Minimization gives weird result (multi-parameter fitting) - numpy

I'm working on fitting of the experimental data. In order to fit it I use the minimization of the function of residual. Everything is quite trivial, but but this time I can't find what's wrong and why the result of fitting is so weird. The example is simplified in comparison with original problem. But anyway it gives wrong parameters even when I set used values of parameters as initial guess.
import matplotlib.pyplot as plt
import numpy as np
import csv
from scipy.optimize import curve_fit, minimize
x=np.arange(0,10,0.5)
a=0.5
b=3
ini_pars=[a, b]
def func(x, a, b):
return a*x+b
plt.plot(x, func(x,a,b))
plt.show()
def fit(pars):
A,B = pars
res = (func(x,a, b)-func(x, *pars))**2
s=sum(res)
return s
bnds=[(0.1,0.5),(1,5)]
x0=[0.1,4]
opt = minimize(fit, x0, bounds=bnds)
new_pars=[opt.x[0], opt.x[0]]
example = fit(ini_pars)
print(example)
example = fit(new_pars)
print(example)
print(new_pars)
plt.plot(x, func(x, *ini_pars))
plt.plot(x, func(x, *new_pars))
plt.show()
```[enter image description here][1]
[1]: https://i.stack.imgur.com/qc1Nu.png

It should be new_pars=[opt.x[0], opt.x[1]] instead of new_pars=[opt.x[0], opt.x[0]]. Note also that you can directly extract the values by new_pars = opt.x.

Related

numpy ndarray error in lmfit when mdel is passed using sympy

I got the following error:
<lambdifygenerated-1>:2: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.return numpy.array((A1exp(-1/2(x - xc1)**2/sigma1**2), 0, 0))
Here I have just one model but this code is written for model combination in fitting by the lmfit Please kindly let me know about it.
import matplotlib.pyplot as plt
import numpy as np
import sympy
from sympy.parsing import sympy_parser
import lmfit
gauss_peak1 = sympy_parser.parse_expr('A1*exp(-(x-xc1)**2/(2*sigma1**2))')
gauss_peak2 = 0
exp_back = 0
model_list = sympy.Array((gauss_peak1, gauss_peak2, exp_back))
model = sum(model_list)
print(model)
model_list_func = sympy.lambdify(list(model_list.free_symbols), model_list)
model_func = sympy.lambdify(list(model.free_symbols), model)
np.random.seed(1)
x = np.linspace(0, 10, 40)
param_values = dict(x=x, A1=2, sigma1=1, xc1=2)
y = model_func(**param_values)
yi = model_list_func(**param_values)
yn = y + np.random.randn(y.size)*0.4
plt.plot(x, yn, 'o')
plt.plot(x, y)
lm_mod = lmfit.Model(model_func, independent_vars=('x'))
res = lm_mod.fit(data=yn, **param_values)
res.plot_fit()
plt.plot(x, y, label='true')
plt.legend()
plt.show()
lmfit.Model takes a model function that is a Python function. It parses the function arguments and expects those to be the Parameters for the model.
I don't think using sympy-created functions will do that. Do you need to use sympy here? I don't see why. The usage here seems designed to make the code more complex than it needs to be. It seems you want to make a model with a Gaussian-like peak, and a constant(?) background. If so, why not do
from lmfit.Models import GaussianModel, ConstantModel
model = GaussianModel(prefix='p1_') + ConstantModel()
params = model.make_params(p1_amplitude=2, p1_center=2, p1_sigma=1, c=0)
That just seems way easier to me, and it is very easy to add a second Gaussian peak to that model.
But even if you have your own preferred mathematical expression, don't use that as a sympy string, use it as Python code:
def myfunction(x, A1, xc1, sigma1):
return A1*exp(-(x-xc1)**2/(2*sigma1**2))
and then
from lmfit import Model
mymodel = Model(myfunction)
params = mymodel.guess(A1=2, xc1=2, sigma1=1)
In short: sympy is an amazing tool, but lmfit does not use it.

matplotlib update figure in loop [duplicate]

I'm having issues with redrawing the figure here. I allow the user to specify the units in the time scale (x-axis) and then I recalculate and call this function plots(). I want the plot to simply update, not append another plot to the figure.
def plots():
global vlgaBuffSorted
cntr()
result = collections.defaultdict(list)
for d in vlgaBuffSorted:
result[d['event']].append(d)
result_list = result.values()
f = Figure()
graph1 = f.add_subplot(211)
graph2 = f.add_subplot(212,sharex=graph1)
for item in result_list:
tL = []
vgsL = []
vdsL = []
isubL = []
for dict in item:
tL.append(dict['time'])
vgsL.append(dict['vgs'])
vdsL.append(dict['vds'])
isubL.append(dict['isub'])
graph1.plot(tL,vdsL,'bo',label='a')
graph1.plot(tL,vgsL,'rp',label='b')
graph2.plot(tL,isubL,'b-',label='c')
plotCanvas = FigureCanvasTkAgg(f, pltFrame)
toolbar = NavigationToolbar2TkAgg(plotCanvas, pltFrame)
toolbar.pack(side=BOTTOM)
plotCanvas.get_tk_widget().pack(side=TOP)
You essentially have two options:
Do exactly what you're currently doing, but call graph1.clear() and graph2.clear() before replotting the data. This is the slowest, but most simplest and most robust option.
Instead of replotting, you can just update the data of the plot objects. You'll need to make some changes in your code, but this should be much, much faster than replotting things every time. However, the shape of the data that you're plotting can't change, and if the range of your data is changing, you'll need to manually reset the x and y axis limits.
To give an example of the second option:
import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(0, 6*np.pi, 100)
y = np.sin(x)
# You probably won't need this if you're embedding things in a tkinter plot...
plt.ion()
fig = plt.figure()
ax = fig.add_subplot(111)
line1, = ax.plot(x, y, 'r-') # Returns a tuple of line objects, thus the comma
for phase in np.linspace(0, 10*np.pi, 500):
line1.set_ydata(np.sin(x + phase))
fig.canvas.draw()
fig.canvas.flush_events()
You can also do like the following:
This will draw a 10x1 random matrix data on the plot for 50 cycles of the for loop.
import matplotlib.pyplot as plt
import numpy as np
plt.ion()
for i in range(50):
y = np.random.random([10,1])
plt.plot(y)
plt.draw()
plt.pause(0.0001)
plt.clf()
This worked for me. Repeatedly calls a function updating the graph every time.
import matplotlib.pyplot as plt
import matplotlib.animation as anim
def plot_cont(fun, xmax):
y = []
fig = plt.figure()
ax = fig.add_subplot(1,1,1)
def update(i):
yi = fun()
y.append(yi)
x = range(len(y))
ax.clear()
ax.plot(x, y)
print i, ': ', yi
a = anim.FuncAnimation(fig, update, frames=xmax, repeat=False)
plt.show()
"fun" is a function that returns an integer.
FuncAnimation will repeatedly call "update", it will do that "xmax" times.
This worked for me:
from matplotlib import pyplot as plt
from IPython.display import clear_output
import numpy as np
for i in range(50):
clear_output(wait=True)
y = np.random.random([10,1])
plt.plot(y)
plt.show()
I have released a package called python-drawnow that provides functionality to let a figure update, typically called within a for loop, similar to Matlab's drawnow.
An example usage:
from pylab import figure, plot, ion, linspace, arange, sin, pi
def draw_fig():
# can be arbitrarily complex; just to draw a figure
#figure() # don't call!
plot(t, x)
#show() # don't call!
N = 1e3
figure() # call here instead!
ion() # enable interactivity
t = linspace(0, 2*pi, num=N)
for i in arange(100):
x = sin(2 * pi * i**2 * t / 100.0)
drawnow(draw_fig)
This package works with any matplotlib figure and provides options to wait after each figure update or drop into the debugger.
In case anyone comes across this article looking for what I was looking for, I found examples at
How to visualize scalar 2D data with Matplotlib?
and
http://mri.brechmos.org/2009/07/automatically-update-a-figure-in-a-loop
(on web.archive.org)
then modified them to use imshow with an input stack of frames, instead of generating and using contours on the fly.
Starting with a 3D array of images of shape (nBins, nBins, nBins), called frames.
def animate_frames(frames):
nBins = frames.shape[0]
frame = frames[0]
tempCS1 = plt.imshow(frame, cmap=plt.cm.gray)
for k in range(nBins):
frame = frames[k]
tempCS1 = plt.imshow(frame, cmap=plt.cm.gray)
del tempCS1
fig.canvas.draw()
#time.sleep(1e-2) #unnecessary, but useful
fig.clf()
fig = plt.figure()
ax = fig.add_subplot(111)
win = fig.canvas.manager.window
fig.canvas.manager.window.after(100, animate_frames, frames)
I also found a much simpler way to go about this whole process, albeit less robust:
fig = plt.figure()
for k in range(nBins):
plt.clf()
plt.imshow(frames[k],cmap=plt.cm.gray)
fig.canvas.draw()
time.sleep(1e-6) #unnecessary, but useful
Note that both of these only seem to work with ipython --pylab=tk, a.k.a.backend = TkAgg
Thank you for the help with everything.
All of the above might be true, however for me "online-updating" of figures only works with some backends, specifically wx. You just might try to change to this, e.g. by starting ipython/pylab by ipython --pylab=wx! Good luck!
Based on the other answers, I wrapped the figure's update in a python decorator to separate the plot's update mechanism from the actual plot. This way, it is much easier to update any plot.
def plotlive(func):
plt.ion()
#functools.wraps(func)
def new_func(*args, **kwargs):
# Clear all axes in the current figure.
axes = plt.gcf().get_axes()
for axis in axes:
axis.cla()
# Call func to plot something
result = func(*args, **kwargs)
# Draw the plot
plt.draw()
plt.pause(0.01)
return result
return new_func
Usage example
And then you can use it like any other decorator.
#plotlive
def plot_something_live(ax, x, y):
ax.plot(x, y)
ax.set_ylim([0, 100])
The only constraint is that you have to create the figure before the loop:
fig, ax = plt.subplots()
for i in range(100):
x = np.arange(100)
y = np.full([100], fill_value=i)
plot_something_live(ax, x, y)

Fitting to Poisson histogram

I am trying to fit a curve over the histogram of a Poisson distribution that looks like this
I have modified the fit function so that it resembles a Poisson distribution, with the parameter t as a variable. But the curve_fit function can not be plotted and I am not sure why.
def histo(bsize):
N = bsize
#binwidth
bw = (dt.max()-dt.min())/(N-1.)
bin1 = dt.min()+ bw*np.arange(N)
#define the array to hold the occurrence count
bincount= np.array([])
for bin in bin1:
count = np.where((dt>=bin)&(dt<bin+bw))[0].size
bincount = np.append(bincount,count)
#bin center
binc = bin1+0.5*bw
plt.figure()
plt.plot(binc,bincount,drawstyle= 'steps-mid')
plt.xlabel("Interval[ticks]")
plt.ylabel("Frequency")
histo(30)
plt.xlim(0,.5e8)
plt.ylim(0,25000)
import numpy as np
from scipy.optimize import curve_fit
delta_t = 1.42e7
def func(x, t):
return t * np.exp(- delta_t/t)
popt, pcov = curve_fit(func, np.arange(0,.5e8),histo(30))
plt.plot(popt)
The problem with your code is that you do not know what the return values of curve_fit are. It is the parameters for the fit-function and their covariance matrix - not something you can plot directly.
Binned Least-Squares Fit
In general you can get everything much, much more easily:
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy.special import factorial
from scipy.stats import poisson
# get poisson deviated random numbers
data = np.random.poisson(2, 1000)
# the bins should be of integer width, because poisson is an integer distribution
bins = np.arange(11) - 0.5
entries, bin_edges, patches = plt.hist(data, bins=bins, density=True, label='Data')
# calculate bin centers
bin_centers = 0.5 * (bin_edges[1:] + bin_edges[:-1])
def fit_function(k, lamb):
'''poisson function, parameter lamb is the fit parameter'''
return poisson.pmf(k, lamb)
# fit with curve_fit
parameters, cov_matrix = curve_fit(fit_function, bin_centers, entries)
# plot poisson-deviation with fitted parameter
x_plot = np.arange(0, 15)
plt.plot(
x_plot,
fit_function(x_plot, *parameters),
marker='o', linestyle='',
label='Fit result',
)
plt.legend()
plt.show()
This is the result:
Unbinned Maximum-Likelihood fit
An even better possibility would be to not use a histogram at all
and instead to carry out a maximum-likelihood fit.
But by closer examination even this is unnecessary, because the
maximum-likelihood estimator for the parameter of the poissonian distribution is the arithmetic mean.
However, if you have other, more complicated PDFs, you can use this as example:
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import minimize
from scipy.special import factorial
from scipy import stats
def poisson(k, lamb):
"""poisson pdf, parameter lamb is the fit parameter"""
return (lamb**k/factorial(k)) * np.exp(-lamb)
def negative_log_likelihood(params, data):
"""
The negative log-Likelihood-Function
"""
lnl = - np.sum(np.log(poisson(data, params[0])))
return lnl
def negative_log_likelihood(params, data):
''' better alternative using scipy '''
return -stats.poisson.logpmf(data, params[0]).sum()
# get poisson deviated random numbers
data = np.random.poisson(2, 1000)
# minimize the negative log-Likelihood
result = minimize(negative_log_likelihood, # function to minimize
x0=np.ones(1), # start value
args=(data,), # additional arguments for function
method='Powell', # minimization method, see docs
)
# result is a scipy optimize result object, the fit parameters
# are stored in result.x
print(result)
# plot poisson-distribution with fitted parameter
x_plot = np.arange(0, 15)
plt.plot(
x_plot,
stats.poisson.pmf(x_plot, result.x),
marker='o', linestyle='',
label='Fit result',
)
plt.legend()
plt.show()
Thank you for the wonderful discussion!
You might want to consider the following:
1) Instead of computing "poisson", compute "log poisson", for better numerical behavior
2) Instead of using "lamb", use the logarithm (let me call it "log_mu"), to avoid the fit "wandering" into negative values of "mu".
So
log_poisson(k, log_mu): return k*log_mu - loggamma(k+1) - math.exp(log_mu)
Where "loggamma" is the scipy.special.loggamma function.
Actually, in the above fit, the "loggamma" term only adds a constant offset to the functions being minimized, so one can just do:
log_poisson_(k, log_mu): return k*log_mu - math.exp(log_mu)
NOTE: log_poisson_() not the same as log_poisson(), but when used for minimization in the manner above, will give the same fitted minimum (the same value of mu, up to numerical issues). The value of the function being minimized will have been offset, but one doesn't usually care about that anyway.

Matplotlib cmap values must be between 0-1

I am having trouble with the code below:
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import numpy as np
from pylab import *
import sys
s = (('408b2e00', '24.21'), ('408b2e0c', '22.51'), ('4089e04a', '23.44'), ('4089e04d', '24.10'))
temp = [x[1] for x in s]
print temp
figure(figsize=(15, 8))
pts = [(886.38864047695108, 349.78744809964849), (1271.1506973277974, 187.65500904929195), (1237.272277227723, 860.38363675077176), (910.58751197700428, 816.82566805067597)]
x = map(lambda x: x[0],pts) # Extract the values from pts
y = map(lambda x: x[1],pts)
t = temp
result = zip(x,y,t)
img = mpimg.imread('floor.png')
imgplot = plt.imshow(img, cmap=cm.hot)
scatter(x, y, marker='h', c=t, s=150, vmin=-20, vmax=40)
print t
# Add cmap
colorbar()
show()
Given the temperature in s - I am trying to set the values of the cmap so I can use temperatures between -10 and 30 instead of having to used values between 1 and 0. I have set the vmin and vmax values but it still gives me the error below:
ValueError: to_rgba: Invalid rgba arg "23.44" to_rgb: Invalid rgb arg "23.44" gray (string) must be in range 0-1
I have use earlier code to simplify the problem and have been successful. This example below works and shows what I am trying to (hopefully) do:
import matplotlib.pyplot as plt
import matplotlib.image as mpimg
import numpy as np
from pylab import *
figure(figsize=(15, 8))
# use ginput to select markers for the sensors
matplotlib.pyplot.hot()
markers = [(269, 792, -5), (1661, 800, 20), (1017, 457, 30)]
x,y,t = zip(*markers)
img = mpimg.imread('floor.png')
imgplot = plt.imshow(img, cmap=cm.hot)
scatter(x, y, marker='h', c=t, s=150, vmin=-10, vmax=30)
colorbar()
show()
Any ideas why only the second solution works? I am working with dynamic values i.e inputs from mysql and user selected points and so the first solution would be much easier to get working later on (the rest of that code is in this question: Full program code )
Any help would be great. Thanks!
You are handing in strings instead of floats, change this line:
temp = [float(x[1]) for x in s]
matplotlib tries to be good about guessing what you mean and lets you define gray as a string of a float between [0, 1] which is what it is trying to do with your string values (and complaining because it is not in than range).

Plotting an exponential distribution with approbriately naming all variables

I want to insert some arrows into a plot of some exponential distributions:
import pylab as pl
import numpy as np
def gauss2d(x,sigma):
return (1/np.sqrt(2*np.pi*sigma ))*np.exp(-1/2*(x/sigma)**2 )
def draw_arrow(zero, sigma, function):
startx = zero
print startx,function(sigma, sigma)
arr = pl.Arrow(startx,function(startx+sigma, sigma), sigma,0,fc="k",ec="k")
ax = pl.gca()
ax.add_patch(arr)
def plot_gauss2d():
x = np.mgrid[115:135:100j]
#x=np.array(zip(range(5)),dtype=float)
sigma = 1
off=1.0
pl.plot(x,gauss2d(x-126.21,3.56), 'b-')
draw_arrow(126.21, 3.56, gauss2d)
pl.plot(x,gauss2d(x-126.71,4.57), 'b-')
pl.plot(x,gauss2d(x-120.64,3.5), 'b-')
pl.ylabel('frequency')
pl.xlabel('ppm of N')
pl.title
pl.show()
def main():
plot_gauss2d()
if __name__ == "__main__":
main()
Somehow I can't seem to get the arrow right. What I essentially would like to have is something like this:
what I simply cannot figure out is how to set the arrow straight to where I want it to be. It should mark the point of the standard deviation in the correct height. The whole thing should of course produce multiple exponential curves.
The problem with arrow is that it uses the figure coordinate as compared to the data coordinates. Hence, as #Paul have suggested, you can use annotate, as
import pylab as pl
import numpy as np
def gauss2d(x,sigma):
return (1/np.sqrt(2*np.pi*sigma ))*np.exp(-1/2*(x/sigma)**2 )
def markParameters(m,s):
p1=gauss2d(s,s)
p2=gauss2d(0,s)
pl.annotate("", xy=(m-s, p1), xycoords='data', xytext=(m+s, p1), textcoords='data', arrowprops=dict(arrowstyle="<->", connectionstyle="arc3"),)
pl.text(m,p1,'sigma',horizontalalignment='center',verticalalignment='top')
pl.annotate("", xy=(m, 0), xycoords='data', xytext=(m, p2), textcoords='data', arrowprops=dict(arrowstyle="<->", connectionstyle="arc3"),)
pl.text(m,p2*0.75,'mean',horizontalalignment='right',verticalalignment='center',rotation=90)
def plot_gauss2d():
x = np.mgrid[115:135:100j]
#x=np.array(zip(range(5)),dtype=float)
m,s=126,3.56
pl.plot(x,gauss2d(x-m,s), 'b-')
markParameters(m,s)
pl.ylabel('frequency')
pl.xlabel('ppm of N')
pl.title
pl.show()
def main():
plot_gauss2d()
if __name__ == "__main__":
main()
check out this demo for the annotate method:
http://matplotlib.sourceforge.net/examples/pylab_examples/annotation_demo.html
That should take care of what you need.