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lmfit - SineModel+ConstantModel appears inaccurate fit

I'm trying to fit a simple sine function to some experimental data using lmfit and I find that the SineModel with a constant model offset returns, what looks like an inaccurate fit to the data (to me). I suppose it may be helpful to highlight that I am most interested in the frequency of the peaks (and I appreciate that I can simply use a scipy.find_peaks() but would prefer to show a fit to the data).
I use the function below for lmfit model:
def Sine(self, x_axis, y_axis):
sine = SineModel()
const = ConstantModel()
x_fit = np.linspace(min(x_axis), max(x_axis), x_axis.size)
guess_sine = sine.guess(y_axis, x=x_fit)
pars = sine.guess(y_axis, x=x_fit)
sine_offset = SineModel() + ConstantModel()
pars.add('c', value=1, vary=True)
result = sine_offset.fit(y_axis, pars, x=x_fit)
return result
Sine function output (graph and report results) are provided here:
SineModel+ConstModel
I then tried to define my own function, defining my own parameters and evaluating in the same lmfit method, providing sensible "guess" initial values etc.
def Sine_User2(self, x_axis, y_axis):
def sine_func(x, amplitude, freq, shift, c):
return amplitude * np.sin(freq * x + shift) + c
sinemodel = Model(sine_func)
# Take a FFT of the data to provide a guess starting location for the curve fitting
x = np.array(x_axis)
y = np.array(y_axis)
ff = np.fft.fftfreq(len(x), (x[1] - x[0])) # assume uniform spacing
Fyy = abs(np.fft.fft(y))
guess_freq = abs(ff[np.argmax(Fyy[1:]) + 1]) * 2. * np.pi
guess_amp = np.std(y) * 2.**0.5
guess_offset = np.mean(y)
x_fit = np.linspace(min(x_axis), max(x_axis), x_axis.size)
params = sinemodel.make_params(amplitude = guess_amp, freq = guess_freq, shift = 0, c = guess_offset )
result = sinemodel.fit(y_axis, params, x = x_fit)
return result
The output of the user defined model appears to provide a much closer fit to the data, however, the report does not provide uncertainties citing a warning that the "Uncertainties could not be estimated":
SineUser2 function outputs (graph and report results) are provided here: User Defined Model
I then tried to include min/max values to the parameters by replacing the "sinmodel.make_params" line with:
params = Parameters()
params.add('amplitude', value=guess_amp, min = 0)
params.add('freq', value=guess_freq, min=0)
params.add('shift', value=0, min=-2*np.pi, max=2*np.pi)
params.add('c', value=guess_offset)
But the results resort back to the SineModel+ConstModel results seen in the first linked graph/report results. Therefore it must be something to do with the way I'm setting initial values.
The fit using the "SineUser2" function appears to be better. Is there a way to improve the fit for "Sine" function in the first block of code.
Why are the uncertainties not calculated in the second function "Sine_User2"?
Data (.csv):
Wavelength (nm),Power (dBm),,,,,
1549.9,-13.76008731,,,,,
1549.905,-13.69423162,,,,,
1549.91,-12.59004339,,,,,
1549.915,-11.31061848,,,,,
1549.92,-10.58731809,,,,,
1549.925,-10.19024329,,,,,
1549.93,-10.07301418,,,,,
1549.935,-10.19513172,,,,,
1549.94,-10.45582159,,,,,
1549.945,-11.15984161,,,,,
1549.95,-12.15876596,,,,,
1549.955,-13.44674933,,,,,
1549.96,-13.56388277,,,,,
1549.965,-12.2513065,,,,,
1549.97,-11.08699015,,,,,
1549.975,-10.43829185,,,,,
1549.98,-10.12861158,,,,,
1549.985,-10.0962929,,,,,
1549.99,-10.1852173,,,,,
1549.995,-10.55438183,,,,,
1550,-11.19555345,,,,,
1550.005,-12.28715299,,,,,
1550.01,-13.5153863,,,,,
1550.015,-13.47019261,,,,,
1550.02,-12.12394732,,,,,
1550.025,-11.01946751,,,,,
1550.03,-10.42138778,,,,,
1550.035,-10.14438079,,,,,
1550.04,-10.05681218,,,,,
1550.045,-10.17148605,,,,,
1550.05,-10.56046759,,,,,
1550.055,-11.11621478,,,,,
1550.06,-12.19930263,,,,,
1550.065,-13.48428349,,,,,
1550.07,-13.43424913,,,,,
1550.075,-12.08019952,,,,,
1550.08,-11.08731704,,,,,
1550.085,-10.45730899,,,,,
1550.09,-10.11278169,,,,,
1550.095,-10.00651194,,,,,
,,,,,,

How to make scipy.optimize.curve_fit result in a better sine regression fit?

I have a problem where I am using scipy.optimize.curve_fit to do a regression fit to a sine/cosine function but the fit does not seem as optimized as I want it to be. How can I change my code to make the fitting better?
I have already tried changing how parameters are tried for the dataset and there is always seemingly a difference in phase-offset of my generated fit or the fitting function is not fitting to the proper minima/maxima.
Here is the code I am using to generate the regression fit. The output (fitfunc) can be plotted to show the result.
def sin_regress(data_x, data_y):
"""Function regression fits data to SIN function; does not need guess of freq.
Parameters
----------
data_x :
Data for X values, most likely a set of voltages.
data_y :
Data for Y values, most likely the resulting powers from voltages.
Returns
-------
__ :
Dictionary containing values for amplitude, angular frequency, phase, offset, frequency, period, fit function, max covariance, initial guess.
"""
data_x = np.array(data_x)
data_y = np.array(data_y)
freqz = np.fft.rfftfreq(len(data_x), (data_x[1] - data_x[0])) # uniform spacing
freq_y = abs(np.fft.rfft(data_y))
guess_freq = abs(freqz[np.argmax(freq_y[1:])+1]) # exclude offset peak
guess_amp = np.std(data_y) * 2.**0.5
guess_offset = np.mean(data_y)
guess = np.array([guess_amp, 2.*np.pi*guess_freq, 0., guess_offset])
def sinfunc(t, A, w, p, c):
"""Raw function to be used to fit data.
Parameters
----------
t :
Voltage array
A :
Amplitude
w :
Angular frequency
p :
Phase
c :
Constant value
Returns
-------
__ :
Formed fit function with provided values.
"""
return A * np.sin(w*t + p) + c
popt, pcov = scipy.optimize.curve_fit(sinfunc, data_x, data_y, p0=guess)
A, w, p, c = popt
f = w/(2.*np.pi)
fitfunc = lambda t: A * np.sin(w*t + p) + c
return {"amp": A, "omega": w, "phase": p, "offset": c, "freq": f, "period": 1./f, "fitfunc": fitfunc, "maxcov": np.max(pcov), "rawres": (guess,popt,pcov)}
With my trial dataset being:
x = np.linspace(3.5,9.5,(9.5-3.5)/0.00625 + 1)
pow1 = [1.8262110863, 1.80944546009, 1.7970185646900003, 1.77120336754, 1.7458101235699999, 1.73597098224, 1.7122529922799998, 1.70015674142, 1.68968617429, 1.6989396515, 1.69760676076, 1.6946375613599998, 1.6895321899, 1.68145658386, 1.68581793183, 1.6920468775900002, 1.6865452951599997, 1.68570953338, 1.6922784791700003, 1.70958957412, 1.71683408637, 1.70360183933, 1.6919669752199997, 1.6669487117300001, 1.6351298032300001, 1.6061729066600001, 1.57344333403, 1.54723708217, 1.5277773737599998, 1.5122628414300001, 1.4962354965200002, 1.4873367459, 1.47567715522, 1.4696584634, 1.46159565032, 1.45320592315, 1.4487225244200002, 1.44572887186, 1.44089260198, 1.4367157657399998, 1.4349226211, 1.43614316806, 1.4381950627400002, 1.43947658627, 1.4483572314200002, 1.4504305909200002, 1.44436990692, 1.43367609757, 1.42637295252, 1.41197427963, 1.4067529511399999, 1.39714414185, 1.38309980493, 1.3730701362500004, 1.3693239836499997, 1.3729558979599998, 1.38291189477, 1.3988274622900003, 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2.16672507523, 2.1595190200499994, 2.15408655871, 2.16100126623, 2.1646243915, 2.16989273172, 2.1760575368399997, 2.18993197141, 2.20082640578, 2.18953400264, 2.1673666182699995, 2.15301331645, 2.1344672799800004, 2.1212936853000004, 2.1081594070399996, 2.08825354625, 2.0697085058700004, 2.045492469, 2.02153998684, 2.0038663723099996, 2.0038828566799998, 2.0085019585599997, 2.0192783851200002, 2.03833670679, 2.05771370034, 2.08050465897, 2.1006803439999997, 2.1263974552, 2.14748327701, 2.17287144288, 2.1941383974899997, 2.19820122981, 2.2003345112000003, 2.20800316408, 2.21184328157, 2.21310867227, 2.21112832057, 2.1998480658600004, 2.1906804089599996, 2.17670294702, 2.1515223983699996, 2.1337058932199997, 2.11742559909, 2.1017357932899996, 2.0798991511200002, 2.05328198125, 2.02510619803, 2.00362619651, 1.98193234731, 1.9618359005700001, 1.9612528146099997, 1.97096636996, 1.9761617414300001, 1.9782324642600002, 1.99263889104, 2.00500029816, 2.01506871685, 2.02912785846, 2.04221860157, 2.06368362263, 2.07491317421, 2.08832055797, 2.09538342956, 2.1084886843899997, 2.1158979036700005, 2.1260576895499996, 2.13639327622, 2.14181249535, 2.1392352295499997, 2.14448495648, 2.1421138235, 2.14009620617, 2.1384934521399996, 2.1319765571600002, 2.1216323962400003, 2.1065051490999998, 2.08999485498, 2.06996758792, 2.05396301646, 2.0366352808700006, 2.023489069, 1.9927697308899996, 1.9807445347400001, 1.97629449536, 1.9772154719699997, 1.9837454333899998, 1.9903514690000002, 1.9990068602399997, 2.0052703762999995, 2.0102515290099996, 2.01071088451, 2.00780344289, 2.00202451671, 1.99526703575, 1.9894158244, 1.9859053554, 1.9872483633099995, 1.99006639085, 2.00697930222, 2.0329301048299997, 2.05059264513, 2.0540770985099996, 2.04176762498, 2.0093012359700007, 1.9757453156100002, 1.94977980597, 1.94015615295, 1.93165724611, 1.9207719523600002, 1.90945249843, 1.89062300491, 1.87690150004, 1.8621346825699998, 1.84607821661, 1.828253313, 1.8169694254700002, 1.8075289169999997, 1.8040289362800004, 1.79267489253, 1.78023102445, 1.7778953016200003, 1.7787011610500003, 1.78226670819, 1.7830425676100004, 1.77486727406, 1.7675372149399997, 1.7575688744100002, 1.7498299871300003, 1.74518012353, 1.73248096246, 1.7160241253800002, 1.70317674164, 1.6978293584500002, 1.6946921121299998, 1.6961595927200002, 1.70211670251, 1.7104493398199998, 1.7203816647499999, 1.7274331496, 1.7311123100199999, 1.73665119714, 1.74750018228, 1.7625600270900001, 1.76829838689, 1.7683754962599998, 1.7604641870999997, 1.7378729159800002, 1.7182883638100002, 1.7072806677199999, 1.7037852573199999, 1.6963237919299996, 1.67904111493, 1.64849412058, 1.61509034869, 1.58860298353, 1.56708077499, 1.5563275906199998, 1.5508352464699997, 1.5448227655799998, 1.53880546048, 1.54041544105, 1.5403843473000003, 1.53577729621, 1.5273169831, 1.51722079097, 1.5010415320300001, 1.4873523904299997, 1.47098713536, 1.45343877476, 1.4333900233299999, 1.4214382256099998, 1.4199358231499999, 1.42357822576, 1.42446916333, 1.4169634987200002, 1.40651060735, 1.39602957147, 1.38608337936, 1.38502109414, 1.38722933647, 1.3877573052599999, 1.38915685615, 1.3879546490299999, 1.38030042971, 1.37484574183, 1.36882917891, 1.36771619056, 1.36598312403, 1.35475238104, 1.3352715984299999, 1.31243304213, 1.29205091175, 1.26981483599, 1.25096920963, 1.23261465755, 1.2107178005399999, 1.1896016271599998, 1.1758782668, 1.17342422369, 1.17358562993, 1.17110207509, 1.1674486178099999, 1.1603703751, 1.1565048865399998, 1.15140617524, 1.15148740571, 1.15832875386, 1.16650391071, 1.1712949266600001, 1.16865191865, 1.16596408644, 1.1661593208199998, 1.16419447693, 1.15754447647, 1.15312982771, 1.1506705697300001, 1.14375644814, 1.13705099847, 1.12589113437, 1.11212277402, 1.10001296849, 1.08946394429, 1.0747068729400002, 1.05980790705, 1.0438431988799999, 1.02497712333, 1.00659505173, 0.98919173016, 0.9715707328300001, 0.95416868081, 0.9416231916500001, 0.92753217501, 0.91364512326, 0.90414607963, 0.8947884227199999, 0.8843405703999998, 0.8769049253500001, 0.8719632452999999, 0.86833484662, 0.8680955887799999, 0.86604049098, 0.86558996362, 0.86372701427, 0.85893691627, 0.85435131048, 0.84886228665, 0.8409088095199999, 0.82732292967, 0.8182398235399999, 0.81298593645, 0.8065804672500001, 0.7963832009099999, 0.7813524576499999, 0.7642633939500001, 0.74891606863, 0.73387495429, 0.72021307831, 0.70711249145, 0.6972523931, 0.68836254874, 0.6789805168, 0.66917573095, 0.65520369872, 0.6405349086200001, 0.6262600443299999, 0.6128265668199999, 0.6004827768800001, 0.58821246352, 0.5763513298499999, 0.56580466895, 0.55820613325, 0.5498382224900001, 0.5432313079700001, 0.5383656045, 0.53169802591];
Here are some additional values for the pow dataset:
(Link to pastebin to not exceed post length limit)
https://pastebin.com/5GP8sj4N
The resulting fit that from the trial dataset (x, pow1) I get is shown here (orange) with the original (pow1) data (blue)
As mentioned, there is an issue with how the phase fits the minima and maxima. Unfortunately the application of getting this fit function correct has very little room for error.
Please help out if you have an idea of how to make this fit the data better!
Edit:
I tried what #Joe mentioned in the comments, with first filtering the data. I utilized a Savitzky-Golay filter and recieved the following result, Original data (blue), the filtered data (green), and the fit to the filtered data (orange). Again the same shift in minima and maxima is still present in the fit function to the filtered data.

Here are my results with more aggressive clipping bounds of 0.5 to 1.75 for each data set.
for pow1:
A = 9.6711505138648990E-01
c = 9.7613787086912507E-01
p = 4.0262076448344617E+00
w = 1.2654001570670070E+00
for pow2:
A = 9.4894637490866129E-01
c = 9.6733405789489280E-01
p = 4.0892433833755097E+00
w = 1.2578627414445132E+00
for pow3:
A = 9.8595630272060597E-01
c = 9.6749868212694512E-01
p = 4.0859456191316230E+00
w = 1.2598547148182329E+00
for pow4:
A = -9.4636707498392481E-01
c = 9.5047597808408602E-01
p = -4.2643913461857056E+02
w = 1.2761107231684055E+00

I think I have this figured out - your data is not a mathematically perfect sine wave + noise, so the fitting software can only come close to modeling a sine function to this data. If you must have more accuracy, try splitting the model into different segments and use a piecewise fit. Here is a close-up of the problem area:

Apply non-linear regression for multi dimension data samples in Python

I have installed Numpy and SciPy, but I'm not quite understand their documentation about polyfit.
For exmpale, Here's my three data samples:
[-0.042780748663101636, -0.0040771571786609945, -0.00506567946276074]
[0.042780748663101636, -0.0044771571786609945, -0.10506567946276074]
[0.542780748663101636, -0.005771571786609945, 0.30506567946276074]
[-0.342780748663101636, -0.0304077157178660995, 0.90506567946276074]
The first two columns are sample features, the third column is output, My target is to get a function that could take two parameters(first two columns) and return its prediction(the output).
Any simple example ?
====================== EDIT ======================
Note that, I need to fit something like a curve, not only straight lines. The polynomial should be something like this ( n = 3):
a*x1^3 + b*x2^2 + c*x3 + d = y
Not:
a*x1 + b*x2 + c*x3 + d = y
x1, x2, x3 are features of one sample, y is the output

Try something like
edit: added an example function that used results of linear regression to estimate output.
import numpy as np
data =np.array(
[[-0.042780748663101636, -0.0040771571786609945, -0.00506567946276074],
[0.042780748663101636, -0.0044771571786609945, -0.10506567946276074],
[0.542780748663101636, -0.005771571786609945, 0.30506567946276074],
[-0.342780748663101636, -0.0304077157178660995, 0.90506567946276074]])
coefficient = data[:,0:2]
dependent = data[:,-1]
x,residuals,rank,s = np.linalg.lstsq(coefficient,dependent)
def f(x,u,v):
return u*x[0] + v*x[1]
for datum in data:
print f(x,*datum[0:2])
Which gives
>>> x
array([ 0.16991146, -30.18923739])
>>> residuals
array([ 0.07941146])
>>> rank
2
>>> s
array([ 0.64490113, 0.02944663])
and the function created with your coefficients gave
0.115817326583
0.142430900298
0.266464019171
0.859743371665
More info can be found at the documentation I posted as a comment.
edit 2: fitting your data to an arbitrary model.
edit 3: made my model a function for ease of understanding.
edit 4: made code more easily read/ changed model to a quadratic fit, but you should be able to read this code and know how to make it minimize any residual you want now.
contrived example:
import numpy as np
from scipy.optimize import leastsq
data =np.array(
[[-0.042780748663101636, -0.0040771571786609945, -0.00506567946276074],
[0.042780748663101636, -0.0044771571786609945, -0.10506567946276074],
[0.542780748663101636, -0.005771571786609945, 0.30506567946276074],
[-0.342780748663101636, -0.0304077157178660995, 0.90506567946276074]])
coefficient = data[:,0:2]
dependent = data[:,-1]
def model(p,x):
a,b,c = p
u = x[:,0]
v = x[:,1]
return (a*u**2 + b*v + c)
def residuals(p, y, x):
a,b,c = p
err = y - model(p,x)
return err
p0 = np.array([2,3,4]) #some initial guess
p = leastsq(residuals, p0, args=(dependent, coefficient))[0]
def f(p,x):
return p[0]*x[0] + p[1]*x[1] + p[2]
for x in coefficient:
print f(p,x)
gives
-0.108798280153
-0.00470479385807
0.570237823475
0.413016072653

Fit two normal distributions (histograms) with MCMC using pymc?

I am trying to fit line profiles as detected with a spectrograph on a CCD. For ease of consideration, I have included a demonstration that, if solved, is very similar to the one I actually want to solve.
I've looked at this:
https://stats.stackexchange.com/questions/46626/fitting-model-for-two-normal-distributions-in-pymc
and various other questions and answers, but they are doing something fundamentally different than what I want to do.
import pymc as mc
import numpy as np
import pylab as pl
def GaussFunc(x, amplitude, centroid, sigma):
return amplitude * np.exp(-0.5 * ((x - centroid) / sigma)**2)
wavelength = np.arange(5000, 5050, 0.02)
# Profile 1
centroid_one = 5025.0
sigma_one = 2.2
height_one = 0.8
profile1 = GaussFunc(wavelength, height_one, centroid_one, sigma_one, )
# Profile 2
centroid_two = 5027.0
sigma_two = 1.2
height_two = 0.5
profile2 = GaussFunc(wavelength, height_two, centroid_two, sigma_two, )
# Measured values
noise = np.random.normal(0.0, 0.02, len(wavelength))
combined = profile1 + profile2 + noise
# If you want to plot what this looks like
pl.plot(wavelength, combined, label="Measured")
pl.plot(wavelength, profile1, color='red', linestyle='dashed', label="1")
pl.plot(wavelength, profile2, color='green', linestyle='dashed', label="2")
pl.title("Feature One and Two")
pl.legend()
My question: Can PyMC (or some variant) give me the mean, amplitude, and sigma for the two components used above?
Please note that the functions that I will actually fit on my real problem are NOT Gaussians -- so please provide the example using a generic function (like GaussFunc in my example), and not a "built-in" pymc.Normal() type function.
Also, I understand model selection is another issue: so with the current noise, 1 component (profile) might be all that is statistically justified. But I'd like to see what the best solution for 1, 2, 3, etc. components would be.
I'm also not wed to the idea of using PyMC -- if scikit-learn, astroML, or some other package seems perfect, please let me know!
EDIT:
I failed a number of ways, but one of the things that I think was on the right track was the following:
sigma_mc_one = mc.Uniform('sig', 0.01, 6.5)
height_mc_one = mc.Uniform('height', 0.1, 2.5)
centroid_mc_one = mc.Uniform('cen', 5015., 5040.)
But I could not construct a mc.model that worked.

Not the most concise PyMC code, but I made that decision to help the reader. This should run, and give (really) accurate results.
I made the decision to use Uniform priors, with liberal ranges, because I really have no idea what we are modelling. But probably one has an idea about the centroid locations, and can use a better priors there.
### Suggested one runs the above code first.
### Unknowns we are interested in
est_centroid_one = mc.Uniform("est_centroid_one", 5000, 5050 )
est_centroid_two = mc.Uniform("est_centroid_two", 5000, 5050 )
est_sigma_one = mc.Uniform( "est_sigma_one", 0, 5 )
est_sigma_two = mc.Uniform( "est_sigma_two", 0, 5 )
est_height_one = mc.Uniform( "est_height_one", 0, 5 )
est_height_two = mc.Uniform( "est_height_two", 0, 5 )
#std deviation of the noise, converted to precision by tau = 1/sigma**2
precision= 1./mc.Uniform("std", 0, 1)**2
#Set up the model's relationships.
#mc.deterministic( trace = False)
def est_profile_1(x = wavelength, centroid = est_centroid_one, sigma = est_sigma_one, height= est_height_one):
return GaussFunc( x, height, centroid, sigma )
#mc.deterministic( trace = False)
def est_profile_2(x = wavelength, centroid = est_centroid_two, sigma = est_sigma_two, height= est_height_two):
return GaussFunc( x, height, centroid, sigma )
#mc.deterministic( trace = False )
def mean( profile_1 = est_profile_1, profile_2 = est_profile_2 ):
return profile_1 + profile_2
observations = mc.Normal("obs", mean, precision, value = combined, observed = True)
model = mc.Model([est_centroid_one,
est_centroid_two,
est_height_one,
est_height_two,
est_sigma_one,
est_sigma_two,
precision])
#always a good idea to MAP it prior to MCMC, so as to start with good initial values
map_ = mc.MAP( model )
map_.fit()
mcmc = mc.MCMC( model )
mcmc.sample( 50000,40000 ) #try running for longer if not happy with convergence.
Important
Keep in mind the algorithm is agnostic to labeling, so the results might show profile1 with all the characteristics from profile2 and vice versa.

fitting an ODE with python leastsq gives a cast error when initial conditions is passed as parameter

I have a set of data that I am trying to fit to an ODE model using scipy's leastsq function. My ODE has parameters beta and gamma, so that it looks for example like this:
# dS/dt = -betaSI
# dI/dt = betaSI - gammaI
# dR/dt = gammaI
# with y0 = y(t=0) = (S(0),I(0),R(0))
The idea is to find beta and gamma so that the numerical integration of my system of ODE's best approximates the data. I am able to do this just fine using leastsq if I know all the points in my initial condition y0.
Now, I am trying to do the same thing but to pass now one of the entries of y0 as an extra parameter. Here is where the Python and me stop communicating...
I did a function so that now the first entry of the parameters that I pass to leastsq is the initial condition of my variable R.
I get the following message:
*Traceback (most recent call last):
File "/Users/Laura/Dropbox/SHIV/shivmodels/test.py", line 73, in <module>
p1,success = optimize.leastsq(errfunc, initguess, args=(simpleSIR,[y0[0]],[Tx],[mydata]))
File "/Library/Frameworks/Python.framework/Versions/7.2/lib/python2.7/site-packages/scipy/optimize/minpack.py", line 283, in leastsq
gtol, maxfev, epsfcn, factor, diag)
TypeError: array cannot be safely cast to required type*
Here is my code. It is a little more involved that what it needs to be for this example because in reality I want to fit another ode with 7 parameters and want to fit to several data sets at once. But I wanted to post here something simpler... Any help will be very very much appreciated! Thank you very much!
import numpy as np
from matplotlib import pyplot as plt
from scipy import optimize
from scipy.integrate import odeint
#define the time span for the ODE integration:
Tx = np.arange(0,50,1)
num_points = len(Tx)
#define a simple ODE to fit:
def simpleSIR(y,t,params):
dydt0 = -params[0]*y[0]*y[1]
dydt1 = params[0]*y[0]*y[1] - params[1]*y[1]
dydt2 = params[1]*y[1]
dydt = [dydt0,dydt1,dydt2]
return dydt
#generate noisy data:
y0 = [1000.,1.,0.]
beta = 12*0.06/1000.0
gamma = 0.25
myparam = [beta,gamma]
sir = odeint(simpleSIR, y0, Tx, (myparam,))
mydata0 = sir[:,0] + 0.05*(-1)**(np.random.randint(num_points,size=num_points))*sir[:,0]
mydata1 = sir[:,1] + 0.05*(-1)**(np.random.randint(num_points,size=num_points))*sir[:,1]
mydata2 = sir[:,2] + 0.05*(-1)**(np.random.randint(num_points,size=num_points))*sir[:,2]
mydata = np.array([mydata0,mydata1,mydata2]).transpose()
#define a function that will run the ode and fit it, the reason I am doing this
#is because I will use several ODE's to see which one fits the data the best.
def fitfunc(myfun,y0,Tx,params):
myfit = odeint(myfun, y0, Tx, args=(params,))
return myfit
#define a function that will measure the error between the fit and the real data:
def errfunc(params,myfun,y0,Tx,y):
"""
INPUTS:
params are the parameters for the ODE
myfun is the function to be integrated by odeint
y0 vector of initial conditions, so that y(t0) = y0
Tx is the vector over which integration occurs, since I have several data sets and each
one has its own vector of time points, Tx is a list of arrays.
y is the data, it is a list of arrays since I want to fit to multiple data sets at once
"""
res = []
for i in range(len(y)):
V0 = params[0][i]
myparams = params[1:]
initCond = np.zeros([3,])
initCond[:2] = y0[i]
initCond[2] = V0
myfit = fitfunc(myfun,initCond,Tx[i],myparams)
res.append(myfit[:,0] - y[i][:,0])
res.append(myfit[:,1] - y[i][:,1])
res.append(myfit[1:,2] - y[i][1:,2])
#end for
all_residuals = np.hstack(res).ravel()
return all_residuals
#end errfunc
#example of the problem:
V0 = [0]
params = [V0,beta,gamma]
y0 = [1000,1]
#this is just to test that my errfunc does work well.
errfunc(params,simpleSIR,[y0],[Tx],[mydata])
initguess = [V0,0.5,0.5]
p1,success = optimize.leastsq(errfunc, initguess, args=(simpleSIR,[y0[0]],[Tx],[mydata]))

The problem is with the variable initguess. The function optimize.leastsq has the following call signature:
http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.leastsq.html
It's second argument, x0, has to be an array. Your list
initguess = [v0,0.5,0.5]
won't be converted to an array because v0 is a list instead of an int or float. So you get an error when you try to convert initguess from a list to an array in the leastsq function.
I would adjust the variable params from
def errfunc(params,myfun,y0,Tx,y):
so that it is a 1-D array. Make the first few entries the values of v0 then append beta and gamma to that.