On Tue, May 1, 2012 at 11:44 AM, <josef.pktd@gmail.com> wrote:

On Tue, May 1, 2012 at 1:31 PM, camille chambon <camillechambon@yahoo.fr> wrote:

...

Hello,

I would like to fit 'a' such as y = a * x**3 + b * x**2 + c * x + d, where x and y are measured data, and b = 0.0, c = -0.00458844157413 and d = 5.8 are fixed.

According to

...

I try to use scipy.optimize.leastsq fit routine like that:

#### CODE #####

from numpy import * from pylab import * from scipy import optimize

# My data points x = array([1078.0, 1117.0, 1212.1, 1368.7, 1686.8, 1880.0]) y = array([5.8, 5.6, 5.4, 4.9, 2.4, 0.0])

b, c, d = 0.0, -0.00458844157413, 5.8 # Fixed parameters

fitfunc = lambda p, x: poly1d([p[0], b, c, d])(x) # Target function errfunc = lambda p, x, y: fitfunc(p, x) - y # Distance to the target function

p0 = [-4.0E-09] # Initial guess for the parameters p1, success = optimize.leastsq(errfunc, p0[:], args=(x, y))

time = linspace(x.min(), x.max(), 100) plot(x, y, "ro", time, fitfunc(p1, time), "r-") # Plot of the data and

http://www.scipy.org/Cookbook/FittingData#head-27373a786baa162a2e8a910ee0b8a... , the

...

fit

title("a fitting") xlabel("time [day]") ylabel("number []") legend(('x position', 'x fit', 'y position', 'y fit'))

show()

################################

But the fit does not work (as one can see on the attached image).

Does someone have any idea of what I'm doing wrong?

Thanks in advance for your help.

my guess would be that the scale is awful, the x are very large

if you only need the to estimate "a", then it's just a very simple linear regression problem dot(x,x)/dot(x,y) or something like this.

as aside numpy.polynomial works very well for fitting a polynomial, but doesn't allow for missing terms

It does recognize NA in devel, but we will see where that goes ;) Chuck

Thanks for your answer. I tried to reduce my problem to a linear regression problem: x = array([1078.0, 1117.0, 1212.1, 1368.7, 1686.8, 1880.0]) y = array([5.8, 5.6, 5.4, 4.9, 2.4, 0.0]) b, c, d =  0.0, -0.00458844157413, 5.8 z = y - b * x**2 - c * x p = numpy.polyfit(x, z, 3) time = linspace(x.min(), x.max(), 100) plot(x, y, "ro", time, numpy.poly1d([p[0], b, c, d])(time), "r-") but it doesn't work (see attached image). Where am I wrong? Cheers, Camille ________________________________ De : "josef.pktd@gmail.com" <josef.pktd@gmail.com> À : camille chambon <camillechambon@yahoo.fr>; SciPy Users List <scipy-user@scipy.org> Envoyé le : Mardi 1 mai 2012 19h44 Objet : Re: [SciPy-User] Least-square fitting of a 3rd degree polynomial On Tue, May 1, 2012 at 1:31 PM, camille chambon <camillechambon@yahoo.fr> wrote:

Hello,

I would like to fit 'a' such as y = a * x**3 + b * x**2 + c * x + d, where x and y are measured data, and b = 0.0, c = -0.00458844157413 and d = 5.8 are fixed.

According to http://www.scipy.org/Cookbook/FittingData#head-27373a786baa162a2e8a910ee0b8a..., I try to use scipy.optimize.leastsq fit routine like that:

#### CODE #####

from numpy import * from pylab import * from scipy import optimize

# My data points x = array([1078.0, 1117.0, 1212.1, 1368.7, 1686.8, 1880.0]) y = array([5.8, 5.6, 5.4, 4.9, 2.4, 0.0])

b, c, d =  0.0, -0.00458844157413, 5.8 # Fixed parameters

fitfunc = lambda p, x: poly1d([p[0], b, c, d])(x) # Target function errfunc = lambda p, x, y: fitfunc(p, x) - y # Distance to the target function

p0 = [-4.0E-09] # Initial guess for the parameters p1, success = optimize.leastsq(errfunc, p0[:], args=(x, y))

time = linspace(x.min(), x.max(), 100) plot(x, y, "ro", time, fitfunc(p1, time), "r-") # Plot of the data and the fit

title("a fitting") xlabel("time [day]") ylabel("number []") legend(('x position', 'x fit', 'y position', 'y fit'))

show()

################################

But the fit does not work (as one can see on the attached image).

Does someone have any idea of what I'm doing wrong?

Thanks in advance for your help.

my guess would be that the scale is awful, the x are very large if you only need the to estimate "a", then it's just a very simple linear regression problem dot(x,x)/dot(x,y) or something like this. as aside numpy.polynomial works very well for fitting a polynomial, but doesn't allow for missing terms Josef

Cheers,

Camille

_______________________________________________ SciPy-User mailing list SciPy-User@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-user

Thanks for your answer.

I tried to reduce my problem to a

Thanks for your answer. I realized I made a mistake with my data. It works much better now. Sorry, I have my head in the clouds... Cheers, Camille ________________________________ De : "josef.pktd@gmail.com" <josef.pktd@gmail.com> À : SciPy Users List <scipy-user@scipy.org> Envoyé le : Mercredi 2 mai 2012 12h45 Objet : Re: [SciPy-User] Re : Least-square fitting of a 3rd degree polynomial On Wed, May 2, 2012 at 3:35 AM, camille chambon <camillechambon@yahoo.fr> wrote: linear regression problem:

x = array([1078.0, 1117.0, 1212.1, 1368.7, 1686.8, 1880.0]) y = array([5.8, 5.6, 5.4, 4.9, 2.4, 0.0]) b, c, d =  0.0, -0.00458844157413, 5.8 z = y - b * x**2 - c * x p = numpy.polyfit(x, z, 3) time = linspace(x.min(), x.max(), 100) plot(x, y, "ro", time, numpy.poly1d([p[0], b, c, d])(time), "r-")

but it doesn't work (see attached image).

Where am I wrong?

Are you sure you got your fixed values b,c,d right? y2 = y - d - c * x - b * x**2

...

...

y2 array([ 4.94634002,  4.92528924,  5.16165003,  5.38019998,  4.33978325,         2.82627016])

It doesn't look like you can fit y2  as a function of x**3 and get a good result. I get a similar plot to your original leastsq solution. import numpy as np import matplotlib.pyplot as plt x = np.array([1078.0, 1117.0, 1212.1, 1368.7, 1686.8, 1880.0]) y = np.array([5.8, 5.6, 5.4, 4.9, 2.4, 0.0]) b, c, d =  0.0, -0.00458844157413, 5.8 y2 = y - d - c * x - b * x**2 x2 = x**3 a = np.dot(x2, y2) / np.dot(x2, x2) #check with statsmodels import statsmodels.api as sm a2 = sm.OLS(y2, x2).fit().params print a, a2[0] xx = np.linspace(x.min(), x.max()) yhat = d + c * xx + b * xx**2 + a * xx**3 plt.plot(x, y, 'o') plt.plot(xx, yhat, '-') plt.figure() plt.plot(x, y2, 'o') plt.show() Josef

Cheers,

Camille

________________________________ De : "josef.pktd@gmail.com" <josef.pktd@gmail.com> À : camille chambon <camillechambon@yahoo.fr>; SciPy Users List <scipy-user@scipy.org> Envoyé le : Mardi 1 mai 2012 19h44 Objet : Re: [SciPy-User] Least-square fitting of a 3rd degree polynomial

On Tue, May 1, 2012 at 1:31 PM, camille chambon <camillechambon@yahoo.fr> wrote:

...

Hello,

I would like to fit 'a' such as y = a * x**3 + b * x**2 + c * x + d, where x and y are measured data, and b = 0.0, c = -0.00458844157413 and d = 5.8 are fixed.

According to

http://www.scipy.org/Cookbook/FittingData#head-27373a786baa162a2e8a910ee0b8a..., I try to use scipy.optimize.leastsq fit routine like that:

#### CODE #####

from numpy import * from pylab import * from scipy import optimize

# My data points x = array([1078.0, 1117.0, 1212.1, 1368.7, 1686.8, 1880.0]) y = array([5.8, 5.6, 5.4, 4.9, 2.4, 0.0])

b, c, d =  0.0, -0.00458844157413, 5.8 # Fixed parameters

fitfunc = lambda p, x: poly1d([p[0], b, c, d])(x) # Target function errfunc = lambda p, x, y: fitfunc(p, x) - y # Distance to the target function

p0 = [-4.0E-09] # Initial guess for the parameters

p1, success = optimize.leastsq(errfunc, p0[:], args=(x, y))

...

time = linspace(x.min(), x.max(), 100) plot(x, y, "ro", time, fitfunc(p1, time), "r-") # Plot of the data and the fit

title("a fitting") xlabel("time [day]") ylabel("number []") legend(('x position', 'x fit', 'y position', 'y fit'))

show()

################################

But the fit does not work (as one can see on the attached image).

Does someone have any idea of what I'm doing wrong?

Thanks in advance for your help.

my guess would be that the scale is awful, the x are very large

if you only need the to estimate "a", then it's just a very simple linear regression problem dot(x,x)/dot(x,y) or something like this.

as aside numpy.polynomial works very well for fitting a polynomial,

but doesn't allow for missing terms

Josef

...

Cheers,

Camille

_______________________________________________ SciPy-User mailing list SciPy-User@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-user

_______________________________________________ SciPy-User mailing list SciPy-User@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-user

_______________________________________________ SciPy-User mailing list SciPy-User@scipy.org http://mail.scipy.org/mailman/listinfo/scipy-user

Thanks for your answer. But I would like to fit 'a' while 'b', 'c' and 'd' are fixed.Your method gives me another b, c and d. Is there any way to fit a polynomial fixing some coefficients? Cheers, Camille ________________________________ De : Charles R Harris <charlesr.harris@gmail.com> À : camille chambon <camillechambon@yahoo.fr>; SciPy Users List <scipy-user@scipy.org> Envoyé le : Mardi 1 mai 2012 19h45 Objet : Re: [SciPy-User] Least-square fitting of a 3rd degree polynomial On Tue, May 1, 2012 at 11:31 AM, camille chambon <camillechambon@yahoo.fr> wrote: Hello,

I would like to fit 'a' such as y = a * x**3 + b * x**2 +

c * x + d,

where x and y are measured data, and b = 0.0, c = -0.00458844157413 and d = 5.8 are fixed.

According to http://www.scipy.org/Cookbook/FittingData#head-27373a786baa162a2e8a910ee0b8a..., I try to use scipy.optimize.leastsq fit routine like that:

#### CODE #####

from numpy import * from pylab import * from scipy import optimize

# My data points x = array([1078.0, 1117.0, 1212.1, 1368.7, 1686.8, 1880.0]) y = array([5.8, 5.6, 5.4, 4.9, 2.4, 0.0])

b, c, d =  0.0, -0.00458844157413, 5.8 # Fixed parameters

fitfunc = lambda p, x: poly1d([p[0], b, c, d])(x) # Target function errfunc = lambda p, x, y: fitfunc(p, x) - y # Distance to the target function

p0 = [-4.0E-09] # Initial guess for the parameters p1, success = optimize.leastsq(errfunc, p0[:], args=(x, y))

time = linspace(x.min(), x.max(), 100) plot(x, y, "ro", time, fitfunc(p1, time), "r-") # Plot of the data and the fit

title("a fitting") xlabel("time [day]") ylabel("number []") legend(('x position', 'x fit', 'y position', 'y fit'))

show()

################################

But the fit does not work (as one can see on the attached image).

Does someone have any idea of what I'm doing wrong?

Thanks in advance for your help.

Cheers,

Camille

You can use numpy for this. In [1]: from numpy.polynomial import Polynomial as P In [2]: x = array([1078.0, 1117.0, 1212.1, 1368.7, 1686.8, 1880.0]) In [3]: y = array([5.8, 5.6, 5.4, 4.9, 2.4, 0.0]) In [4]: p = P.fit(x,y,3) In [5]: plot(*p.linspace()) Out[5]: [<matplotlib.lines.Line2D at 0x2e51ad0>] In [6]: plot(x, y, '.') Out[6]: [<matplotlib.lines.Line2D at 0x2e62c90>] In [7]: p.mapparms() Out[7]: (-3.6882793017456361, 0.0024937655860349127) Note two things, the coefficients go from degree zero upwards and you need to make the substitution x <- -3.6882793017456361 + 0024937655860349127*x if you want to use them in a publication. Chuck