def nonlinear_fit(d, e, initial_guess):
"""
d : list of values of the set of discretization
parameters in each experiment:
d = ((d_1,d_2,d_3),(d_1,d_2,d_3,),...)
d[i] provides the values of the discretization
parameters in experiement no. i
e : list of error values; e = (e_1, e_2, ...)
e[i] is the error associated with the parameters
d[i]
initial_guess is the starting value for the unknown
parameters vector.
"""
if len(d) != len(e):
raise ValueError, 'len(d) != len(e)'
# transform d and e to the data format required by
# the Scientific package:
data = []
for d_i, e_i in zip(d, e):
if isinstance(d_i, (float, int)):
data.append(((d_i,), e_i))
else: # d_i is tuple, list, array, NumArray, ...
data.append((d_i, e_i))
sol = leastSquaresFit(ManyDiscretizationPrm.error_model,
initial_guess, data)
# return list of fitted parameters (p in error_model)
# (sol[1] is a measure of the quality of the fit)
return sol[0]
def analyze(self, task):
self.initialGuess(task)
p = [self.coeff[c] for c in self.varCoeffs]
(p, self.chisq) = leastSquaresFit(self.func, p, self.chooseXY(task))
for i in range(len(self.varCoeffs)):
self.coeff[self.varCoeffs[i]] = p[i]
del self.func
def nonlinear_fit(d, e, initial_guess):
"""
d : list of values of the (single) discretization
parameter in each experiment:
d[i] provides the values of the discretization
parameter in experiement no. i
e : list of error values; e = (e_1, e_2, ...)
e[i] is the error associated with the parameters
d[i]
initial_guess is the starting value for the unknown
parameters vector.
"""
if len(d) != len(e):
raise ValueError, 'd and e must have the same length'
if not isinstance(d[0], (float,int)):
raise TypeError, \
'd must be an array of numbers, not %s' % str(type(d[0]))
# transform d and e to the data format required by
# the Scientific package:
data = []
for d_i, e_i in zip(d, e):
data.append(((d_i,) , e_i)) # recall (a,) conversion to tuple
sol = leastSquaresFit(OneDiscretizationPrm.error_model,
initial_guess, data)
return sol[0]
def fit(self):
self.setStartParam()
fitParam, chi = leastSquaresFit(self.func, self.startParam, self.data)
fitData, akaike = self.akaike(fitParam)
# wszystkie model oczekuja parametrow >= 0
if fitParam[0] <= 0:
raise Exception, "alfa %f mniejsza od 0! " % fitParam[0]
if len(fitParam) > 1 and fitParam[1] <= 0:
raise Exception, "beta %f mniejsza od 0! " % fitParam[1]
return (fitParam, chi, fitData, akaike)
def __call__(self, t, data, param = [10000, 200, 300000, 2000]):
"""
Sets the Star object parameters to the best fit. param can be changed
for better performance. Be aware that there might be more than one fix
point for each data-set, so inspect the result to see wheter it is a
realistic fit. Usually this is no problem if the initializing parameters
are sensible.
"""
# create list of tuples
values = [];
print len(data);
print len(t);
for i in range(len(t)):
values.append([t[i], data[i]]);
values = np.asarray(values);
return leastSquaresFit(self.modelFunction, param, values)
def __call__(self, t, data, param=[10000, 200, 300000, 2000]):
"""
Sets the Star object parameters to the best fit. param can be changed
for better performance. Be aware that there might be more than one fix
point for each data-set, so inspect the result to see wheter it is a
realistic fit. Usually this is no problem if the initializing parameters
are sensible.
"""
# create list of tuples
values = []
print len(data)
print len(t)
for i in range(len(t)):
values.append([t[i], data[i]])
values = np.asarray(values)
return leastSquaresFit(self.modelFunction, param, values)
def equilibrate(atoms, dyn, temp):
print "Equilibrating ..."
tstart = time.time()
temperatures = []
for i in xrange(1,nequil/nminor+1):
dyn.run(nminor)
ekin = atoms.get_kinetic_energy() / len(atoms)
temperatures.append((i*nminor*timestep, 2.0/3.0 * ekin))
if i % nequilprint == 0:
#data = array(temperatures)
#print data.shape
try:
(a, b, c) = leastSquaresFit(targetfunc, (0.1, 2*frict, temp),
temperatures)[0]
except OverflowError:
print "leastSquaresFit failed (this is OK)."
a = b = c = 0.0
print "%.6f T_inf = %.6f (goal: %f) k = %.6f" % \
(ekin, c, temp, b)
tequil = time.time() - tstart
print "This took %.1f minutes." % (tequil / 60)
print "Taking data - this takes", repeats*nsteps/nequil, "times longer!"
C = 1
a = 2
D = 2
b = 1
p = (C, a, D, b)
dx = 0.5
dt = 1.0
for i in range(7):
dx /= 2
dt /= 2
e = error_model(p, (dx, dt)) # use the model to generate data
e += random.gauss(0, 0.01 * e) # perturb data randomly
data.append(((dx, dt), e))
from Scientific.Functions.LeastSquares import leastSquaresFit
parameter_guess = (1, 2, 2, 1) # exact guess...
r = leastSquaresFit(error_model, parameter_guess, data)
print r
# try different initial guesses:
array_output_precision(4)
for i in range(6):
pg = array(p,
Float) + i * 0.1 * sign(random.uniform(-1, 1)) * ones(4, Float)
r = leastSquaresFit(error_model, pg, data)
print "guess:", str(pg)
deviation = array(p) - array(r[0])
print " deviation:", deviation
import sys
sys.exit(0)
def rateFilter(sampledRGB, filterRadius, exposedTime, flowRate, bcgradient, gradient, parenttags=None, level=logging.ERROR):
''' Computes the BCArea and BCVolume subject to the params
Keyword arguments:
sampledRGB -- The sampled RGB values of the BCFilter
exposedTime -- The duration for which the filter was exposed to air from the pump
flowRate -- The flow rate of the pump
bcgradient -- The calibration value obtained from the database
gradient -- The values corresponding to the color values from GrayBar objects
parenttags -- The tag string of the calling function
level -- The logging level
Returns:
BCCResult object
'''
# Set the logging level
log.setLevel(level)
tags = parenttags + " BCCCOMPUTATION"
try:
fitParam = BCCCalculatorConstants.FittingParameters
stop = BCCCalculatorConstants.StoppingLimit
expmod = Rating.expmod
rsquared = Rating.rsquared
# The results of this computation
bccResult = BCCResult()
# separate by color leaving off the black and white
gradientRed, gradientGreen, gradientBlue = zip(*gradient[1:-1])
# fit the gradient
bccResult.fitRed, chi = leastSquaresFit(expmod, fitParam, zip(gradientRed, bcgradient), stopping_limit=stop)
bccResult.fitGreen, chi = leastSquaresFit(expmod, fitParam, zip(gradientGreen, bcgradient), stopping_limit=stop)
bccResult.fitBlue, chi = leastSquaresFit(expmod, fitParam, zip(gradientBlue, bcgradient), stopping_limit=stop)
# compute the rsquared value
bccResult.rSquaredRed = rsquared(expmod, bccResult.fitRed, pylab.array(gradientRed), bcgradient)
bccResult.rSquaredGreen = rsquared(expmod, bccResult.fitGreen, pylab.array(gradientRed), bcgradient)
bccResult.rSquaredBlue = rsquared(expmod, bccResult.fitBlue, pylab.array(gradientRed), bcgradient)
red, green, blue = sampledRGB
bccResult.BCAreaRed = expmod(bccResult.fitRed, red)
bccResult.BCAreaGreen = expmod(bccResult.fitGreen, green)
bccResult.BCAreaBlue = expmod(bccResult.fitBlue, blue)
log.info('Computing Black Carbon Concentration: ', extra=tags)
bccResult.BCVolRed = computeBCC(filterRadius, bccResult.BCAreaRed, exposedTime ,flowRate)
bccResult.BCVolGreen = computeBCC(filterRadius, bccResult.BCAreaGreen, exposedTime, flowRate)
bccResult.BCVolBlue = computeBCC(filterRadius, bccResult.BCAreaBlue, exposedTime, flowRate)
log.info('Black carbon per cm^2: %s', ([bccResult.BCAreaRed, bccResult.BCAreaGreen, bccResult.BCAreaBlue],), extra=tags)
log.info('Black carbon per cm^3: %s', ([bccResult.BCVolRed, bccResult.BCVolGreen, bccResult.BCVolBlue],), extra=tags)
log.info('Done Computing Black Carbon Concentration: ', extra=tags)
return bccResult, ExitCode.Success
except Exception, err:
log.error('Error %s' % str(err), extra=tags)
return None, ExitCode.BCCComputationError
def fit(self):
"""
Determine of data for optimal fit and fit
"""
Yr = [x.real for x in self.admitance]
maxYr = max(Yr)
maxYrIndex = Yr.index(maxYr)
fRes = self.frequency[maxYrIndex]
# Hladanie P% +- bodov
P = 10
minYr = min(Yr)
hod = maxYr - (((maxYr - minYr) / 100) * P)
lava = maxYrIndex
for i in range(maxYrIndex, 0, -1):
if Yr[i] > hod:
lava = i
prava = maxYrIndex
for i in range(maxYrIndex, len(self.frequency), 1):
if Yr[i] > hod:
prava = i
#prava = maxYrIndex + (maxYrIndex - lava)
# vyrez
self.vyrez = Yr[lava:prava]
self.vyref = self.frequency[lava:prava]
self.vyref_fit = []
for i in range(len(self.vyref)):
self.vyref_fit.append(i)
# Fitovanie Realnej zlozky admitancie
datafit = []
for i in range(len(self.vyref)):
datafit.append((i, self.vyrez[i]))
guess = (1, 1, 1)
fit_params, fit_error = leastSquaresFit(func, guess, datafit)
#print fit_params, fit_error
self.fResonanceFit = (- fit_params[1] ) / (2 * fit_params[0]) * ((self.vyref[-1] - self.vyref[0]) / (len(self.vyref) - 1)) + self.vyref[0]
#print self.fResonanceFit
for i in range(len(self.vyref)):
self.yre_fit.append(func(fit_params, i))
maxY = max(self.yre_fit)
indexmax = self.yre_fit.index(max(self.yre_fit))
self.fResonance = self.vyref[indexmax]
# fitovanie Imaginarnej zlozky admitancie
Yi = [x.imag for x in self.admitance]
self.vyrezimag = Yi[lava:prava]
datafitimag = []
for i in range(len(self.vyref)):
datafitimag.append((i, self.vyrezimag[i]))
guessimag = (-1.0, 1.0)
fit_params, fit_error = leastSquaresFit(funcimag, guessimag, datafitimag)
#print fit_params, fit_error
xim = []
for i in range(len(self.vyref)):
xim.append(self.vyref[i])
self.yim_fit.append(funcimag(fit_params, i))
Yimag = self.yim_fit[indexmax]
# Determine R1
self.R1 = 1.0 / maxY
# Determine C0
w0 = 2 * math.pi * self.fResonance
self.C0 = Yimag / w0
# Find X1
w = []
for f in self.frequency[lava:prava]:
w.append(2 * math.pi * f)
Yinn = [] # z ofitovanych hodnot real a imag urobi komplexne cislo...
for i in range(len(self.vyref)):
Yinn.append(self.yre_fit[i] + 1j * self.yim_fit[i])
X1 = []
for i in range(len(self.frequency[lava:prava])):
X1.append((1 / (Yinn[i] - 1j * w[i] * self.C0)).imag)
# Determine C1
C1 = []
f1 = []
for i in range(len(X1)):
try:
C1.append((((w[i] / w0) ** 2) - 1) / (w[i] * X1[i]))
f1.append(self.frequency[lava + i])
except ZeroDivisionError:
pass
#self.C1 = Numeric.average(C1) ISVOSA - OLD
self.C1 = numpy.average(C1)
#Determine L1
self.L1 = 1.0 / (self.C1 * (w0 ** 2))
D = 2
b = 1
p = (C, a, D, b)
dx = 0.5
dt = 1.0
for i in range(7):
dx /= 2
dt /= 2
e = error_model(p, (dx, dt)) # use the model to generate data
e += random_number.gauss(0, 0.01 * e) # perturb data randomly
data.append(((dx, dt), e))
from Scientific.Functions.LeastSquares import leastSquaresFit
parameter_guess = (1, 2, 2, 1) # exact guess...
r = leastSquaresFit(error_model, parameter_guess, data)
print r
# try different initial guesses:
for i in range(6):
# exact p +/- [1-6]*(randomly chosen -1 or 1):
pg = array(p, float) + i * 0.05 * sign(random_number.uniform(-1, 1)) * ones(4)
r = leastSquaresFit(error_model, pg, data)
print "guess:", str(pg)
deviation = array(p) - array(r[0])
print " deviation:", deviation
print "\n\nTesting statistical computations:"
import Scientific.Statistics as S
nsamples = 100000
data = random.normal(1.0, 0.5, nsamples)
def test(temp, frict):
output = file('Langevin.dat', 'w')
# Make a small perturbation of the momenta
atoms.set_momenta(1e-6 * np.random.random([len(atoms), 3]))
print 'Initializing ...'
predyn = VelocityVerlet(atoms, 0.5)
predyn.run(2500)
dyn = Langevin(atoms, timestep, temp, frict)
print ''
print ('Testing Langevin dynamics with T = %f eV and lambda = %f' %
(temp, frict))
ekin = atoms.get_kinetic_energy()/len(atoms)
print ekin
output.write('%.8f\n' % ekin)
print 'Equilibrating ...'
# Initial guesses for least-squares fit
a = 0.04
b = 2*frict
c = temp
params = (a,b,c)
fitdata = [(0, 2.0 / 3.0 * ekin)]
tstart = time.time()
for i in xrange(1,nequil+1):
dyn.run(nminor)
ekin = atoms.get_kinetic_energy() / len(atoms)
fitdata.append((i*nminor*timestep, 2.0/3.0 * ekin))
if usescipy and i % nequilprint == 0:
(params, chisq) = leastSquaresFit(targetfunc, params, fitdata)
print '%.6f T_inf = %.6f (goal: %f), tau = %.2f, k = %.6f' % \
(ekin, params[2], temp, 1.0/params[1], params[0])
output.write('%.8f\n' % ekin)
tequil = time.time() - tstart
print 'This took %s minutes.' % (tequil / 60)
output.write('&\n')
assert abs(temp-params[2]) < 0.25*temp, 'Least-squares fit is way off'
assert nequil*nminor*timestep > 3.0/params[1], 'Equiliberation was too short'
fitdata = np.array(fitdata)
print 'Recording statistical data - this takes ten times longer!'
temperatures = []
tstart = time.time()
for i in xrange(1,nsteps+1):
dyn.run(nminor)
ekin = atoms.get_kinetic_energy() / len(atoms)
temperatures.append(2.0/3.0 * ekin)
if i % nprint == 0:
tnow = time.time() - tstart
tleft = (nsteps-i) * tnow / i
print '%.6f (time left: %.1f minutes)' % (ekin, tleft/60)
output.write('%.8f\n' % ekin)
output.write('&\n')
output.close()
temperatures = np.array(temperatures)
mean = sum(temperatures) / len(temperatures)
print 'Mean temperature:', mean, 'eV'
print
print 'This test is statistical, and may in rare cases fail due to a'
print 'statistical fluctuation.'
print
assert abs(mean - temp) <= reltol*temp, 'Deviation is too large.'
print 'Mean temperature:', mean, ' in ', temp, ' +/- ', reltol*temp
return fitdata, params, temperatures