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Package random (in random.i) -

Index of documented functions or symbols:


DOCUMENT build_dimlist, dimlist, next_argument
  build a DIMLIST, as used in the array function.  Use like this:

func your_function
    while (more_args()) build_dimlist, dimlist, next_arg();

  After this, DIMLIST will be an array of the form
  [#dims, dim1, dim2, ...], compounded from the multiple arguments
  in the same way as the array function.  If no DIMLIST arguments
  given, DIMLIST will be [] instead of [0], which will act the
  same in most situations.  If that possibility is unacceptible,
  you may add
    if (is_void(dimlist)) dimlist= [0];
  after the while loop.


DOCUMENT model= ipq_setup(x, u)
      or model= ipq_setup(x, u, power=[pleft,prght])
      or model= ipq_setup(x, u, power=[pleft,prght], slope=[sleft,srght])

  compute a model for the ipq_compute function, which computes the
  inverse of a piecewise quadratic function.  This function occurs
  when computing random numbers distributed according to a piecewise
  linear function.  The piecewise linear function is u(x), determined
  by the discrete points X and U input to ipq_setup.  None of the
  values of U may be negative, and X must be strictly increasing,
  X(i)0 while SRGHT<0.  If either power is greater than or equal to
  100, an exponential tail will be used.  As a convenience, you may
  also specify PLEFT or PRGHT of 0 to get an exponential tail.

  Note: ipq_function(model, xp) returns the function values u(xp) at
  the points xp, including the tails (if any).  ipq_compute(model, yp)
  returns the xp for which (integral from -infinity to xp) of u(x)
  equals yp; i.e.- the inverse of the piecewise quadratic.

SEE ALSO: random_ipq, random_rej


DOCUMENT poisson(navg)

  returns a Poisson distributed random value with mean NAVG.
  (This is the integer number of events which actually occur
   in some time interval, when the probability per unit time of
   an event is constant, and the average number of events during
   the interval is NAVG.)
  The return value has the same dimensions as the input NAVG.
  The return value is an integer, but its type is double.
  The algorithm is taken from Numerical Recipes by Press, et. al.

SEE ALSO: random, random_n


DOCUMENT random_ipq(ipq_model, dimlist)

  returns an array of double values with the given DIMLIST (see array
  function, nil for a scalar result).  The numbers are distributed
  according to a piecewise linear function (possibly with power law
  or exponential tails) specified by the IPQ_MODEL.  The "IPQ" stands
  for "inverse piecewise quadratic", which the type of function
  required to transform a uniform random deviate into the piecewise
  linear distribution.  Use the ipq_setup function to compute

SEE ALSO: random, random_x, random_u, random_n, random_rej, ipq_setup


DOCUMENT random_n(dimlist)

  returns an array of normally distributed random double values with
  the given DIMLIST (see array function, nil for a scalar result).
  The mean is 0.0 and the standard deviation is 1.0.
  The algorithm follows the Box-Muller method (see Numerical Recipes
  by Press et al.).

SEE ALSO: random, random_x, random_u, random_ipq, random_rej, poisson


DOCUMENT random_rej(target_dist, ipq_model, dimlist)
      or random_rej(target_dist, bounding_dist, bounding_rand, dimlist)

  returns an array of double values with the given DIMLIST (see array
  function, nil for a scalar result).  The numbers are distributed
  according to the TARGET_DIST function:
func target_dist
  returning u(x)>=0 of same number and dimensionality as x, normalized
  so that the integral of target_dist(x) from -infinity to +infinity
  is 1.0.  The BOUNDING_DIST function must have the same calling
  sequence as TARGET_DIST:
func bounding_dist
  returning b(x)>=u(x) everywhere.  Since u(x) is normalized, the
  integral of b(x) must be >=1.0.  Finally, BOUNDING_RAND is a
  function which converts an array of uniformly distributed random
  numbers on (0,1) -- as returned by random -- into an array
  distributed according to BOUNDING_DIST:
func bounding_rand
  Mathematically, BOUNDING_RAND is the inverse of the integral of
  BOUNDING_DIST from -infinity to x, with its input scaled to (0,1).

  If BOUNDING_DIST is not a function, then it must be an IPQ_MODEL
  returned by the ipq_setup function.  In this case BOUNDING_RAND is
  omitted -- ipq_compute will be used automatically.

SEE ALSO: random, random_x, random_u, random_n, random_ipq, ipq_setup


DOCUMENT random_u(a, b, dimlist)

  return uniformly distributed random numbers between A and B.
  (Will never exactly equal A or B.)  The DIMLIST is as for the
  array function.  Same as (b-a)*random(dimlist)+a.  If A==0,
  you are better off just writing B*random(dimlist).

SEE ALSO: random, random_x, random_n, random_ipq, random_rej


DOCUMENT random_x(dimlist)

  same as random(DIMLIST), except that random_x calls random
  twice at each point, to avoid the defect that random only
  can produce about 2.e9 numbers on the interval (0.,1.) (see
  random for an explanation of these bins).

  You may set random=random_x to get these "better" random
  numbers in every call to random.

  Unlike random, there is a chance in 1.e15 or so that random_x
  may return exactly 1.0 or 0.0 (the latter may not be possible
  with IEEE standard arithmetic, while the former apparently is).
  Since cosmic rays are far more likely, you may as well not
  worry about this.  Also, because of rounding errors, some bit
  patterns may still be more likely than others, but the 0.5e-9
  wide bins of random will be absent.

SEE ALSO: random