1128 lines
40 KiB
Python
1128 lines
40 KiB
Python
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"""
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Python wrappers for Orthogonal Distance Regression (ODRPACK).
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Notes
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=====
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* Array formats -- FORTRAN stores its arrays in memory column first, i.e. an
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array element A(i, j, k) will be next to A(i+1, j, k). In C and, consequently,
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NumPy, arrays are stored row first: A[i, j, k] is next to A[i, j, k+1]. For
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efficiency and convenience, the input and output arrays of the fitting
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function (and its Jacobians) are passed to FORTRAN without transposition.
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Therefore, where the ODRPACK documentation says that the X array is of shape
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(N, M), it will be passed to the Python function as an array of shape (M, N).
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If M==1, the one-dimensional case, then nothing matters; if M>1, then your
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Python functions will be dealing with arrays that are indexed in reverse of
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the ODRPACK documentation. No real biggie, but watch out for your indexing of
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the Jacobians: the i,j'th elements (@f_i/@x_j) evaluated at the n'th
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observation will be returned as jacd[j, i, n]. Except for the Jacobians, it
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really is easier to deal with x[0] and x[1] than x[:,0] and x[:,1]. Of course,
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you can always use the transpose() function from scipy explicitly.
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* Examples -- See the accompanying file test/test.py for examples of how to set
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up fits of your own. Some are taken from the User's Guide; some are from
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other sources.
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* Models -- Some common models are instantiated in the accompanying module
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models.py . Contributions are welcome.
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Credits
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=======
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* Thanks to Arnold Moene and Gerard Vermeulen for fixing some killer bugs.
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Robert Kern
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robert.kern@gmail.com
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"""
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from __future__ import division, print_function, absolute_import
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import numpy
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from warnings import warn
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from scipy.odr import __odrpack
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__all__ = ['odr', 'OdrWarning', 'OdrError', 'OdrStop',
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'Data', 'RealData', 'Model', 'Output', 'ODR',
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'odr_error', 'odr_stop']
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odr = __odrpack.odr
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class OdrWarning(UserWarning):
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"""
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Warning indicating that the data passed into
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ODR will cause problems when passed into 'odr'
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that the user should be aware of.
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"""
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pass
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class OdrError(Exception):
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"""
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Exception indicating an error in fitting.
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This is raised by `scipy.odr` if an error occurs during fitting.
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"""
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pass
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class OdrStop(Exception):
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"""
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Exception stopping fitting.
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You can raise this exception in your objective function to tell
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`scipy.odr` to stop fitting.
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"""
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pass
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# Backwards compatibility
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odr_error = OdrError
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odr_stop = OdrStop
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__odrpack._set_exceptions(OdrError, OdrStop)
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def _conv(obj, dtype=None):
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""" Convert an object to the preferred form for input to the odr routine.
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"""
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if obj is None:
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return obj
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else:
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if dtype is None:
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obj = numpy.asarray(obj)
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else:
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obj = numpy.asarray(obj, dtype)
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if obj.shape == ():
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# Scalar.
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return obj.dtype.type(obj)
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else:
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return obj
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def _report_error(info):
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""" Interprets the return code of the odr routine.
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Parameters
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----------
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info : int
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The return code of the odr routine.
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Returns
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-------
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problems : list(str)
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A list of messages about why the odr() routine stopped.
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"""
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stopreason = ('Blank',
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'Sum of squares convergence',
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'Parameter convergence',
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'Both sum of squares and parameter convergence',
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'Iteration limit reached')[info % 5]
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if info >= 5:
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# questionable results or fatal error
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I = (info//10000 % 10,
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info//1000 % 10,
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info//100 % 10,
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info//10 % 10,
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info % 10)
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problems = []
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if I[0] == 0:
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if I[1] != 0:
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problems.append('Derivatives possibly not correct')
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if I[2] != 0:
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problems.append('Error occurred in callback')
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if I[3] != 0:
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problems.append('Problem is not full rank at solution')
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problems.append(stopreason)
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elif I[0] == 1:
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if I[1] != 0:
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problems.append('N < 1')
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if I[2] != 0:
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problems.append('M < 1')
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if I[3] != 0:
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problems.append('NP < 1 or NP > N')
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if I[4] != 0:
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problems.append('NQ < 1')
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elif I[0] == 2:
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if I[1] != 0:
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problems.append('LDY and/or LDX incorrect')
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if I[2] != 0:
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problems.append('LDWE, LD2WE, LDWD, and/or LD2WD incorrect')
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if I[3] != 0:
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problems.append('LDIFX, LDSTPD, and/or LDSCLD incorrect')
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if I[4] != 0:
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problems.append('LWORK and/or LIWORK too small')
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elif I[0] == 3:
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if I[1] != 0:
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problems.append('STPB and/or STPD incorrect')
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if I[2] != 0:
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problems.append('SCLB and/or SCLD incorrect')
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if I[3] != 0:
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problems.append('WE incorrect')
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if I[4] != 0:
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problems.append('WD incorrect')
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elif I[0] == 4:
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problems.append('Error in derivatives')
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elif I[0] == 5:
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problems.append('Error occurred in callback')
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elif I[0] == 6:
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problems.append('Numerical error detected')
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return problems
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else:
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return [stopreason]
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class Data(object):
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"""
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The data to fit.
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Parameters
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----------
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x : array_like
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Observed data for the independent variable of the regression
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y : array_like, optional
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If array-like, observed data for the dependent variable of the
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regression. A scalar input implies that the model to be used on
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the data is implicit.
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we : array_like, optional
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If `we` is a scalar, then that value is used for all data points (and
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all dimensions of the response variable).
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If `we` is a rank-1 array of length q (the dimensionality of the
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response variable), then this vector is the diagonal of the covariant
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weighting matrix for all data points.
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If `we` is a rank-1 array of length n (the number of data points), then
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the i'th element is the weight for the i'th response variable
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observation (single-dimensional only).
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If `we` is a rank-2 array of shape (q, q), then this is the full
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covariant weighting matrix broadcast to each observation.
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If `we` is a rank-2 array of shape (q, n), then `we[:,i]` is the
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diagonal of the covariant weighting matrix for the i'th observation.
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If `we` is a rank-3 array of shape (q, q, n), then `we[:,:,i]` is the
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full specification of the covariant weighting matrix for each
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observation.
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If the fit is implicit, then only a positive scalar value is used.
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wd : array_like, optional
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If `wd` is a scalar, then that value is used for all data points
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(and all dimensions of the input variable). If `wd` = 0, then the
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covariant weighting matrix for each observation is set to the identity
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matrix (so each dimension of each observation has the same weight).
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If `wd` is a rank-1 array of length m (the dimensionality of the input
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variable), then this vector is the diagonal of the covariant weighting
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matrix for all data points.
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If `wd` is a rank-1 array of length n (the number of data points), then
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the i'th element is the weight for the i'th input variable observation
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(single-dimensional only).
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If `wd` is a rank-2 array of shape (m, m), then this is the full
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covariant weighting matrix broadcast to each observation.
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If `wd` is a rank-2 array of shape (m, n), then `wd[:,i]` is the
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diagonal of the covariant weighting matrix for the i'th observation.
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If `wd` is a rank-3 array of shape (m, m, n), then `wd[:,:,i]` is the
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full specification of the covariant weighting matrix for each
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observation.
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fix : array_like of ints, optional
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The `fix` argument is the same as ifixx in the class ODR. It is an
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array of integers with the same shape as data.x that determines which
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input observations are treated as fixed. One can use a sequence of
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length m (the dimensionality of the input observations) to fix some
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dimensions for all observations. A value of 0 fixes the observation,
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a value > 0 makes it free.
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meta : dict, optional
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Free-form dictionary for metadata.
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Notes
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-----
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Each argument is attached to the member of the instance of the same name.
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The structures of `x` and `y` are described in the Model class docstring.
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If `y` is an integer, then the Data instance can only be used to fit with
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implicit models where the dimensionality of the response is equal to the
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specified value of `y`.
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The `we` argument weights the effect a deviation in the response variable
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has on the fit. The `wd` argument weights the effect a deviation in the
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input variable has on the fit. To handle multidimensional inputs and
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responses easily, the structure of these arguments has the n'th
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dimensional axis first. These arguments heavily use the structured
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arguments feature of ODRPACK to conveniently and flexibly support all
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options. See the ODRPACK User's Guide for a full explanation of how these
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weights are used in the algorithm. Basically, a higher value of the weight
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for a particular data point makes a deviation at that point more
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detrimental to the fit.
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"""
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def __init__(self, x, y=None, we=None, wd=None, fix=None, meta={}):
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self.x = _conv(x)
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if not isinstance(self.x, numpy.ndarray):
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raise ValueError(("Expected an 'ndarray' of data for 'x', "
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"but instead got data of type '{name}'").format(
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name=type(self.x).__name__))
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self.y = _conv(y)
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self.we = _conv(we)
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self.wd = _conv(wd)
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self.fix = _conv(fix)
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self.meta = meta
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def set_meta(self, **kwds):
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""" Update the metadata dictionary with the keywords and data provided
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by keywords.
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Examples
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||
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--------
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::
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data.set_meta(lab="Ph 7; Lab 26", title="Ag110 + Ag108 Decay")
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"""
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self.meta.update(kwds)
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def __getattr__(self, attr):
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""" Dispatch attribute access to the metadata dictionary.
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"""
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if attr in self.meta:
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return self.meta[attr]
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else:
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raise AttributeError("'%s' not in metadata" % attr)
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class RealData(Data):
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"""
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The data, with weightings as actual standard deviations and/or
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covariances.
|
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|
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Parameters
|
||
|
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----------
|
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|
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x : array_like
|
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|
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Observed data for the independent variable of the regression
|
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|
|
y : array_like, optional
|
||
|
|
If array-like, observed data for the dependent variable of the
|
||
|
|
regression. A scalar input implies that the model to be used on
|
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|
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the data is implicit.
|
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|
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sx : array_like, optional
|
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Standard deviations of `x`.
|
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`sx` are standard deviations of `x` and are converted to weights by
|
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dividing 1.0 by their squares.
|
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sy : array_like, optional
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Standard deviations of `y`.
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`sy` are standard deviations of `y` and are converted to weights by
|
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dividing 1.0 by their squares.
|
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covx : array_like, optional
|
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|
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Covariance of `x`
|
||
|
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`covx` is an array of covariance matrices of `x` and are converted to
|
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weights by performing a matrix inversion on each observation's
|
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|
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covariance matrix.
|
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covy : array_like, optional
|
||
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Covariance of `y`
|
||
|
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`covy` is an array of covariance matrices and are converted to
|
||
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weights by performing a matrix inversion on each observation's
|
||
|
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covariance matrix.
|
||
|
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fix : array_like, optional
|
||
|
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The argument and member fix is the same as Data.fix and ODR.ifixx:
|
||
|
|
It is an array of integers with the same shape as `x` that
|
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|
|
determines which input observations are treated as fixed. One can
|
||
|
|
use a sequence of length m (the dimensionality of the input
|
||
|
|
observations) to fix some dimensions for all observations. A value
|
||
|
|
of 0 fixes the observation, a value > 0 makes it free.
|
||
|
|
meta : dict, optional
|
||
|
|
Free-form dictionary for metadata.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
The weights `wd` and `we` are computed from provided values as follows:
|
||
|
|
|
||
|
|
`sx` and `sy` are converted to weights by dividing 1.0 by their squares.
|
||
|
|
For example, ``wd = 1./numpy.power(`sx`, 2)``.
|
||
|
|
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`covx` and `covy` are arrays of covariance matrices and are converted to
|
||
|
|
weights by performing a matrix inversion on each observation's covariance
|
||
|
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matrix. For example, ``we[i] = numpy.linalg.inv(covy[i])``.
|
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These arguments follow the same structured argument conventions as wd and
|
||
|
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we only restricted by their natures: `sx` and `sy` can't be rank-3, but
|
||
|
|
`covx` and `covy` can be.
|
||
|
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Only set *either* `sx` or `covx` (not both). Setting both will raise an
|
||
|
|
exception. Same with `sy` and `covy`.
|
||
|
|
|
||
|
|
"""
|
||
|
|
|
||
|
|
def __init__(self, x, y=None, sx=None, sy=None, covx=None, covy=None,
|
||
|
|
fix=None, meta={}):
|
||
|
|
if (sx is not None) and (covx is not None):
|
||
|
|
raise ValueError("cannot set both sx and covx")
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||
|
|
if (sy is not None) and (covy is not None):
|
||
|
|
raise ValueError("cannot set both sy and covy")
|
||
|
|
|
||
|
|
# Set flags for __getattr__
|
||
|
|
self._ga_flags = {}
|
||
|
|
if sx is not None:
|
||
|
|
self._ga_flags['wd'] = 'sx'
|
||
|
|
else:
|
||
|
|
self._ga_flags['wd'] = 'covx'
|
||
|
|
if sy is not None:
|
||
|
|
self._ga_flags['we'] = 'sy'
|
||
|
|
else:
|
||
|
|
self._ga_flags['we'] = 'covy'
|
||
|
|
|
||
|
|
self.x = _conv(x)
|
||
|
|
|
||
|
|
if not isinstance(self.x, numpy.ndarray):
|
||
|
|
raise ValueError(("Expected an 'ndarray' of data for 'x', "
|
||
|
|
"but instead got data of type '{name}'").format(
|
||
|
|
name=type(self.x).__name__))
|
||
|
|
|
||
|
|
self.y = _conv(y)
|
||
|
|
self.sx = _conv(sx)
|
||
|
|
self.sy = _conv(sy)
|
||
|
|
self.covx = _conv(covx)
|
||
|
|
self.covy = _conv(covy)
|
||
|
|
self.fix = _conv(fix)
|
||
|
|
self.meta = meta
|
||
|
|
|
||
|
|
def _sd2wt(self, sd):
|
||
|
|
""" Convert standard deviation to weights.
|
||
|
|
"""
|
||
|
|
|
||
|
|
return 1./numpy.power(sd, 2)
|
||
|
|
|
||
|
|
def _cov2wt(self, cov):
|
||
|
|
""" Convert covariance matrix(-ices) to weights.
|
||
|
|
"""
|
||
|
|
|
||
|
|
from numpy.dual import inv
|
||
|
|
|
||
|
|
if len(cov.shape) == 2:
|
||
|
|
return inv(cov)
|
||
|
|
else:
|
||
|
|
weights = numpy.zeros(cov.shape, float)
|
||
|
|
|
||
|
|
for i in range(cov.shape[-1]): # n
|
||
|
|
weights[:,:,i] = inv(cov[:,:,i])
|
||
|
|
|
||
|
|
return weights
|
||
|
|
|
||
|
|
def __getattr__(self, attr):
|
||
|
|
lookup_tbl = {('wd', 'sx'): (self._sd2wt, self.sx),
|
||
|
|
('wd', 'covx'): (self._cov2wt, self.covx),
|
||
|
|
('we', 'sy'): (self._sd2wt, self.sy),
|
||
|
|
('we', 'covy'): (self._cov2wt, self.covy)}
|
||
|
|
|
||
|
|
if attr not in ('wd', 'we'):
|
||
|
|
if attr in self.meta:
|
||
|
|
return self.meta[attr]
|
||
|
|
else:
|
||
|
|
raise AttributeError("'%s' not in metadata" % attr)
|
||
|
|
else:
|
||
|
|
func, arg = lookup_tbl[(attr, self._ga_flags[attr])]
|
||
|
|
|
||
|
|
if arg is not None:
|
||
|
|
return func(*(arg,))
|
||
|
|
else:
|
||
|
|
return None
|
||
|
|
|
||
|
|
|
||
|
|
class Model(object):
|
||
|
|
"""
|
||
|
|
The Model class stores information about the function you wish to fit.
|
||
|
|
|
||
|
|
It stores the function itself, at the least, and optionally stores
|
||
|
|
functions which compute the Jacobians used during fitting. Also, one
|
||
|
|
can provide a function that will provide reasonable starting values
|
||
|
|
for the fit parameters possibly given the set of data.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
fcn : function
|
||
|
|
fcn(beta, x) --> y
|
||
|
|
fjacb : function
|
||
|
|
Jacobian of fcn wrt the fit parameters beta.
|
||
|
|
|
||
|
|
fjacb(beta, x) --> @f_i(x,B)/@B_j
|
||
|
|
fjacd : function
|
||
|
|
Jacobian of fcn wrt the (possibly multidimensional) input
|
||
|
|
variable.
|
||
|
|
|
||
|
|
fjacd(beta, x) --> @f_i(x,B)/@x_j
|
||
|
|
extra_args : tuple, optional
|
||
|
|
If specified, `extra_args` should be a tuple of extra
|
||
|
|
arguments to pass to `fcn`, `fjacb`, and `fjacd`. Each will be called
|
||
|
|
by `apply(fcn, (beta, x) + extra_args)`
|
||
|
|
estimate : array_like of rank-1
|
||
|
|
Provides estimates of the fit parameters from the data
|
||
|
|
|
||
|
|
estimate(data) --> estbeta
|
||
|
|
implicit : boolean
|
||
|
|
If TRUE, specifies that the model
|
||
|
|
is implicit; i.e `fcn(beta, x)` ~= 0 and there is no y data to fit
|
||
|
|
against
|
||
|
|
meta : dict, optional
|
||
|
|
freeform dictionary of metadata for the model
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
Note that the `fcn`, `fjacb`, and `fjacd` operate on NumPy arrays and
|
||
|
|
return a NumPy array. The `estimate` object takes an instance of the
|
||
|
|
Data class.
|
||
|
|
|
||
|
|
Here are the rules for the shapes of the argument and return
|
||
|
|
arrays of the callback functions:
|
||
|
|
|
||
|
|
`x`
|
||
|
|
if the input data is single-dimensional, then `x` is rank-1
|
||
|
|
array; i.e. ``x = array([1, 2, 3, ...]); x.shape = (n,)``
|
||
|
|
If the input data is multi-dimensional, then `x` is a rank-2 array;
|
||
|
|
i.e., ``x = array([[1, 2, ...], [2, 4, ...]]); x.shape = (m, n)``.
|
||
|
|
In all cases, it has the same shape as the input data array passed to
|
||
|
|
`odr`. `m` is the dimensionality of the input data, `n` is the number
|
||
|
|
of observations.
|
||
|
|
`y`
|
||
|
|
if the response variable is single-dimensional, then `y` is a
|
||
|
|
rank-1 array, i.e., ``y = array([2, 4, ...]); y.shape = (n,)``.
|
||
|
|
If the response variable is multi-dimensional, then `y` is a rank-2
|
||
|
|
array, i.e., ``y = array([[2, 4, ...], [3, 6, ...]]); y.shape =
|
||
|
|
(q, n)`` where `q` is the dimensionality of the response variable.
|
||
|
|
`beta`
|
||
|
|
rank-1 array of length `p` where `p` is the number of parameters;
|
||
|
|
i.e. ``beta = array([B_1, B_2, ..., B_p])``
|
||
|
|
`fjacb`
|
||
|
|
if the response variable is multi-dimensional, then the
|
||
|
|
return array's shape is `(q, p, n)` such that ``fjacb(x,beta)[l,k,i] =
|
||
|
|
d f_l(X,B)/d B_k`` evaluated at the i'th data point. If `q == 1`, then
|
||
|
|
the return array is only rank-2 and with shape `(p, n)`.
|
||
|
|
`fjacd`
|
||
|
|
as with fjacb, only the return array's shape is `(q, m, n)`
|
||
|
|
such that ``fjacd(x,beta)[l,j,i] = d f_l(X,B)/d X_j`` at the i'th data
|
||
|
|
point. If `q == 1`, then the return array's shape is `(m, n)`. If
|
||
|
|
`m == 1`, the shape is (q, n). If `m == q == 1`, the shape is `(n,)`.
|
||
|
|
|
||
|
|
"""
|
||
|
|
|
||
|
|
def __init__(self, fcn, fjacb=None, fjacd=None,
|
||
|
|
extra_args=None, estimate=None, implicit=0, meta=None):
|
||
|
|
|
||
|
|
self.fcn = fcn
|
||
|
|
self.fjacb = fjacb
|
||
|
|
self.fjacd = fjacd
|
||
|
|
|
||
|
|
if extra_args is not None:
|
||
|
|
extra_args = tuple(extra_args)
|
||
|
|
|
||
|
|
self.extra_args = extra_args
|
||
|
|
self.estimate = estimate
|
||
|
|
self.implicit = implicit
|
||
|
|
self.meta = meta
|
||
|
|
|
||
|
|
def set_meta(self, **kwds):
|
||
|
|
""" Update the metadata dictionary with the keywords and data provided
|
||
|
|
here.
|
||
|
|
|
||
|
|
Examples
|
||
|
|
--------
|
||
|
|
set_meta(name="Exponential", equation="y = a exp(b x) + c")
|
||
|
|
"""
|
||
|
|
|
||
|
|
self.meta.update(kwds)
|
||
|
|
|
||
|
|
def __getattr__(self, attr):
|
||
|
|
""" Dispatch attribute access to the metadata.
|
||
|
|
"""
|
||
|
|
|
||
|
|
if attr in self.meta:
|
||
|
|
return self.meta[attr]
|
||
|
|
else:
|
||
|
|
raise AttributeError("'%s' not in metadata" % attr)
|
||
|
|
|
||
|
|
|
||
|
|
class Output(object):
|
||
|
|
"""
|
||
|
|
The Output class stores the output of an ODR run.
|
||
|
|
|
||
|
|
Attributes
|
||
|
|
----------
|
||
|
|
beta : ndarray
|
||
|
|
Estimated parameter values, of shape (q,).
|
||
|
|
sd_beta : ndarray
|
||
|
|
Standard errors of the estimated parameters, of shape (p,).
|
||
|
|
cov_beta : ndarray
|
||
|
|
Covariance matrix of the estimated parameters, of shape (p,p).
|
||
|
|
delta : ndarray, optional
|
||
|
|
Array of estimated errors in input variables, of same shape as `x`.
|
||
|
|
eps : ndarray, optional
|
||
|
|
Array of estimated errors in response variables, of same shape as `y`.
|
||
|
|
xplus : ndarray, optional
|
||
|
|
Array of ``x + delta``.
|
||
|
|
y : ndarray, optional
|
||
|
|
Array ``y = fcn(x + delta)``.
|
||
|
|
res_var : float, optional
|
||
|
|
Residual variance.
|
||
|
|
sum_square : float, optional
|
||
|
|
Sum of squares error.
|
||
|
|
sum_square_delta : float, optional
|
||
|
|
Sum of squares of delta error.
|
||
|
|
sum_square_eps : float, optional
|
||
|
|
Sum of squares of eps error.
|
||
|
|
inv_condnum : float, optional
|
||
|
|
Inverse condition number (cf. ODRPACK UG p. 77).
|
||
|
|
rel_error : float, optional
|
||
|
|
Relative error in function values computed within fcn.
|
||
|
|
work : ndarray, optional
|
||
|
|
Final work array.
|
||
|
|
work_ind : dict, optional
|
||
|
|
Indices into work for drawing out values (cf. ODRPACK UG p. 83).
|
||
|
|
info : int, optional
|
||
|
|
Reason for returning, as output by ODRPACK (cf. ODRPACK UG p. 38).
|
||
|
|
stopreason : list of str, optional
|
||
|
|
`info` interpreted into English.
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
Takes one argument for initialization, the return value from the
|
||
|
|
function `odr`. The attributes listed as "optional" above are only
|
||
|
|
present if `odr` was run with ``full_output=1``.
|
||
|
|
|
||
|
|
"""
|
||
|
|
|
||
|
|
def __init__(self, output):
|
||
|
|
self.beta = output[0]
|
||
|
|
self.sd_beta = output[1]
|
||
|
|
self.cov_beta = output[2]
|
||
|
|
|
||
|
|
if len(output) == 4:
|
||
|
|
# full output
|
||
|
|
self.__dict__.update(output[3])
|
||
|
|
self.stopreason = _report_error(self.info)
|
||
|
|
|
||
|
|
def pprint(self):
|
||
|
|
""" Pretty-print important results.
|
||
|
|
"""
|
||
|
|
|
||
|
|
print('Beta:', self.beta)
|
||
|
|
print('Beta Std Error:', self.sd_beta)
|
||
|
|
print('Beta Covariance:', self.cov_beta)
|
||
|
|
if hasattr(self, 'info'):
|
||
|
|
print('Residual Variance:',self.res_var)
|
||
|
|
print('Inverse Condition #:', self.inv_condnum)
|
||
|
|
print('Reason(s) for Halting:')
|
||
|
|
for r in self.stopreason:
|
||
|
|
print(' %s' % r)
|
||
|
|
|
||
|
|
|
||
|
|
class ODR(object):
|
||
|
|
"""
|
||
|
|
The ODR class gathers all information and coordinates the running of the
|
||
|
|
main fitting routine.
|
||
|
|
|
||
|
|
Members of instances of the ODR class have the same names as the arguments
|
||
|
|
to the initialization routine.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
data : Data class instance
|
||
|
|
instance of the Data class
|
||
|
|
model : Model class instance
|
||
|
|
instance of the Model class
|
||
|
|
|
||
|
|
Other Parameters
|
||
|
|
----------------
|
||
|
|
beta0 : array_like of rank-1
|
||
|
|
a rank-1 sequence of initial parameter values. Optional if
|
||
|
|
model provides an "estimate" function to estimate these values.
|
||
|
|
delta0 : array_like of floats of rank-1, optional
|
||
|
|
a (double-precision) float array to hold the initial values of
|
||
|
|
the errors in the input variables. Must be same shape as data.x
|
||
|
|
ifixb : array_like of ints of rank-1, optional
|
||
|
|
sequence of integers with the same length as beta0 that determines
|
||
|
|
which parameters are held fixed. A value of 0 fixes the parameter,
|
||
|
|
a value > 0 makes the parameter free.
|
||
|
|
ifixx : array_like of ints with same shape as data.x, optional
|
||
|
|
an array of integers with the same shape as data.x that determines
|
||
|
|
which input observations are treated as fixed. One can use a sequence
|
||
|
|
of length m (the dimensionality of the input observations) to fix some
|
||
|
|
dimensions for all observations. A value of 0 fixes the observation,
|
||
|
|
a value > 0 makes it free.
|
||
|
|
job : int, optional
|
||
|
|
an integer telling ODRPACK what tasks to perform. See p. 31 of the
|
||
|
|
ODRPACK User's Guide if you absolutely must set the value here. Use the
|
||
|
|
method set_job post-initialization for a more readable interface.
|
||
|
|
iprint : int, optional
|
||
|
|
an integer telling ODRPACK what to print. See pp. 33-34 of the
|
||
|
|
ODRPACK User's Guide if you absolutely must set the value here. Use the
|
||
|
|
method set_iprint post-initialization for a more readable interface.
|
||
|
|
errfile : str, optional
|
||
|
|
string with the filename to print ODRPACK errors to. *Do Not Open
|
||
|
|
This File Yourself!*
|
||
|
|
rptfile : str, optional
|
||
|
|
string with the filename to print ODRPACK summaries to. *Do Not
|
||
|
|
Open This File Yourself!*
|
||
|
|
ndigit : int, optional
|
||
|
|
integer specifying the number of reliable digits in the computation
|
||
|
|
of the function.
|
||
|
|
taufac : float, optional
|
||
|
|
float specifying the initial trust region. The default value is 1.
|
||
|
|
The initial trust region is equal to taufac times the length of the
|
||
|
|
first computed Gauss-Newton step. taufac must be less than 1.
|
||
|
|
sstol : float, optional
|
||
|
|
float specifying the tolerance for convergence based on the relative
|
||
|
|
change in the sum-of-squares. The default value is eps**(1/2) where eps
|
||
|
|
is the smallest value such that 1 + eps > 1 for double precision
|
||
|
|
computation on the machine. sstol must be less than 1.
|
||
|
|
partol : float, optional
|
||
|
|
float specifying the tolerance for convergence based on the relative
|
||
|
|
change in the estimated parameters. The default value is eps**(2/3) for
|
||
|
|
explicit models and ``eps**(1/3)`` for implicit models. partol must be less
|
||
|
|
than 1.
|
||
|
|
maxit : int, optional
|
||
|
|
integer specifying the maximum number of iterations to perform. For
|
||
|
|
first runs, maxit is the total number of iterations performed and
|
||
|
|
defaults to 50. For restarts, maxit is the number of additional
|
||
|
|
iterations to perform and defaults to 10.
|
||
|
|
stpb : array_like, optional
|
||
|
|
sequence (``len(stpb) == len(beta0)``) of relative step sizes to compute
|
||
|
|
finite difference derivatives wrt the parameters.
|
||
|
|
stpd : optional
|
||
|
|
array (``stpd.shape == data.x.shape`` or ``stpd.shape == (m,)``) of relative
|
||
|
|
step sizes to compute finite difference derivatives wrt the input
|
||
|
|
variable errors. If stpd is a rank-1 array with length m (the
|
||
|
|
dimensionality of the input variable), then the values are broadcast to
|
||
|
|
all observations.
|
||
|
|
sclb : array_like, optional
|
||
|
|
sequence (``len(stpb) == len(beta0)``) of scaling factors for the
|
||
|
|
parameters. The purpose of these scaling factors are to scale all of
|
||
|
|
the parameters to around unity. Normally appropriate scaling factors
|
||
|
|
are computed if this argument is not specified. Specify them yourself
|
||
|
|
if the automatic procedure goes awry.
|
||
|
|
scld : array_like, optional
|
||
|
|
array (scld.shape == data.x.shape or scld.shape == (m,)) of scaling
|
||
|
|
factors for the *errors* in the input variables. Again, these factors
|
||
|
|
are automatically computed if you do not provide them. If scld.shape ==
|
||
|
|
(m,), then the scaling factors are broadcast to all observations.
|
||
|
|
work : ndarray, optional
|
||
|
|
array to hold the double-valued working data for ODRPACK. When
|
||
|
|
restarting, takes the value of self.output.work.
|
||
|
|
iwork : ndarray, optional
|
||
|
|
array to hold the integer-valued working data for ODRPACK. When
|
||
|
|
restarting, takes the value of self.output.iwork.
|
||
|
|
|
||
|
|
Attributes
|
||
|
|
----------
|
||
|
|
data : Data
|
||
|
|
The data for this fit
|
||
|
|
model : Model
|
||
|
|
The model used in fit
|
||
|
|
output : Output
|
||
|
|
An instance if the Output class containing all of the returned
|
||
|
|
data from an invocation of ODR.run() or ODR.restart()
|
||
|
|
|
||
|
|
"""
|
||
|
|
|
||
|
|
def __init__(self, data, model, beta0=None, delta0=None, ifixb=None,
|
||
|
|
ifixx=None, job=None, iprint=None, errfile=None, rptfile=None,
|
||
|
|
ndigit=None, taufac=None, sstol=None, partol=None, maxit=None,
|
||
|
|
stpb=None, stpd=None, sclb=None, scld=None, work=None, iwork=None):
|
||
|
|
|
||
|
|
self.data = data
|
||
|
|
self.model = model
|
||
|
|
|
||
|
|
if beta0 is None:
|
||
|
|
if self.model.estimate is not None:
|
||
|
|
self.beta0 = _conv(self.model.estimate(self.data))
|
||
|
|
else:
|
||
|
|
raise ValueError(
|
||
|
|
"must specify beta0 or provide an estimater with the model"
|
||
|
|
)
|
||
|
|
else:
|
||
|
|
self.beta0 = _conv(beta0)
|
||
|
|
|
||
|
|
self.delta0 = _conv(delta0)
|
||
|
|
# These really are 32-bit integers in FORTRAN (gfortran), even on 64-bit
|
||
|
|
# platforms.
|
||
|
|
# XXX: some other FORTRAN compilers may not agree.
|
||
|
|
self.ifixx = _conv(ifixx, dtype=numpy.int32)
|
||
|
|
self.ifixb = _conv(ifixb, dtype=numpy.int32)
|
||
|
|
self.job = job
|
||
|
|
self.iprint = iprint
|
||
|
|
self.errfile = errfile
|
||
|
|
self.rptfile = rptfile
|
||
|
|
self.ndigit = ndigit
|
||
|
|
self.taufac = taufac
|
||
|
|
self.sstol = sstol
|
||
|
|
self.partol = partol
|
||
|
|
self.maxit = maxit
|
||
|
|
self.stpb = _conv(stpb)
|
||
|
|
self.stpd = _conv(stpd)
|
||
|
|
self.sclb = _conv(sclb)
|
||
|
|
self.scld = _conv(scld)
|
||
|
|
self.work = _conv(work)
|
||
|
|
self.iwork = _conv(iwork)
|
||
|
|
|
||
|
|
self.output = None
|
||
|
|
|
||
|
|
self._check()
|
||
|
|
|
||
|
|
def _check(self):
|
||
|
|
""" Check the inputs for consistency, but don't bother checking things
|
||
|
|
that the builtin function odr will check.
|
||
|
|
"""
|
||
|
|
|
||
|
|
x_s = list(self.data.x.shape)
|
||
|
|
|
||
|
|
if isinstance(self.data.y, numpy.ndarray):
|
||
|
|
y_s = list(self.data.y.shape)
|
||
|
|
if self.model.implicit:
|
||
|
|
raise OdrError("an implicit model cannot use response data")
|
||
|
|
else:
|
||
|
|
# implicit model with q == self.data.y
|
||
|
|
y_s = [self.data.y, x_s[-1]]
|
||
|
|
if not self.model.implicit:
|
||
|
|
raise OdrError("an explicit model needs response data")
|
||
|
|
self.set_job(fit_type=1)
|
||
|
|
|
||
|
|
if x_s[-1] != y_s[-1]:
|
||
|
|
raise OdrError("number of observations do not match")
|
||
|
|
|
||
|
|
n = x_s[-1]
|
||
|
|
|
||
|
|
if len(x_s) == 2:
|
||
|
|
m = x_s[0]
|
||
|
|
else:
|
||
|
|
m = 1
|
||
|
|
if len(y_s) == 2:
|
||
|
|
q = y_s[0]
|
||
|
|
else:
|
||
|
|
q = 1
|
||
|
|
|
||
|
|
p = len(self.beta0)
|
||
|
|
|
||
|
|
# permissible output array shapes
|
||
|
|
|
||
|
|
fcn_perms = [(q, n)]
|
||
|
|
fjacd_perms = [(q, m, n)]
|
||
|
|
fjacb_perms = [(q, p, n)]
|
||
|
|
|
||
|
|
if q == 1:
|
||
|
|
fcn_perms.append((n,))
|
||
|
|
fjacd_perms.append((m, n))
|
||
|
|
fjacb_perms.append((p, n))
|
||
|
|
if m == 1:
|
||
|
|
fjacd_perms.append((q, n))
|
||
|
|
if p == 1:
|
||
|
|
fjacb_perms.append((q, n))
|
||
|
|
if m == q == 1:
|
||
|
|
fjacd_perms.append((n,))
|
||
|
|
if p == q == 1:
|
||
|
|
fjacb_perms.append((n,))
|
||
|
|
|
||
|
|
# try evaluating the supplied functions to make sure they provide
|
||
|
|
# sensible outputs
|
||
|
|
|
||
|
|
arglist = (self.beta0, self.data.x)
|
||
|
|
if self.model.extra_args is not None:
|
||
|
|
arglist = arglist + self.model.extra_args
|
||
|
|
res = self.model.fcn(*arglist)
|
||
|
|
|
||
|
|
if res.shape not in fcn_perms:
|
||
|
|
print(res.shape)
|
||
|
|
print(fcn_perms)
|
||
|
|
raise OdrError("fcn does not output %s-shaped array" % y_s)
|
||
|
|
|
||
|
|
if self.model.fjacd is not None:
|
||
|
|
res = self.model.fjacd(*arglist)
|
||
|
|
if res.shape not in fjacd_perms:
|
||
|
|
raise OdrError(
|
||
|
|
"fjacd does not output %s-shaped array" % repr((q, m, n)))
|
||
|
|
if self.model.fjacb is not None:
|
||
|
|
res = self.model.fjacb(*arglist)
|
||
|
|
if res.shape not in fjacb_perms:
|
||
|
|
raise OdrError(
|
||
|
|
"fjacb does not output %s-shaped array" % repr((q, p, n)))
|
||
|
|
|
||
|
|
# check shape of delta0
|
||
|
|
|
||
|
|
if self.delta0 is not None and self.delta0.shape != self.data.x.shape:
|
||
|
|
raise OdrError(
|
||
|
|
"delta0 is not a %s-shaped array" % repr(self.data.x.shape))
|
||
|
|
|
||
|
|
if self.data.x.size == 0:
|
||
|
|
warn(("Empty data detected for ODR instance. "
|
||
|
|
"Do not expect any fitting to occur"),
|
||
|
|
OdrWarning)
|
||
|
|
|
||
|
|
def _gen_work(self):
|
||
|
|
""" Generate a suitable work array if one does not already exist.
|
||
|
|
"""
|
||
|
|
|
||
|
|
n = self.data.x.shape[-1]
|
||
|
|
p = self.beta0.shape[0]
|
||
|
|
|
||
|
|
if len(self.data.x.shape) == 2:
|
||
|
|
m = self.data.x.shape[0]
|
||
|
|
else:
|
||
|
|
m = 1
|
||
|
|
|
||
|
|
if self.model.implicit:
|
||
|
|
q = self.data.y
|
||
|
|
elif len(self.data.y.shape) == 2:
|
||
|
|
q = self.data.y.shape[0]
|
||
|
|
else:
|
||
|
|
q = 1
|
||
|
|
|
||
|
|
if self.data.we is None:
|
||
|
|
ldwe = ld2we = 1
|
||
|
|
elif len(self.data.we.shape) == 3:
|
||
|
|
ld2we, ldwe = self.data.we.shape[1:]
|
||
|
|
else:
|
||
|
|
# Okay, this isn't precisely right, but for this calculation,
|
||
|
|
# it's fine
|
||
|
|
ldwe = 1
|
||
|
|
ld2we = self.data.we.shape[1]
|
||
|
|
|
||
|
|
if self.job % 10 < 2:
|
||
|
|
# ODR not OLS
|
||
|
|
lwork = (18 + 11*p + p*p + m + m*m + 4*n*q + 6*n*m + 2*n*q*p +
|
||
|
|
2*n*q*m + q*q + 5*q + q*(p+m) + ldwe*ld2we*q)
|
||
|
|
else:
|
||
|
|
# OLS not ODR
|
||
|
|
lwork = (18 + 11*p + p*p + m + m*m + 4*n*q + 2*n*m + 2*n*q*p +
|
||
|
|
5*q + q*(p+m) + ldwe*ld2we*q)
|
||
|
|
|
||
|
|
if isinstance(self.work, numpy.ndarray) and self.work.shape == (lwork,)\
|
||
|
|
and self.work.dtype.str.endswith('f8'):
|
||
|
|
# the existing array is fine
|
||
|
|
return
|
||
|
|
else:
|
||
|
|
self.work = numpy.zeros((lwork,), float)
|
||
|
|
|
||
|
|
def set_job(self, fit_type=None, deriv=None, var_calc=None,
|
||
|
|
del_init=None, restart=None):
|
||
|
|
"""
|
||
|
|
Sets the "job" parameter is a hopefully comprehensible way.
|
||
|
|
|
||
|
|
If an argument is not specified, then the value is left as is. The
|
||
|
|
default value from class initialization is for all of these options set
|
||
|
|
to 0.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
fit_type : {0, 1, 2} int
|
||
|
|
0 -> explicit ODR
|
||
|
|
|
||
|
|
1 -> implicit ODR
|
||
|
|
|
||
|
|
2 -> ordinary least-squares
|
||
|
|
deriv : {0, 1, 2, 3} int
|
||
|
|
0 -> forward finite differences
|
||
|
|
|
||
|
|
1 -> central finite differences
|
||
|
|
|
||
|
|
2 -> user-supplied derivatives (Jacobians) with results
|
||
|
|
checked by ODRPACK
|
||
|
|
|
||
|
|
3 -> user-supplied derivatives, no checking
|
||
|
|
var_calc : {0, 1, 2} int
|
||
|
|
0 -> calculate asymptotic covariance matrix and fit
|
||
|
|
parameter uncertainties (V_B, s_B) using derivatives
|
||
|
|
recomputed at the final solution
|
||
|
|
|
||
|
|
1 -> calculate V_B and s_B using derivatives from last iteration
|
||
|
|
|
||
|
|
2 -> do not calculate V_B and s_B
|
||
|
|
del_init : {0, 1} int
|
||
|
|
0 -> initial input variable offsets set to 0
|
||
|
|
|
||
|
|
1 -> initial offsets provided by user in variable "work"
|
||
|
|
restart : {0, 1} int
|
||
|
|
0 -> fit is not a restart
|
||
|
|
|
||
|
|
1 -> fit is a restart
|
||
|
|
|
||
|
|
Notes
|
||
|
|
-----
|
||
|
|
The permissible values are different from those given on pg. 31 of the
|
||
|
|
ODRPACK User's Guide only in that one cannot specify numbers greater than
|
||
|
|
the last value for each variable.
|
||
|
|
|
||
|
|
If one does not supply functions to compute the Jacobians, the fitting
|
||
|
|
procedure will change deriv to 0, finite differences, as a default. To
|
||
|
|
initialize the input variable offsets by yourself, set del_init to 1 and
|
||
|
|
put the offsets into the "work" variable correctly.
|
||
|
|
|
||
|
|
"""
|
||
|
|
|
||
|
|
if self.job is None:
|
||
|
|
job_l = [0, 0, 0, 0, 0]
|
||
|
|
else:
|
||
|
|
job_l = [self.job // 10000 % 10,
|
||
|
|
self.job // 1000 % 10,
|
||
|
|
self.job // 100 % 10,
|
||
|
|
self.job // 10 % 10,
|
||
|
|
self.job % 10]
|
||
|
|
|
||
|
|
if fit_type in (0, 1, 2):
|
||
|
|
job_l[4] = fit_type
|
||
|
|
if deriv in (0, 1, 2, 3):
|
||
|
|
job_l[3] = deriv
|
||
|
|
if var_calc in (0, 1, 2):
|
||
|
|
job_l[2] = var_calc
|
||
|
|
if del_init in (0, 1):
|
||
|
|
job_l[1] = del_init
|
||
|
|
if restart in (0, 1):
|
||
|
|
job_l[0] = restart
|
||
|
|
|
||
|
|
self.job = (job_l[0]*10000 + job_l[1]*1000 +
|
||
|
|
job_l[2]*100 + job_l[3]*10 + job_l[4])
|
||
|
|
|
||
|
|
def set_iprint(self, init=None, so_init=None,
|
||
|
|
iter=None, so_iter=None, iter_step=None, final=None, so_final=None):
|
||
|
|
""" Set the iprint parameter for the printing of computation reports.
|
||
|
|
|
||
|
|
If any of the arguments are specified here, then they are set in the
|
||
|
|
iprint member. If iprint is not set manually or with this method, then
|
||
|
|
ODRPACK defaults to no printing. If no filename is specified with the
|
||
|
|
member rptfile, then ODRPACK prints to stdout. One can tell ODRPACK to
|
||
|
|
print to stdout in addition to the specified filename by setting the
|
||
|
|
so_* arguments to this function, but one cannot specify to print to
|
||
|
|
stdout but not a file since one can do that by not specifying a rptfile
|
||
|
|
filename.
|
||
|
|
|
||
|
|
There are three reports: initialization, iteration, and final reports.
|
||
|
|
They are represented by the arguments init, iter, and final
|
||
|
|
respectively. The permissible values are 0, 1, and 2 representing "no
|
||
|
|
report", "short report", and "long report" respectively.
|
||
|
|
|
||
|
|
The argument iter_step (0 <= iter_step <= 9) specifies how often to make
|
||
|
|
the iteration report; the report will be made for every iter_step'th
|
||
|
|
iteration starting with iteration one. If iter_step == 0, then no
|
||
|
|
iteration report is made, regardless of the other arguments.
|
||
|
|
|
||
|
|
If the rptfile is None, then any so_* arguments supplied will raise an
|
||
|
|
exception.
|
||
|
|
"""
|
||
|
|
if self.iprint is None:
|
||
|
|
self.iprint = 0
|
||
|
|
|
||
|
|
ip = [self.iprint // 1000 % 10,
|
||
|
|
self.iprint // 100 % 10,
|
||
|
|
self.iprint // 10 % 10,
|
||
|
|
self.iprint % 10]
|
||
|
|
|
||
|
|
# make a list to convert iprint digits to/from argument inputs
|
||
|
|
# rptfile, stdout
|
||
|
|
ip2arg = [[0, 0], # none, none
|
||
|
|
[1, 0], # short, none
|
||
|
|
[2, 0], # long, none
|
||
|
|
[1, 1], # short, short
|
||
|
|
[2, 1], # long, short
|
||
|
|
[1, 2], # short, long
|
||
|
|
[2, 2]] # long, long
|
||
|
|
|
||
|
|
if (self.rptfile is None and
|
||
|
|
(so_init is not None or
|
||
|
|
so_iter is not None or
|
||
|
|
so_final is not None)):
|
||
|
|
raise OdrError(
|
||
|
|
"no rptfile specified, cannot output to stdout twice")
|
||
|
|
|
||
|
|
iprint_l = ip2arg[ip[0]] + ip2arg[ip[1]] + ip2arg[ip[3]]
|
||
|
|
|
||
|
|
if init is not None:
|
||
|
|
iprint_l[0] = init
|
||
|
|
if so_init is not None:
|
||
|
|
iprint_l[1] = so_init
|
||
|
|
if iter is not None:
|
||
|
|
iprint_l[2] = iter
|
||
|
|
if so_iter is not None:
|
||
|
|
iprint_l[3] = so_iter
|
||
|
|
if final is not None:
|
||
|
|
iprint_l[4] = final
|
||
|
|
if so_final is not None:
|
||
|
|
iprint_l[5] = so_final
|
||
|
|
|
||
|
|
if iter_step in range(10):
|
||
|
|
# 0..9
|
||
|
|
ip[2] = iter_step
|
||
|
|
|
||
|
|
ip[0] = ip2arg.index(iprint_l[0:2])
|
||
|
|
ip[1] = ip2arg.index(iprint_l[2:4])
|
||
|
|
ip[3] = ip2arg.index(iprint_l[4:6])
|
||
|
|
|
||
|
|
self.iprint = ip[0]*1000 + ip[1]*100 + ip[2]*10 + ip[3]
|
||
|
|
|
||
|
|
def run(self):
|
||
|
|
""" Run the fitting routine with all of the information given and with ``full_output=1``.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
output : Output instance
|
||
|
|
This object is also assigned to the attribute .output .
|
||
|
|
"""
|
||
|
|
|
||
|
|
args = (self.model.fcn, self.beta0, self.data.y, self.data.x)
|
||
|
|
kwds = {'full_output': 1}
|
||
|
|
kwd_l = ['ifixx', 'ifixb', 'job', 'iprint', 'errfile', 'rptfile',
|
||
|
|
'ndigit', 'taufac', 'sstol', 'partol', 'maxit', 'stpb',
|
||
|
|
'stpd', 'sclb', 'scld', 'work', 'iwork']
|
||
|
|
|
||
|
|
if self.delta0 is not None and self.job % 1000 // 10 == 1:
|
||
|
|
# delta0 provided and fit is not a restart
|
||
|
|
self._gen_work()
|
||
|
|
|
||
|
|
d0 = numpy.ravel(self.delta0)
|
||
|
|
|
||
|
|
self.work[:len(d0)] = d0
|
||
|
|
|
||
|
|
# set the kwds from other objects explicitly
|
||
|
|
if self.model.fjacb is not None:
|
||
|
|
kwds['fjacb'] = self.model.fjacb
|
||
|
|
if self.model.fjacd is not None:
|
||
|
|
kwds['fjacd'] = self.model.fjacd
|
||
|
|
if self.data.we is not None:
|
||
|
|
kwds['we'] = self.data.we
|
||
|
|
if self.data.wd is not None:
|
||
|
|
kwds['wd'] = self.data.wd
|
||
|
|
if self.model.extra_args is not None:
|
||
|
|
kwds['extra_args'] = self.model.extra_args
|
||
|
|
|
||
|
|
# implicitly set kwds from self's members
|
||
|
|
for attr in kwd_l:
|
||
|
|
obj = getattr(self, attr)
|
||
|
|
if obj is not None:
|
||
|
|
kwds[attr] = obj
|
||
|
|
|
||
|
|
self.output = Output(odr(*args, **kwds))
|
||
|
|
|
||
|
|
return self.output
|
||
|
|
|
||
|
|
def restart(self, iter=None):
|
||
|
|
""" Restarts the run with iter more iterations.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
iter : int, optional
|
||
|
|
ODRPACK's default for the number of new iterations is 10.
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
output : Output instance
|
||
|
|
This object is also assigned to the attribute .output .
|
||
|
|
"""
|
||
|
|
|
||
|
|
if self.output is None:
|
||
|
|
raise OdrError("cannot restart: run() has not been called before")
|
||
|
|
|
||
|
|
self.set_job(restart=1)
|
||
|
|
self.work = self.output.work
|
||
|
|
self.iwork = self.output.iwork
|
||
|
|
|
||
|
|
self.maxit = iter
|
||
|
|
|
||
|
|
return self.run()
|