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8RH r c " e Zd ZdZ fdZ xZS )_MultilinearModela
Arbitrary-dimensional linear model
.. deprecated:: 1.17.0
`scipy.odr` is deprecated and will be removed in SciPy 1.19.0. Please use
`pypi.org/project/odrpack/ `_
instead.
This model is defined by :math:`y=\beta_0 + \sum_{i=1}^m \beta_i x_i`
Examples
--------
We can calculate orthogonal distance regression with an arbitrary
dimensional linear model:
>>> from scipy import odr
>>> import numpy as np
>>> x = np.linspace(0.0, 5.0)
>>> y = 10.0 + 5.0 * x
>>> data = odr.Data(x, y)
>>> odr_obj = odr.ODR(data, odr.multilinear)
>>> output = odr_obj.run()
>>> print(output.beta)
[10. 5.]
c
t t t t t
dddd d S )Nz Arbitrary-dimensional Linearz y = B_0 + Sum[i=1..m, B_i * x_i]z&$y=\beta_0 + \sum_{i=1}^m \beta_i x_i$nameequTeXequ)fjacbfjacdestimatemeta)super__init__r r! r$ r+ self __class__s r rR z_MultilinearModel.__init__o sQ
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Factory function for a general polynomial model.
.. deprecated:: 1.17.0
`scipy.odr` is deprecated and will be removed in SciPy 1.19.0. Please use
`pypi.org/project/odrpack/ `_
instead.
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 data using orthogonal distance regression (ODR) with
a polynomial model:
>>> import numpy as np
>>> 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
>>> data = odr.Data(x, y)
>>> odr_obj = odr.ODR(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 data")
>>> plt.plot(x, poly_y, label="polynomial ODR")
>>> plt.legend()
>>> plt.show()
r c 8 t j |ft S )N)r r r )r) len_betas r _poly_estz polynomial.._poly_est s w{E***r zSorta-general Polynomialz$y = B_0 + Sum[i=1..%s, B_i * (x**i)]z)$y=\beta_0 + \sum_{i=1}^{%s} \beta_i x^i$rI )rN rM rO
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Exponential model
.. deprecated:: 1.17.0
`scipy.odr` is deprecated and will be removed in SciPy 1.19.0. Please use
`pypi.org/project/odrpack/ `_
instead.
This model is defined by :math:`y=\beta_0 + e^{\beta_1 x}`
Examples
--------
We can calculate orthogonal distance regression with an exponential model:
>>> from scipy import odr
>>> import numpy as np
>>> x = np.linspace(0.0, 5.0)
>>> y = -10.0 + np.exp(0.5*x)
>>> data = odr.Data(x, y)
>>> odr_obj = odr.ODR(data, odr.exponential)
>>> output = odr_obj.run()
>>> print(output.beta)
[-10. 0.5]
c
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_quadraticrx s& a!fqtm qt ##r c 0 d|z | d z | d z S r& r^ r: s r _quad_fjdrz s Q3qt8ad?r c t j ||z |t j |j t f }| d|j z S )N) rq rr s r _quad_fjbr} sB
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instead.
This model is defined by :math:`y = \beta_0 x + \beta_1`
Examples
--------
We can calculate orthogonal distance regression with an unilinear model:
>>> from scipy import odr
>>> import numpy as np
>>> x = np.linspace(0.0, 5.0)
>>> y = 1.0 * x + 2.0
>>> data = odr.Data(x, y)
>>> odr_obj = odr.ODR(data, odr.unilinear)
>>> output = odr_obj.run()
>>> print(output.beta)
[1. 2.]
c
t t t t t
dddd d S )NzUnivariate Linearzy = B_0 * x + B_1z$y = \beta_0 x + \beta_1$rI rj )rQ rR rm ro rt rv rS s r rR z_UnilinearModel.__init__ sQ
;"-':&9)F H H I I I I Ir rV r\ s @r r r sK 4I I I I I I I I Ir r c " e Zd ZdZ fdZ xZS )_QuadraticModela
Quadratic model
.. deprecated:: 1.17.0
`scipy.odr` is deprecated and will be removed in SciPy 1.19.0. Please use
`pypi.org/project/odrpack/ `_
instead.
This model is defined by :math:`y = \beta_0 x^2 + \beta_1 x + \beta_2`
Examples
--------
We can calculate orthogonal distance regression with a quadratic model:
>>> from scipy import odr
>>> import numpy as np
>>> x = np.linspace(0.0, 5.0)
>>> y = 1.0 * x ** 2 + 2.0 * x + 3.0
>>> data = odr.Data(x, y)
>>> odr_obj = odr.ODR(data, odr.quadratic)
>>> output = odr_obj.run()
>>> print(output.beta)
[1. 2. 3.]
c
t t t t t
dddd d S )N Quadraticzy = B_0*x**2 + B_1*x + B_2z&$y = \beta_0 x^2 + \beta_1 x + \beta_2rI rj )rQ rR rx rz r} r rS s r rR z_QuadraticModel.__init__E sQ
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