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""" |
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Orthogonal distance regression (:mod:`scipy.odr`) |
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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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polynomial -- Factory function for a general polynomial model. |
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exponential -- Exponential model |
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multilinear -- Arbitrary-dimensional linear model |
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unilinear -- Univariate linear model |
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quadratic -- Quadratic model |
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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 multidimensional. 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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from ._odrpack import * |
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from ._models import * |
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from . import _add_newdocs |
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from . import models, odrpack |
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__all__ = [s for s in dir() |
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if not (s.startswith('_') or s in ('odr_stop', 'odr_error'))] |
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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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