Project 3

import pandas as pd import matplotlib.pyplot as pl import numpy as np

f = [100, 500, 1000, 2000, 5000, 7000, 8000, 9000, 10000] amp = [976, 800, 560, 320, 160, 128, 120, 104, 104] g = [2, 1.639, 1.148, 0.656, 0.328, 0.262, 0.246, 0.213, 0.213] omega = 2*np.pi*np.array(f) R=1000 C=.22e-6 X = 1.0/(omega*C) Z = np.sqrt(R**2 + X**2) G = 2.0*X/Z pl.loglog(f, G,'r-',label='theory') pl.loglog(f,g,'b.',label='exp') pl.grid() pl.legend()

G

N=10000 Tau=10.0 r = np.random.rand(N) t = -Tau*np.log(1.0-r) n,_,_ =pl.hist(t, bins=np.linspace(0,50,41)) pl.title("Exponentially distributed 't's") pl.xlabel("t (min)") pl.ylabel("Number (out of %d)" % N)

pl.plot(np.linspace(0,50,41)[:-1],np.log(n),'b.') pl.grid()

t = -Tau*np.log(1.0-np.random.rand(100)) # get 100 intervals between defects pl.hist(t)

print("Total time:", t.sum()) print("Average time:", t.mean())

delta2 = t[:-1] + t[1:] pl.hist(delta2)#make it delta 2 and sum of two slices not three - Tariq print("Minimum time between three successive defects:", min(delta2)) ThreeInLessThan10 = delta2<10#check for delta 2 less then ten - Tariq print("times less than 10:", delta2[np.nonzero(ThreeInLessThan10)]) print("Number of times 3 defects happened in less than 10 minutes:", len(delta2[np.nonzero(ThreeInLessThan10)]))

finalTime = 480 # run for one hour processTime = 10.0 # how long does it take to process an currTime = 0.0 # what time is it now? nextTime = processTime # when will the last defect be finished? (it takes 10 minutes to handle a defect) defectsProcessed = 0 # how many defects have been processed? defectsOccurred = 0 for delta in t: currTime = currTime + delta # when does the next defect appear? if currTime > finalTime: break # OK, it's the end of the 1 hour shift, break out. defectsOccurred += 1 # count the number of defects that have happened. if currTime > nextTime: nextTime = currTime + processTime # process immediately else: nextTime = nextTime + processTime # process after this one. if nextTime<finalTime: defectsProcessed += 1 print("Defects Occurred:", defectsOccurred) print("Defects Processed:", defectsProcessed) print("Backlog:", defectsOccurred-defectsProcessed)

!pip install pymc3

import pymc3 as pm import arviz as az with pm.Model() as model: tau = pm.Uniform('tau',lower=0,upper=100) # set up a prior for tau, somewhere between 0 and 100 t_obs = pm.Exponential('t_obs',lam=1/tau, observed=t) # add the observed data trace = pm.sample(1000, return_inferencedata=True) # check the results

az.plot_trace(trace) az.summary(trace, kind="stats")