Revision c3f5615648978f9fdc82237c443ed29eadb2fc15 authored by Andrew Plested on 29 January 2023, 12:31:28 UTC, committed by GitHub on 29 January 2023, 12:31:28 UTC
1 parent 65a26ea
quantal.py
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
from scipy import optimize
import pandas as pd
from scipy.stats import binom, poisson
def cdf(x, func, max, step, *fargs):
"""calculate cdf for function. extra arguments (after x) for func in should be given in fargs
func is the abitrary function to calculate the cdf"""
#print ("Len (x) = {}".format(len(x)))
#print (x, step)
_denom = 0
for d in np.arange(0, max, step):
_denom += func(d, *fargs)
f = []
for xi in x:
_num = 0
#print ("xi: {} step: {}".format(xi, step))
for d in np.arange(0, xi, step):
_num += func(d, *fargs)
f.append(_num / _denom)
f_array = np.array(f)
#print (f_array)
return f_array
def gaussian(x, height, center, width, offset):
"""x is an array or a scalar"""
return 0.399 * height / width * np.exp(-(x - center)**2 / (2 * width ** 2)) + offset
def nprGaussians(x, n, q, widths, scale, pr):
"""heights come from binomial (Pr) and an optimised scale parameter (number of events)"""
g = gaussian (x, 0, 0, 1, 0) # create a blank in the correct x
for k in range(n+1):
b = binom.pmf(k, n, pr)
g += gaussian(x, b * scale, k * q, widths, 0)
#print ("Binomial k {}, n {}, pr {} = {}. q {}, w {}, scale {}".format(k, n, pr, b, q, widths, scale))
return g
def fit_PoissonGaussians_global(num, q, ws, hy, hx, fixedW=False):
# hy and hx are matrixes of n columns for the n histograms
#print (hy.shape)
nh = hy.shape[1] # how many columns = how many functions
mu = np.full(nh, 2) # mean release rate, no bound (will be bounded 0 to num)
_scale = 10 # a scale factor depending on total no. of events measured
if fixedW==False:
guesses = np.array([q, ws, _scale, *mu])
l_bounds = np.zeros (nh + 3)
u_bounds = np.concatenate((np.full((3), np.inf), np.full(nh, num) ))
return optimize.least_squares(globalErrFuncP, guesses, bounds = (l_bounds, u_bounds),
args=(num, nh, hx.flatten(), hy.flatten()))
else:
guesses = np.array([q, _scale, *mu])
l_bounds = np.zeros (nh + 2)
u_bounds = np.concatenate((np.full((2), np.inf), np.full(nh, num) )) #maximum value of mu is num
return optimize.least_squares(globalErrFuncPW, guesses, bounds = (l_bounds, u_bounds),
args=(num, ws, nh, hx.flatten(), hy.flatten()))
def poissonGaussians(x, n, q, widths, scale, mu):
"""Heights come from poisson with mean mu and an optimised scale parameter (no. of events)"""
g = gaussian (x, 0, 0, 1, 0) # create a blank
for k in range(n):
b = poisson.pmf(k, mu)
g += gaussian(x, b * scale, k * q, (k+1) * widths, 0)
#print ("Poisson k {}, n {}, mu {} = {}. q {}, w {}, scale {}".format(k, n, mu, b, q, widths, scale))
return g
def globalErrFuncPW(pa, num, ws, nh, hx, hy):
"""global poisson stats fit with fixed ws"""
# 1-D function so hx and hy are passed flat
# assume that pa is a list.
_errfunc_list = []
_hxr = hx.reshape(-1, nh) # rows are inferred
_hyr = hy.reshape(-1, nh)
_q = pa[0]
_scale = pa[1]
# loop for each column
for i in range(nh):
_hx = _hxr[:, i]
_hxc = np.mean(np.vstack([_hx[0:-1], _hx[1:]]), axis=0)
# pa[i+2] is the relevant mu
#_e_i = (poissonGaussians(_hxc, num, _q, ws, _scale, pa[i+2]) - _hyr[:, i])**2
# JUST RESIDUAL!
_e_i = (poissonGaussians(_hxc, num, _q, ws, _scale, pa[i+2]) - _hyr[:, i])
_errfunc_list.append(_e_i)
return np.concatenate(_errfunc_list) # FLAT -works for unknown n
def globalErrFuncP(pa, num, nh, hx, hy):
"""global multi-gaussian fit with poisson stats"""
# 1-D function so hx and hy are passed flat
# assume that pa is a list...
_errfunc_list = []
_hxr = hx.reshape(-1, nh) # rows are inferred
_hyr = hy.reshape(-1, nh)
_q = pa[0]
_ws = pa[1]
_scale = pa[2]
# loop for each column
for i in range(nh):
_hx = _hxr[:, i]
_hxc = np.mean(np.vstack([_hx[0:-1], _hx[1:]]), axis=0)
# pa[i+3] is the relevant mu
#_e_i = (poissonGaussians(_hxc, num, _q, _ws, _scale, pa[i+3]) - _hyr[:, i])**2
#just residual
_e_i = (poissonGaussians(_hxc, num, _q, _ws, _scale, pa[i+3]) - _hyr[:, i])
_errfunc_list.append(_e_i)
return np.concatenate(_errfunc_list) #FLAT -should work for unknown n
def nGaussians(x, n, spacing, widths, *heights):
g = gaussian (x, 0, 0, 1, 0) # create a blank
for j in range(n):
g += gaussian(x, heights[j], j * spacing, widths, 0)
return g
def fit_nGaussians (num, q, ws, hy, hx):
"""heights are fitted"""
h = np.random.rand(num) * np.average(hy) # array of guesses for heights
guesses = np.array([q, ws, *h])
errfunc = lambda pa, x, y: (nGaussians(x, num, *pa) - y)**2
# JUST RESIDUAL!
errfunc = lambda pa, x, y: (nGaussians(x, num, *pa) - y)
# loss="soft_l1" is bad!
return optimize.least_squares(errfunc, guesses, bounds = (0, np.inf), args=(hx, hy))
def globalErrFuncBW(pa, num, ws, nh, hx, hy):
"""global binomial stats fit with fixed ws"""
# 1-D function so hx and hy are passed flat
# assume for now that pa is a list... it should be!
_errfunc_list = []
_hxr = hx.reshape(-1, nh) # rows are inferred
_hyr = hy.reshape(-1, nh)
_q = pa[0]
_scale = pa[1]
# loop for each column
for i in range(nh):
_hx = _hxr[:, i]
_hxc = np.mean(np.vstack([_hx[0:-1], _hx[1:]]), axis=0)
# pa[i+2] is the relevant Pr
#_e_i = (nprGaussians(_hxc, num, _q, ws, _scale, pa[i+2]) - _hyr[:, i])**2
# just residual
_e_i = (nprGaussians(_hxc, num, _q, ws, _scale, pa[i+2]) - _hyr[:, i])
_errfunc_list.append(_e_i)
return np.concatenate(_errfunc_list) #FLAT -should work for unknown n
def globalErrFuncB(pa, num, nh, hx, hy):
# 1-D function so hx and hy are passed flat
# assume for now that pa is a list... it should be!
_errfunc_list = []
_hxr = hx.reshape(-1, nh) # rows are inferred
_hyr = hy.reshape(-1, nh)
_q = pa[0]
_ws = pa[1]
_scale = pa[2]
# loop for each column
for i in range(nh):
_hx = _hxr[:, i]
_hxc = np.mean(np.vstack([_hx[0:-1], _hx[1:]]), axis=0)
# pa[i+3] is the relevant Pr
#_e_i = (nprGaussians(_hxc, num, _q, _ws, _scale, pa[i+3]) - _hyr[:, i])**2
#JUST RESIDUAL
_e_i = (nprGaussians(_hxc, num, _q, _ws, _scale, pa[i+3]) - _hyr[:, i])
_errfunc_list.append(_e_i)
return np.concatenate(_errfunc_list) #FLAT -should work for unknown n
def fit_nprGaussians_global(num, q, ws, hy, hx, fixedW=False):
# hy and hx are matrixes of n columns for the n histograms
nh = hy.shape[1] # how many columns = how many functions
#print (hy.shape, nh)
#l = np.arange(nh, dtype=np.double)
pr = np.full(nh, 0.5) # release probabilities (will be bounded 0 to 1)
_scale = 10 # a scale factor depending on no. of events measured
if fixedW==False:
guesses = np.array([q, ws, _scale, *pr])
l_bounds = np.zeros (nh + 3)
u_bounds = np.concatenate((np.full((3), np.inf), np.ones (nh)))
return optimize.least_squares(globalErrFuncB, guesses, bounds = (l_bounds, u_bounds),
args=(num, nh, hx.flatten(), hy.flatten()))
else:
guesses = np.array([q, _scale, *pr])
l_bounds = np.zeros (nh + 2)
u_bounds = np.concatenate((np.full((2), np.inf), np.ones (nh)))
return optimize.least_squares(globalErrFuncBW, guesses, bounds = (l_bounds, u_bounds),
args=(num, ws, nh, hx.flatten(), hy.flatten()))
def fit_nprGaussians (num, q, ws, hy, hx):
# with fixed number of gaussians, q, ws
_scale = 10 # a scale factor depending on no. of events measured
pr = 0.5 # release probability (will be bounded 0 to 1)
guesses = np.array([_scale, pr])
#errfunc = lambda pa, x, y: (nprGaussians(x, num, q, ws, *pa) - y)**2
# just residual
errfunc = lambda pa, x, y: (nprGaussians(x, num, q, ws, *pa) - y)
return optimize.least_squares(errfunc, guesses, bounds = ([0,0], [np.inf, 1]), args=(hx, hy))
def PoissonGaussians_display (hx, num, q, ws, optix):
"""oversample the Gaussian functions for a better display"""
# optix being a 2-list or a 2-array, the x attribute of opti (from optimise). Scale, mu?
# the ratio of the G. width to the histogram bin width tells us how much to oversample
oversam = int(10 * (hx[1]-hx[0]) / ws)
if oversam == 0:
oversam = 2
hx_u = np.linspace(0, hx[-1], len(hx)*oversam, endpoint=False)
hy_u = poissonGaussians(hx_u, num, q, ws, *list(optix))
return hx_u, hy_u
def nprGaussians_display (hx, num, q, ws, optix, verbose=False):
"""oversample the Gaussian functions for a better display"""
# optix being a 2-list or a 2-array, the x attribute of opti (from optimise).
# the ratio of the G. width to the histogram bin width tells us how much to oversample
oversam = int(10 * (hx[1]-hx[0]) / ws)
if oversam == 0:
oversam = 2
if verbose: print ("nprGaussians_display", num, q, ws, optix, oversam)
hx_o = np.linspace(0, hx[-1], len(hx)*oversam, endpoint=False)
hy_o = nprGaussians(hx_o, num, q, ws, *list(optix))
return hx_o, hy_o
def nGaussians_display (hx, num, optix, verbose=False):
"""oversample the Gaussian functions for a better display"""
# optix being a 2-list, the x attribute of opti (from optimise).
# the ratio of the G. width to the histogram bin width tells us how much to oversample
oversam = int(10 * (hx[1]-hx[0]) / optix[1])
if oversam == 0:
oversam = 2
if verbose: print ("nGaussians_display", num, optix, oversam)
hx_o = np.linspace(0, hx[-1], len(hx)*oversam, endpoint=False)
hy_o = nGaussians(hx_o, num, *list(optix))
return hx_o, hy_o
if __name__ == "__main__":
# trial code
mpl.rcParams['pdf.fonttype'] = 42
data = pd.read_csv('r47.txt', sep="\t", header=None)
data=data.as_matrix()
#print (data)
hx = data[:,0]
hy = data[:,1]
#these parameters are not optimised (in nprgaussians)
num = 8 # number of gaussians (will not be optimised
q = .062 # quantal size
ws = .015 # width of the gaussian
# just a straight line at the moment.
opti = fit_poissGaussians_global(num, q, ws, hy, hx)
#opti = fit_nprGaussians(num, q, ws, hy, hx)
print (opti)
plt.bar(hx, hy, color='orange', label='Peaks', width=(hx[1]-hx[0])*.95, alpha=0.4, edgecolor='black')
#hx_u = np.linspace(0, hx[-1], len(hx)*10, endpoint=False) #oversample to get nice gaussians
#fitp = ('q = {:.3f}\nw = {:.3f}'.format(opti.x[0], opti.x[1]))
fitp = ('Pr = {:.3f}'.format(opti.x[0]))
#hx_u, hy_u = nGaussians_display(hx, num, opti)
hx_u, hy_u = nprGaussians_display(hx, num, q, ws, opti)
plt.plot(hx_u, hy_u,
c='black', label='Fit of {} Gaussians'.format(num))
plt.title("Optical quantal analysis of glutamate release")
plt.ylabel("No. of events")
plt.xlabel("dF/F")
plt.legend(loc='upper right')
plt.annotate(fitp,xy=(.85, .65), xycoords='figure fraction',
horizontalalignment='right', verticalalignment='top',
fontsize=10)
#plt.show()
plt.savefig('res{}.pdf'.format(num))
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