-2 Inf], "single");
%! assert (result, single ([NaN NaN]));
 
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   randg ("state", 12);
%!   a = 0.1;
%!   x = randg (a, 100_000, 1);
%!   assert (mean (x),     a,          0.01);
%!   assert (var (x),      a,          0.01);
%!   assert (skewness (x), 2/sqrt (a), 1);
%!   assert (kurtosis (x), 6/a,        50);
%! endif
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   randg ("state", 12);
%!   a = 0.95;
%!   x = randg (a, 100_000, 1);
%!   assert (mean (x),     a,          0.01);
%!   assert (var (x),      a,          0.04);
%!   assert (skewness (x), 2/sqrt (a), 0.2);
%!   assert (kurtosis (x), 6/a,        2);
%! endif
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   randg ("state", 12);
%!   a = 1;
%!   x = randg (a, 100_000, 1);
%!   assert (mean (x),     a,          0.01);
%!   assert (var (x),      a,          0.04);
%!   assert (skewness (x), 2/sqrt (a), 0.2);
%!   assert (kurtosis (x), 6/a,        2);
%! endif
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   randg ("state", 12);
%!   a = 10;
%!   x = randg (a, 100_000, 1);
%!   assert (mean (x),     a,          0.1);
%!   assert (var (x),      a,          0.5);
%!   assert (skewness (x), 2/sqrt (a), 0.1);
%!   assert (kurtosis (x), 6/a,        0.5);
%! endif
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   randg ("state", 12);
%!   a = 100;
%!   x = randg (a, 100_000, 1);
%!   assert (mean (x),     a,          0.2);
%!   assert (var (x),      a,          2);
%!   assert (skewness (x), 2/sqrt (a), 0.05);
%!   assert (kurtosis (x), 6/a,        0.2);
%! endif
%!test
%! randg ("seed", 12);
%! assert (randg ([-inf, -1, 0, inf, nan]), [nan, nan, nan, nan, nan]);
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   randg ("seed", 12);
%!   a = 0.1;
%!   x = randg (a, 100_000, 1);
%!   assert (mean (x),     a,          0.01);
%!   assert (var (x),      a,          0.01);
%!   assert (skewness (x), 2/sqrt (a), 1);
%!   assert (kurtosis (x), 6/a,        50);
%! endif
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   randg ("seed", 12);
%!   a = 0.95;
%!   x = randg (a, 100_000, 1);
%!   assert (mean (x),     a,          0.01);
%!   assert (var (x),      a,          0.04);
%!   assert (skewness (x), 2/sqrt (a), 0.2);
%!   assert (kurtosis (x), 6/a,        2);
%! endif
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   randg ("seed", 12);
%!   a = 1;
%!   x = randg (a, 100_000, 1);
%!   assert (mean (x),     a,          0.01);
%!   assert (var (x),      a,          0.04);
%!   assert (skewness (x), 2/sqrt (a), 0.2);
%!   assert (kurtosis (x), 6/a,        2);
%! endif
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   randg ("seed", 12);
%!   a = 10;
%!   x = randg (a, 100_000, 1);
%!   assert (mean (x),     a,          0.1);
%!   assert (var (x),      a,          0.5);
%!   assert (skewness (x), 2/sqrt (a), 0.1);
%!   assert (kurtosis (x), 6/a,        0.5);
%! endif
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   randg ("seed", 12);
%!   a = 100;
%!   x = randg (a, 100_000, 1);
%!   assert (mean (x),     a,          0.2);
%!   assert (var (x),      a,          2);
%!   assert (skewness (x), 2/sqrt (a), 0.05);
%!   assert (kurtosis (x), 6/a,        0.2);
%! endif
*/
 
DEFUN (randp, args, ,
       doc: /* -*- texinfo -*-
@deftypefn  {} {@var{x} =} randp (@var{l}, @var{n})
@deftypefnx {} {@var{x} =} randp (@var{l}, @var{m}, @var{n}, @dots{})
@deftypefnx {} {@var{x} =} randp (@var{l}, [@var{m} @var{n} @dots{}])
@deftypefnx {} {@var{x} =} randp (@dots{}, "single")
@deftypefnx {} {@var{x} =} randp (@dots{}, "double")
@deftypefnx {} {@var{v} =} randp ("state")
@deftypefnx {} {} randp ("state", @var{v})
@deftypefnx {} {} randp ("state", "reset")
@deftypefnx {} {@var{v} =} randp ("seed")
@deftypefnx {} {} randp ("seed", @var{v})
@deftypefnx {} {} randp ("seed", "reset")
Return a matrix with Poisson distributed random elements with mean value
parameter given by the first argument, @var{l}.
 
The arguments are handled the same as the arguments for @code{rand}, except
for the argument @var{l}.
 
Five different algorithms are used depending on the range of @var{l} and
whether or not @var{l} is a scalar or a matrix.
 
@table @asis
@item For scalar @var{l} @leq{} 12, use direct method.
W.H. Press, et al., @cite{Numerical Recipes in C},
Cambridge University Press, 1992.
 
@item For scalar @var{l} > 12, use rejection method.[1]
W.H. Press, et al., @cite{Numerical Recipes in C},
Cambridge University Press, 1992.
 
@item For matrix @var{l} @leq{} 10, use inversion method.[2]
@nospell{E. Stadlober, et al., WinRand source code}, available via FTP.
 
@item For matrix @var{l} > 10, use patchwork rejection method.
@nospell{E. Stadlober, et al., WinRand source code}, available via FTP, or
@nospell{H. Zechner}, @cite{Efficient sampling from continuous and discrete
unimodal distributions}, Doctoral Dissertation, 156pp., Technical
University @nospell{Graz}, Austria, 1994.
 
@item For @var{l} > 1e8, use normal approximation.
@nospell{L. Montanet}, et al., @cite{Review of Particle Properties},
Physical Review D 50 p1284, 1994.
@end table
 
The class of the value returned can be controlled by a trailing
@qcode{"double"} or @qcode{"single"} argument.  These are the only valid
classes.
@seealso{rand, randn, rande, randg}
@end deftypefn */)
{
  int nargin = args.length ();
 
  if (nargin < 1)
    error ("randp: insufficient arguments");
 
  return do_rand (args, nargin, "randp", "poisson", true);
}
 
/*
%!test
%! randp ("state", 12);
%! assert (randp ([-inf, -1, 0, inf, nan]), [nan, nan, 0, nan, nan]);
%!test
%! ## Test a known fixed state
%! randp ("state", 1);
%! assert (randp (5, 1, 6), [5 5 3 7 7 3]);
%!test
%! ## Test a known fixed state
%! randp ("state", 1);
%! assert (randp (15, 1, 6), [13 15 8 18 18 15]);
%!test
%! ## Test a known fixed state
%! randp ("state", 1);
%! assert (randp (1e9, 1, 6),
%!         [999915677 999976657 1000047684 1000019035 999985749 999977692],
%!         -1e-6);
%!test
%! ## Test a known fixed seed
%! randp ("seed", 1);
%! %%assert (randp (5, 1, 6), [8 2 3 6 6 8])
%! assert (randp (5, 1, 5), [8 2 3 6 6]);
%!test
%! ## Test a known fixed seed
%! randp ("seed", 1);
%! assert (randp (15, 1, 6), [15 16 12 10 10 12]);
%!test
%! ## Test a known fixed seed
%! randp ("seed", 1);
%! assert (randp (1e9, 1, 6),
%!         [1000006208 1000012224 999981120 999963520 999963072 999981440],
%!         -1e-6);
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   randp ("state", 12);
%!   for a = [5, 15, 1e9; 0.03, 0.03, -5e-3; 0.03, 0.03, 0.03]
%!     x = randp (a (1), 100_000, 1);
%!     assert (min (x) >= 0);   # *** Please report this!!! ***
%!     assert (mean (x), a(1), a(2));
%!     assert (var (x), a(1), 0.02*a(1));
%!     assert (skewness (x), 1/sqrt (a(1)), a(3));
%!     assert (kurtosis (x), 1/a(1), 3*a(3));
%!   endfor
%! endif
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   randp ("state", 12);
%!   for a = [5, 15, 1e9; 0.03, 0.03, -5e-3; 0.03, 0.03, 0.03]
%!     x = randp (a(1)* ones (100_000, 1), 100_000, 1);
%!     assert (min (x) >= 0);   # *** Please report this!!! ***
%!     assert (mean (x), a(1), a(2));
%!     assert (var (x), a(1), 0.02*a(1));
%!     assert (skewness (x), 1/sqrt (a(1)), a(3));
%!     assert (kurtosis (x), 1/a(1), 3*a(3));
%!   endfor
%! endif
%!test
%! randp ("seed", 12);
%! assert (randp ([-inf, -1, 0, inf, nan]), [nan, nan, 0, nan, nan]);
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   randp ("seed", 12);
%!   for a = [5, 15, 1e9; 0.03, 0.03, -5e-3; 0.03, 0.03, 0.03]
%!     x = randp (a(1), 100_000, 1);
%!     assert (min (x) >= 0);   # *** Please report this!!! ***
%!     assert (mean (x), a(1), a(2));
%!     assert (var (x), a(1), 0.02*a(1));
%!     assert (skewness (x), 1/sqrt (a(1)), a(3));
%!     assert (kurtosis (x), 1/a(1), 3*a(3));
%!   endfor
%! endif
%!test
%! if (__random_statistical_tests__)
%!   ## statistical tests may fail occasionally.
%!   randp ("seed", 12);
%!   for a = [5, 15, 1e9; 0.03, 0.03, -5e-3; 0.03, 0.03, 0.03]
%!     x = randp (a(1)* ones (100_000, 1), 100_000, 1);
%!     assert (min (x) >= 0);   # *** Please report this!!! ***
%!     assert (mean (x), a(1), a(2));
%!     assert (var (x), a(1), 0.02*a(1));
%!     assert (skewness (x), 1/sqrt (a(1)), a(3));
%!     assert (kurtosis (x), 1/a(1), 3*a(3));
%!   endfor
%! endif
*/
 
DEFUN (randperm, args, ,
       doc: /* -*- texinfo -*-
@deftypefn  {} {@var{v} =} randperm (@var{n})
@deftypefnx {} {@var{v} =} randperm (@var{n}, @var{m})
Return a row vector containing a random permutation of @code{1:@var{n}}.
 
If @var{m} is supplied, return @var{m} unique entries, sampled without
replacement from @code{1:@var{n}}.
 
The complexity is O(@var{n}) in memory and O(@var{m}) in time, unless
@var{m} < @var{n}/5, in which case O(@var{m}) memory is used as well.  The
randomization is performed using rand().  All permutations are equally
likely.
@seealso{perms}
@end deftypefn */)
{
  int nargin = args.length ();
 
  if (nargin < 1 || nargin > 2)
    print_usage ();
 
  octave_idx_type n = args(0).idx_type_value (true);
  octave_idx_type m = (nargin == 2) ? args(1).idx_type_value (true) : n;
 
  if (m < 0 || n < 0)
    error ("randperm: M and N must be non-negative");
 
  if (m > n)
    error ("randperm: M must be less than or equal to N");
 
  // Quick and dirty heuristic to decide if we allocate or not the
  // whole vector for tracking the truncated shuffle.
  bool short_shuffle = m < n/5;
 
  // Generate random numbers.
  NDArray r = rand::nd_array (dim_vector (1, m));
  double *rvec = r.fortran_vec ();
 
  octave_idx_type idx_len = (short_shuffle ? m : n);
  Array<octave_idx_type> idx;
  try
    {
      idx = Array<octave_idx_type> (dim_vector (1, idx_len));
    }
  catch (const std::bad_alloc&)
    {
      // Looks like n is too big and short_shuffle is false.
      // Let's try again, but this time with the alternative.
      idx_len = m;
      short_shuffle = true;
      idx = Array<octave_idx_type> (dim_vector (1, idx_len));
    }
 
  octave_idx_type *ivec = idx.fortran_vec ();
 
  for (octave_idx_type i = 0; i < idx_len; i++)
    ivec[i] = i;
 
  if (short_shuffle)
    {
      std::unordered_map<octave_idx_type, octave_idx_type> map (m);
 
      // Perform the Knuth shuffle only keeping track of moved
      // entries in the map
      for (octave_idx_type i = 0; i < m; i++)
        {
          octave_idx_type k = i + std::floor (rvec[i] * (n - i));
 
          // For shuffling first m entries, no need to use extra storage
          if (k < m)
            {
              std::swap (ivec[i], ivec[k]);
            }
          else
            {
              if (map.find (k) == map.end ())
                map[k] = k;
 
              std::swap (ivec[i], map[k]);
            }
        }
    }
  else
    {
      // Perform the Knuth shuffle of the first m entries
      for (octave_idx_type i = 0; i < m; i++)
        {
          octave_idx_type k = i + std::floor (rvec[i] * (n - i));
          std::swap (ivec[i], ivec[k]);
        }
    }
 
  // Convert to doubles, reusing r.
  for (octave_idx_type i = 0; i < m; i++)
    rvec[i] = ivec[i] + 1;
 
  if (m < n)
    idx.resize (dim_vector (1, m));
 
  // Now create an array object with a cached idx_vector.
  return ovl (new octave_matrix (r, idx_vector (idx)));
}
 
/*
%!assert (sort (randperm (20)), 1:20)
%!assert (length (randperm (20,10)), 10)
 
## Test biggish N
%!assert <*39378> (length (randperm (30_000^2, 100_000)), 100_000)
 
%!test
%! rand ("seed", 0);
%! for i = 1:100
%!   p = randperm (305, 30);
%!   assert (length (unique (p)), 30);
%! endfor
*/
 
OCTAVE_END_NAMESPACE(octave)