def odRegress(x, y, weights=[], linreg=None):
# Produce Orthogonal Data Reduction (fit) for the passed x,y pairings.
# Returns: [fit parameters] , [parm. errors], [[covariance matrix]],
# [estimated error in x vars], [estimated error in y vars]
# Code modified from: Robin Wilson, see the site for copyright notice:
# http://blog.rtwilson.com/orthogonal-distance-regression-in-python/
#
# x,y both arrays of same length
assert len(x) == len(y)
if linreg is None:
linreg = stats.linregress(x, y)
# Linear function defined above
model = odr.Model(Linear)
if len(weights) != len(x):
data = odr.Data(x, y=y)
else:
data = odr.Data(x, y=y, we=weights)
# Bad variable naming, I know...so caps to avoid(?) confusion. :P
ODR = odr.ODR(data, model, beta0=linreg[0:2])
out = ODR.run()
return out.beta, out.sd_beta, out.cov_beta, out.delta, out.eps
def __init__(self, list_of_points, pointcloud):
self.points = list_of_points
model = odr.Model(odr_linear_definition)
#extract coordinates from list of points
x = [pointcloud.points[p][0] for p in list_of_points]
y = [pointcloud.points[p][1] for p in list_of_points]
#calculate standard errors along dimensions or something
wd = 1/(np.std(x)**2) #FIXME: I have no idea what this is
we = 1/(np.std(y)**2) #or if I did it right
#fit ODR
data = odr.Data(x, y, wd=wd, we=we)
self.odr = odr.ODR(data, model, beta0=[1., 1.])
self.odr.run()
params = self.odr.output.beta
#apply bounds for start and end point
bounds = []
for index in [-1, 0]:
m, b = params
p_x, p_y = pointcloud.points[self.points[index]]
bounds.append(self._find_closest_input_val(m, b, p_x, p_y))
bounds.sort()
#save the params in nice formats
params = {"m": params[0], "b": params[1], "low": bounds[0], "high": bounds[1]}
self.params = params
self.start_point = [params["low"], params["low"] * params["m"] + params["b"]]
self.end_point = [params["high"], params["high"] * params["m"] + params["b"]]
def fitLine(data):
start = 0
end = 0
rest = 0
listOfSpeeds = []
errors = []
frameNo = []
metEnd = False
for i in xrange(len(data) - 1):
rest += 1
frameNo.append(i)
if data[i + 1] < data[i] and metEnd == False:
start = i + 9
metEnd = True
if data[i + 1] > data[i] and rest > 10:
metEnd = False
rest = 0
end = i
x = frameNo[start:end]
y = data[start:end]
myodr = odr.ODR(odr.Data(frameNo[start:end], data[start:end]),
odr.Model(str8Line),
beta0=[-0.5, 70])
result = myodr.run()
fitLine = result.beta[0] * frameNo[start:end] + result.beta[1]
listOfSpeeds.append(result.beta[0])
errors.append(result.sd_beta[0])
return np.mean(listOfSpeeds), np.mean(errors)
def optimize_odr(self, data):
"""
Calculate the orthogonal distance regression for a dataset fitted to a circle
Parameters
----------
data: 2D array
x-y coordinates of all datapoints in all images
Returns
-------
calibration: float array
array of midpoint coordinates and respective radii
"""
self.grid = data[0][1]
self.grid_stack = np.array(list(self.grid) * len(data))
x = np.array(data)[:, 0, :].flatten()
lsc_data = odr.Data(x, y=1)
lsc_model = odr.Model(fcn=self.f_odr_multivariate,
implicit=True,
estimate=self.calc_estimate_odr_multivariate)
lsc_odr = odr.ODR(lsc_data, lsc_model)
lsc_out = lsc_odr.run()
lsc_out.pprint()
opt = lsc_out.beta
calibration = []
for i in range(len(data)):
xc = opt[i * 2]
yc = opt[i * 2 + 1]
r = opt[-1]
package = [xc, yc, r]
calibration.append(package)
return calibration
def autoCorrelation(xData,maxRange):
"""
A function to calculate the auto correlation time of a data set.
:xData: the data for which the time is found.
:maxRange: the range over which an exponential decay is fitted(=100).
"""
maxTp = maxRange # the maximum distance between values in a list, eg List[0] and List[100]
xMean = np.average(xData) # finds the mean of all values
C = np.zeros(maxTp) # numpy arrays to hold Correlation
tPr = np.zeros(maxTp) # different Correlation times, t', No of elements between values
for i in xrange(maxTp):
xLen = xData.shape[0]
runTot = 0
for j in xrange(xLen-i):
runTot+=xData[j]*xData[j+i] # checks how correlated each bit is
C[i]=(float(runTot)/float(xLen-i))
tPr[i]=(i)
C = C - xMean**2.
lnC = np.log(C)
myodr = odr.ODR(odr.Data(tPr,lnC), odr.Model(str8Line), beta0=[-1.0, -1.0])
result = myodr.run()
fitLine = result.beta[0]*tPr + result.beta[1]
#pl.plot(tPr,lnC)
#pl.plot(tPr,fitLine)
#pl.show()
correlationTime = -1.0/result.beta[0]
if np.isnan(correlationTime):return 700
return correlationTime
def autoCorrelation(xData):
maxTp = 400
xMean = np.average(xData)
C = np.zeros(maxTp)
tPr = np.zeros(maxTp)
for i in xrange(maxTp):
xLen = xData.shape[0]
runTot = 0
for j in xrange(xLen - i):
runTot += xData[j] * xData[j + i]
C[i] = (float(runTot) / float(xLen - i))
tPr[i] = (i)
C = C - xMean**2.
lnC = np.log(C)
myodr = odr.ODR(odr.Data(tPr, lnC),
odr.Model(str8Line),
beta0=[-0.00558, -1.0])
result = myodr.run()
fitLine = result.beta[0] * tPr + result.beta[1]
pl.plot(tPr, lnC)
pl.plot(tPr, fitLine)
pl.show()
correlationTime = -1.0 / result.beta[0]
print correlationTime
return correlationTime
def fit_ellipse(self,
beta_i,
num_fitting_pts=5000,
ring_width=40,
num_high_pix=20):
'''
Fit an ellipse to a ring image
==============================
beta_i - float tuple , ( x_center, y_center, x_radius, y_radius )
num_fitting_pts - int, number of pixels to include in fit
ring_width - int, width ring-like region on image that contains ring of interest (pixels units)
num_high_pix - int, remove this many pixels before running fit (removes artificial high pixels that might bias the fit)
'''
r = sqrt((self.x - beta_i[0])**2 + (self.y - beta_i[1])**2)
self.img[r > beta_i[2] + ring_width / 2] = 0
self.img[r < beta_i[2] - ring_width / 2] = 0
img1 = self.img.ravel()
self._remove_highest(img1, num_high_pix)
num_pts = where(img1 > 0)[0].shape[0]
if num_fitting_pts >= num_pts:
num_fitting_pts = num_pts / 2
inds = argsort(img1)[::-1][:num_fitting_pts]
pts = row_stack([self.x1[inds], self.y1[inds]])
lsc_data = odr.Data(pts, y=1)
lsc_odr = odr.ODR(lsc_data, self.ellipse_model, beta_i)
lsc_out = lsc_odr.run()
return lsc_out.beta
def perform_odr(x, y, sx, sy):
linear = odr.Model(f)
mydata = odr.Data(x, y, wd=1./np.power(sx,2), we=1./np.power(sy,2))
myodr = odr.ODR(mydata, linear, beta0=linreg[0:2])
output = myodr.run()
output.pprint()
return output
def odr(self, i, plot=False, eps=2):
"""Orthogonal distance regression for temporally concurrent points of overlapping time series. Uses :mod:`scipy.odr`.
:param i: the 'join' index (``0`` is the index of the join between series ``0`` and ``1`` etc.)
:param plot: whether or not to plot the given join
:param eps: the ``eps`` param to be handed down to the :meth:`.dbscan` method for outlier detection
:returns: dictionary with computed statistics, including the additive offset (key ``offs``)
:rtype: :obj:`dict`
"""
c = self.var.iloc[:, i:i + 2].dropna(0, 'any')
# outliers are detected from the differenc between the two series
diff = c.diff(1, 1).values[:, 1]
k, labels = self.dbscan(diff, True, True, eps=eps)
x, y = c.iloc[k].values.T
o = odr.ODR(odr.Data(x, y), odr.models.unilinear, beta0=[1, 0]).run()
diff = diff[k]
offs = np.nanmean(diff)
m = np.argmin(abs(diff - offs)) + np.where(k)[0].min()
self.starts[i + 1] += m
self.ends[i] = self.starts[i + 1] - 1
if plot:
fig, axs = plt.subplots(1, 2, figsize=(12, 5))
t = c.index.values.astype('datetime64[s]').astype(float).reshape(
(-1, 1))
x, y = c.values.T
for h in labels:
pl = axs[0].plot(t[h], x[h], 'x')[0]
axs[0].plot(t[h], y[h], '*', color=pl.get_color())
axs[1].plot(x[h], y[h], 'x')
axs[1].plot(o.xplus, o.y, 'r-')
axs[1].plot(x, y, 'mo', mfc='none')
axs[1].yaxis.tick_right()
plt.show()
else:
idx = c.index.symmetric_difference(c.index[k])
j = np.where(np.diff(idx) != self.delta)[0]
if len(j) > 1:
print('Complex outlier structure deteced at knot {}'.format(i))
elif len(
j
) == 1: # means there are outliers on either end of the overlap
self.out.loc[idx[:j[0] + 1], 'outliers'] = i + 1
self.out.loc[idx[j[0] + 1:], 'outliers'] = i
elif len(
idx
) > 0: # means there are outliers only in one of the two series
self.out.loc[idx, 'outliers'] = i + int(idx[0] == c.index[0])
return {
'offs': offs,
'kind': 'mean',
'stdev': diff.std() / np.sqrt(len(diff)),
'odr_slope': o.beta[0],
'odr_offs': o.beta[1],
'RSS1': np.mean(o.delta**2),
'RSS2': np.mean(o.eps**2),
}
def fit_circle(points):
"""
fits a circle to the given points. The method has been adapted from
http://wiki.scipy.org/Cookbook/Least_Squares_Circle
The function returns an instance of Circle
"""
def calc_dist(xc, yc):
""" calculate the distance of each point from the center (xc, yc) """
return np.linalg.norm(points - np.array([[xc, yc]]), axis=0)
def circle_implicit(beta, x):
""" implicit definition of the circle """
return (x[0] - beta[0])**2 + (x[1] - beta[1])**2 - beta[2]**2
# coordinates of the bary center
x_m, y_m = np.mean(points, axis=0)
# initial guess for parameters
R_m = calc_dist(x_m, y_m).mean()
beta0 = [x_m, y_m, R_m]
# for implicit function :
# data.x contains both coordinates of the points (data.x = [x, y])
# data.y is the dimensionality of the response
lsc_data = odr.Data(points.T, y=1)
lsc_model = odr.Model(circle_implicit, implicit=True)
lsc_odr = odr.ODR(lsc_data, lsc_model, beta0)
lsc_out = lsc_odr.run()
# collect result
xc, yc, R = lsc_out.beta
return shapes.Circle(xc, yc, R)
def fiting_test():
a = 2.
b = 3.
N = 10
x = np.linspace(-a, a, N)
y = b * np.sqrt(1. - (x / a)**2)
x += (2. * np.random.random(N) - 1.) * 0.1
y += (2. * np.random.random(N) - 1.) * 0.1
xx = np.array([x, y])
mdr = odr.Model(f, implicit=True)
mydata = odr.Data(xx, y=1)
myodr = odr.ODR(mydata, mdr, beta0=[1., 2.])
myoutput = myodr.run()
myoutput.pprint()
ax = plt.subplot(111, aspect='equal')
plt.scatter(x, y) # raw data with randomness
ell = Ellipse(xy=(0., 0.),
width=2. * myoutput.beta[0],
height=2. * myoutput.beta[1],
angle=0.0)
ell.set_facecolor('none')
ax.add_artist(ell) # fitted curve
plt.show()
def fit_circle(x, y):
x_m = np.mean(x)
y_m = np.mean(y)
def calc_R(xc, yc):
""" calculate the distance of each 2D points from the center (xc, yc) """
return np.sqrt((x - xc)**2 + (y - yc)**2)
def f_3(beta, x):
""" implicit definition of the circle """
return (x[0] - beta[0])**2 + (x[1] - beta[1])**2 - beta[2]**2
# initial guess for parameters
R_m = calc_R(x_m, y_m).mean()
beta0 = [x_m, y_m, R_m]
# for implicit function :
# data.x contains both coordinates of the points (data.x = [x, y])
# data.y is the dimensionality of the response
lsc_data = odr.Data(np.row_stack([x, y]), y=1)
lsc_model = odr.Model(f_3, implicit=True)
lsc_odr = odr.ODR(lsc_data, lsc_model, beta0)
lsc_out = lsc_odr.run()
xc_3, yc_3, R_3 = lsc_out.beta
Ri_3 = calc_R(xc_3, yc_3)
residu_3 = sum((Ri_3 - R_3)**2)
return xc_3, yc_3, R_3, residu_3
def fit_odr(data, correlant, odr_function, poly_order, weights):
if weights == 'relative':
std = 0.1
mydata = _odr.RealData(
data, correlant, sx=data * std, sy=correlant *
std) # , wd=1. / self.sx ** 2, we=1. / self.sy ** 2)
elif weights == 'absolute':
sx, sy = (1, 1)
mydata = _odr.Data(data,
correlant,
wd=1. / sx**2,
we=1. / sy**2)
else:
raise ValueError('weights has to be scalar or absolute')
if odr_function != 'linear':
raise (
'only "linear" allowed at this point, programming required!'
)
model = _odr.polynomial(poly_order)
myodr = _odr.ODR(mydata, model)
myoutput = myodr.run()
odr_res = {
'model': myodr,
'output': myoutput,
'function': _np.polynomial.Polynomial(myoutput.beta)
}
return odr_res
def perform_odr(x, y, xerr, yerr):
quadr = odr.Model(odr_line)
mydata = odr.Data(x, y, wd=1. / xerr, we=1. / yerr)
#mydata = odr.Data(x, y)
myodr = odr.ODR(mydata, quadr, beta0=[0., 0.])
output = myodr.run()
return output
def _fit_a_model(self, model, param_guess):
# use odr module to fit data to model
self.pts = np.row_stack( [self.x1D[ self.fit_indices],
self.y1D[ self.fit_indices]])
lsc_data = odr.Data( self.pts , y=1)
lsc_odr = odr.ODR( lsc_data, model, param_guess)
lsc_out = lsc_odr.run()
self.beta_fit = lsc_out.beta
def getOutput(xa, ya):
def f(B, x):
return B[0]*x+B[1]
linear = odr.Model(f)
mydata = odr.Data(xa, ya)
myodr = odr.ODR(mydata, linear, beta0=[1., 10.])
myoutput = myodr.run()
return myoutput
def lin_fit(self, C):
''' Perform orthogonal linear regression on this Cluster.
The slope and intercept are stored as a tuple in the field <linear>'''
linear_fit = odr.Model(lin_func)
data = odr.Data(C * self.t_co, self.v_co) # y-axis is frequency
odr_inst = odr.ODR(data, linear_fit, beta0=[0.0, self.v_mean])
output = odr_inst.run()
(slope, intercept) = output.beta[0], output.beta[1]
self.linear = (C * slope, intercept)
def gap_filler(x, y, R, center, fill_density=0.1):
"""
Returns N points to fill in a gap
Parameters
----------
x: sequence
x = (x_left, x_right)
y: sequence
y = (y_left, y_right)
R: float
initial guess at average radius
center: `np.ndarray`
initial guess at the center of the ellipse
N: int
The number of points to return, defaults to 15
Returns: `np.ndarray`
A 2xN `np.ndarray` [x_vals, y_vals]
"""
xl, xr = x
yl, yr = y
R2 = R * R
a = c = 1 / R2
b = 0
d = -center[0] / R2
f = -center[1] / R2
p0 = (a, b, c, d, f)
data = sodr.Data((np.hstack(x), np.hstack(y)), 1)
model = sodr.Model(_e_funx, implicit=1)
worker = sodr.ODR(data, model, p0)
out = worker.run()
#out = worker.restart()
ap, bp, t0, x0, y0 = gen_to_parm(out.beta)
if np.any(np.isnan([ap, bp, t0, x0, y0])):
# print out.beta
# print ap, bp, t0, x0, y0
raise EllipseException('parameters contain NaN')
theta_start = np.mod(np.arctan2(yl[-1] - y0, xl[-1] - x0), 2 * np.pi)
theta_end = np.mod(np.arctan2(yr[0] - y0, xr[0] - x0), 2 * np.pi)
if theta_end < theta_start:
theta_end += 2 * np.pi
N = int((theta_end - theta_start) * fill_density * (ap + bp) / 2)
# print theta_start, theta_end, (ap + bp) / 2, N
if N < 1:
print('gap_filler: under fill')
N = 1
theta_list = np.linspace(theta_start, theta_end, N + 2)[1:-1]
return gen_ellipse(ap, bp, t0, x0, y0, theta_list)
def autoCorrelation(xData, maxRange, plot, col):
"""
A function to calculate the auto correlation time of a data set.
:xData: the data for which the time is found.
:maxRange: the range over which an exponential decay is fitted(=100).
"""
maxTp = maxRange # the maximum distance between values in a list, eg List[0] and List[100]
xMean = np.average(xData) # finds the mean of all values
C = np.zeros(maxTp) # numpy arrays to hold Correlation
tPr = np.zeros(
maxTp
) # different Correlation times, t', No of elements between values
for i in xrange(maxTp):
xLen = xData.shape[0]
runTot = 0
for j in xrange(xLen - i):
runTot += xData[j] * xData[j +
i] # checks how correlated each bit is
C[i] = (float(runTot) / float(xLen - i))
tPr[i] = (i)
C = C - xMean**2.
lnC = np.log(np.absolute(C))
myodr = odr.ODR(odr.Data(tPr, lnC),
odr.Model(str8Line),
beta0=[-0.00558, -1.0])
print myodr.beta0
result = myodr.run()
print result.beta
print result.sd_beta
print result.sd_beta / (result.beta**2.0)
chisq = result.res_var
print chisq
if chisq < 0.001: chisq = 1.09
fitLine = result.beta[0] * tPr + result.beta[1]
correlationTime = -1.0 / result.beta[0]
axarr[plot].plot(tPr,
lnC,
color=col,
label="t*={:.1f}".format(correlationTime))
axarr[plot].plot(tPr,
fitLine,
"k--",
label=("$\chi^{2}$=" + "{:.2f}".format(chisq)),
linewidth=3)
axarr[plot].legend(loc="best")
return correlationTime
def fit_odr(self, p0):
from scipy import odr
model = odr.Model(self.func)
data = odr.Data(self._xdata, self._ydata)
fit = odr.ODR(data, model, p0, maxit=100)
fit.set_job(fit_type=0) #0 = LSQ, 1 = EXPlicit
out = fit.run()
self._fit_params = out.beta
self._fit_err = out.sd_beta
return self._fit_params
def _fit_a_model_fast(self, model, param_guess):
# use odr module to fit data to model
self.pts = np.row_stack( [self.x1D[ self.fit_indices],
self.y1D[ self.fit_indices]])
lsc_data = odr.Data( self.pts , y=1)
lsc_odr = odr.ODR(lsc_data, model)# param_guess)
lsc_odr.set_job(deriv=3)
lsc_odr.set_iprint(iter=1, iter_step=1)
lsc_out = lsc_odr.run()
self.beta_fit = lsc_out.beta
def linear_fit(x, y, xerr=None, yerr=None):
from scipy import odr
linear = odr.Model(f)
if xerr == None: xerr = np.ones(len(x))
if yerr == None: yerr = np.ones(len(y))
for i, e in enumerate(yerr):
if e == 0: yerr[i] = 1
mydata = odr.Data(x, y, wd=1 / xerr, we=1 / yerr)
myodr = odr.ODR(mydata, linear, beta0=[-1., 0.])
myoutput = myodr.run()
return (myoutput.beta[0], myoutput.beta[1], myoutput.sd_beta[0],
myoutput.sd_beta[1])
def DM_fit(self, tstart, v_max_index):
''' Perform orthogonal DM (inverse square) regression on this Cluster.
The fitted DM value is stored in the field <DM>.'''
# Note: frequency axis is flipped, because high freqs correspond to low array indices
t_co = (self.t_co * tsamp * dt) + tstart
v_co = ((v_max_index - self.v_co) * vsamp * dv) + vlow
#print(DM_func([560.0*kDM], v_co, t_co[0], v_co[0]))
data = odr.Data(v_co, t_co) # y-axis is time
DM_mod = odr.Model(DM_func, extra_args=(t_co[0], v_co[0]))
# Note: beta0 is initial estimate of DM*kDM
odr_inst = odr.ODR(data, DM_mod, beta0=[560.0 * kDM])
output = odr_inst.run()
self.DM = output.beta[0] / kDM
def OrthReg(self, Deg=1):
"""
Orthogonal regressiong of a polynomial of
arbitrary degree.
"""
B0 = np.ones(Deg+1)
PF = odr.Model(PolyFun)
if (self.Xw.all() == 0) and (self.Yw.all() == 0):
Data = odr.Data(self.X, self.Y)
else:
Wx = 1./np.power(self.Xw,2)
Wy = 1./np.power(self.Yw,2)
Data = odr.Data(self.X, self.Y, Wx, Wy)
Out = odr.ODR(Data, PF, beta0=B0)
Out.run()
self.B = Out.output.beta
self.E = Out.output.sd_beta
def faceON(table):
index, = np.where(table['flag']>0)
table0 = trim(table, index)
index, = np.where(table0['flag']<3)
table0 = trim(table0, index)
#### for test not face-on
###index, = np.where(table['Sqlt']>3)
###table0 = trim(table, index)
###index, = np.where(table0['Wqlt']>3)
###table0 = trim(table0, index)
###index, = np.where(table0['flag']==0)
###table0 = trim(table0, index)
###index, = np.where(table0['inc']>80)
###table0 = trim(table0, index)
###index, = np.where(table0['inc']<90)
###table0 = trim(table0, index)
#### end test
logWimx = table0['logWimx']
r_w1 = table0['r_w1']
c21w = table0['c21w']
Ec21w = table0['Ec21w']
AB, cov = np.polyfit(logWimx,r_w1, 1, cov=True, full = False)
a0, b0 = AB[0],AB[1]
a = 1./a0
b = -1.*b0/a0
print "AB: ", a0, b0
print "Covariance AB: ", cov
delta = r_w1-(a0*logWimx+b0)
a, b, c = np.polyfit(c21w,delta, 2)
x = c21w
y = delta
mydata = odr.Data(x, y, wd=Ec21w, we=delta*0.+0.1)
F = odr.Model(Fdelta)
myodr = odr.ODR(mydata, F, beta0=[a,b,c])
myoutput = myodr.run()
print "Delta: ", myoutput.beta
print"Std Error Delta: ", myoutput.sd_beta
return [a0,b0], myoutput.beta, table0, cov, myoutput.sd_beta
def TLS_regresssion(stock_1, stock_2):
def f(B, x):
'''Linear function y = m*x + b'''
# B is a vector of the parameters.
# x is an array of the current x values.
# x is in the same format as the x passed to Data or RealData.
# Return an array in the same format as y passed to Data or RealData.
return B[0] * x + B[1]
linear_model = odr.Model(f)
used_data = odr.Data(stock_1, stock_2)
TLS_regression_model = odr.ODR(used_data, linear_model, beta0=[1., 2.])
result = TLS_regression_model.run()
return result
def reldist_odr(x, y):
import scipy.odr as odr
def f(B, xx):
return B[0] * xx + B[1]
linear = odr.Model(f)
data = odr.Data(x, y, wd=1, we=1)
res = odr.ODR(data, linear, beta0=[.4, .0])
res = res.run()
b = res.beta[0]
b = np.array([b, 1 / b])[np.argmin(np.abs([b, 1 / b]))]
# print reldist_type2(x,y),b
return b
def fit_circle(arc_contour):
"""
Fit the circle with feeding points
Algorithm from scipy-cookbook: http://scipy-cookbook.readthedocs.io/items/Least_Squares_Circle.html
:param arc_contour:
:return: (x, y, r)
"""
from scipy import odr
x = np.array([i[0][0] for i in arc_contour])
y = np.array([i[0][1] for i in arc_contour])
def calc_R(c):
""" calculate the distance of each 2D points from the center c=(xc, yc) """
return np.sqrt((x - c[0])**2 + (y - c[1])**2)
def circlemodel(beta, x):
""" implicit function of the circle """
xc, yc, r = beta
return (x[0] - xc)**2 + (x[1] - yc)**2 - r**2
def calc_estimate(data):
""" Return a first estimation on the parameter from the data """
xc0, yc0 = data.x.mean(axis=1)
r0 = np.sqrt((data.x[0] - xc0)**2 + (data.x[1] - yc0)**2).mean()
return xc0, yc0, r0
# for implicit function :
# data.x contains both coordinates of the points
# data.y is the dimensionality of the response
lsc_data = odr.Data(np.row_stack([x, y]), y=1)
lsc_model = odr.Model(circlemodel,
implicit=True,
estimate=calc_estimate)
lsc_odr = odr.ODR(lsc_data, lsc_model)
lsc_out = lsc_odr.run()
xc_3, yc_3, R_3 = lsc_out.beta
print('lsc_out.sum_square = ', lsc_out.sum_square)
# Ri_3 = calc_R([xc_3, yc_3])
# residu_3 = sum((Ri_3 - R_3) ** 2)
# residu2_3 = sum((Ri_3 ** 2 - R_3 ** 2) ** 2)
# print('residu_3 :', residu_3 )
# print('residu2_3 :', residu2_3)
return xc_3, yc_3, R_3
def __init__(self, x, y, xerr=None, yerr=None):
self.n = len(x)
self.data = odr.Data(x, y, wd=xerr, we=yerr)
self.odr = odr.ODR(self.data, odr.unilinear).run()
self.beta = self.odr.beta
self.cov_beta = self.odr.cov_beta
self.stderr_beta = self.odr.sd_beta
self.xhat = np.sort(x)
self.yhat = self.predict(self.xhat)
self.r2 = self._calc_r2()
self.rmse = self._calc_rmse()
self.pval = self._calc_pval()
def findCurvatureR(x, y):
# for implicit function :
# data.x contains both coordinates of the points
# data.y is the dimensionality of the response
lsc_data = odr.Data(np.row_stack([x, y]), y=1)
lsc_model = odr.Model(f_3, implicit=True, estimate=calc_estimate)
lsc_odr = odr.ODR(lsc_data, lsc_model)
lsc_out = lsc_odr.run()
xc_3, yc_3, R_3 = lsc_out.beta
Ri_3 = calc_R([xc_3, yc_3], x, y)
residu_3 = sum((Ri_3 - R_3)**2)
residu2_3 = sum((Ri_3**2 - R_3**2)**2)
#ncalls_3 = f_3.ncalls
#print ('lsc_out.sum_square = ',lsc_out.sum_square)
return ([xc_3, yc_3, R_3])