Fitting data with python - Revision history

Roux: /* Curve fitting */

2016-01-31T14:01:42Z

Curve fitting

← Older revision		Revision as of 16:01, 31 January 2016
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	<source lang="py">		<source lang="py">
	fitfunc = lambda x, a, b: anp.sin(bx)		fitfunc = lambda x, a, b: anp.sin(bx)
	p, pcov = curve_fit(fitfunc,xb,yb,p0 = p0)		p, pcov = curve_fit(fitfunc,xb,yb,p0 = [1.0,1.0])
	print p, np.sqrt(np.diag(pcov))		print p, np.sqrt(np.diag(pcov))
	</source>		</source>

Roux: /* Curve fitting */

2016-01-31T14:00:56Z

Curve fitting

← Older revision		Revision as of 16:00, 31 January 2016
Line 12:		Line 12:
	Using a polynomial fit that is based on generalized linear regression algorithm, solving a linear system.		Using a polynomial fit that is based on generalized linear regression algorithm, solving a linear system.
	<source lang="py">		<source lang="py">
	~~print "polynomial fit"~~
	from numpy.polynomial import polynomial as P		from numpy.polynomial import polynomial as P
	coeff, stats = P.polyfit(xb,yb,9,full=True)		coeff, stats = P.polyfit(xb,yb,9,full=True)
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	Using curve-fit that calls leastsq algorithm, taking a step-by-step search for the minimum.		Using curve-fit that calls leastsq algorithm, taking a step-by-step search for the minimum.
	<source lang="py">		<source lang="py">
	~~print "with curve_fit"~~
	fitfunc = lambda x, a, b: anp.sin(bx)		fitfunc = lambda x, a, b: anp.sin(bx)
	p, pcov = curve_fit(fitfunc,xb,yb,p0 = p0)		p, pcov = curve_fit(fitfunc,xb,yb,p0 = p0)
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	The last lines provides the found optimal parameters and their uncertainties.		The last lines provides the found optimal parameters and their uncertainties.
	It is worth trying several guesses p0.		It is worth trying several guesses p0.


	Plotting the results:		Plotting the results:

Roux at 14:00, 31 January 2016

2016-01-31T14:00:09Z

← Older revision		Revision as of 16:00, 31 January 2016
Line 1:		Line 1:
			== Curve fitting ==

			Preparing noisy data:
			<source lang="py">
			Npoints = 30
			x = np.linspace(1,10,100)
			xb = np.linspace(1,10,Npoints)
			f = lambda x: np.sin(x)
			yb = f(xb) + 0.3*np.random.normal(size=len(xb))
			</source>

			Using a polynomial fit that is based on generalized linear regression algorithm, solving a linear system.
			<source lang="py">
			print "polynomial fit"
			from numpy.polynomial import polynomial as P
			coeff, stats = P.polyfit(xb,yb,9,full=True)
			fitpoly = P.Polynomial(coeff)
			print stats
			</source>
			fitpoly is a function and coeff are the coefficients of the optimal polynomial.

			Using curve-fit that calls leastsq algorithm, taking a step-by-step search for the minimum.
			<source lang="py">
			print "with curve_fit"
			fitfunc = lambda x, a, b: anp.sin(bx)
			p, pcov = curve_fit(fitfunc,xb,yb,p0 = p0)
			print p, np.sqrt(np.diag(pcov))
			</source>
			The last lines provides the found optimal parameters and their uncertainties.
			It is worth trying several guesses p0.


			Plotting the results:
			<source lang="py">
			import matplotlib.pyplot as plt
			plt.scatter(xb,yb)
			plt.plot(x,f(x))
			plt.plot(x,fitpoly(x))
			plt.plot(x,fitfunc(x,p[0],p[1]))
			plt.show()
			</source>

			== Using the least-square function directly ==

	The basic syntax is the following:		The basic syntax is the following:
	<source lang="py">		<source lang="py">

Roux: Created page with "The basic syntax is the following: #!/usr/bin/python from scipy import optimize from numpy import array # your data as lists x = [0.0, 1.0, 2.0, 3.0] y = [1..."

2011-10-20T13:24:09Z

Created page with "The basic syntax is the following: <source lang="py"> #!/usr/bin/python from scipy import optimize from numpy import array # your data as lists x = [0.0, 1.0, 2.0, 3.0] y = [1..."

New page

The basic syntax is the following:
<source lang="py">
#!/usr/bin/python

from scipy import optimize
from numpy import array

# your data as lists
x = [0.0, 1.0, 2.0, 3.0]
y = [1.0, 0.5, 0.0, -1.0]
# define a fitting function and the corresponding error function that must be minimized
# use the lambda shortcut or define standard functions with def fit():
# p is the list of parameters
fit = lambda p, x: p[0] + p[1]*(x) + p[2]*(x)**2
err = lambda p, x, y: fit(p,x) - y
# initial guess
p0 = [1.0,1.0,1.0]
# calls optimize.leastsq to find optimal parameters, converts lists into numpy.array on the fly
p, success = optimize.leastsq(err, p0, args=(array(x), array(y)), ftol=5e-9, xtol=5e-9)
# some info about convergence is in success and the optimized parameters in p
</source>