def tanh_fit(x, y, iqr_multiplier=None):
from scitbx.math import curve_fitting
tf = curve_fitting.tanh_fit(x, y)
f = curve_fitting.tanh(*tf.params)
if iqr_multiplier is not None:
assert iqr_multiplier > 0
yc = f(x)
dy = y - yc
from scitbx.math import five_number_summary
min_x, q1_x, med_x, q3_x, max_x = five_number_summary(dy)
iqr_x = q3_x - q1_x
cut_x = iqr_multiplier * iqr_x
outliers = (dy > q3_x + cut_x) | (dy < q1_x - cut_x)
if outliers.count(True) > 0:
xo = x.select(~outliers)
yo = y.select(~outliers)
tf = curve_fitting.tanh_fit(xo, yo)
f = curve_fitting.tanh(*tf.params)
return f(x)
def tanh_fit(x, y, iqr_multiplier=None):
"""
Fit a tanh function to the values y(x) and return this fit
x, y should be iterables containing floats of the same size. This is used for
fitting a curve to CC½.
"""
tf = curve_fitting.tanh_fit(x, y)
f = curve_fitting.tanh(*tf.params)
if iqr_multiplier:
assert iqr_multiplier > 0
yc = f(x)
dy = y - yc
min_x, q1_x, med_x, q3_x, max_x = five_number_summary(dy)
iqr_x = q3_x - q1_x
cut_x = iqr_multiplier * iqr_x
outliers = (dy > q3_x + cut_x) | (dy < q1_x - cut_x)
if outliers.count(True) > 0:
xo = x.select(~outliers)
yo = y.select(~outliers)
tf = curve_fitting.tanh_fit(xo, yo)
f = curve_fitting.tanh(*tf.params)
return f(x)
def exercise_tanh_fit():
# Curve fitting as used by Aimless for fitting CC1/2 plot:
# Curve fitting as suggested by Ed Pozharski to a tanh function
# of the form (1/2)(1 - tanh(z)) where z = (s - d0)/r,
# s = 1/d^2, d0 is the value of s at the half-falloff value, and r controls
# the steepness of falloff
d = flex.double(
[2.71, 2.15, 1.88, 1.71, 1.59, 1.49, 1.42, 1.36, 1.31, 1.26])
x_obs = 1 / d**2
y_obs = flex.double(
[0.999, 0.996, 0.993, 0.984, 0.972, 0.948, 0.910, 0.833, 0.732, 0.685])
fit = curve_fitting.tanh_fit(x_obs, y_obs, r=1, s0=1)
r, s0 = fit.params
f = curve_fitting.tanh(r, s0)
y_calc = flex.double(f(x_obs))
residual = flex.sum(flex.pow2(y_obs - y_calc))
assert approx_equal(residual, 0.0023272873437026106)
assert approx_equal(fit.params, (0.17930695756689238, 0.6901032957705017))