307 lines
7.5 KiB
Python
307 lines
7.5 KiB
Python
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""" Collection of Model instances for use with the odrpack fitting package.
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"""
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import numpy as np
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from scipy.odr.odrpack import Model
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__all__ = ['Model', 'exponential', 'multilinear', 'unilinear', 'quadratic',
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'polynomial']
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def _lin_fcn(B, x):
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a, b = B[0], B[1:]
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b.shape = (b.shape[0], 1)
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return a + (x*b).sum(axis=0)
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def _lin_fjb(B, x):
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a = np.ones(x.shape[-1], float)
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res = np.concatenate((a, x.ravel()))
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res.shape = (B.shape[-1], x.shape[-1])
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return res
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def _lin_fjd(B, x):
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b = B[1:]
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b = np.repeat(b, (x.shape[-1],)*b.shape[-1], axis=0)
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b.shape = x.shape
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return b
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def _lin_est(data):
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# Eh. The answer is analytical, so just return all ones.
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# Don't return zeros since that will interfere with
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# ODRPACK's auto-scaling procedures.
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if len(data.x.shape) == 2:
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m = data.x.shape[0]
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else:
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m = 1
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return np.ones((m + 1,), float)
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def _poly_fcn(B, x, powers):
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a, b = B[0], B[1:]
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b.shape = (b.shape[0], 1)
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return a + np.sum(b * np.power(x, powers), axis=0)
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def _poly_fjacb(B, x, powers):
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res = np.concatenate((np.ones(x.shape[-1], float),
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np.power(x, powers).flat))
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res.shape = (B.shape[-1], x.shape[-1])
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return res
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def _poly_fjacd(B, x, powers):
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b = B[1:]
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b.shape = (b.shape[0], 1)
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b = b * powers
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return np.sum(b * np.power(x, powers-1), axis=0)
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def _exp_fcn(B, x):
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return B[0] + np.exp(B[1] * x)
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def _exp_fjd(B, x):
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return B[1] * np.exp(B[1] * x)
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def _exp_fjb(B, x):
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res = np.concatenate((np.ones(x.shape[-1], float), x * np.exp(B[1] * x)))
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res.shape = (2, x.shape[-1])
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return res
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def _exp_est(data):
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# Eh.
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return np.array([1., 1.])
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class _MultilinearModel(Model):
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r"""
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Arbitrary-dimensional linear model
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This model is defined by :math:`y=\beta_0 + \sum_{i=1}^m \beta_i x_i`
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Examples
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--------
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We can calculate orthogonal distance regression with an arbitrary
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dimensional linear model:
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>>> from scipy import odr
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>>> x = np.linspace(0.0, 5.0)
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>>> y = 10.0 + 5.0 * x
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>>> data = odr.Data(x, y)
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>>> odr_obj = odr.ODR(data, odr.multilinear)
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>>> output = odr_obj.run()
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>>> print(output.beta)
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[10. 5.]
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"""
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def __init__(self):
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super().__init__(
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_lin_fcn, fjacb=_lin_fjb, fjacd=_lin_fjd, estimate=_lin_est,
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meta={'name': 'Arbitrary-dimensional Linear',
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'equ': 'y = B_0 + Sum[i=1..m, B_i * x_i]',
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'TeXequ': r'$y=\beta_0 + \sum_{i=1}^m \beta_i x_i$'})
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multilinear = _MultilinearModel()
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def polynomial(order):
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"""
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Factory function for a general polynomial model.
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Parameters
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----------
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order : int or sequence
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If an integer, it becomes the order of the polynomial to fit. If
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a sequence of numbers, then these are the explicit powers in the
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polynomial.
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A constant term (power 0) is always included, so don't include 0.
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Thus, polynomial(n) is equivalent to polynomial(range(1, n+1)).
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Returns
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-------
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polynomial : Model instance
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Model instance.
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Examples
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--------
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We can fit an input data using orthogonal distance regression (ODR) with
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a polynomial model:
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>>> import matplotlib.pyplot as plt
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>>> from scipy import odr
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>>> x = np.linspace(0.0, 5.0)
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>>> y = np.sin(x)
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>>> poly_model = odr.polynomial(3) # using third order polynomial model
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>>> data = odr.Data(x, y)
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>>> odr_obj = odr.ODR(data, poly_model)
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>>> output = odr_obj.run() # running ODR fitting
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>>> poly = np.poly1d(output.beta[::-1])
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>>> poly_y = poly(x)
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>>> plt.plot(x, y, label="input data")
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>>> plt.plot(x, poly_y, label="polynomial ODR")
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>>> plt.legend()
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>>> plt.show()
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"""
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powers = np.asarray(order)
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if powers.shape == ():
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# Scalar.
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powers = np.arange(1, powers + 1)
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powers.shape = (len(powers), 1)
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len_beta = len(powers) + 1
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def _poly_est(data, len_beta=len_beta):
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# Eh. Ignore data and return all ones.
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return np.ones((len_beta,), float)
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return Model(_poly_fcn, fjacd=_poly_fjacd, fjacb=_poly_fjacb,
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estimate=_poly_est, extra_args=(powers,),
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meta={'name': 'Sorta-general Polynomial',
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'equ': 'y = B_0 + Sum[i=1..%s, B_i * (x**i)]' % (len_beta-1),
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'TeXequ': r'$y=\beta_0 + \sum_{i=1}^{%s} \beta_i x^i$' %
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(len_beta-1)})
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class _ExponentialModel(Model):
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r"""
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Exponential model
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This model is defined by :math:`y=\beta_0 + e^{\beta_1 x}`
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Examples
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--------
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We can calculate orthogonal distance regression with an exponential model:
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>>> from scipy import odr
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>>> x = np.linspace(0.0, 5.0)
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>>> y = -10.0 + np.exp(0.5*x)
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>>> data = odr.Data(x, y)
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>>> odr_obj = odr.ODR(data, odr.exponential)
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>>> output = odr_obj.run()
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>>> print(output.beta)
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[-10. 0.5]
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"""
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def __init__(self):
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super().__init__(_exp_fcn, fjacd=_exp_fjd, fjacb=_exp_fjb,
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estimate=_exp_est,
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meta={'name': 'Exponential',
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'equ': 'y= B_0 + exp(B_1 * x)',
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'TeXequ': r'$y=\beta_0 + e^{\beta_1 x}$'})
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exponential = _ExponentialModel()
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def _unilin(B, x):
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return x*B[0] + B[1]
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def _unilin_fjd(B, x):
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return np.ones(x.shape, float) * B[0]
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def _unilin_fjb(B, x):
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_ret = np.concatenate((x, np.ones(x.shape, float)))
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_ret.shape = (2,) + x.shape
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return _ret
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def _unilin_est(data):
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return (1., 1.)
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def _quadratic(B, x):
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return x*(x*B[0] + B[1]) + B[2]
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def _quad_fjd(B, x):
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return 2*x*B[0] + B[1]
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def _quad_fjb(B, x):
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_ret = np.concatenate((x*x, x, np.ones(x.shape, float)))
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_ret.shape = (3,) + x.shape
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return _ret
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def _quad_est(data):
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return (1.,1.,1.)
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class _UnilinearModel(Model):
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r"""
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Univariate linear model
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This model is defined by :math:`y = \beta_0 x + \beta_1`
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Examples
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--------
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We can calculate orthogonal distance regression with an unilinear model:
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>>> from scipy import odr
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>>> x = np.linspace(0.0, 5.0)
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>>> y = 1.0 * x + 2.0
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>>> data = odr.Data(x, y)
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>>> odr_obj = odr.ODR(data, odr.unilinear)
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>>> output = odr_obj.run()
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>>> print(output.beta)
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[1. 2.]
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"""
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def __init__(self):
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super().__init__(_unilin, fjacd=_unilin_fjd, fjacb=_unilin_fjb,
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estimate=_unilin_est,
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meta={'name': 'Univariate Linear',
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'equ': 'y = B_0 * x + B_1',
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'TeXequ': '$y = \\beta_0 x + \\beta_1$'})
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unilinear = _UnilinearModel()
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class _QuadraticModel(Model):
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r"""
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Quadratic model
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This model is defined by :math:`y = \beta_0 x^2 + \beta_1 x + \beta_2`
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Examples
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--------
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We can calculate orthogonal distance regression with a quadratic model:
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>>> from scipy import odr
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>>> x = np.linspace(0.0, 5.0)
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>>> y = 1.0 * x ** 2 + 2.0 * x + 3.0
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>>> data = odr.Data(x, y)
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>>> odr_obj = odr.ODR(data, odr.quadratic)
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>>> output = odr_obj.run()
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>>> print(output.beta)
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[1. 2. 3.]
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"""
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def __init__(self):
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super().__init__(
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_quadratic, fjacd=_quad_fjd, fjacb=_quad_fjb, estimate=_quad_est,
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meta={'name': 'Quadratic',
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'equ': 'y = B_0*x**2 + B_1*x + B_2',
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'TeXequ': '$y = \\beta_0 x^2 + \\beta_1 x + \\beta_2'})
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quadratic = _QuadraticModel()
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