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dna_paint_data_fitting.py
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dna_paint_data_fitting.py
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"""
dna_paint_data_fitting.py
Library of functions for fitting model relative position distributions (RPDs)
to relative positions obtained from localisations appearing to be arranged
on a relatively simple geometric pattern, i.e. polyhedra.
Created on Mon Jul 29 15:41:31 2019
Alistair Curd
University of Leeds
30 July 2018
Software Engineering practices applied
Joanna Leng (an EPSRC funded Research Software Engineering Fellow (EP/R025819/1)
University of Leeds
January 2019
---
Copyright 2018 Peckham Lab
Licensed under the Apache License, Version 2.0 (the "License"); you may not use
this file except in compliance with the License. You may obtain a copy of the
License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software distributed
under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR
CONDITIONS OF ANY KIND, either express or implied. See the License for the
specific language governing permissions and limitations under the License.
"""
from scipy.optimize import curve_fit
import numpy as np
import matplotlib.pyplot as plt
import polyhedramodelling as poly
import modelstats as stats
import modelling_general as models
from modelling_general import ModelWithFitSettings
from modelling_general import stdev_of_model
def create_default_fitting_params_dicts():
"""Create lists for initial guesses and bounds for parameters during
fitting. Sets the defaults for scipy.optimise.curve_fit
Returns:
lower_bound_dict (dict):
Dictionary of default lower bound options for parameter values.
upper_bound_dict (dict):
Dictionary of default upper bound options for parameter values.
initial_params_dict (dict):
Dictionary of default initial parameter value options.
"""
lower_bound_dict = {'side_1': 0,
'side_2': 0,
'side_3': 0,
'loc_prec_sd': 0,
'loc_prec_amp': 0,
'vertices_amp': 0,
'vertices_sd': 0,
'substruct_amp': 0,
'substruct_sd': 0,
'square_grid_spacing': 0,
'square_grid_amp': 0,
'square_grid_sd': 0,
'bg_slope': 0,
}
upper_bound_dict = {'side_1': 200,
'side_2': 200,
'side_3': 200,
'loc_prec_sd': 100,
'loc_prec_amp': 100,
'vertices_amp': 100,
'vertices_sd': 100,
'substruct_amp': 100,
'substruct_sd': 100,
'square_grid_spacing': 400,
'square_grid_amp': 1000,
'square_grid_sd': 100,
'bg_slope': 0.1,
}
initial_params_dict = {'side_1': 100,
'side_2': 100,
'side_3': 100,
'loc_prec_sd': 10,
'loc_prec_amp': 10,
'vertices_amp': 10,
'vertices_sd': 10,
'substruct_amp': 10,
'substruct_sd': 10,
'square_grid_spacing': 200,
'square_grid_amp': 100,
'square_grid_sd': 10,
'bg_slope': 0.001,
}
return lower_bound_dict, upper_bound_dict, initial_params_dict
def set_up_tri_prism_on_grid_1_length_2disobg_substruct_with_fit_info():
"""Set up the RPD model with fitting settings,
for a rotationally symmetric model with spread due to repeated
localisations and spread to unresolvable substructure.
The fitting settings are to pass to scipy's
curve_fit, and the vector-input version of the model is for
differentiation and error propagation with numdifftools.
Args:
None
Returns:
A ModelWithFitSettings object containing:
model_rpd (function name):
Relative position density as a function of separation
between localisations.
initial_params (list):
Starting guesses for the parameter values by
scipy.optimize.curve_fit
lower_bounds (list), upper_bounds (list):
The bounds on allowable parameter values as
scipy.optimize.curve_fit runs.
"""
model_with_info = (
ModelWithFitSettings(
model_rpd=poly.tri_prism_on_grid_1_length_2disobg_substruct_rpd
)
)
# Add fitting parameters to ModelWithFitSettings object
(lower_bound_dict,
upper_bound_dict,
initial_params_dict) = create_default_fitting_params_dicts()
# Can optionally modify these dictionaries here:
initial_params = [initial_params_dict['side_1'],
initial_params_dict['loc_prec_amp'],
initial_params_dict['loc_prec_sd'],
initial_params_dict['vertices_amp'],
initial_params_dict['vertices_sd'],
initial_params_dict['substruct_amp'],
initial_params_dict['substruct_sd'],
initial_params_dict['square_grid_spacing'],
initial_params_dict['square_grid_amp'],
initial_params_dict['square_grid_sd'],
initial_params_dict['bg_slope']
]
lower_bounds = [lower_bound_dict['side_1'],
lower_bound_dict['loc_prec_amp'],
lower_bound_dict['loc_prec_sd'],
lower_bound_dict['vertices_amp'],
lower_bound_dict['vertices_sd'],
lower_bound_dict['substruct_amp'],
lower_bound_dict['substruct_sd'],
lower_bound_dict['square_grid_spacing'],
lower_bound_dict['square_grid_amp'],
lower_bound_dict['square_grid_sd'],
lower_bound_dict['bg_slope']
]
upper_bounds = [upper_bound_dict['side_1'],
upper_bound_dict['loc_prec_amp'],
upper_bound_dict['loc_prec_sd'],
upper_bound_dict['vertices_amp'],
upper_bound_dict['vertices_sd'],
upper_bound_dict['substruct_amp'],
upper_bound_dict['substruct_sd'],
upper_bound_dict['square_grid_spacing'],
upper_bound_dict['square_grid_amp'],
upper_bound_dict['square_grid_sd'],
upper_bound_dict['bg_slope']
]
bounds = (lower_bounds, upper_bounds)
model_with_info.initial_params = (
initial_params
)
model_with_info.param_bounds = (
bounds
)
model_with_info.vector_input_model = (
poly.tri_prism_on_grid_1_length_2disobg_substruct_rpd_vectorargs
)
return model_with_info
def set_up_tri_prism_on_grid_1_length_substruct_with_fit_info():
"""Set up the RPD model with fitting settings,
for a rotationally symmetric model with spread due to repeated
localisations and spread to unresolvable substructure.
The fitting settings are to pass to scipy's
curve_fit, and the vector-input version of the model is for
differentiation and error propagation with numdifftools.
Args:
None
Returns:
A ModelWithFitSettings object containing:
model_rpd (function name):
Relative position density as a function of separation
between localisations.
initial_params (list):
Starting guesses for the parameter values by
scipy.optimize.curve_fit
lower_bounds (list), upper_bounds (list):
The bounds on allowable parameter values as
scipy.optimize.curve_fit runs.
"""
model_with_info = (
ModelWithFitSettings(
model_rpd=poly.tri_prism_on_grid_1_length_substructure_rpd
)
)
# Add fitting parameters to ModelWithFitSettings object
(lower_bound_dict,
upper_bound_dict,
initial_params_dict) = create_default_fitting_params_dicts()
# Can optionally modify these dictionaries here:
initial_params = [initial_params_dict['side_1'],
initial_params_dict['loc_prec_amp'],
initial_params_dict['loc_prec_sd'],
initial_params_dict['vertices_amp'],
initial_params_dict['vertices_sd'],
initial_params_dict['substruct_amp'],
initial_params_dict['substruct_sd'],
initial_params_dict['square_grid_spacing'],
initial_params_dict['square_grid_amp'],
initial_params_dict['square_grid_sd'],
]
lower_bounds = [lower_bound_dict['side_1'],
lower_bound_dict['loc_prec_amp'],
lower_bound_dict['loc_prec_sd'],
lower_bound_dict['vertices_amp'],
lower_bound_dict['vertices_sd'],
lower_bound_dict['substruct_amp'],
lower_bound_dict['substruct_sd'],
lower_bound_dict['square_grid_spacing'],
lower_bound_dict['square_grid_amp'],
lower_bound_dict['square_grid_sd'],
]
upper_bounds = [upper_bound_dict['side_1'],
upper_bound_dict['loc_prec_amp'],
upper_bound_dict['loc_prec_sd'],
upper_bound_dict['vertices_amp'],
upper_bound_dict['vertices_sd'],
upper_bound_dict['substruct_amp'],
upper_bound_dict['substruct_sd'],
upper_bound_dict['square_grid_spacing'],
upper_bound_dict['square_grid_amp'],
upper_bound_dict['square_grid_sd'],
]
bounds = (lower_bounds, upper_bounds)
model_with_info.initial_params = (
initial_params
)
model_with_info.param_bounds = (
bounds
)
#model_with_info.vector_input_model = (
# poly.tri_prism_on_grid_1_length_2disobg_substruct_rpd_vectorargs
# )
return model_with_info
def set_up_tri_prism_on_grid_1_length_3disobg_substruct_with_fit_info():
"""Set up the RPD model with fitting settings,
for a rotationally symmetric model with spread due to repeated
localisations and spread to unresolvable substructure.
The fitting settings are to pass to scipy's
curve_fit, and the vector-input version of the model is for
differentiation and error propagation with numdifftools.
Args:
None
Returns:
A ModelWithFitSettings object containing:
model_rpd (function name):
Relative position density as a function of separation
between localisations.
initial_params (list):
Starting guesses for the parameter values by
scipy.optimize.curve_fit
lower_bounds (list), upper_bounds (list):
The bounds on allowable parameter values as
scipy.optimize.curve_fit runs.
"""
model_with_info = (
ModelWithFitSettings(
model_rpd=poly.tri_prism_on_grid_1_length_3disobg_substruct_rpd
)
)
# Add fitting parameters to ModelWithFitSettings object
(lower_bound_dict,
upper_bound_dict,
initial_params_dict) = create_default_fitting_params_dicts()
# Can optionally modify these dictionaries here:
initial_params = [initial_params_dict['side_1'],
initial_params_dict['loc_prec_amp'],
initial_params_dict['loc_prec_sd'],
initial_params_dict['vertices_amp'],
initial_params_dict['vertices_sd'],
initial_params_dict['substruct_amp'],
initial_params_dict['substruct_sd'],
initial_params_dict['square_grid_spacing'],
initial_params_dict['square_grid_amp'],
initial_params_dict['square_grid_sd'],
initial_params_dict['bg_slope'] # Use this as the bg_scale
]
lower_bounds = [lower_bound_dict['side_1'],
lower_bound_dict['loc_prec_amp'],
lower_bound_dict['loc_prec_sd'],
lower_bound_dict['vertices_amp'],
lower_bound_dict['vertices_sd'],
lower_bound_dict['substruct_amp'],
lower_bound_dict['substruct_sd'],
#lower_bound_dict['square_grid_spacing'],
200.,
lower_bound_dict['square_grid_amp'],
lower_bound_dict['square_grid_sd'],
lower_bound_dict['bg_slope'] # Use this as the bg_scale
]
upper_bounds = [upper_bound_dict['side_1'],
upper_bound_dict['loc_prec_amp'],
upper_bound_dict['loc_prec_sd'],
upper_bound_dict['vertices_amp'],
upper_bound_dict['vertices_sd'],
upper_bound_dict['substruct_amp'],
upper_bound_dict['substruct_sd'],
upper_bound_dict['square_grid_spacing'],
upper_bound_dict['square_grid_amp'],
upper_bound_dict['square_grid_sd'],
upper_bound_dict['bg_slope'] # Use this as the bg_scale
]
bounds = (lower_bounds, upper_bounds)
model_with_info.initial_params = (
initial_params
)
model_with_info.param_bounds = (
bounds
)
#model_with_info.vector_input_model = (
# poly.tri_prism_on_grid_1_length_2disobg_substruct_rpd_vectorargs
# )
return model_with_info
def set_up_tri_prism_1_length_3disobg_substruct_with_fit_info():
"""Set up the RPD model with fitting settings,
for a rotationally symmetric model with spread due to repeated
localisations and spread to unresolvable substructure.
The fitting settings are to pass to scipy's
curve_fit, and the vector-input version of the model is for
differentiation and error propagation with numdifftools.
Args:
None
Returns:
A ModelWithFitSettings object containing:
model_rpd (function name):
Relative position density as a function of separation
between localisations.
initial_params (list):
Starting guesses for the parameter values by
scipy.optimize.curve_fit
lower_bounds (list), upper_bounds (list):
The bounds on allowable parameter values as
scipy.optimize.curve_fit runs.
"""
model_with_info = (
ModelWithFitSettings(
model_rpd=poly.tri_prism_1_length_3disobg_substruct_rpd
)
)
# Add fitting parameters to ModelWithFitSettings object
(lower_bound_dict,
upper_bound_dict,
initial_params_dict) = create_default_fitting_params_dicts()
# Can optionally modify these dictionaries here:
initial_params = [initial_params_dict['side_1'],
initial_params_dict['loc_prec_amp'],
initial_params_dict['loc_prec_sd'],
initial_params_dict['vertices_amp'],
initial_params_dict['vertices_sd'],
initial_params_dict['substruct_amp'],
initial_params_dict['substruct_sd'],
initial_params_dict['bg_slope'] # Use this as the bg_scale
]
lower_bounds = [lower_bound_dict['side_1'],
lower_bound_dict['loc_prec_amp'],
lower_bound_dict['loc_prec_sd'],
lower_bound_dict['vertices_amp'],
lower_bound_dict['vertices_sd'],
lower_bound_dict['substruct_amp'],
lower_bound_dict['substruct_sd'],
lower_bound_dict['bg_slope'] # Use this as the bg_scale
]
upper_bounds = [upper_bound_dict['side_1'],
upper_bound_dict['loc_prec_amp'],
upper_bound_dict['loc_prec_sd'],
upper_bound_dict['vertices_amp'],
upper_bound_dict['vertices_sd'],
upper_bound_dict['substruct_amp'],
upper_bound_dict['substruct_sd'],
upper_bound_dict['bg_slope'] # Use this as the bg_scale
]
bounds = (lower_bounds, upper_bounds)
model_with_info.initial_params = (
initial_params
)
model_with_info.param_bounds = (
bounds
)
#model_with_info.vector_input_model = (
# poly.tri_prism_on_grid_1_length_2disobg_substruct_rpd_vectorargs
# )
return model_with_info
def set_up_model_tri_prism_on_grid_2disobg_substructure_with_fit_info():
"""Set up the RPD model with fitting settings,
for a rotationally symmetric model with spread due to repeated
localisations and spread to unresolvable substructure.
The fitting settings are to pass to scipy's
curve_fit, and the vector-input version of the model is for
differentiation and error propagation with numdifftools.
Args:
None
Returns:
A ModelWithFitSettings object containing:
model_rpd (function name):
Relative position density as a function of separation
between localisations.
initial_params (list):
Starting guesses for the parameter values by
scipy.optimize.curve_fit
lower_bounds (list), upper_bounds (list):
The bounds on allowable parameter values as
scipy.optimize.curve_fit runs.
"""
model_with_info = (
ModelWithFitSettings(
model_rpd=poly.tri_prism_on_grid_2disobg_substructure_rpd
)
)
# Add fitting parameters to ModelWithFitSettings object
(lower_bound_dict,
upper_bound_dict,
initial_params_dict) = create_default_fitting_params_dicts()
# Can optionally modify these dictionaries here:
initial_params = [initial_params_dict['side_1'],
initial_params_dict['side_2'],
initial_params_dict['loc_prec_amp'],
initial_params_dict['loc_prec_sd'],
initial_params_dict['vertices_amp'],
initial_params_dict['vertices_sd'],
initial_params_dict['substruct_amp'],
initial_params_dict['substruct_sd'],
initial_params_dict['square_grid_spacing'],
initial_params_dict['square_grid_amp'],
initial_params_dict['square_grid_sd'],
initial_params_dict['bg_slope']
]
lower_bounds = [lower_bound_dict['side_1'],
lower_bound_dict['side_2'],
lower_bound_dict['loc_prec_amp'],
lower_bound_dict['loc_prec_sd'],
lower_bound_dict['vertices_amp'],
lower_bound_dict['vertices_sd'],
lower_bound_dict['substruct_amp'],
lower_bound_dict['substruct_sd'],
lower_bound_dict['square_grid_spacing'],
lower_bound_dict['square_grid_amp'],
lower_bound_dict['square_grid_sd'],
lower_bound_dict['bg_slope']
]
upper_bounds = [upper_bound_dict['side_1'],
upper_bound_dict['side_2'],
upper_bound_dict['loc_prec_amp'],
upper_bound_dict['loc_prec_sd'],
upper_bound_dict['vertices_amp'],
upper_bound_dict['vertices_sd'],
upper_bound_dict['substruct_amp'],
upper_bound_dict['substruct_sd'],
upper_bound_dict['square_grid_spacing'],
upper_bound_dict['square_grid_amp'],
upper_bound_dict['square_grid_sd'],
upper_bound_dict['bg_slope']
]
bounds = (lower_bounds, upper_bounds)
model_with_info.initial_params = (
initial_params
)
model_with_info.param_bounds = (
bounds
)
model_with_info.vector_input_model = (
poly.tri_prism_on_grid_2disobg_substructure_rpd_vectorargs
)
return model_with_info
def set_up_model_cuboid_on_grid_2disobg_substructure_with_fit_info():
"""Set up the RPD model with fitting settings,
for a rotationally symmetric model with spread due to repeated
localisations and spread to unresolvable substructure.
The fitting settings are to pass to scipy's
curve_fit, and the vector-input version of the model is for
differentiation and error propagation with numdifftools.
Args:
None
Returns:
A ModelWithFitSettings object containing:
model_rpd (function name):
Relative position density as a function of separation
between localisations.
initial_params (list):
Starting guesses for the parameter values by
scipy.optimize.curve_fit
lower_bounds (list), upper_bounds (list):
The bounds on allowable parameter values as
scipy.optimize.curve_fit runs.
"""
model_with_info = (
ModelWithFitSettings(
model_rpd=poly.cuboid_on_grid_2disobg_substructure_rpd
)
)
# Add fitting parameters to ModelWithFitSettings object
(lower_bound_dict,
upper_bound_dict,
initial_params_dict) = create_default_fitting_params_dicts()
# Can optionally modify these dictionaries here:
initial_params = [initial_params_dict['side_1'],
initial_params_dict['side_2'],
initial_params_dict['side_3'],
initial_params_dict['loc_prec_amp'],
initial_params_dict['loc_prec_sd'],
initial_params_dict['vertices_amp'],
initial_params_dict['vertices_sd'],
initial_params_dict['substruct_amp'],
initial_params_dict['substruct_sd'],
initial_params_dict['square_grid_spacing'],
initial_params_dict['square_grid_amp'],
initial_params_dict['square_grid_sd'],
initial_params_dict['bg_slope']
]
lower_bounds = [lower_bound_dict['side_1'],
lower_bound_dict['side_2'],
lower_bound_dict['side_3'],
lower_bound_dict['loc_prec_amp'],
lower_bound_dict['loc_prec_sd'],
lower_bound_dict['vertices_amp'],
lower_bound_dict['vertices_sd'],
lower_bound_dict['substruct_amp'],
lower_bound_dict['substruct_sd'],
lower_bound_dict['square_grid_spacing'],
lower_bound_dict['square_grid_amp'],
lower_bound_dict['square_grid_sd'],
lower_bound_dict['bg_slope']
]
upper_bounds = [upper_bound_dict['side_1'],
upper_bound_dict['side_2'],
upper_bound_dict['side_3'],
upper_bound_dict['loc_prec_amp'],
upper_bound_dict['loc_prec_sd'],
upper_bound_dict['vertices_amp'],
upper_bound_dict['vertices_sd'],
upper_bound_dict['substruct_amp'],
upper_bound_dict['substruct_sd'],
upper_bound_dict['square_grid_spacing'],
upper_bound_dict['square_grid_amp'],
upper_bound_dict['square_grid_sd'],
upper_bound_dict['bg_slope']
]
bounds = (lower_bounds, upper_bounds)
model_with_info.initial_params = (
initial_params
)
model_with_info.param_bounds = (
bounds
)
# model_with_info.vector_input_model = (
# poly.tri_prism_on_grid_2disobg_substructure_rpd_vectorargs
# )
return model_with_info
def set_up_model_tri_pyramid_on_grid_2disobg_substructure_with_fit_info():
"""Set up the RPD model with fitting settings,
for a rotationally symmetric model with spread due to repeated
localisations and spread to unresolvable substructure.
The fitting settings are to pass to scipy's
curve_fit, and the vector-input version of the model is for
differentiation and error propagation with numdifftools.
Args:
None
Returns:
A ModelWithFitSettings object containing:
model_rpd (function name):
Relative position density as a function of separation
between localisations.
initial_params (list):
Starting guesses for the parameter values by
scipy.optimize.curve_fit
lower_bounds (list), upper_bounds (list):
The bounds on allowable parameter values as
scipy.optimize.curve_fit runs.
"""
model_with_info = (
ModelWithFitSettings(
model_rpd=poly.tri_pyramid_on_grid_2disobg_substructure_rpd
)
)
# Add fitting parameters to ModelWithFitSettings object
(lower_bound_dict,
upper_bound_dict,
initial_params_dict) = create_default_fitting_params_dicts()
# Can optionally modify these dictionaries here:
initial_params = [initial_params_dict['side_1'],
initial_params_dict['side_2'],
initial_params_dict['loc_prec_amp'],
initial_params_dict['loc_prec_sd'],
initial_params_dict['vertices_amp'],
initial_params_dict['vertices_sd'],
initial_params_dict['substruct_amp'],
initial_params_dict['substruct_sd'],
initial_params_dict['square_grid_spacing'],
initial_params_dict['square_grid_amp'],
initial_params_dict['square_grid_sd'],
initial_params_dict['bg_slope']
]
lower_bounds = [lower_bound_dict['side_1'],
lower_bound_dict['side_2'],
lower_bound_dict['loc_prec_amp'],
lower_bound_dict['loc_prec_sd'],
lower_bound_dict['vertices_amp'],
lower_bound_dict['vertices_sd'],
lower_bound_dict['substruct_amp'],
lower_bound_dict['substruct_sd'],
lower_bound_dict['square_grid_spacing'],
lower_bound_dict['square_grid_amp'],
lower_bound_dict['square_grid_sd'],
lower_bound_dict['bg_slope']
]
upper_bounds = [upper_bound_dict['side_1'],
upper_bound_dict['side_2'],
upper_bound_dict['loc_prec_amp'],
upper_bound_dict['loc_prec_sd'],
upper_bound_dict['vertices_amp'],
upper_bound_dict['vertices_sd'],
upper_bound_dict['substruct_amp'],
upper_bound_dict['substruct_sd'],
upper_bound_dict['square_grid_spacing'],
upper_bound_dict['square_grid_amp'],
upper_bound_dict['square_grid_sd'],
upper_bound_dict['bg_slope']
]
bounds = (lower_bounds, upper_bounds)
model_with_info.initial_params = (
initial_params
)
model_with_info.param_bounds = (
bounds
)
# model_with_info.vector_input_model = (
# poly.tri_prism_on_grid_2disobg_substructure_rpd_vectorargs
# )
return model_with_info
def fitmodel_to_hist(
distancehist,
model=poly.tri_prism_on_grid_1_length_2disobg_substruct_rpd,
fitlength=400.):
"""Fit model RPD to distance histogram. Designed to allow user editting of
parameter guesses and bounds for models of RPDs for simple polyhedra,
as in polyhedramodelling.py.
Args:
distancehist (numpy array):
An array of Euclidean distances between localisations.
model:
The model RPD to be fitted.
fitlength:
The maximum distance between localisations used for the fit.
Returns:
popt:
perr
"""
params_optimised, params_covar = curve_fit(
model, np.arange(fitlength) + 0.5, distancehist,
p0=(100., 100., #100., # a, b, c
10., 10., # locamp, locprec
10., 10., # structamp, spread
10., 10., # substructamp, substructspread
200., 100., 10., # gridspace, gridamp, gridspread
0.001), # bgslope
bounds=(
[0., 0., #0., # a, b, c
0., 0., # locamp, locprec
0., 0., # structamp, spread
0., 0., # substructamp, substructspread
0., 0., 0., # gridspace, gridamp, gridspread
0.], # bgslope
[200., 200., #200., # a, b, c
100., 100., # locamp, locprec
100., 100., # structamp, spread
100., 100., # substructamp, substructspread
400., 1000., 100., # gridspace, gridamp, gridspread
0.1]) # bgslope
)
# plt.plot(np.arange(fitlength) + 0.5,
# model(np.arange(fitlength) + 0.5, *params_optimised))
params_1sd_error = np.sqrt(np.diag(params_covar))
params_table = np.column_stack((params_optimised, params_1sd_error))
print(params_table)
# No. free parameters, including var. of residuals for least squares fit.
k = float(len(params_optimised) + 1)
# Calculate AICc
ssr = np.sum((model(np.arange(fitlength) + 0.5, *params_optimised) -
distancehist) ** 2)
aic = fitlength * np.log(ssr / fitlength) + 2 * k
aiccorr = aic + 2 * k * (k + 1) / (fitlength - k - 1)
print('SSR =', ssr)
print('AIC =', aic)
print('AICcorr =', aiccorr)
return params_optimised, params_covar, params_1sd_error
def plot_xyz_distance_histogram(distances, fitlength, color='gray'):
"""Plot histogram of experimental distances, with 1 nm bins.
Scales counts, so that mean = 1, to suit scipy.optimize.curve_fit
Args:
distances (numpy array-like):
Set of distances (nm) to plot.
fitlength (float):
The distance upto which the histogram will be calculated.
color (string):
Colour for the matplotlib histogram.
Returns:
hist_values (numpy array):
Histogram bin values.
bin_edges (numpy array):
Histogram bin edge positions.
"""
# Histogram figure with 1-nm bins
histfig = plt.figure()
histaxes = histfig.add_subplot(111)
hist_values, bin_edges = histaxes.hist(
distances,
bins=np.arange(fitlength + 1),
weights=np.repeat(float(fitlength) / len(distances),
len(distances)
),
color=color, alpha=0.5
)[0:2] # 2 not required
histaxes.set_xlim([0, fitlength])
histaxes.set_title('Histogram')
histaxes.set_xlabel(r'$\Delta$XYZ (nm)')
histaxes.set_ylabel('Counts (scaled: mean = 1)')
return hist_values, bin_edges
def plot_distance_hist_and_fit(distances,
fitlength,
params_optimised,
params_covar,
model_with_info,
plot_95ci=False,
color='xkcd:red'):
# Use only distances within fitlength
distances = distances[distances <= fitlength]
fig = plt.figure()
axes = plt.subplot(111)
histogram_output = axes.hist(distances,
bins=np.arange(fitlength + 1),
weights=np.repeat(float(fitlength)
/ len(distances),
len(distances)
),
color='gray', alpha=0.5
)
bin_edges = histogram_output[1]
bin_centres = (bin_edges[0:(len(bin_edges) - 1)] + bin_edges[1:]) / 2
axes.plot(distances,
model_with_info.model_rpd(distances, *params_optimised),
color=color,
lw=0.75
)
axes.set_xlim([0, fitlength])
axes.set_xlabel(r'$\Delta$XYZ (nm)')
axes.set_ylabel('Counts (scaled: mean = 1)')
axes.set_title('Model: ' +model_with_info.model_rpd.__name__)
# Get 1 SD uncertainty on model result from uncertainty on parameters
# and plot 95% CI.
if plot_95ci is True:
stdev = stdev_of_model(bin_centres,
params_optimised,
params_covar,
model_with_info.vector_input_model
)
axes.fill_between(bin_centres,
model_with_info.model_rpd(bin_centres,
*params_optimised)
- stdev * 1.96,
model_with_info.model_rpd(bin_centres,
*params_optimised)
+ stdev * 1.96,
facecolor=color,
alpha=0.25
)
return fig, axes
def plot_model_components_tri_prism(fitlength,
side_length,
locamp, locprec,
structamp, spread,
substructamp, substructspread,
gridspace, gridamp, gridspread,
bgslope):
"""
fitlength: distance upto to which the model fit was performed
side_length: side length of the triangular prism (all sides equal)
locamp: Amplitude of sinlge molecule localisation precision component
locprec: Average single molecule localisation precision
structamp: Amplitude of components reflecting the structural features
of the complex.
spread: Spread owing to unresolvable complexity or inhomogeneity between
complexes.
substructamp: Amplitude of component reflecting unresolvable substructure
at one vertex.
substructspread: Spread in localisations at one vertex, as a result of
unresolvable substructure there.
gridspace: The spacing of a square grid the complexes are found on.
gridamp: Amplitude of components reflecting the nieghbouring complexes at
nearby grid points.
gridspread: Spread owing to different orientation at different grid points.
bgslope: Approximate background to 2D (relatively flat); this is the
linear slope.
"""
distance_values = np.arange(0, fitlength + 1, 1)
fig = plt.figure()
axes = plt.subplot(111)
axes.set_xlim([0, fitlength])
axes.set_xlabel(r'$\Delta$XYZ (nm)')
axes.set_ylabel('Counts (scaled: mean = 1)')
axes.set_title('Model: Triangular pyramid, equal side lengths')
# Background term
bg_term = distance_values * bgslope
plt.plot(distance_values, bg_term)
# Repeated localisations term
rep_locs_term = (locamp
* models.pairwise_correlation_3d(distance_values,
0.,
np.sqrt(2) * locprec
)
)
plt.plot(distance_values, rep_locs_term)
# Plot substructure term
substructure_term = (substructamp
* models.pairwise_correlation_3d(distance_values,
0.,
np.sqrt(2) * locprec
)
)
plt.plot(distance_values, substructure_term)
# Triangular prism peaks:
# Set up triangular prism
verts = poly.tri_prism_vertices(side_length, side_length)
relpos = poly.get_1d_relpos_no_filter(verts)
# Get unique distances
xyz_distances = np.sqrt(relpos[:, 0] ** 2 + relpos[:, 1] ** 2 + relpos[:, 2] ** 2)
xyz_distances = np.unique(xyz_distances)
# Two peaks:
# 3 x shorter distance x 6 vertices
tri_prism_peak_1 = (18 * structamp
* models.pairwise_correlation_3d(distance_values,
xyz_distances[0],
spread
)
)
plt.plot(distance_values, tri_prism_peak_1)
# 2 x longer distance x 6 vertices
tri_prism_peak_2 = (12 * structamp
* models.pairwise_correlation_3d(distance_values,
xyz_distances[1],
spread
)
)
plt.plot(distance_values, tri_prism_peak_2)
# Plot square grid componenet
square_grid_component = (
gridamp * models.pairwise_correlation_2d(distance_values,
gridspace,
gridspread
)
+ gridamp * models.pairwise_correlation_2d(distance_values,
gridspace * np.sqrt(2),
gridspread
)
)
plt.plot(distance_values, square_grid_component)
# Plot total model
total_model = (bg_term