Odr

Data¶

Module Scipy.Odr.Data wraps Python class scipy.odr.Data.

type t

create¶

constructor and attributes create

val create :
  ?y:[>`Ndarray] Np.Obj.t ->
  ?we:[>`Ndarray] Np.Obj.t ->
  ?wd:[>`Ndarray] Np.Obj.t ->
  ?fix:Py.Object.t ->
  ?meta:Py.Object.t ->
  x:[>`Ndarray] Np.Obj.t ->
  unit ->
  t

The data to fit.

Parameters

x : array_like Observed data for the independent variable of the regression
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 the data is implicit.
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 ith 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 ith 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 Free-form 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.

set_meta¶

method set_meta

val set_meta :
  ?kwds:(string * Py.Object.t) list ->
  [> tag] Obj.t ->
  Py.Object.t

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')

to_string¶

method to_string

val to_string: t -> string

Print the object to a human-readable representation.

show¶

method show

val show: t -> string

Print the object to a human-readable representation.

pp¶

method pp

val pp: Format.formatter -> t -> unit

Pretty-print the object to a formatter.

Model¶

Module Scipy.Odr.Model wraps Python class scipy.odr.Model.

type t

create¶

constructor and attributes create

val create :
  ?fjacb:Py.Object.t ->
  ?fjacd:Py.Object.t ->
  ?extra_args:Py.Object.t ->
  ?estimate:Py.Object.t ->
  ?implicit:bool ->
  ?meta:Py.Object.t ->
  fcn:Py.Object.t ->
  unit ->
  t

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 ~scipy.odr.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 ith 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 ith 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,).

set_meta¶

method set_meta

val set_meta :
  ?kwds:(string * Py.Object.t) list ->
  [> tag] Obj.t ->
  Py.Object.t

Update the metadata dictionary with the keywords and data provided here.

Examples

set_meta(name='Exponential', equation='y = a exp(b x) + c')

to_string¶

method to_string

val to_string: t -> string

Print the object to a human-readable representation.

show¶

method show

val show: t -> string

Print the object to a human-readable representation.

pp¶

method pp

val pp: Format.formatter -> t -> unit

Pretty-print the object to a formatter.

ODR¶

Module Scipy.Odr.ODR wraps Python class scipy.odr.ODR.

type t

create¶

constructor and attributes create

val create :
  ?beta0:Py.Object.t ->
  ?delta0:Py.Object.t ->
  ?ifixb:Py.Object.t ->
  ?ifixx:Py.Object.t ->
  ?job:Py.Object.t ->
  ?iprint:Py.Object.t ->
  ?errfile:Py.Object.t ->
  ?rptfile:Py.Object.t ->
  ?ndigit:Py.Object.t ->
  ?taufac:Py.Object.t ->
  ?sstol:Py.Object.t ->
  ?partol:Py.Object.t ->
  ?maxit:Py.Object.t ->
  ?stpb:Py.Object.t ->
  ?stpd:Py.Object.t ->
  ?sclb:Py.Object.t ->
  ?scld:Py.Object.t ->
  ?work:Py.Object.t ->
  ?iwork:Py.Object.t ->
  data:Py.Object.t ->
  model:Py.Object.t ->
  unit ->
  t

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()

restart¶

method restart

val restart :
  ?iter:int ->
  [> tag] Obj.t ->
  Py.Object.t

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 .

run¶

method run

val run :
  [> tag] Obj.t ->
  Py.Object.t

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 .

set_iprint¶

method set_iprint

val set_iprint :
  ?init:Py.Object.t ->
  ?so_init:Py.Object.t ->
  ?iter:Py.Object.t ->
  ?so_iter:Py.Object.t ->
  ?iter_step:Py.Object.t ->
  ?final:Py.Object.t ->
  ?so_final:Py.Object.t ->
  [> tag] Obj.t ->
  Py.Object.t

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.

set_job¶

method set_job

val set_job :
  ?fit_type:[`PyObject of Py.Object.t | `One] ->
  ?deriv:[`PyObject of Py.Object.t | `One | `Two] ->
  ?var_calc:[`PyObject of Py.Object.t | `One] ->
  ?del_init:Py.Object.t ->
  ?restart:Py.Object.t ->
  [> tag] Obj.t ->
  Py.Object.t

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.

data¶

attribute data

val data : t -> Py.Object.t
val data_opt : t -> (Py.Object.t) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

model¶

attribute model

val model : t -> Py.Object.t
val model_opt : t -> (Py.Object.t) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

output¶

attribute output

val output : t -> Py.Object.t
val output_opt : t -> (Py.Object.t) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

to_string¶

method to_string

val to_string: t -> string

Print the object to a human-readable representation.

show¶

method show

val show: t -> string

Print the object to a human-readable representation.

pp¶

method pp

val pp: Format.formatter -> t -> unit

Pretty-print the object to a formatter.

OdrError¶

Module Scipy.Odr.OdrError wraps Python class scipy.odr.OdrError.

type t

with_traceback¶

method with_traceback

val with_traceback :
  tb:Py.Object.t ->
  [> tag] Obj.t ->
  Py.Object.t

Exception.with_traceback(tb) -- set self.traceback to tb and return self.

to_string¶

method to_string

val to_string: t -> string

Print the object to a human-readable representation.

show¶

method show

val show: t -> string

Print the object to a human-readable representation.

pp¶

method pp

val pp: Format.formatter -> t -> unit

Pretty-print the object to a formatter.

OdrStop¶

Module Scipy.Odr.OdrStop wraps Python class scipy.odr.OdrStop.

type t

with_traceback¶

method with_traceback

val with_traceback :
  tb:Py.Object.t ->
  [> tag] Obj.t ->
  Py.Object.t

Exception.with_traceback(tb) -- set self.traceback to tb and return self.

to_string¶

method to_string

val to_string: t -> string

Print the object to a human-readable representation.

show¶

method show

val show: t -> string

Print the object to a human-readable representation.

pp¶

method pp

val pp: Format.formatter -> t -> unit

Pretty-print the object to a formatter.

OdrWarning¶

Module Scipy.Odr.OdrWarning wraps Python class scipy.odr.OdrWarning.

type t

with_traceback¶

method with_traceback

val with_traceback :
  tb:Py.Object.t ->
  [> tag] Obj.t ->
  Py.Object.t

Exception.with_traceback(tb) -- set self.traceback to tb and return self.

to_string¶

method to_string

val to_string: t -> string

Print the object to a human-readable representation.

show¶

method show

val show: t -> string

Print the object to a human-readable representation.

pp¶

method pp

val pp: Format.formatter -> t -> unit

Pretty-print the object to a formatter.

Output¶

Module Scipy.Odr.Output wraps Python class scipy.odr.Output.

type t

create¶

constructor and attributes create

val create :
  Py.Object.t ->
  t

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 ~scipy.odr.odr. The attributes listed as 'optional' above are only present if ~scipy.odr.odr was run with full_output=1.

pprint¶

method pprint

val pprint :
  [> tag] Obj.t ->
  Py.Object.t

Pretty-print important results.

beta¶

attribute beta

val beta : t -> [`ArrayLike|`Ndarray|`Object] Np.Obj.t
val beta_opt : t -> ([`ArrayLike|`Ndarray|`Object] Np.Obj.t) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

sd_beta¶

attribute sd_beta

val sd_beta : t -> [`ArrayLike|`Ndarray|`Object] Np.Obj.t
val sd_beta_opt : t -> ([`ArrayLike|`Ndarray|`Object] Np.Obj.t) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

cov_beta¶

attribute cov_beta

val cov_beta : t -> [`ArrayLike|`Ndarray|`Object] Np.Obj.t
val cov_beta_opt : t -> ([`ArrayLike|`Ndarray|`Object] Np.Obj.t) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

delta¶

attribute delta

val delta : t -> [`ArrayLike|`Ndarray|`Object] Np.Obj.t
val delta_opt : t -> ([`ArrayLike|`Ndarray|`Object] Np.Obj.t) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

eps¶

attribute eps

val eps : t -> [`ArrayLike|`Ndarray|`Object] Np.Obj.t
val eps_opt : t -> ([`ArrayLike|`Ndarray|`Object] Np.Obj.t) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

xplus¶

attribute xplus

val xplus : t -> [`ArrayLike|`Ndarray|`Object] Np.Obj.t
val xplus_opt : t -> ([`ArrayLike|`Ndarray|`Object] Np.Obj.t) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

y¶

attribute y

val y : t -> [`ArrayLike|`Ndarray|`Object] Np.Obj.t
val y_opt : t -> ([`ArrayLike|`Ndarray|`Object] Np.Obj.t) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

res_var¶

attribute res_var

val res_var : t -> float
val res_var_opt : t -> (float) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

sum_square¶

attribute sum_square

val sum_square : t -> float
val sum_square_opt : t -> (float) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

sum_square_delta¶

attribute sum_square_delta

val sum_square_delta : t -> float
val sum_square_delta_opt : t -> (float) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

sum_square_eps¶

attribute sum_square_eps

val sum_square_eps : t -> float
val sum_square_eps_opt : t -> (float) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

inv_condnum¶

attribute inv_condnum

val inv_condnum : t -> float
val inv_condnum_opt : t -> (float) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

rel_error¶

attribute rel_error

val rel_error : t -> float
val rel_error_opt : t -> (float) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

work¶

attribute work

val work : t -> [`ArrayLike|`Ndarray|`Object] Np.Obj.t
val work_opt : t -> ([`ArrayLike|`Ndarray|`Object] Np.Obj.t) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

work_ind¶

attribute work_ind

val work_ind : t -> Py.Object.t
val work_ind_opt : t -> (Py.Object.t) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

info¶

attribute info

val info : t -> int
val info_opt : t -> (int) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

stopreason¶

attribute stopreason

val stopreason : t -> string list
val stopreason_opt : t -> (string list) option

This attribute is documented in create above. The first version raises Not_found if the attribute is None. The _opt version returns an option.

to_string¶

method to_string

val to_string: t -> string

Print the object to a human-readable representation.

show¶

method show

val show: t -> string

Print the object to a human-readable representation.

pp¶

method pp

val pp: Format.formatter -> t -> unit

Pretty-print the object to a formatter.

RealData¶

Module Scipy.Odr.RealData wraps Python class scipy.odr.RealData.

type t

create¶

constructor and attributes create

val create :
  ?y:[>`Ndarray] Np.Obj.t ->
  ?sx:[>`Ndarray] Np.Obj.t ->
  ?sy:[>`Ndarray] Np.Obj.t ->
  ?covx:[>`Ndarray] Np.Obj.t ->
  ?covy:[>`Ndarray] Np.Obj.t ->
  ?fix:[>`Ndarray] Np.Obj.t ->
  ?meta:Py.Object.t ->
  x:[>`Ndarray] Np.Obj.t ->
  unit ->
  t

The data, with weightings as actual standard deviations and/or covariances.

Parameters

x : array_like Observed data for the independent variable of the regression
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 the data is implicit.
sx : 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, optional 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, 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).

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.

set_meta¶

method set_meta

val set_meta :
  ?kwds:(string * Py.Object.t) list ->
  [> tag] Obj.t ->
  Py.Object.t

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')

to_string¶

method to_string

val to_string: t -> string

Print the object to a human-readable representation.

show¶

method show

val show: t -> string

Print the object to a human-readable representation.

pp¶

method pp

val pp: Format.formatter -> t -> unit

Pretty-print the object to a formatter.

Models¶

Module Scipy.Odr.Models wraps Python module scipy.odr.models.

polynomial¶

function polynomial

val polynomial :
  [`Sequence of Py.Object.t | `I of int] ->
  Py.Object.t

Factory function for a general polynomial model.

Parameters

order : int or sequence If an integer, it becomes the order of the polynomial to fit. If a sequence of numbers, then these are the explicit powers in the polynomial. A constant term (power 0) is always included, so don't include 0. Thus, polynomial(n) is equivalent to polynomial(range(1, n+1)).

Returns

polynomial : Model instance Model instance.

Examples

We can fit an input data using orthogonal distance regression (ODR) with a polynomial model:

>>> import matplotlib.pyplot as plt
>>> from scipy import odr
>>> x = np.linspace(0.0, 5.0)
>>> y = np.sin(x)
>>> poly_model = odr.polynomial(3)  # using third order polynomial model
>>> data = odr.Data(x, y)
>>> odr_obj = odr.ODR(data, poly_model)
>>> output = odr_obj.run()  # running ODR fitting
>>> poly = np.poly1d(output.beta[::-1])
>>> poly_y = poly(x)
>>> plt.plot(x, y, label='input data')
>>> plt.plot(x, poly_y, label='polynomial ODR')
>>> plt.legend()
>>> plt.show()

Odrpack¶

Module Scipy.Odr.Odrpack wraps Python module scipy.odr.odrpack.

odr¶

function odr

val odr :
  ?we:Py.Object.t ->
  ?wd:Py.Object.t ->
  ?fjacb:Py.Object.t ->
  ?fjacd:Py.Object.t ->
  ?extra_args:Py.Object.t ->
  ?ifixx:Py.Object.t ->
  ?ifixb:Py.Object.t ->
  ?job:Py.Object.t ->
  ?iprint:Py.Object.t ->
  ?errfile:Py.Object.t ->
  ?rptfile:Py.Object.t ->
  ?ndigit:Py.Object.t ->
  ?taufac:Py.Object.t ->
  ?sstol:Py.Object.t ->
  ?partol:Py.Object.t ->
  ?maxit:Py.Object.t ->
  ?stpb:Py.Object.t ->
  ?stpd:Py.Object.t ->
  ?sclb:Py.Object.t ->
  ?scld:Py.Object.t ->
  ?work:Py.Object.t ->
  ?iwork:Py.Object.t ->
  ?full_output:Py.Object.t ->
  fcn:Py.Object.t ->
  beta0:Py.Object.t ->
  y:Py.Object.t ->
  x:Py.Object.t ->
  unit ->
  Py.Object.t

odr(fcn, beta0, y, x, we=None, wd=None, fjacb=None, fjacd=None, extra_args=None, ifixx=None, ifixb=None, job=0, iprint=0, errfile=None, rptfile=None, ndigit=0, taufac=0.0, sstol=-1.0, partol=-1.0, maxit=-1, stpb=None, stpd=None, sclb=None, scld=None, work=None, iwork=None, full_output=0)

Low-level function for ODR.

Notes

This is a function performing the same operation as the ODR, Model, and Data classes together. The parameters of this function are explained in the class documentation.

warn¶

function warn

val warn :
  ?category:Py.Object.t ->
  ?stacklevel:Py.Object.t ->
  ?source:Py.Object.t ->
  message:Py.Object.t ->
  unit ->
  Py.Object.t

Issue a warning, or maybe ignore it or raise an exception.

odr¶

function odr

val odr :
  ?we:Py.Object.t ->
  ?wd:Py.Object.t ->
  ?fjacb:Py.Object.t ->
  ?fjacd:Py.Object.t ->
  ?extra_args:Py.Object.t ->
  ?ifixx:Py.Object.t ->
  ?ifixb:Py.Object.t ->
  ?job:Py.Object.t ->
  ?iprint:Py.Object.t ->
  ?errfile:Py.Object.t ->
  ?rptfile:Py.Object.t ->
  ?ndigit:Py.Object.t ->
  ?taufac:Py.Object.t ->
  ?sstol:Py.Object.t ->
  ?partol:Py.Object.t ->
  ?maxit:Py.Object.t ->
  ?stpb:Py.Object.t ->
  ?stpd:Py.Object.t ->
  ?sclb:Py.Object.t ->
  ?scld:Py.Object.t ->
  ?work:Py.Object.t ->
  ?iwork:Py.Object.t ->
  ?full_output:Py.Object.t ->
  fcn:Py.Object.t ->
  beta0:Py.Object.t ->
  y:Py.Object.t ->
  x:Py.Object.t ->
  unit ->
  Py.Object.t

odr(fcn, beta0, y, x, we=None, wd=None, fjacb=None, fjacd=None, extra_args=None, ifixx=None, ifixb=None, job=0, iprint=0, errfile=None, rptfile=None, ndigit=0, taufac=0.0, sstol=-1.0, partol=-1.0, maxit=-1, stpb=None, stpd=None, sclb=None, scld=None, work=None, iwork=None, full_output=0)

Low-level function for ODR.

Notes

This is a function performing the same operation as the ODR, Model, and Data classes together. The parameters of this function are explained in the class documentation.

polynomial¶

function polynomial

val polynomial :
  [`Sequence of Py.Object.t | `I of int] ->
  Py.Object.t

Factory function for a general polynomial model.

Parameters

order : int or sequence If an integer, it becomes the order of the polynomial to fit. If a sequence of numbers, then these are the explicit powers in the polynomial. A constant term (power 0) is always included, so don't include 0. Thus, polynomial(n) is equivalent to polynomial(range(1, n+1)).

Returns

polynomial : Model instance Model instance.

Examples

We can fit an input data using orthogonal distance regression (ODR) with a polynomial model:

>>> import matplotlib.pyplot as plt
>>> from scipy import odr
>>> x = np.linspace(0.0, 5.0)
>>> y = np.sin(x)
>>> poly_model = odr.polynomial(3)  # using third order polynomial model
>>> data = odr.Data(x, y)
>>> odr_obj = odr.ODR(data, poly_model)
>>> output = odr_obj.run()  # running ODR fitting
>>> poly = np.poly1d(output.beta[::-1])
>>> poly_y = poly(x)
>>> plt.plot(x, y, label='input data')
>>> plt.plot(x, poly_y, label='polynomial ODR')
>>> plt.legend()
>>> plt.show()