def test_odr_model_default_meta(self):
def func(b, x):
return b[0] + b[1] * x
p = Model(func)
p.set_meta(name='Sample Model Meta', ref='ODRPACK')
assert_equal(p.meta, {'name': 'Sample Model Meta', 'ref': 'ODRPACK'})
def chi2_iterative(k, k_nn, Foward=True):
"""
Esta funcion agarra un eje X (k), un eje Y (k_nn) y busca los parametros para
ajustar la mejor recta, buscando el regimen lineal de la curva. Esto lo hace
sacando puntos de la curva, ajustando la curva resultante, y luego comparando
los parametros de los distintos ajustes, seleccionando el de menor chi2.
Si Foward=True entonces la funcion va a ir sacando puntos del final para
encontrar kmax. Si Foward=False, la funcion va a sacar puntos del principio para
calcular kmin. El punto va a estar dado por k[index].
Returns: m, b, chi2_stat, index
m: pendiente de la recta resultante
b: ordenada de la recta resultante
chi2: estadistico de chi2 de la recta resultante
index: indice del elemento donde empieza/termina el regimen lineal.
.
.
"""
chi2_list = []
m_list = []
b_list = []
if Foward == True:
for j in range(0, len(k) - 3):
k_nn_temp = k_nn[:len(k_nn) - j]
k_temp = k[:len(k) - j]
linear_model = Model(linear)
data = RealData(k_temp, k_nn_temp)
odr = ODR(data, linear_model, beta0=[0., 1.])
out = odr.run()
chi2_list.append(out.res_var)
m_list.append(out.beta[0])
b_list.append(out.beta[1])
else:
for j in range(0, len(k) - 3):
k_nn_temp = k_nn[j:]
k_temp = k[j:]
linear_model = Model(linear)
data = RealData(k_temp, k_nn_temp)
odr = ODR(data, linear_model, beta0=[0., 1.])
out = odr.run()
chi2_list.append(out.res_var)
m_list.append(out.beta[0])
b_list.append(out.beta[1])
#index = ClosestToOne(chi2_list)
index = chi2_list.index(min(chi2_list))
m = m_list[index]
b = b_list[index]
chi2 = chi2_list[index]
return m, b, chi2, index
def test_explicit(self):
explicit_mod = Model(
self.explicit_fcn,
fjacb=self.explicit_fjb,
fjacd=self.explicit_fjd,
meta=dict(name='Sample Explicit Model',
ref='ODRPACK UG, pg. 39'),
)
explicit_dat = Data([0.,0.,5.,7.,7.5,10.,16.,26.,30.,34.,34.5,100.],
[1265.,1263.6,1258.,1254.,1253.,1249.8,1237.,1218.,1220.6,
1213.8,1215.5,1212.])
explicit_odr = ODR(explicit_dat, explicit_mod, beta0=[1500.0, -50.0, -0.1],
ifixx=[0,0,1,1,1,1,1,1,1,1,1,0])
explicit_odr.set_job(deriv=2)
explicit_odr.set_iprint(init=0, iter=0, final=0)
out = explicit_odr.run()
assert_array_almost_equal(
out.beta,
np.array([1.2646548050648876e+03, -5.4018409956678255e+01,
-8.7849712165253724e-02]),
)
assert_array_almost_equal(
out.sd_beta,
np.array([1.0349270280543437, 1.583997785262061, 0.0063321988657267]),
)
assert_array_almost_equal(
out.cov_beta,
np.array([[4.4949592379003039e-01, -3.7421976890364739e-01,
-8.0978217468468912e-04],
[-3.7421976890364739e-01, 1.0529686462751804e+00,
-1.9453521827942002e-03],
[-8.0978217468468912e-04, -1.9453521827942002e-03,
1.6827336938454476e-05]]),
)
def test_output_file_overwrite(self):
"""
Verify fix for gh-1892
"""
def func(b, x):
return b[0] + b[1] * x
p = Model(func)
data = Data(np.arange(10), 12 * np.arange(10))
tmp_dir = tempfile.mkdtemp()
error_file_path = os.path.join(tmp_dir, "error.dat")
report_file_path = os.path.join(tmp_dir, "report.dat")
try:
ODR(data,
p,
beta0=[0.1, 13],
errfile=error_file_path,
rptfile=report_file_path).run()
ODR(data,
p,
beta0=[0.1, 13],
errfile=error_file_path,
rptfile=report_file_path,
overwrite=True).run()
finally:
# remove output files for clean up
shutil.rmtree(tmp_dir)
def orthoregress(x, y):
"""Perform an Orthogonal Distance Regression on the given data,
using the same interface as the standard scipy.stats.linregress function.
Adapted from https://gist.github.com/robintw/d94eb527c44966fbc8b9#file-orthoregress-py
Arguments:
x: x data
y: y data
Returns:
[slope, intercept, residual]
Uses standard ordinary least squares to estimate the starting parameters
then uses the scipy.odr interface to the ODRPACK Fortran code to do the
orthogonal distance calculations.
"""
def f(p, x):
"""Basic linear regression 'model' for use with ODR"""
return (p[0] * x) + p[1]
linreg = stats.linregress(x, y)
mod = Model(f)
dat = Data(x, y)
od = ODR(dat, mod, beta0=linreg[0:2])
out = od.run()
return list(out.beta) + [out.res_var]
def fit_slope(X, Y, eX=None, eY=None):
"""Will fit a Y vs X with errors using the scipy
ODR functionalities and a linear fitting function
Args:
X:
Y: input arrays
eX:
eY: input uncertaintites [None]
Returns:
odr output
"""
# First filtering the Nan
good = ~np.isnan(X)
if eX is None: eX_good = None
else: eX_good = eX[good]
if eY is None: eY_good = None
else: eY_good = eY[good]
linear = Model(linear_fit)
odr_data = RealData(X[good], Y[good], sx=eX_good, sy=eY_good)
odr_run = ODR(odr_data, linear, beta0=[2., 1.])
return odr_run.run()
def do_the_fit(obs, **kwargs):
global print_output, beta0
func = kwargs.get('function')
yerr = kwargs.get('yerr')
length = len(yerr)
xerr = kwargs.get('xerr')
if length == len(obs):
assert 'x_constants' in kwargs
data = RealData(kwargs.get('x_constants'), obs, sy=yerr)
fit_type = 2
elif length == len(obs) // 2:
data = RealData(obs[:length], obs[length:], sx=xerr, sy=yerr)
fit_type = 0
else:
raise Exception('x and y do not fit together.')
model = Model(func)
odr = ODR(data, model, beta0, partol=np.finfo(np.float64).eps)
odr.set_job(fit_type=fit_type, deriv=1)
output = odr.run()
if print_output and not silent:
print(*output.stopreason)
print('chisquare/d.o.f.:', output.res_var)
print_output = 0
beta0 = output.beta
return output.beta[kwargs.get('n')]
def meanResiduals(pts):
f = lambda B, x: B[0] * x + B[1]
model = Model(f)
data = RealData(list(p.x() for p in pts), list(p.y() for p in pts))
odr = ODR(data, model, beta0=[0., 1.])
out = odr.run()
return out.sum_square / len(pts)
def __init__(self, recebe_x, recebe_y, recebe_x_erro,
recebe_y_erro): #construtor da classe
super().__init__(
recebe_x, recebe_y, recebe_x_erro,
recebe_y_erro) #chama o construtor da classe Fit_curve
self.model = Model(
self.funcao) #cria uma classe model com a função racional
def regress_odr(x, y, sx, sy, beta0=[0., 1.]):
"""Return an ODR linear fit
"""
linear = Model(my_linear)
mydata = RealData(x.ravel(), y.ravel(), sx=sx.ravel(), sy=sy.ravel())
myodr = ODR(mydata, linear, beta0=beta0)
return myodr.run()
def voltage_current_regression():
# read data from datafile
df = pd.read_table(os.path.join(os.path.dirname(__file__), DATA_PATH,
'1_a_soneloid.dat'),
delim_whitespace=True,
names=['current', 'voltage_min', 'voltage_max'],
decimal=',',
comment='#')
# add columns for voltage mean and error
df['voltage_mean'] = 0.5 * (df['voltage_min'] + df['voltage_max'])
df['voltage_error'] = df['voltage_max'] - df['voltage_min']
# Create a model for fitting.
linear_model = Model(regression_func)
x = np.array(df['current'])
y = np.array(df['voltage_mean'])
sy = np.array(df['voltage_error'])
data = RealData(x, y, sy=sy)
odr = ODR(data, linear_model, beta0=[0., 1.])
out = odr.run()
return out
def find_c13(self):
'''
Find the c13 parameter by fitting a curve to
the measured group velocities using the scipy
ODR library. Since c13 is par tof the equation
for the curve, the c13 value corresponding to
the best fit curve is the result of the inversion.
'''
self.c13_max = np.sqrt(
self.c33 *
(self.c11)) #The most physically reasonable maximum for c13
self.c13_min = np.sqrt(self.c33 * (self.c11 - 2 * self.c66) +
self.c66**2) - self.c66
self.c13_0 = self.c13_min * 1.2
model = Model(self.forward_model,
estimate=[self.c13_0, self.theta0, self.c11, self.c33])
data = RealData(self.group_angles,
self.group_vels,
sy=self.group_vel_err)
fit = ODR(data,
model,
beta0=[self.c13_0, self.theta0, self.c11, self.c33],
ifixb=[1, 1, 1, 1])
output = fit.run()
best_fit = output.beta
errors = output.sd_beta
self.c13 = best_fit[0]
self.c13_err = errors[0]
self.theta0 = best_fit[1]
def graph(a,toc): #a:odr with xerrors or curvefit without? toc: number of the figure
plt.figure(toc,figsize=(15,10))
for tickLabel in plt.gca().get_xticklabels()+plt.gca().get_yticklabels():
tickLabel.set_fontsize(15)
plt.title("Number of coincidence counts in the peak of $Na^{22}$ wrt angle",fontsize=17)
plt.xlabel(r'Angle $\theta$ (°)',fontsize=17)
plt.ylabel('# coincidence events',fontsize=17)
plt.scatter(Ld,res,label='\n Data with parameters'+\
' \n $16$ $cm$ source-detectors'+\
' \n $150$ $s/points$')
if a==False:
par, par_va = curve_fit(simplegaussian, Ld, res, p0=[70000, 180, 10,1000],sigma=err_res,absolute_sigma=True)
chi2=round(sum(((res - simplegaussian(Ld,*par) )/ err_res) ** 2)/(len(Ld)-3),2)
plt.plot(Lc,simplegaussian(Lc, *par),color='gold',label='Fit with '+r'$A\exp\{\frac{-(\theta-\mu)^2}{2\sigma^2}\}+Cst$'+\
' \n $A =$%s'%int(par[0])+' $ \pm$ %s'%int(np.sqrt(np.diag(par_va)[0]))+' #'+\
' \n $\mu =$ %s'%round(par[1],1)+' $\pm$ %s'%round(np.sqrt(np.diag(par_va)[1]),1)+'°'+\
' \n $\sigma =$ %s'%round(par[2],1)+ '$\pm$ %s'%round(np.sqrt(np.diag(par_va)[2]),1)+'°'+\
' \n $Cst=$ %s'%int(par[3])+' $\pm$ %s'%int(np.sqrt(np.diag(par_va)[3]))+' #'+\
' \n $\chi^2/dof = $ %s'%chi2)
plt.errorbar(Ld, res, err_res,fmt='.',label=r'$y=\sqrt{counts}$ '+\
'\n $x=0°$', color='black',ecolor='lightgray', elinewidth=3, capsize=0)
else:
data = RealData(Ld,res,err_resx,err_res)
model = Model(simplegaussianl)
odr = ODR(data, model, [73021, 183, 11,1208])
odr.set_job(fit_type=2)
output = odr.run()
xn = Lc
yn = simplegaussianl(output.beta, xn)
#pl.hold(True)
#plot(Ld,res,'ro')
#print(x,y)
plt.plot(xn,yn,'k-',label=' ODR leastsq fit'+\
' \n $\chi^2/dof = $ %s'%round(output.sum_square/(len(Ld)-3),2)+'\n')
odr.set_job(fit_type=0)
output = odr.run()
par,par_va=output.beta,output.cov_beta
yn = simplegaussianl(output.beta, xn)
plt.plot(xn,yn,color='gold',label='ODR fit '+r'$A\exp\{\frac{-(\theta-\mu)^2}{2\sigma^2}\}+Cst$'+\
' \n $A =$%s'%int(par[0])+' $ \pm$ %s'%int(np.sqrt(np.diag(par_va)[0]))+' #'+\
' \n $\mu =$ %s'%round(par[1],1)+' $\pm$ %s'%round(np.sqrt(np.diag(par_va)[1]),1)+'°'+\
' \n $\sigma =$ %s'%round(par[2],1)+ '$\pm$ %s'%round(np.sqrt(np.diag(par_va)[2]),1)+'°'+\
' \n $Cst=$ %s'%int(par[3])+' $\pm$ %s'%int(np.sqrt(np.diag(par_va)[3]))+' #'+\
' \n Sum of squares/dof $= $ %s'%round(output.sum_square/(len(Ld)-3),2))
plt.legend(loc=0)
plt.errorbar(Ld, res, err_res,err_resx,label=r'$y=\sqrt{counts}$ '+\
'\n $x=$%s'%errx+'°',fmt='.', color='black',ecolor='lightgray', elinewidth=3, capsize=0)
plt.gca().set_xlim(140,220)
plt.legend(bbox_to_anchor=(0.68, 0.58), loc=1, borderaxespad=0.,prop={'size':14})
plt.yscale('log')
plt.ylim(1e2,1e5)
def ortho_regress(x, y):
linreg = linregress(x, y)
mod = Model(f)
dat = Data(x, y)
od = ODR(dat, mod, beta0=linreg[0:2])
out = od.run()
#print(list(out.beta))
#return list(out.beta) + [np.nan, np.nan, np.nan]
return(list(out.beta))
def test_empty_data(self):
beta0 = [0.02, 0.0]
linear = Model(self.empty_data_func)
empty_dat = Data([], [])
assert_warns(OdrWarning, ODR, empty_dat, linear, beta0=beta0)
empty_dat = RealData([], [])
assert_warns(OdrWarning, ODR, empty_dat, linear, beta0=beta0)
def fit(self, x, y):
# Initial estimate of betas
linreg = linregress(x, y)
linear = Model(self.model)
mydata = Data(x, y)
myodr = ODR(mydata, linear, beta0=linreg[0:2])
myoutput = myodr.run()
self.betas = myoutput.beta
def orthogonal_distance_regression(func, data, err, beta0=None):
"""Fit the function using scipy.odr and return fit output."""
if not beta0:
beta0 = _start_values(data)
model = Model(func)
rdata = _real_data(data, err)
fit = ODR(rdata, model, beta0=beta0)
output = fit.run()
print(output.beta)
return output
def sigma(X, Y, X_err, Y_err):
linear_model = Model(Linear)
data = RealData(X, Y, sx=X_err, sy=Y_err)
odr = ODR(data, linear_model, beta0=[0., 1.])
out = odr.run()
m = out.beta[0]
b = out.beta[1]
recta = [(I[i] - (V[i] * m + b)) for i in range(len(I))]
return len(recta), f.dispersion(recta)
def orthoregress(x, y, xerr, yerr):
linreg = linregress(x, y)
mod = Model(f)
dat = RealData(x, y, sx=xerr, sy=yerr)
od = ODR(dat, mod, beta0=linreg[0:2])
out = od.run()
return list(out.beta)
def test_lorentz(self):
l_sy = np.array([.29] * 18)
l_sx = np.array([
.000972971, .000948268, .000707632, .000706679, .000706074,
.000703918, .000698955, .000456856, .000455207, .000662717,
.000654619, .000652694, .000000859202, .00106589, .00106378,
.00125483, .00140818, .00241839
])
l_dat = RealData(
[
3.9094, 3.85945, 3.84976, 3.84716, 3.84551, 3.83964, 3.82608,
3.78847, 3.78163, 3.72558, 3.70274, 3.6973, 3.67373, 3.65982,
3.6562, 3.62498, 3.55525, 3.41886
],
[
652, 910.5, 984, 1000, 1007.5, 1053, 1160.5, 1409.5, 1430,
1122, 957.5, 920, 777.5, 709.5, 698, 578.5, 418.5, 275.5
],
sx=l_sx,
sy=l_sy,
)
l_mod = Model(self.lorentz, meta=dict(name='Lorentz Peak'))
l_odr = ODR(l_dat, l_mod, beta0=(1000., .1, 3.8))
out = l_odr.run()
assert_array_almost_equal(
out.beta,
np.array([
1.4306780846149925e+03, 1.3390509034538309e-01,
3.7798193600109009e+00
]),
)
assert_array_almost_equal(
out.sd_beta,
np.array([
7.3621186811330963e-01, 3.5068899941471650e-04,
2.4451209281408992e-04
]),
)
assert_array_almost_equal(
out.cov_beta,
np.array([[
2.4714409064597873e-01, -6.9067261911110836e-05,
-3.1236953270424990e-05
],
[
-6.9067261911110836e-05, 5.6077531517333009e-08,
3.6133261832722601e-08
],
[
-3.1236953270424990e-05, 3.6133261832722601e-08,
2.7261220025171730e-08
]]),
)
def orth_regression(obs, model):
linear = Model(f)
mydata = RealData(obs, model)
myodr = ODR(mydata, linear, beta0=[1., 0.])
myoutput = myodr.run()
params = myoutput.beta
gradient = params[0]
y_intercept = params[1]
res_var = myoutput.res_var
return np.around(gradient, 2), np.around(y_intercept,
2), np.around(res_var, 2)
def run(self):
fit_data = RealData(self.data['ref_spd'].values.flatten(), self.data['target_spd'].values.flatten())
p, res = lstsq(np.nan_to_num(fit_data.x[:, np.newaxis] ** [1, 0]), np.nan_to_num(np.asarray(fit_data.y)
[:, np.newaxis]))[0:2]
self._model = ODR(fit_data, Model(OrthogonalLeastSquares.linear_func), beta0=[p[0][0], p[1][0]])
self.out = self._model.run()
self.params = {'slope': self.out.beta[0], 'offset': self.out.beta[1]}
self.params['r2'] = self.get_r2()
self.params['Num data points'] = self.num_data_pts
# print("Model output:", self.out.pprint())
self.show_params()
def ODR_fitting(xdata, ydata, fitfunction, beta, fix):
bpl_all = Model(fitfunction)
data_all = RealData(xdata,
ydata,
sx=np.cov([xdata, ydata])[0][1],
sy=np.cov([xdata, ydata])[0][1])
odr_all = ODR(data_all, bpl_all, beta0=beta, ifixb=fix)
odr_all.set_job(fit_type=0)
output_all = odr_all.run()
#output_all.pprint()
return (output_all.beta, output_all.sd_beta)
def test_ifixx(self):
x1 = [-2.01, -0.99, -0.001, 1.02, 1.98]
x2 = [3.98, 1.01, 0.001, 0.998, 4.01]
fix = np.vstack((np.zeros_like(x1, dtype=int), np.ones_like(x2, dtype=int)))
data = Data(np.vstack((x1, x2)), y=1, fix=fix)
model = Model(lambda beta, x: x[1, :] - beta[0] * x[0, :]**2., implicit=True)
odr1 = ODR(data, model, beta0=np.array([1.]))
sol1 = odr1.run()
odr2 = ODR(data, model, beta0=np.array([1.]), ifixx=fix)
sol2 = odr2.run()
assert_equal(sol1.beta, sol2.beta)
def _run_odr(self):
"""Run an ODR regression"""
linear = Model(self._modelODR)
mydata = Data(ravel(self._datax), ravel(self._datay), 1)
myodr = ODR(mydata, linear, beta0=self._guess, maxit=10000)
myoutput = myodr.run()
self._result = myoutput.beta
self._stdev = myoutput.sd_beta
self._covar = myoutput.cov_beta
self._odr = myoutput
def test_ticket_1253(self):
def linear(c, x):
return c[0] * x + c[1]
c = [2.0, 3.0]
x = np.linspace(0, 10)
y = linear(c, x)
model = Model(linear)
data = Data(x, y, wd=1.0, we=1.0)
job = ODR(data, model, beta0=[1.0, 1.0])
result = job.run()
assert_equal(result.info, 2)
def ODR_Fit(function, x, y, x_err, y_err):
print('Fit:\t', function.__name__, '\n')
# Create a model for fitting.
model = Model(function)
# Create a RealData object using our initiated data from above.
D = RealData(x, y, sx=x_err, sy=y_err)
# Set up ODR with the model and data.
odr = ODR(D, model, beta0=[0.7, 0.])
# Run the regression.
out = odr.run()
# Use the in-built pprint method to give us results.
out.pprint()
print('\n')
return out
def fit_xy(x, y):
# Create a model for fitting.
linear_model = Model(linear_func)
# Create a RealData object using our initiated data from above.
data = RealData(x, y)
# Set up ODR with the model and data.
odr = ODR(data, linear_model, beta0=[0., 1.])
# Run the regression.
out = odr.run()
return out.beta
def linear_regression(data, err):
"""Calculate a linear regression using scipy.odr and return fit output."""
print('Fitting with')
print(data[:, 0], data[:, 1])
print('and Error')
print(err[:, 0], err[:, 1])
beta0 = get_start_values(data)
model = Model(linear_model)
rdata = RealData(data[:, 0], data[:, 1], sx=err[:, 0], sy=err[:, 1])
# TODO: check different errors
fit = ODR(rdata, model, beta0=beta0)
output = fit.run()
print(output.beta)
return output
def odr_inversion(self, initial_guess=None):
'''
Just another curve fit/inversion method
to find c13, using scipy's ODR class. Does
the same job as curve_fit.
'''
def odr_forward_model(parameters, xdata):
c13, c11, c33, c55, c66, theta = parameters
return self.forward_model(xdata, c13, c11, c33, c55, c66, theta)
from scipy.odr import ODR, RealData, Model
c13_max = np.sqrt(self.c33 * (self.c11 - self.c66))
c13_min = np.sqrt(self.c33 *
(self.c11 - 2 * self.c66) + self.c66**2) - self.c66
if not initial_guess:
initial_guess = c13_min * 1.1
print(self.c11, self.c33, self.c55, self.c66, self.theta0)
print('ok', round(c13_min / 1e9), round(c13_max / 1e9))
parameters = ['c11', 'c33', 'c55', 'c66', 'theta0']
fixed_params = [0, 0, 0, 0, 0]
for i, item in enumerate(parameters):
if item in self.parameters_to_invert:
fixed_params[i] = 1
fixed_params = [
1, 1, 1, 0, 0, 1
] #MAKE THIS [1]+fixed_params. I'M FORCING C55 NOT TO BE INVERTED
model = Model(odr_forward_model,
estimate=[
initial_guess, self.c11, self.c33, self.c55,
self.c66, self.theta0
])
data = RealData(self.group_angles,
self.group_vels,
sy=self.group_vel_err)
fit = ODR(data,
model,
beta0=[
initial_guess, self.c11, self.c33, self.c55, self.c66,
self.theta0
],
ifixb=fixed_params)
output = fit.run()
best_fit = output.beta
errors = output.sd_beta
return best_fit, errors
