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@*
PoissonianRandomVariable.tmpl
Created by Joe Hope on 2009-08-22.
Copyright (c) 2009-2012, Joe Hope
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 2 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
*@
@extends xpdeint.ScriptElement
@from xpdeint.CallOnceGuards import callOnceGuard
@def splitNoise($function)
@*doc:
Return the code to generate a new smaller poissonian noise from a previous noise.
The previous noise had a time step of ``_old_smallest_step`` a variable available in the C
code, not in the template itself.
*@
@#
@set noiseVector = $parent
// Split a poissonian noise
const real _new_var = 1.0 / (${noiseVector.spatiallyIndependentVolumeElement} * _new_step);
const real _old_volume = (${noiseVector.spatiallyIndependentVolumeElement} * _old_step);
@capture loopString
@silent nonUniformDimReps = noiseVector.nonUniformDimReps
@if nonUniformDimReps
@set volumeFixup = ' * '.join('%s * (%s)' % (dimRep.stepSize, dimRep.volumePrefactor) for dimRep in nonUniformDimReps)
@set varFixup = ' / (' + volumeFixup + ')'
@set volumeFixup = ' * ' + volumeFixup
@else
@set volumeFixup = ''
@set varFixup = ''
@end if
@for componentNumber, component in enumerate(noiseVector.components)
${component} = _new_var${varFixup} * _poisplit_${noiseVector.id}(_new_step/_old_step, lrint(_old_array[_${noiseVector.id}_index_pointer + ${componentNumber}] * _old_volume${volumeFixup}));
@end for
@end capture
${loopOverFieldInBasisWithVectorsAndInnerContent(noiseVector.field, noiseVector.initialBasis, [noiseVector], loopString)}@slurp
@#
@end def
@def makeNoises
@*doc:
Return the code for the contents of the makeNoises function for
a poissonian random variable, by which we mean a jump process.
Much of this is likely to change when we implement triggered filters
to model jump processes efficiently.
*@
@#
@set noiseVector = $parent
@#
const real _dVdt = ${noiseVector.spatiallyIndependentVolumeElement}@slurp
@if not noiseVector.static:
* _step@slurp
@end if
;
const real _var = 1.0 / _dVdt;
@capture loopString
@silent nonUniformDimReps = noiseVector.nonUniformDimReps
@if nonUniformDimReps
@set volumeFixup = ' * '.join('%s * (%s)' % (dimRep.stepSize, dimRep.volumePrefactor) for dimRep in nonUniformDimReps)
@set varFixup = ' / (' + volumeFixup + ')'
@set volumeFixup = ' * ' + volumeFixup
@else
@set volumeFixup = ''
@set varFixup = ''
@end if
@for component in noiseVector.components
${component} = _var${varFixup} * _poidev_${noiseVector.id}(${noiseMeanRate} * _dVdt${volumeFixup});
@end for
@end capture
${loopOverFieldInBasisWithVectorsAndInnerContent(noiseVector.field, noiseVector.initialBasis, [noiseVector], loopString)}@slurp
@#
@end def
@def functionPrototypes
@#
@super
@#
@set noiseVector = $parent
@#
real _poidev_${noiseVector.id}(real xm);
real _poisplit_${noiseVector.id}(real pp, int n);
@#
@end def
@def functionImplementations
@#
@super
@#
@set noiseVector = $parent
@#
real _poidev_${noiseVector.id}(real xm)
{
real sq, alxm, g, em, t, y;
if (xm < 12.0) { // Use direct method
g = exp(-xm);
em = -1.0;
t = 1.0;
// Instead of adding exponential deviates it is equivalent
// to multiply uniform deviates. We never actually have to
// take the log, merely compare to the pre-computed exponential
do {
++em;
t *= ${generator.zeroToOneRandomNumber()};
} while (t > g);
} else {
// Use rejection method
sq = sqrt(2.0*xm);
alxm = log(xm);
g = xm*alxm - lgamma(xm + 1.0);
do {
do {
// y is a deviate from a Lorenzian comparison function
y = tan(M_PI*${generator.zeroToOneRandomNumber()});
// em is y, shifted and scaled
em = sq*y + xm;
} while (em < 0.0); // Reject if in regime of zero probability
em = floor(em); // The trick for integer-valued distributions
t = 0.9*(1.0 + y*y)*exp(em*alxm - lgamma(em + 1.0) - g);
// The ratio of the desired distribution to the comparison
// function; we reject by comparing it to another uniform
// deviate. The factor 0.9 so that t never exceeds 1.
} while (${generator.zeroToOneRandomNumber()} > t);
}
return em;
}
real _poisplit_${noiseVector.id}(real pp, int n)
{
/*
Returns as a floating-point number an integer value that is a random deviate drawn from
a binomial distribution of n trials each of probability pp, using erand48(_generator) as a source of
uniform random deviates. This is exactly the distribution that must be sampled when a poissonian process is split over two smaller time steps
*/
long j;
real am, em, g, p, bnl, sq, t, y;
static real pc, plog, pclog, en, oldg;
// The binomial distribution is invariant under changing pp to 1-pp,
// if we also change the answer to n minus itself; we do this at the end.
p = (pp <= 0.5 ? pp : 1.0-pp);
// This is the mean of the deviate to be produced.
am = n * p;
if (n < 25) {
// Use the direct method while n is not too large. This can require up to 25 calls to erand48(_generator).
bnl = 0.0;
for (j = 1; j <= n; j++)
if (${generator.zeroToOneRandomNumber()} < p)
++bnl;
} else if (am < 1.0) {
// If fewer than one event is expected out of 25 or more trials, then the distribution is quite accurately Poisson. Use direct Poisson method.
g = exp(-am);
t = 1.0;
for (j = 0; j <= n; j++) {
t *= ${generator.zeroToOneRandomNumber()};
if (t < g)
break;
}
bnl = (j <= n ? j : n);
} else {
en = n;
oldg = lgamma(en + 1.0);
pc = 1.0 - p;
plog = log(p);
pclog = log(pc);
sq = sqrt(2.0*am*pc);
// The following code should by now seem familiar: rejection method with a Lorentzian comparison function.
do {
do {
y = tan(M_PI*${generator.zeroToOneRandomNumber()});
em = sq*y + am;
} while (em < 0.0 || em >= (en+1.0)); // Reject.
em = floor(em); // Trick for integer-valued distribution.
t = 1.2 * sq * (1.0 + y*y) * exp(oldg - lgamma(em + 1.0) - lgamma(en - em + 1.0) + em*plog + (en - em)*pclog);
} while (${generator.zeroToOneRandomNumber()} > t); // Reject. This happens about 1.5 times per deviate, on average.
bnl = em;
}
if (p != pp) bnl = n - bnl; // Remember to undo the symmetry transformation.
return bnl;
}
@#
@end def
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