Model(fcn, fjacb=None, fjacd=None, extra_args=None, estimate=None, implicit=0, meta=None)¶
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.
- 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
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:
- if the input data is single-dimensional, then x is rank-1
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.
- 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.
- rank-1 array of length p where p is the number of parameters;
beta = array([B_1, B_2, ..., B_p])
- 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_kevaluated at the i’th data point. If q == 1, then the return array is only rank-2 and with shape (p, n).
- as with fjacb, only the return array’s shape is (q, m, n)
fjacd(x,beta)[l,j,i] = d f_l(X,B)/d X_jat 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,).
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