CODEWITHSUNDEEP
pythonscipycurve-fitting
Chris
Chris

Reputation: 461

Better way to create fit functions with changing number of parameters in Python with Scipy curve_fit

I am looking for a better way to use scipy's curve_fit()

I am currently using it to fit linear combinations of the parameters and a vector x.

For example, here is a fitting function I pass for trying the fit with 5 parameters, m0-m4:

def degFour(x, m0, m1, m2, m3, m4):
    return x[0]*m0 + x[1]*m1 + x[2]*m2 + x[3]*m3 + x[4]*m4

I have made more of these up to degTen using the same pattern. It does work, too.

My x vector:

[[ 1.          1.          1.          1.          1.        ]
 [ 1.          0.99990931  0.99963727  0.99918392  0.99854935]
 [ 1.          0.94872591  0.80016169  0.56954235  0.28051747]
 [ 1.          0.84717487  0.43541052 -0.10943716 -0.62083535]
 [ 1.          0.77991807  0.21654439 -0.44214431 -0.90621706]
 [ 1.          0.73162055  0.07053725 -0.62840754 -0.99004899]
 [ 1.          0.68866877 -0.05147065 -0.75956123 -0.99470154]
 [ 1.          0.64892616 -0.15778967 -0.85371386 -0.95020484]
 [ 1.          0.6114128  -0.25234877 -0.91999134 -0.8726402 ]
 [ 1.          0.57600247 -0.33644232 -0.96358568 -0.77361313]
 [ 1.          0.54225052 -0.41192874 -0.98898767 -0.66062942]
 [ 1.          0.29541145 -0.82546415 -0.78311458  0.36278212]
 [ 1.          0.09546594 -0.98177251 -0.28291761  0.92775452]
 [ 1.         -0.07539697 -0.9886306   0.22447646  0.95478091]
 [ 1.         -0.22050008 -0.90275943  0.61861713  0.62994918]
 [ 1.         -0.33964821 -0.76927818  0.86221613  0.18357784]
 [ 1.         -0.54483185 -0.40631651  0.9875802  -0.66981378]
 [ 1.         -0.71937092  0.03498904  0.66903073 -0.99755153]
 [ 1.         -1.          1.         -1.          1.        ]]

My y data:

[  3.50032   3.5007    3.6328    3.94564   4.12814   4.2651    4.39586
   4.51982   4.64394   4.76738   4.88654   5.90314   6.93304   7.99074
   9.04278  10.02426  12.01392  14.0592   18.1689 ]

Using curve_fit(degFour, xdata.T, ydata), I get the correct coefficients:

[ 9.14562709 -7.05004692  1.66932215 -0.27868686  0.02097462]

I recreate the x data depending on the degree, so I will always pass in data with the correct shape.

I tried a version of fbstj's answer regarding variable input parameters.

I used this:

def vararg(x, *args):
    return sum(a * x[i] for i, a in enumerate(args))

and ended up with this:

Traceback (most recent call last):
  File "D:/Libraries/Desktop/PScratch2/vararg.py", line 18, in <module>
    print(curve_fit(vararg, deg4kary.T, deg4ydata))
  File "C:\Python35\lib\site-packages\scipy\optimize\minpack.py", line 606, in curve_fit
    raise ValueError("Unable to determine number of fit parameters.")
ValueError: Unable to determine number of fit parameters.

As you can see from the trace, I just passed the function itself. I am stuck.

Upvotes: 0

Views: 871

Answers (1)

ali_m
ali_m

Reputation: 74182

You are fitting a multivariate linear model to your data. This can be expressed as a dot product between your x vector, with shape (npoints, nparams), and a single (nparams,) vector of coefficients, say m:

def linear(x, m):
    return x.dot(m)

x = np.random.randn(100, 5)
m = np.random.randn(5)

y = linear(x, m)

There's really no need to use curve_fit to get the m coefficients - it's simpler and more efficient to use np.linalg.lstsq to solve linear systems such as this:

m_hat, residuals, rank, singular_vals = np.linalg.lstsq(x, y)

Here, m_hat will be an (n_params,) vector containing the least-squares estimates of m0, m1, m2 etc. This will work for any number of coefficients.

Upvotes: 2

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