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# Copyright 2014-2016 by Marco Galardini. All rights reserved.
# This code is part of the Biopython distribution and governed by its
# license. Please see the LICENSE file that should have been included
# as part of this package.
"""Growth curves fitting and parameters extraction for phenotype data
This module provides functions to perform sigmoid functions fitting to
Phenotype Microarray data. This module depends on scipy curve_fit function.
If not available, a warning is raised.
Functions:
logistic Logistic growth model.
gompertz Gompertz growth model.
richards Richards growth model.
guess_plateau Guess the plateau point to improve sigmoid fitting.
guess_lag Guess the lag point to improve sigmoid fitting.
fit Sigmoid functions fit.
get_area Calculate the area under the PM curve."""
import numpy as np
try:
from scipy.optimize.minpack import curve_fit
from scipy.integrate import trapz
except ImportError:
from Bio import MissingPythonDependencyError
raise MissingPythonDependencyError(
'Install scipy to extract curve parameters.')
def logistic(x, A, u, d, v, y0):
"""Logistic growth model
Proposed in Zwietering et al., 1990 (PMID: 16348228)
"""
y = (A / (1 + np.exp((((4 * u) / A) * (d - x)) + 2))) + y0
return y
def gompertz(x, A, u, d, v, y0):
"""Gompertz growth model
Proposed in Zwietering et al., 1990 (PMID: 16348228)
"""
y = (A * np.exp(-np.exp((((u * np.e) / A) * (d - x)) + 1))) + y0
return y
def richards(x, A, u, d, v, y0):
"""Gompertz growth model (equivalent to Stannard)
Proposed in Zwietering et al., 1990 (PMID: 16348228)
"""
y = (A * pow(1 + (v + (np.exp(1 + v) * np.exp((u / A) *
(1 + v) * (1 + (1 / v)) * (d - x)))), -(1 / v))) + y0
return y
def guess_lag(x, y):
"""Given two axes returns a guess of the lag point.
The lag point is defined as the x point where the difference in y
with the next point is higher then the mean differences between
the points plus one standard deviation. If such point is not found
or x and y have different lengths the function returns zero.
"""
if len(x) != len(y):
return 0
diffs = []
indexes = range(len(x))
for i in indexes:
if i + 1 not in indexes:
continue
diffs.append(y[i + 1] - y[i])
diffs = np.array(diffs)
flex = x[-1]
for i in indexes:
if i + 1 not in indexes:
continue
if (y[i + 1] - y[i]) > (diffs.mean() + (diffs.std())):
flex = x[i]
break
return flex
def guess_plateau(x, y):
"""Given two axes returns a guess of the plateau point.
The plateau point is defined as the x point where the y point
is near one standard deviation of the differences between the y points to
the maximum y value. If such point is not found or x and y have
different lengths the function returns zero.
"""
if len(x) != len(y):
return 0
diffs = []
indexes = range(len(y))
for i in indexes:
if i + 1 not in indexes:
continue
diffs.append(y[i + 1] - y[i])
diffs = np.array(diffs)
ymax = y[-1]
for i in indexes:
if y[i] > (ymax - diffs.std()) and y[i] < (ymax + diffs.std()):
ymax = y[i]
break
return ymax
def fit(function, x, y):
"""Fit the provided functrion to the x and y values.
The function parameters and the parameters covariance."""
# Compute guesses for the parameters
# This is necessary to get significant fits
p0 = [guess_plateau(x, y), 4.0, guess_lag(x, y), 0.1, min(y)]
params, pcov = curve_fit(function, x, y, p0=p0)
return params, pcov
def get_area(y, x):
"""Get the area under the curve"""
return trapz(y=y, x=x)
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