def interpolate(x, y, half_window=10):
perm = flex.sort_permutation(x)
x = x.select(perm)
y = y.select(perm)
x_all = flex.double()
y_all = flex.double()
for i in range(x.size()):
x_all.append(x[i])
y_all.append(y[i])
if i < x.size()-1 and (x[i+1] - x[i]) > 1:
window_left = min(half_window, i)
window_right = min(half_window, x.size() - i)
x_ = x[i-window_left:i+window_right]
y_ = y[i-window_left:i+window_right]
from scitbx.math import curve_fitting
# fit a 2nd order polynomial through the missing points
polynomial = curve_fitting.univariate_polynomial(1, 1)
fit = curve_fitting.lbfgs_minimiser([polynomial], x_,y_).functions[0]
missing_x = flex.double(range(int(x[i]+1), int(x[i+1])))
x_all.extend(missing_x)
y_all.extend(fit(missing_x))
perm = flex.sort_permutation(x_all)
x_all = x_all.select(perm)
y_all = y_all.select(perm)
return x_all, y_all
def log_fit(x, y, degree=5):
"""Fit the values log(y(x)) then return exp() to this fit.
x, y should be iterables containing floats of the same size. The order is the order
of polynomial to use for this fit. This will be useful for e.g. I/sigma."""
fit = curve_fitting.univariate_polynomial_fit(
x, flex.log(y), degree=degree, max_iterations=100
)
f = curve_fitting.univariate_polynomial(*fit.params)
return flex.exp(f(x))
def log_inv_fit(x, y, degree=5):
"""Fit the values log(1 / y(x)) then return the inverse of this fit.
x, y should be iterables, the order of the polynomial for the transformed
fit needs to be specified. This will be useful for e.g. Rmerge."""
fit = curve_fitting.univariate_polynomial_fit(
x, flex.log(1 / y), degree=degree, max_iterations=100
)
f = curve_fitting.univariate_polynomial(*fit.params)
return 1 / flex.exp(f(x))
def polynomial_fit(x, y, degree=5):
"""
Fit a polynomial to the values y(x) and return this fit
x, y should be iterables containing floats of the same size. The order is the order
of polynomial to use for this fit. This will be useful for e.g. I/sigma.
"""
fit = curve_fitting.univariate_polynomial_fit(
x, y, degree=degree, max_iterations=100
)
f = curve_fitting.univariate_polynomial(*fit.params)
return f(x)
def exercise_polynomial_fit():
def do_polynomial_fit(x, params):
n_terms = len(params)
y = flex.double(x.size())
for i in range(len(params)):
y += params[i] * flex.pow(x, i)
fit = curve_fitting.univariate_polynomial_fit(x, y, degree=n_terms - 1)
assert approx_equal(params, fit.params, eps=1e-4)
x = flex.double(range(-50, 50))
do_polynomial_fit(x, (2, 3, 5)) # y = 2 + 3x + 5x^2
do_polynomial_fit(x, (-0.0002, -1000)) # y = -0.0002 -1000x
for n_terms in range(1, 6):
params = [100 * random.random() for i in range(n_terms)]
x = flex.double(
frange(-random.randint(1, 10), random.randint(1, 10), 0.1))
functor = curve_fitting.univariate_polynomial(*params)
fd_grads = finite_differences(functor, x)
assert approx_equal(functor.partial_derivatives(x), fd_grads, 1e-4)
do_polynomial_fit(x, params)
def exercise_polynomial_fit():
def do_polynomial_fit(x, params):
n_terms = len(params)
y = flex.double(x.size())
for i in range(len(params)):
y += params[i] * flex.pow(x, i)
fit = curve_fitting.univariate_polynomial_fit(x, y, degree=n_terms-1)
assert approx_equal(params, fit.params, eps=1e-4)
x = flex.double(range(-50,50))
do_polynomial_fit(x, (2,3,5)) # y = 2 + 3x + 5x^2
do_polynomial_fit(x, (-0.0002, -1000)) # y = -0.0002 -1000x
for n_terms in range(1, 6):
params = [100*random.random() for i in range(n_terms)]
x = flex.double(frange(-random.randint(1,10), random.randint(1,10), 0.1))
functor = curve_fitting.univariate_polynomial(*params)
fd_grads = finite_differences(functor, x)
assert approx_equal(functor.partial_derivatives(x), fd_grads, 1e-4)
do_polynomial_fit(x, params)
