functions in random.i -

             build_dimlist, dimlist, next_argument  
 
     build a DIMLIST, as used in the array function.  Use like this:  
     func your_function(arg1, arg2, etc, dimlist, ..)  
     {  
       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.  

             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.  

             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.  

             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  
     IPQ_MODEL.  

             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.).  

             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(x)  
     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(x)  
     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(uniform_x_01)  
     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.  

             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).  

             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.