functions in random.i - r

 
random_ipq

    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.  
Interpreted function, defined at i/random.i   line 179  

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

random_n

    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.).  
Interpreted function, defined at i/random.i   line 130  

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

random_rej

    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.  
Interpreted function, defined at i/random.i   line 199  

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

random_u

    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).  
Interpreted function, defined at i/random.i   line 113  

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

random_x

    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.  
Interpreted function, defined at i/random.i   line 74  

SEE ALSO: random