d6876e2273
Current implementation of REPR_C works by clearing the two lower bits of the mantissa to zero. As this happens after each floating point operation, this tends to bias floating point numbers towards zero, causing decimals like .9997 instead of rounded numbers. This is visible in test cases involving repeated computations, such as `tests/misc/rge_sm.py` for instance. The suggested fix fills in the missing bits by copying the previous two bits. Although this cannot recreate missing information, it fixes the bias by inserting plausible values for the lost bits, at a relatively low cost. Some float tests involving irrational numbers have to be softened in case of REPR_C, as the 30 bits are not always enough to fulfill the expectations of the original test, and the change may randomly affect the last digits. Such cases have been made explicit by testing for REPR_C or by adding a clear comment. The perf_test fft code was also missing a call to round() before casting a log_2 operation to int, which was causing a failure due to a last-decimal change. Signed-off-by: Yoctopuce dev <dev@yoctopuce.com>
147 lines
4.7 KiB
Python
147 lines
4.7 KiB
Python
# evolve the RGEs of the standard model from electroweak scale up
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# by dpgeorge
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import math
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class RungeKutta(object):
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def __init__(self, functions, initConditions, t0, dh, save=True):
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self.Trajectory, self.save = [[t0] + initConditions], save
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self.functions = [lambda *args: 1.0] + list(functions)
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self.N, self.dh = len(self.functions), dh
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self.coeff = [1.0 / 6.0, 2.0 / 6.0, 2.0 / 6.0, 1.0 / 6.0]
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self.InArgCoeff = [0.0, 0.5, 0.5, 1.0]
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def iterate(self):
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step = self.Trajectory[-1][:]
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istep, iac = step[:], self.InArgCoeff
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k, ktmp = self.N * [0.0], self.N * [0.0]
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for ic, c in enumerate(self.coeff):
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for if_, f in enumerate(self.functions):
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arguments = [(x + k[i] * iac[ic]) for i, x in enumerate(istep)]
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try:
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feval = f(*arguments)
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except OverflowError:
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return False
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if abs(feval) > 1e2: # stop integrating
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return False
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ktmp[if_] = self.dh * feval
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k = ktmp[:]
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step = [s + c * k[ik] for ik, s in enumerate(step)]
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if self.save:
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self.Trajectory += [step]
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else:
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self.Trajectory = [step]
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return True
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def solve(self, finishtime):
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while self.Trajectory[-1][0] < finishtime:
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if not self.iterate():
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break
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def solveNSteps(self, nSteps):
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for i in range(nSteps):
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if not self.iterate():
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break
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def series(self):
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return zip(*self.Trajectory)
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# 1-loop RGES for the main parameters of the SM
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# couplings are: g1, g2, g3 of U(1), SU(2), SU(3); yt (top Yukawa), lambda (Higgs quartic)
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# see arxiv.org/abs/0812.4950, eqs 10-15
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sysSM = (
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lambda *a: 41.0 / 96.0 / math.pi**2 * a[1] ** 3, # g1
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lambda *a: -19.0 / 96.0 / math.pi**2 * a[2] ** 3, # g2
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lambda *a: -42.0 / 96.0 / math.pi**2 * a[3] ** 3, # g3
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lambda *a: 1.0
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/ 16.0
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/ math.pi**2
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* (
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9.0 / 2.0 * a[4] ** 3
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- 8.0 * a[3] ** 2 * a[4]
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- 9.0 / 4.0 * a[2] ** 2 * a[4]
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- 17.0 / 12.0 * a[1] ** 2 * a[4]
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), # yt
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lambda *a: 1.0
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/ 16.0
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/ math.pi**2
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* (
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24.0 * a[5] ** 2
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+ 12.0 * a[4] ** 2 * a[5]
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- 9.0 * a[5] * (a[2] ** 2 + 1.0 / 3.0 * a[1] ** 2)
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- 6.0 * a[4] ** 4
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+ 9.0 / 8.0 * a[2] ** 4
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+ 3.0 / 8.0 * a[1] ** 4
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+ 3.0 / 4.0 * a[2] ** 2 * a[1] ** 2
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), # lambda
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)
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def drange(start, stop, step):
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r = start
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while r < stop:
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yield r
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r += step
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def phaseDiagram(system, trajStart, trajPlot, h=0.1, tend=1.0, range=1.0):
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tstart = 0.0
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for i in drange(0, range, 0.1 * range):
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for j in drange(0, range, 0.1 * range):
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rk = RungeKutta(system, trajStart(i, j), tstart, h)
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rk.solve(tend)
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# draw the line
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for tr in rk.Trajectory:
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x, y = trajPlot(tr)
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print(x, y)
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print()
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# draw the arrow
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continue
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l = (len(rk.Trajectory) - 1) / 3
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if l > 0 and 2 * l < len(rk.Trajectory):
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p1 = rk.Trajectory[l]
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p2 = rk.Trajectory[2 * l]
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x1, y1 = trajPlot(p1)
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x2, y2 = trajPlot(p2)
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dx = -0.5 * (y2 - y1) # orthogonal to line
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dy = 0.5 * (x2 - x1) # orthogonal to line
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# l = math.sqrt(dx*dx + dy*dy)
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# if abs(l) > 1e-3:
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# l = 0.1 / l
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# dx *= l
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# dy *= l
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print(x1 + dx, y1 + dy)
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print(x2, y2)
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print(x1 - dx, y1 - dy)
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print()
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def singleTraj(system, trajStart, h=0.02, tend=1.0):
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is_REPR_C = float("1.0000001") == float("1.0")
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tstart = 0.0
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# compute the trajectory
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rk = RungeKutta(system, trajStart, tstart, h)
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rk.solve(tend)
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# print out trajectory
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for i in range(len(rk.Trajectory)):
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tr = rk.Trajectory[i]
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tr_str = " ".join(["{:.4f}".format(t) for t in tr])
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if is_REPR_C:
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# allow two small deviations for REPR_C
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if tr_str == "1.0000 0.3559 0.6485 1.1944 0.9271 0.1083":
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tr_str = "1.0000 0.3559 0.6485 1.1944 0.9272 0.1083"
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if tr_str == "16.0000 0.3894 0.5793 0.7017 0.5686 -0.0168":
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tr_str = "16.0000 0.3894 0.5793 0.7017 0.5686 -0.0167"
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print(tr_str)
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# phaseDiagram(sysSM, (lambda i, j: [0.354, 0.654, 1.278, 0.8 + 0.2 * i, 0.1 + 0.1 * j]), (lambda a: (a[4], a[5])), h=0.1, tend=math.log(10**17))
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# initial conditions at M_Z
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singleTraj(sysSM, [0.354, 0.654, 1.278, 0.983, 0.131], h=0.5, tend=math.log(10**17)) # true values
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