129 lines
4.1 KiB
Python
129 lines
4.1 KiB
Python
|
"""
|
||
|
|
=================================================
|
||
|
|
Orthogonal distance regression (:mod:`scipy.odr`)
|
||
|
|
=================================================
|
||
|
|
|
||
|
|
.. currentmodule:: scipy.odr
|
||
|
|
|
||
|
|
Package Content
|
||
|
|
===============
|
||
|
|
|
||
|
|
.. autosummary::
|
||
|
|
:toctree: generated/
|
||
|
|
|
||
|
|
Data -- The data to fit.
|
||
|
|
RealData -- Data with weights as actual std. dev.s and/or covariances.
|
||
|
|
Model -- Stores information about the function to be fit.
|
||
|
|
ODR -- Gathers all info & manages the main fitting routine.
|
||
|
|
Output -- Result from the fit.
|
||
|
|
odr -- Low-level function for ODR.
|
||
|
|
|
||
|
|
OdrWarning -- Warning about potential problems when running ODR.
|
||
|
|
OdrError -- Error exception.
|
||
|
|
OdrStop -- Stop exception.
|
||
|
|
|
||
|
|
polynomial -- Factory function for a general polynomial model.
|
||
|
|
exponential -- Exponential model
|
||
|
|
multilinear -- Arbitrary-dimensional linear model
|
||
|
|
unilinear -- Univariate linear model
|
||
|
|
quadratic -- Quadratic model
|
||
|
|
|
||
|
|
Usage information
|
||
|
|
=================
|
||
|
|
|
||
|
|
Introduction
|
||
|
|
------------
|
||
|
|
|
||
|
|
Why Orthogonal Distance Regression (ODR)? Sometimes one has
|
||
|
|
measurement errors in the explanatory (a.k.a., "independent")
|
||
|
|
variable(s), not just the response (a.k.a., "dependent") variable(s).
|
||
|
|
Ordinary Least Squares (OLS) fitting procedures treat the data for
|
||
|
|
explanatory variables as fixed, i.e., not subject to error of any kind.
|
||
|
|
Furthermore, OLS procedures require that the response variables be an
|
||
|
|
explicit function of the explanatory variables; sometimes making the
|
||
|
|
equation explicit is impractical and/or introduces errors. ODR can
|
||
|
|
handle both of these cases with ease, and can even reduce to the OLS
|
||
|
|
case if that is sufficient for the problem.
|
||
|
|
|
||
|
|
ODRPACK is a FORTRAN-77 library for performing ODR with possibly
|
||
|
|
non-linear fitting functions. It uses a modified trust-region
|
||
|
|
Levenberg-Marquardt-type algorithm [1]_ to estimate the function
|
||
|
|
parameters. The fitting functions are provided by Python functions
|
||
|
|
operating on NumPy arrays. The required derivatives may be provided
|
||
|
|
by Python functions as well, or may be estimated numerically. ODRPACK
|
||
|
|
can do explicit or implicit ODR fits, or it can do OLS. Input and
|
||
|
|
output variables may be multidimensional. Weights can be provided to
|
||
|
|
account for different variances of the observations, and even
|
||
|
|
covariances between dimensions of the variables.
|
||
|
|
|
||
|
|
The `scipy.odr` package offers an object-oriented interface to
|
||
|
|
ODRPACK, in addition to the low-level `odr` function.
|
||
|
|
|
||
|
|
Additional background information about ODRPACK can be found in the
|
||
|
|
`ODRPACK User's Guide
|
||
|
|
<https://docs.scipy.org/doc/external/odrpack_guide.pdf>`_, reading
|
||
|
|
which is recommended.
|
||
|
|
|
||
|
|
Basic usage
|
||
|
|
-----------
|
||
|
|
|
||
|
|
1. Define the function you want to fit against.::
|
||
|
|
|
||
|
|
def f(B, x):
|
||
|
|
'''Linear function y = m*x + b'''
|
||
|
|
# B is a vector of the parameters.
|
||
|
|
# x is an array of the current x values.
|
||
|
|
# x is in the same format as the x passed to Data or RealData.
|
||
|
|
#
|
||
|
|
# Return an array in the same format as y passed to Data or RealData.
|
||
|
|
return B[0]*x + B[1]
|
||
|
|
|
||
|
|
2. Create a Model.::
|
||
|
|
|
||
|
|
linear = Model(f)
|
||
|
|
|
||
|
|
3. Create a Data or RealData instance.::
|
||
|
|
|
||
|
|
mydata = Data(x, y, wd=1./power(sx,2), we=1./power(sy,2))
|
||
|
|
|
||
|
|
or, when the actual covariances are known::
|
||
|
|
|
||
|
|
mydata = RealData(x, y, sx=sx, sy=sy)
|
||
|
|
|
||
|
|
4. Instantiate ODR with your data, model and initial parameter estimate.::
|
||
|
|
|
||
|
|
myodr = ODR(mydata, linear, beta0=[1., 2.])
|
||
|
|
|
||
|
|
5. Run the fit.::
|
||
|
|
|
||
|
|
myoutput = myodr.run()
|
||
|
|
|
||
|
|
6. Examine output.::
|
||
|
|
|
||
|
|
myoutput.pprint()
|
||
|
|
|
||
|
|
|
||
|
|
References
|
||
|
|
----------
|
||
|
|
.. [1] P. T. Boggs and J. E. Rogers, "Orthogonal Distance Regression,"
|
||
|
|
in "Statistical analysis of measurement error models and
|
||
|
|
applications: proceedings of the AMS-IMS-SIAM joint summer research
|
||
|
|
conference held June 10-16, 1989," Contemporary Mathematics,
|
||
|
|
vol. 112, pg. 186, 1990.
|
||
|
|
|
||
|
|
"""
|
||
|
|
# version: 0.7
|
||
|
|
# author: Robert Kern <robert.kern@gmail.com>
|
||
|
|
# date: 2006-09-21
|
||
|
|
|
||
|
|
from .odrpack import *
|
||
|
|
from .models import *
|
||
|
|
from . import _add_newdocs
|
||
|
|
|
||
|
|
__all__ = [s for s in dir()
|
||
|
|
if not (s.startswith('_') or s in ('odr_stop', 'odr_error'))]
|
||
|
|
|
||
|
|
from scipy._lib._testutils import PytestTester
|
||
|
|
test = PytestTester(__name__)
|
||
|
|
del PytestTester
|