python - scipy 和 numpy 中切比雪夫多项式实现的区别

Question

谁能告诉我 numpy 中的 Chebyshev 之间的区别-

numpy.polynomial.Chebyshev.basis(deg) 

和切比雪夫的 scipy 解释-

scipy.special.chebyt(deg)

这会很有帮助。提前致谢!

Answer 1

scipy.special 多项式函数使用np.poly1d，which is outdated and error prone - 特别是，它将 x0 的索引存储在 poly.coeffs[-1]

中

numpy.polynomial.Chebyshev 不仅以更合理的顺序存储系数，而且按照它们的基础来保存它们，从而提高精度。您可以使用 cast 方法进行转换:

>>> from numpy.polynomial import Chebyshev, Polynomial

# note loss of precision
>>> sc_che = scipy.special.chebyt(4); sc_che
poly1d([  8.000000e+00,   0.000000e+00,  -8.000000e+00, 8.881784e-16,   1.000000e+00])

# using the numpy functions - note that the result is just in terms of basis 4
>>> np_che = Chebyshev.basis(4); np_che
Chebyshev([ 0.,  0.,  0.,  0.,  1.], [-1.,  1.], [-1.,  1.])

# converting to a standard polynomial - note that these store the
# coefficient of x^i in .coeffs[i] - so are reversed when compared to above
>>> Polynomial.cast(np_che)
Polynomial([ 1.,  0., -8.,  0.,  8.], [-1.,  1.], [-1.,  1.])