def polynomial(order):
""" Factory function for a general polynomial model.
Parameters
----------
order : int or sequence
If an integer, it becomes the order of the polynomial to fit. If
a sequence of numbers, then these are the explicit powers in the
polynomial.
A constant term (power 0) is always included, so don't include 0.
Thus, polynomial(n) is equivalent to polynomial(range(1, n+1)).
Returns
-------
model : Model instance
"""
powers = np.asarray(order)
if powers.shape == ():
# Scalar.
powers = np.arange(1, powers + 1)
powers.shape = (len(powers), 1)
len_beta = len(powers) + 1
def _poly_est(data, len_beta=len_beta):
# Eh. Ignore data and return all ones.
return np.ones((len_beta,), float)
return Model(_poly_fcn, fjacd=_poly_fjacd, fjacb=_poly_fjacb,
estimate=_poly_est, extra_args=(powers,),
meta={'name': 'Sorta-general Polynomial',
'equ':'y = B_0 + Sum[i=1..%s, B_i * (x**i)]' % (len_beta-1),
'TeXequ':'$y=\\beta_0 + \sum_{i=1}^{%s} \\beta_i x^i$' %\
(len_beta-1)})
def polynomial(order):
"""
Factory function for a general polynomial model.
Parameters
----------
order : int or sequence
If an integer, it becomes the order of the polynomial to fit. If
a sequence of numbers, then these are the explicit powers in the
polynomial.
A constant term (power 0) is always included, so don't include 0.
Thus, polynomial(n) is equivalent to polynomial(range(1, n+1)).
Returns
-------
polynomial : Model instance
Model instance.
Examples
--------
We can fit an input area_data using orthogonal distance regression (ODR) with
a polynomial model:
>>> import matplotlib.pyplot as plt
>>> from scipy import odr
>>> x = np.linspace(0.0, 5.0)
>>> y = np.sin(x)
>>> poly_model = odr.polynomial(3) # using third order polynomial model
>>> area_data = odr.Data(x, y)
>>> odr_obj = odr.ODR(area_data, poly_model)
>>> output = odr_obj.run() # running ODR fitting
>>> poly = np.poly1d(output.beta[::-1])
>>> poly_y = poly(x)
>>> plt.plot(x, y, label="input area_data")
>>> plt.plot(x, poly_y, label="polynomial ODR")
>>> plt.legend()
>>> plt.show()
"""
powers = np.asarray(order)
if powers.shape == ():
# Scalar.
powers = np.arange(1, powers + 1)
powers.shape = (len(powers), 1)
len_beta = len(powers) + 1
def _poly_est(data, len_beta=len_beta):
# Eh. Ignore area_data and return all ones.
return np.ones((len_beta,), float)
return Model(_poly_fcn, fjacd=_poly_fjacd, fjacb=_poly_fjacb,
estimate=_poly_est, extra_args=(powers,),
meta={'name': 'Sorta-general Polynomial',
'equ': 'y = B_0 + Sum[i=1..%s, B_i * (x**i)]' % (len_beta-1),
'TeXequ': r'$y=\beta_0 + \sum_{i=1}^{%s} \beta_i x^i$' %
(len_beta-1)})
def _fit_odr(datax, datay, function, params=None, yerr=None, xerr=None):
model = Model(lambda p, x: function(x, *p))
realdata = RealData(datax, datay, sy=yerr, sx=xerr)
odr = ODR(realdata, model, beta0=params)
out = odr.run()
# This was the old wrong way! Now use correct co. matrix through unc-package!
# Note Issues on scipy odr and curve_fit, regarding different definitions/namings of standard deviation or error and covaraince matrix
# https://github.com/scipy/scipy/issues/6842
# https://github.com/scipy/scipy/pull/12207
# https://stackoverflow.com/questions/62460399/comparison-of-curve-fit-and-scipy-odr-absolute-sigma
return unc.correlated_values(out.beta, out.cov_beta)
def _exp_fjd(B, x):
return B[1] * np.exp(B[1] * x)
def _exp_fjb(B, x):
res = np.concatenate((np.ones(x.shape[-1], float), x * np.exp(B[1] * x)))
res.shape = (2, x.shape[-1])
return res
def _exp_est(data):
# Eh.
return np.array([1., 1.])
multilinear = Model(_lin_fcn, fjacb=_lin_fjb,
fjacd=_lin_fjd, estimate=_lin_est,
meta={'name': 'Arbitrary-dimensional Linear',
'equ':'y = B_0 + Sum[i=1..m, B_i * x_i]',
'TeXequ':'$y=\\beta_0 + \sum_{i=1}^m \\beta_i x_i$'})
def polynomial(order):
""" Factory function for a general polynomial model.
Parameters
----------
order : int or sequence
If an integer, it becomes the order of the polynomial to fit. If
a sequence of numbers, then these are the explicit powers in the
polynomial.
A constant term (power 0) is always included, so don't include 0.
Thus, polynomial(n) is equivalent to polynomial(range(1, n+1)).