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quantal.py
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quantal.py
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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))