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functions in random.i -
build_dimlist
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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.
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ipq_setup
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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.
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SEE ALSO:
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random_ipq,
random_rej
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poisson
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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.
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SEE ALSO:
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random,
random_n
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random_ipq
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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.
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SEE ALSO:
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random,
random_x,
random_u,
random_n,
random_rej,
ipq_setup
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random_n
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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.).
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SEE ALSO:
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random,
random_x,
random_u,
random_ipq,
random_rej,
poisson
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random_rej
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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.
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SEE ALSO:
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random,
random_x,
random_u,
random_n,
random_ipq,
ipq_setup
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random_u
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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).
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SEE ALSO:
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random,
random_x,
random_n,
random_ipq,
random_rej
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random_x
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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.
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SEE ALSO:
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random
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