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- y(x) = p[0]* x^7 + p[1]*x^6 + p[2]*x^5 + p[3]*x^4 + p[4]*x^3 + p[5]*x^2 + p[6]*x^1 + p[7]
- x(y) = p[0]*y^n + p[1]*y^n-1 + .... + p[n]*y^0
- import numpy as np
- # generate a random coefficient vector a
- degree = 1
- a = 2 * np.random.random(degree+1) - 1
- # an assumed true polynomial y(x)
- def y_of_x(x, coeff_vector):
- """
- Evaluate a polynomial with coeff_vector and degree len(coeff_vector)-1 using Horner's method.
- Coefficients are ordered by increasing degree, from the constant term at coeff_vector[0],
- to the linear term at coeff_vector[1], to the n-th degree term at coeff_vector[n]
- """
- coeff_rev = coeff_vector[::-1]
- b = 0
- for a in coeff_rev:
- b = b * x + a
- return b
- # generate some data
- my_x = np.arange(-1, 1, 0.01)
- my_y = y_of_x(my_x, a)
- # verify that polyfit in the "traditional" direction gives the correct result
- # [::-1] b/c polyfit returns coeffs in backwards order rel. to y_of_x()
- p_test = np.polyfit(my_x, my_y, deg=degree)[::-1]
- print p_test, a
- # fit the data using polyfit but with y as the independent var, x as the dependent var
- p = np.polyfit(my_y, my_x, deg=degree)[::-1]
- # define x as a function of y
- def x_of_y(yy, a):
- return y_of_x(yy, a)
- # compare results
- import matplotlib.pyplot as plt
- %matplotlib inline
- plt.plot(my_x, my_y, '-b', x_of_y(my_y, p), my_y, '-r')
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