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"""
Python wrappers for Orthogonal Distance Regression (ODRPACK).
Classes
=======
Data -- stores the data and weights to fit against
RealData -- stores data with standard deviations and covariance matrices
Model -- stores the model and its related information
Output -- stores all of the output from an ODR run
ODR -- collects all data and runs the fitting routine
Exceptions
==========
`odr_error` :
error sometimes raised inside odr() and can be raised in the
fitting functions to tell ODRPACK to halt the procedure
`odr_stop` :
error to raise in fitting functions to tell ODRPACK that the data or
parameters given are invalid
Use
===
Basic use:
1) Define the function you want to fit against.
::
def f(B, x):
''' Linear function y = m*x + b '''
return B[0]*x + B[1]
# B is a vector of the parameters.
# x is an array of the current x values.
# x is same format as the x passed to Data or RealData.
# Return an array in the same format as y passed to Data or RealData.
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
::
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()
Read the docstrings and the accompanying tests for more advanced usage.
Notes
=====
* Array formats -- FORTRAN stores its arrays in memory column first, i.e. an
array element A(i, j, k) will be next to A(i+1, j, k). In C and, consequently,
NumPy, arrays are stored row first: A[i, j, k] is next to A[i, j, k+1]. For
efficiency and convenience, the input and output arrays of the fitting
function (and its Jacobians) are passed to FORTRAN without transposition.
Therefore, where the ODRPACK documentation says that the X array is of shape
(N, M), it will be passed to the Python function as an array of shape (M, N).
If M==1, the one-dimensional case, then nothing matters; if M>1, then your
Python functions will be dealing with arrays that are indexed in reverse of
the ODRPACK documentation. No real biggie, but watch out for your indexing of
the Jacobians: the i,j'th elements (@f_i/@x_j) evaluated at the n'th
observation will be returned as jacd[j, i, n]. Except for the Jacobians, it
really is easier to deal with x[0] and x[1] than x[:,0] and x[:,1]. Of course,
you can always use the transpose() function from scipy explicitly.
* Examples -- See the accompanying file test/test.py for examples of how to set
up fits of your own. Some are taken from the User's Guide; some are from
other sources.
* Models -- Some common models are instantiated in the accompanying module
models.py . Contributions are welcome.
Credits
=======
* Thanks to Arnold Moene and Gerard Vermeulen for fixing some killer bugs.
Robert Kern
robert.kern@gmail.com
"""
import numpy
from scipy.odr import __odrpack
__all__ = ['odr', 'odr_error', 'odr_stop', 'Data', 'RealData', 'Model',
'Output', 'ODR']
odr = __odrpack.odr
odr_error = __odrpack.odr_error
odr_stop = __odrpack.odr_stop
def _conv(obj, dtype=None):
""" Convert an object to the preferred form for input to the odr routine.
"""
if obj is None:
return obj
else:
if dtype is None:
obj = numpy.asarray(obj)
else:
obj = numpy.asarray(obj, dtype)
if obj.shape == ():
# Scalar.
return obj.dtype.type(obj)
else:
return obj
def _report_error(info):
""" Interprets the return code of the odr routine.
Parameters
----------
info : int
The return code of the odr routine.
Returns
-------
problems : list(str)
A list of messages about why the odr() routine stopped.
"""
stopreason = ('Blank',
'Sum of squares convergence',
'Parameter convergence',
'Both sum of squares and parameter convergence',
'Iteration limit reached')[info % 5]
if info >= 5:
# questionable results or fatal error
I = (info/10000 % 10,
info/1000 % 10,
info/100 % 10,
info/10 % 10,
info % 10)
problems = []
if I[0] == 0:
if I[1] != 0:
problems.append('Derivatives possibly not correct')
if I[2] != 0:
problems.append('Error occurred in callback')
if I[3] != 0:
problems.append('Problem is not full rank at solution')
problems.append(stopreason)
elif I[0] == 1:
if I[1] != 0:
problems.append('N < 1')
if I[2] != 0:
problems.append('M < 1')
if I[3] != 0:
problems.append('NP < 1 or NP > N')
if I[4] != 0:
problems.append('NQ < 1')
elif I[0] == 2:
if I[1] != 0:
problems.append('LDY and/or LDX incorrect')
if I[2] != 0:
problems.append('LDWE, LD2WE, LDWD, and/or LD2WD incorrect')
if I[3] != 0:
problems.append('LDIFX, LDSTPD, and/or LDSCLD incorrect')
if I[4] != 0:
problems.append('LWORK and/or LIWORK too small')
elif I[0] == 3:
if I[1] != 0:
problems.append('STPB and/or STPD incorrect')
if I[2] != 0:
problems.append('SCLB and/or SCLD incorrect')
if I[3] != 0:
problems.append('WE incorrect')
if I[4] != 0:
problems.append('WD incorrect')
elif I[0] == 4:
problems.append('Error in derivatives')
elif I[0] == 5:
problems.append('Error occurred in callback')
elif I[0] == 6:
problems.append('Numerical error detected')
return problems
else:
return [stopreason]
class Data(object):
"""
scipy.odr.Data(x, y=None, we=None, wd=None, fix=None, meta={})
The Data class stores the data to fit.
Parameters
----------
x : array_like
Input data for regression.
y : array_like, optional
Input data for regression.
we : array_like, optional
If `we` is a scalar, then that value is used for all data points (and
all dimensions of the response variable).
If `we` is a rank-1 array of length q (the dimensionality of the
response variable), then this vector is the diagonal of the covariant
weighting matrix for all data points.
If `we` is a rank-1 array of length n (the number of data points), then
the i'th element is the weight for the i'th response variable
observation (single-dimensional only).
If `we` is a rank-2 array of shape (q, q), then this is the full
covariant weighting matrix broadcast to each observation.
If `we` is a rank-2 array of shape (q, n), then `we[:,i]` is the
diagonal of the covariant weighting matrix for the i'th observation.
If `we` is a rank-3 array of shape (q, q, n), then `we[:,:,i]` is the
full specification of the covariant weighting matrix for each
observation.
If the fit is implicit, then only a positive scalar value is used.
wd : array_like, optional
If `wd` is a scalar, then that value is used for all data points
(and all dimensions of the input variable). If `wd` = 0, then the
covariant weighting matrix for each observation is set to the identity
matrix (so each dimension of each observation has the same weight).
If `wd` is a rank-1 array of length m (the dimensionality of the input
variable), then this vector is the diagonal of the covariant weighting
matrix for all data points.
If `wd` is a rank-1 array of length n (the number of data points), then
the i'th element is the weight for the i'th input variable observation
(single-dimensional only).
If `wd` is a rank-2 array of shape (m, m), then this is the full
covariant weighting matrix broadcast to each observation.
If `wd` is a rank-2 array of shape (m, n), then `wd[:,i]` is the
diagonal of the covariant weighting matrix for the i'th observation.
If `wd` is a rank-3 array of shape (m, m, n), then `wd[:,:,i]` is the
full specification of the covariant weighting matrix for each
observation.
fix : array_like of ints, optional
The `fix` argument is the same as ifixx in the class ODR. It is 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.
meta : dict, optional
Freeform dictionary for metadata.
Notes
-----
Each argument is attached to the member of the instance of the same name.
The structures of `x` and `y` are described in the Model class docstring.
If `y` is an integer, then the Data instance can only be used to fit with
implicit models where the dimensionality of the response is equal to the
specified value of `y`.
The `we` argument weights the effect a deviation in the response variable
has on the fit. The `wd` argument weights the effect a deviation in the
input variable has on the fit. To handle multidimensional inputs and
responses easily, the structure of these arguments has the n'th
dimensional axis first. These arguments heavily use the structured
arguments feature of ODRPACK to conveniently and flexibly support all
options. See the ODRPACK User's Guide for a full explanation of how these
weights are used in the algorithm. Basically, a higher value of the weight
for a particular data point makes a deviation at that point more
detrimental to the fit.
"""
def __init__(self, x, y=None, we=None, wd=None, fix=None, meta={}):
self.x = _conv(x)
self.y = _conv(y)
self.we = _conv(we)
self.wd = _conv(wd)
self.fix = _conv(fix)
self.meta = meta
def set_meta(self, **kwds):
""" Update the metadata dictionary with the keywords and data provided
by keywords.
Examples
--------
data.set_meta(lab="Ph 7; Lab 26", title="Ag110 + Ag108 Decay")
"""
self.meta.update(kwds)
def __getattr__(self, attr):
""" Dispatch aatribute access to the metadata dictionary.
"""
if attr in self.meta.keys():
return self.meta[attr]
else:
raise AttributeError("'%s' not in metadata" % attr)
class RealData(Data):
"""
The RealData class stores the weightings as actual standard deviations
and/or covariances.
Parameters
----------
x : array_like
x
y : array_like, optional
y
sx, sy : array_like, optional
Standard deviations of `x`.
`sx` are standard deviations of `x` and are converted to weights by
dividing 1.0 by their squares.
sy : array_like, optional
Standard deviations of `y`.
`sy` are standard deviations of `y` and are converted to weights by
dividing 1.0 by their squares.
covx : array_like, optional
Covariance of `x`
`covx` is an array of covariance matrices of `x` and are converted to
weights by performing a matrix inversion on each observation's
covariance matrix.
covy : array_like, optional
Covariance of `y`
`covy` is an array of covariance matrices and are converted to
weights by performing a matrix inversion on each observation's
covariance matrix.
fix : array_like
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
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
Meta
Notes
-----
The weights needed for ODRPACK are generated on-the-fly with
``__getattr__`` trickery.
`sx` and `sy` are converted to weights by dividing 1.0 by their squares.
For example, ``wd = 1./numpy.power(`sx`, 2)``.
`covx` and `covy` are arrays of covariance matrices and are converted to
weights by performing a matrix inversion on each observation's covariance
matrix. For example, ``we[i] = numpy.linalg.inv(covy[i])``.
These arguments follow the same structured argument conventions as wd and
we only restricted by their natures: `sx` and `sy` can't be rank-3, but
`covx` and `covy` can be.
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")
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)
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.keys():
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 apply(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 :
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] =
@f_l(X,B)/@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] = @f_l(X,B)/@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.keys():
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.
Takes one argument for initialization, the return value from the
function `odr`.
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_sqare : 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
-----
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
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.
output : Output class instance
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 odr_error("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 odr_error("an explicit model needs response data")
self.set_job(fit_type=1)
if x_s[-1] != y_s[-1]:
raise odr_error("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 odr_error("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 odr_error(
"fjacd does not output %s-shaped array" % (q, m, n))
if self.model.fjacb is not None:
res = self.model.fjacb(*arglist)
if res.shape not in fjacb_perms:
raise odr_error(
"fjacb does not output %s-shaped array" % (q, p, n))
# check shape of delta0
if self.delta0 is not None and self.delta0.shape != self.data.x.shape:
raise odr_error(
"delta0 is not a %s-shaped array" % self.data.x.shape)
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 odr_error(
"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.
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(apply(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 odr_error("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()
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