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