def hessian_compute_fit_old(self, lm_lambda=None):
"take one Hessian fitting step if lm_lambda undefined, otherwise make Levenberg-Marquardt adjustment"
if hasattr(self, 'fitmat'):
del self.fitmat
# if we are recycing, thoroughly clean up possibly huge objects
self.collect()
n = self.pointcount
fxarray = self.derivs()
self.set_weights()
fxwarray = self.weights_multiply(Numeric.transpose(fxarray))
self.fitmat = dot(fxwarray, fxarray)
# make Levenberg-Marquardt correction to inverse-covariance matrix
if lm_lambda is not None:
for i in range(self.param_count):
self.fitmat[i, i] *= (1.0 + lm_lambda)
for i in range(self.param_count): # handle frozen parameters
if self.frozen[i]:
self.fitmat[i, :] = 0.0
self.fitmat[:, i] = 0.0
self.fitmat[i, i] = 1.0
if (self.firstpass):
self.funcvals = self.compute_funcvals()
self.firstpass = 0
self.fitvector = solve_linear_equations(
self.fitmat, dot(fxwarray, self.yarray[:n] - self.funcvals))
self.funcparams = self.funcparams + self.fitvector * (1 - self.frozen)
self.funcvals = self.compute_funcvals()
self.compute_chi2()
def hessian_compute_fit(self, lm_lambda=None): "take one Hessian fitting step if lm_lambda undefined, otherwise make Levenberg-Marquardt adjustment" if hasattr(self, 'fitmat'): del self.fitmat self.collect() #if we are recycing, thoroughly clean up possibly huge objects n=self.pointcount fxarray=self.derivs() self.set_weights() fxwarray=self.weights_multiply(Numeric.transpose(fxarray)) self.fitmat=dot(fxwarray, fxarray) if lm_lambda is not None: #make Levenberg-Marquardt correction to inverse-covariance matrix for i in range(self.param_count): self.fitmat[i,i]*=(1.0+lm_lambda) for i in range(self.param_count): #handle frozen parameters if self.frozen[i]: self.fitmat[i,:]=0.0 self.fitmat[:,i]=0.0 self.fitmat[i,i]=1.0 if(self.firstpass): self.funcvals=self.compute_funcvals() self.firstpass=0 self.fitvector=solve_linear_equations(self.fitmat, dot(fxwarray, self.yarray[:n]-self.funcvals) ) self.funcparams=self.funcparams+self.fitvector*(1-self.frozen) self.funcvals=self.compute_funcvals() self.compute_chi2()
def lowess(x, y, f=2./3., iter=3):
"""lowess(x, y, f=2./3., iter=3) -> yest
Lowess smoother: Robust locally weighted regression.
The lowess function fits a nonparametric regression curve to a scatterplot.
The arrays x and y contain an equal number of elements; each pair
(x[i], y[i]) defines a data point in the scatterplot. The function returns
the estimated (smooth) values of y.
The smoothing span is given by f. A larger value for f will result in a
smoother curve. The number of robustifying iterations is given by iter. The
function will run faster with a smaller number of iterations."""
n = len(x)
r = int(ceil(f*n))
h = [sort(abs(x-x[i]))[r] for i in range(n)]
w = clip(abs(([x]-transpose([x]))/h),0.0,1.0)
w = 1-w*w*w
w = w*w*w
yest = zeros(n,'d')
delta = ones(n,'d')
for iteration in range(iter):
for i in range(n):
weights = delta * w[:,i]
b = array([sum(weights*y), sum(weights*y*x)])
A = array([[sum(weights), sum(weights*x)],
[sum(weights*x), sum(weights*x*x)]])
beta = solve_linear_equations(A,b)
yest[i] = beta[0] + beta[1]*x[i]
residuals = y-yest
s = median(abs(residuals))
delta = clip(residuals/(6*s),-1,1)
delta = 1-delta*delta
delta = delta*delta
return yest
def hessian_compute_fit(self, lm_lambda=None):
"take one Hessian fitting step if lm_lambda undefined, otherwise make Levenberg-Marquardt adjustment"
if hasattr(self, 'fitmat'):
del self.fitmat
# if we are recycing, thoroughly clean up possibly huge objects
self.collect()
n = self.pointcount
fxarray = self.derivs()
self.set_weights()
fxwarray = self.weights_multiply(Numeric.transpose(fxarray))
self.fitmat = dot(fxwarray, fxarray)
# make Levenberg-Marquardt correction to inverse-covariance matrix
if lm_lambda is not None:
for i in range(self.param_count):
self.fitmat[i, i] *= (1.0 + lm_lambda)
for i in range(self.param_count): # handle frozen parameters
if self.frozen[i]:
self.fitmat[i, :] = 0.0
self.fitmat[:, i] = 0.0
self.fitmat[i, i] = 1.0
mask = 1 - self.frozen
# compress out rows & columns of frozen parameters, to make fit much faster
if numpy.any(self.frozen):
fitmat = self.fitmat.compress(mask, 0).compress(mask, 1)
else:
fitmat = self.fitmat
if self.firstpass:
self.funcvals = self.compute_funcvals()
self.firstpass = 0
# compress corresponding elements out of the 'y' array
yarray = dot(fxwarray, self.yarray[:n] - self.funcvals).compress(mask)
fitvector = solve_linear_equations(fitmat, yarray)
fullfit = Numeric.zeros_like(self.funcparams)
# uncompress fit vector
idx = 0
for i in xrange(self.param_count):
if mask[i]:
fullfit[i] = fitvector[idx]
idx += 1
self.funcparams = self.funcparams + fullfit * (1 - self.frozen)
self.funcvals = self.compute_funcvals()
self.compute_chi2()
def hessian_compute_fit(self, lm_lambda=None):
"take one Hessian fitting step if lm_lambda undefined, otherwise make Levenberg-Marquardt adjustment"
if hasattr(self, 'fitmat'):
del self.fitmat
# if we are recycing, thoroughly clean up possibly huge objects
self.collect()
n = self.pointcount
fxarray = self.derivs()
self.set_weights()
fxwarray = self.weights_multiply(Numeric.transpose(fxarray))
self.fitmat = dot(fxwarray, fxarray)
# make Levenberg-Marquardt correction to inverse-covariance matrix
if lm_lambda is not None:
for i in range(self.param_count):
self.fitmat[i, i] *= (1.0 + lm_lambda)
for i in range(self.param_count): # handle frozen parameters
if self.frozen[i]:
self.fitmat[i, :] = 0.0
self.fitmat[:, i] = 0.0
self.fitmat[i, i] = 1.0
mask = 1 - self.frozen
# compress out rows & columns of frozen parameters, to make fit much faster
if numpy.any(self.frozen):
fitmat = self.fitmat.compress(mask, 0).compress(mask, 1)
else:
fitmat = self.fitmat
if self.firstpass:
self.funcvals = self.compute_funcvals()
self.firstpass = 0
# compress corresponding elements out of the 'y' array
yarray = dot(fxwarray, self.yarray[:n] - self.funcvals).compress(mask)
fitvector = solve_linear_equations(fitmat, yarray)
fullfit = Numeric.zeros_like(self.funcparams)
# uncompress fit vector
idx = 0
for i in xrange(self.param_count):
if mask[i]:
fullfit[i] = fitvector[idx]
idx += 1
self.funcparams = self.funcparams + fullfit * (1 - self.frozen)
self.funcvals = self.compute_funcvals()
self.compute_chi2()
def planepoint(v, i, j, k):
mat = V(polyMat[i], polyMat[j], polyMat[k])
vec = V(v[i], v[j], v[k])
return solve_linear_equations(mat, vec)
def CoordinatesFromCartesianCoordinates(self, coordinates):
from LinearAlgebra import solve_linear_equations
return solve_linear_equations(transpose(self.GetBasis()),
asarray(coordinates))
def planepoint(v,i,j,k):
mat = V(polyMat[i],polyMat[j],polyMat[k])
vec = V(v[i],v[j],v[k])
return solve_linear_equations(mat, vec)
def CoordinatesFromCartesianCoordinates(self,coordinates): from LinearAlgebra import solve_linear_equations return solve_linear_equations(transpose(self.GetBasis()),asarray(coordinates))
