def Smooth(x,y): """return: smoothed funciton s(x) and estimation of sigma of y for one data point""" #define segments to do spline smoothing t=np.linspace(0,len(x),3)[1:-1] sr = LSQUnivariateSpline(x, y.real, t) si = LSQUnivariateSpline(x, y.imag, t) return sr(x)+si(x)*1j, (sr.get_residual()/len(x))**0.5+(si.get_residual()/len(x))**0.5*1j
def Smooth(x,y): """return: smoothed funciton s(x) and estimation of sigma of y for one data point""" #define segments to do spline smoothing t=np.linspace(0,len(x),3)[1:-1] sr = LSQUnivariateSpline(x, y.real, t) si = LSQUnivariateSpline(x, y.imag, t) return sr(x)+si(x)*1j, (sr.get_residual()/len(x))**0.5+(si.get_residual()/len(x))**0.5*1j
def fun_residuals(params, xnor, ynor, w, bbox, k, ext): """Compute fit residuals""" spl = LSQUnivariateSpline(x=xnor, y=ynor, t=[item.value for item in params.values()], w=w, bbox=bbox, k=k, ext=ext, check_finite=False) return spl.get_residual()
def pval(self, index): ### In practice we'd implement some actual error scheme for this knotsDel = np.delete(self.knots, index) interpDel = LSQUnivariateSpline(self.x, self.y, knotsDel, k=1, w=self.weights) resid = self.interp.get_residual() residDel = interpDel.get_residual() dof = len(self.x) - len( self.knots ) - 2 # -2 because there are 2 parameters in a 1-knot k=1 fit. dofdel = dof + 1 if dof == 0: self.knotPvals[index] = -np.inf else: self.knotPvals[index] = abs(residDel / dofdel - 1) - abs(resid / dof - 1) print(self.knotPvals[index], resid / dof, residDel / dofdel, resid, dof)
class fitfunc: def __init__(self, x, y, errors=None): if errors is not None: self.errors = errors else: grad = np.gradient(y) ms = grad**2 ms2 = np.zeros(len(ms) + 4) ms2[0] = ms[0] ms2[1] = ms[0] ms2[2:-2] = ms ms2[-2] = ms[-1] ms2[-1] = ms[-1] ms = ms2 ms = np.convolve(ms, np.ones((5, )) / 5, mode='valid') ms /= 2 # Correction for difference of uncorrelated errors self.errors = np.sqrt(ms) self.errors = np.copy(np.sqrt(np.abs(y))) self.weights = self.errors**2 # Save inputs and enforce sorting along x inds = np.argsort(x) self.x = np.copy(x)[inds] + 1e-10 * np.array(range( len(x))) # This prevents duplicates in x self.y = np.copy(y)[inds] # Setup knots self.knots = np.copy(self.x[1:-1]) self.knotInd = np.array(range(len(self.knots))) self.knotPvals = None # Iteratively fit and remove knots self.interp = None self.fit() self.pvals() done = False while not done and len(self.knots) > 2: choice = np.random.choice(range(len(self.knots)), len(self.knots), replace=False) for i in choice: if self.knotPvals[i] < 0: self.removeKnot(i) self.fit() self.pvals() break else: done = True self.interpDeriv = self.interp.derivative(1) print('Converged with ', len(self.knots), 'knots.') print(self.knotPvals, self.interp.get_residual()) def fit(self): self.knotPvals = np.zeros(len(self.knots)) self.interp = LSQUnivariateSpline(self.x, self.y, self.knots, k=1, w=self.weights) def pvals(self): for i in range(len(self.knots)): self.pval(i) def pval(self, index): ### In practice we'd implement some actual error scheme for this knotsDel = np.delete(self.knots, index) interpDel = LSQUnivariateSpline(self.x, self.y, knotsDel, k=1, w=self.weights) resid = self.interp.get_residual() residDel = interpDel.get_residual() dof = len(self.x) - len( self.knots ) - 2 # -2 because there are 2 parameters in a 1-knot k=1 fit. dofdel = dof + 1 if dof == 0: self.knotPvals[index] = -np.inf else: self.knotPvals[index] = abs(residDel / dofdel - 1) - abs(resid / dof - 1) print(self.knotPvals[index], resid / dof, residDel / dofdel, resid, dof) def removeKnot(self, index): # Note that index can be a list of indices, or even # a smart-indexing tool. self.knots = np.delete(self.knots, index) self.knotInd = np.delete(self.knotInd, index) self.slope = None self.intercept = None self.knotPvals = None def evalY(self, x): return self.interp(x) def evalDeriv(self, x): return self.interpDeriv(x)