Pseudo-random numbers from a variety of distributions may be generated with the Random class. Multiple random number generators are provided; low level access to the mcell_ran4 generator is described in:
Random()
Random(seed)
Random(seed, size)
The Random class provides commonly used random distributions which are useful for stochastic simulations. The default distribution is normal with mean = 0 and standard deviation = 1.
This class is an interface to the RNG class from the gnu c++ class library. As of version 5.2, a cryptographic quality RNG class wrapper for mcell_ran4() was added and is available with the Random.MCellRan4() method. The current default random generator is Random.ACG().
As of version 7.3, a more versatile cryptographic quality generator, Random123, is available with the Random.Random123() method. This generator uses a 34bit counter, up to 3 32 bit identifiers, and a 32 bit global index and is most suitable for managing separate independent, reproducible, restartable streams that are unique to individual cell and synapses in large parallel network models. See: http://www.thesalmons.org/john/random123/papers/random123sc11.pdf
Note that multiple instances of the Random class will produce different streams of random numbers only if their seeds are different.
One can switch distributions at any time but if the distribution is stationary then it is more efficient to use Random.repick() to avoid constructor/destructor overhead.
Example:
from neuron import h r = h.Random() for i in range(1,11): print r.uniform(30, 50) # not as efficient as for i in range(1,11): print r.repick() # thisprints 20 random numbers ranging in value between 30 and 50.
r.ACG()
r.ACG(seed)
r.ACG(seed, size)
r.MLCG()
r.MLCG(seed1)
r.MLCG(seed1, seed2)
highindex = r.MCellRan4()
highindex = r.MCellRan4(highindex)
highindex = r.MCellRan4(highindex, lowindex)
Use the MCell variant of the Ran4 generator. See mcell_ran4(). In the no argument case or if the highindex is 0, then the system selects an index which is the random 32 bit integer resulting from an mcell_ran4 call with an index equal to the the number of instances of the Random generator that had been created. Thus, each stream should be statistically independent as long as the highindex values differ by more than the eventual length of the stream. In any case, the initial highindex is returned and can be used to restart an instance of the generator. Use mcell_ran4_init() to set the (global) low 32 bit index of the generator. The Random.seq() method is useful for getting the current sequence number and restarting at that sequence number (highindex). If the lowindex arg is present and nonzero, then that lowindex is used instead of the global one specified by mcell_ran4_init(). This allows 2^32-1 independent streams that do not overlap.
Note that for reproducibility, the distribution should be defined AFTER setting the seed since some distributions, such as Random.normal(), hold state information from a previous pick from the uniform distribution.
See also
Example:
from neuron import h, gui r = h.Random() index = h.ref(r.MCellRan4()) r.uniform(0, 2) vec = h.Vector(1000) g1 = h.Graph() g2 = h.Graph() g1.size(0, 1000, 0, 2) g2.size(0, 2, 0, 150) def doit(): g1.erase() g2.erase() vec.setrand(r) hist = vec.histogram(0, 2, 0.2) vec.line(g1) hist.line(g2, .2) g1.flush() g2.flush() def set_index_then_doit(): r.MCellRan4(index[0]) doit() doit() h.xpanel("MCellRan4 test") h.xbutton("Sample", doit) h.xvalue("Original index", index, 1, set_index_then_doit) h.xpanel()
Use the Random123 generator (currently philox4x32 is the crypotgraphic hash used) with the stream identified by the identifiers 0 <= id1,2,3 < 2^32 and the global index (see Random.Random123_globalindex()). The counter, which increments from 0 to 2^34-1, is initialized to 0 (see Random.seq()). If any of the up to 3 arguments are missing, it is assumed 0.
The generators should be usable in the context of threads as long as no instance is used in more than one thread.
This generator uses a 34bit counter, 3 32 bit identifiers, and a 32 bit global index and is most suitable for managing separate independent, reproducible, restartable streams that are unique to individual cell and synapses in large parallel network models. See: http://www.thesalmons.org/john/random123/papers/random123sc11.pdf
For MCellRan4, Gets and sets the current highindex value when the Random.MCellRan4() is in use. This allows restarting the generator at any specified point. Note that the currenthighindex value is incremented every Random.repick(). Usually the increment is 1 but some distributions, e.g. Random.poisson() can increment by more. Also, some distributions, e.g. Random.normal(), pick twice on the first repick but once thereafter.
For Random123, Gets and sets the counter value which ranges from 0 to 2^34-1. The reason the the greater range is that the internal Random123 generators return 4 uint32 values on each call. So that is done only every 4 picks from the generator.
Example:
from neuron import h r = h.Random() r.negexp(1) h.mcell_ran4_init(1) r.MCellRan4(1) for i in range(11): print i, r.repick() r.MCellRan4(1) for i in range(6): print i, r.repick() idum = r.seq() print "idum = ", idum for i in range(6, 11): print i, r.repick() print "restarting" r.seq(idum) for i in range(6, 11): print i, r.repick() print "restarting" r.seq(idum) for i in range(6, 11): print i, r.repick()
At the beginning of every call to fadvance() and finitialize() var is set to a new value equivalent to
var = r.repick()
(but with no interpreter overhead). This is similar in concept to Vector.play(). Play may be called several times for different variables and each variable will get an independent random value but with the same distribution. To disconnect the Random object from its list of variables, either the variables or the Random object must be destroyed.
Example:
Example:
objref r, vec, g1, g2, hist r = h.Random() r.uniform(0, 2) vec = h.Vector(1000) vec.setrand(r) hist = vec.histogram(0, 2, 0.2) g1 = h.Graph() g2 = h.Graph() g1.size(0, 1000, 0, 2) g2.size(0, 2, 0, 150) vec.plot(g1) hist.plot(g2, .2)
Example:
from neuron import h, gui r = h.Random() r.normal(-1, .5) vec = h.Vector() vec.indgen(-3, 2, .1) # x-axis for plot hist = h.Vector(vec.size()) g = h.Graph() g.size(-3, 2, 0, 50) hist.plot(g, vec) i = 0 while (i<500): x = r.repick() print i, x j = int((x+3)*10) # -3 to 2 -> 0 to 50 i+=1 if j >= 0: hist.x[j] = hist.x[j]+1 g.flush() doNotify()
Example:
r = h.Random() r.lognormal(5,2) n=20 xvec = h.Vector(n*3) # bins look like discrete spikes for i in range(n): xvec.x[3*i] = i-.1 xvec.x[3*i+1] = i xvec.x[3*i+2] = i+.1 hist = h.Vector(xvec.size()) g = h.Graph() g.size(0, 15, 0, 120) hist.plot(g, xvec) i = 0 while (i<500): x = r.repick() print i, x j = int(x) j = 3*j+1 i=i+1 if j >= hist.size(): # don't let any off the edge j = hist.size() -1 hist.x[j] = hist.x[j]+1 g.flush() doNotify()
Example:
r = h.Random() r.poisson(3) n=20 xvec = h.Vector(n*3) for i in range(n): xvec.x[3*i] = i-.1 xvec.x[3*i+1] = i xvec.x[3*i+2] = i+.1 hist = h.Vector(xvec.size()) g = h.Graph() g.size(0, 15, 0, 120) hist.plot(g, xvec) i = 0 while (i<500): x = r.repick() print i, x i += 1 j = int(x) j = 3*j+1 if j >= hist.size(): j = hist.size() -1 hist.x[j] = hist.x[j]+1 g.flush() doNotify()
Create a binomial distribution. Returns the number of "successes" after N trials when the probability of a success after one trial is p. (n>0, 0<=p<=1).
P(n, N, p) = p * P(n-1, N-1, p) + (1 - p) * P(n, N-1, p)
Example:
r = h.Random() r.binomial(20, .5) g = h.Graph() g.size(0, 20, 0, 100) hist = h.Vector(20) hist.plot(g) i = 0 while (i<500): j = r.repick() hist.x[j] = hist.x[j]+1 i += 1 g.flush() doNotify()
Example:
from neuron import h, gui objref r, hist, g r = h.Random() r.geometric(.8) hist = new Vector(1000) def sample(): hist = h.Vector(1000) hist.setrand(r) hist = hist.histogram(0,100,1) hist.plot(g) g = h.Graph() g.size(0,40,0,200) sample() h.xpanel("Resample") h.xbutton("Resample", "sample()") h.xpanel()
Example:
from neuron import h, gui r = h.Random() r.negexp(2.5) hist = h.Vector(1000) def sample(): hist = h.Vector(1000) hist.setrand(r) hist = hist.histogram(0,20,.1) hist.plot(g, .1) g = h.Graph() g.size(0,20,0,50) sample() h.xpanel("Resample") h.xbutton("Resample", "sample()") h.xpanel()