How to Use NumPy 1.4 Polynomial Class to Fit Values

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How do you use the new Polynomials sub-package in numpy to give it new x values and get an output of y values? https://numpy.org/doc/stable/reference/routines.polynomials.package.html

In prior versions of numpy it went something like this:

poly = np.poly1d(np.polyfit(x, y, 3)
new_x = np.linspace(0, 100)
new_y = poly(new_x)

The new version I am struggling to give it x values that give me the y values of each?

from numpy.polynomial import Polynomial

poly = Polynomial(Polynomial.fit(x, y, 3))

When I give it an array of x it just returns the coefficients.

numpy python
2 Answers

You can directly call the resulting series to evaluate it:

from numpy.polynomial import Polynomial
poly = Polynomial.fit(x, y, 3)

new_y = poly(new_x)

Check this page of the documentation it has several examples.

user_8673950

Unfortunately, the answer by @Joan Charmant and the supportive comment @rh109019 do not work.

The intuitive way suggested by @Joan Charmant is, basically, what the question's about: it doesn't work.

Evidently, there is a new method introduced in numpy.polynomial.polynomial devoted specifically to evaluating polynomials. See here.

Here's my code where I'm comparing the two approaches.

import numpy as np

Pgauge = np.asarray([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0])
NIST = np.asarray([1.1, 2.1, 3.1, 4.1, 5.1, 6.1, 7.1, 8.1])

calibrationCurve = np.polynomial.polynomial.Polynomial.fit(Pgauge,
                                                           NIST,
                                                           deg=1
)

print("The polynomial: {}".format(calibrationCurve))

x = np.asarray([0, 1]) # values of x to evaluate the polynomial at
c = calibrationCurve.coef # coefficients of the polynomial

print("The intuitive (wrong) way: {}".format(calibrationCurve(x)))
print("The correct way: {}".format(np.polynomial.polynomial.polyval(x, c)))

The first print command prints out the polynomial:4.6+3.5x.

If we want to evaluate it at the points 0 and 1 (x = np.asarray([0, 1])), we expect to get 4.6 and 8.1 respectively.

The second print command (that reads "The intuitive (wrong) way"), uses the method suggested by @Joan Charmant. It gives [0.1, 1.1] as the result. Which is wrong. Though seemingly, it looks ok: it gives two numbers as expected. But the numbers themselves are wrong. I don't know how these numbers were calculated. But if I had a bigger series of data, I wouldn't go with a calculator through it and assume I've got a correct result.

The last print command makes use of the polyval method suggested in the user manual that I cited above. And it works perfectly well. It gives [4.6, 8.1] as the result.

It so happens that my answer is wrong as well (see all the comments below by @user2357112 supports Monica).

But still, I'll leave it here for the folks who, like me, fell the victim of the confusing new numpy.polynomial library.

FIRST: why my code is wrong?

Everything's ok with it. But the line print("The polynomial: {}".format(calibrationCurve)) doesn't give me what, I think, it must give me. It takes the correct polynomial, changes its coefficients somehow and prints out a new polynomial with the changed coefficients. Still, it does store the correct polynomial in its memory and when you do the thing suggested by @Joan Charmant it may give you the correct answer if you ask it properly.

SECOND: how to use the new numpy.polynomial library in order to get a correct result?

Due to that peculiarity, you have to introduce a new line of code. Namely, do the Polynomial.fit() and immediately afterwards use the .convert() method. Then work with the converted polynomial only.

Here's my code that works correctly now.

import numpy as np

Pgauge = np.asarray([1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0])
NIST = np.asarray([1.1, 2.1, 3.1, 4.1, 5.1, 6.1, 7.1, 8.1])

calibrationCurveMessedUp = np.polynomial.polynomial.Polynomial.fit(Pgauge,
                                                                   NIST,
                                                                   deg=1
)

calibrationCurve = calibrationCurveMessedUp.convert()

print("The polynomial: {}".format(calibrationCurve))
print("The rounded polynomial coefficients: {}".format(calibrationCurve.coef))

x = np.asarray([0, 1]) # values of x to evaluate the polynomial at
print(calibrationCurve(x))

THIRD: a little note.

Apparently, there is a possibility to get the correct polynomial without the additional line of code. Probably, you have to give the correct window and domain parameters to the Polynomial.fit() function. Or may be there is another way.

If anybody knows such a way, you're welcome to edit my current answer and add your code.

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