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minpack.cpython-35.opt-1.pyc
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Z! m" Z" d d l# m$ Z$ m% Z% m& Z& d d l' m( Z( d d l) m* Z* d d l+ m, Z, e j- Z- d d d d g Z. d d d � Z/ f d d d d d d d d d d d � Z0 f d d d d d d d d d d � Z1 f d d d d d d d d d d d d � Z2 d d � Z3 d d � Z4 d d � Z5 d d d d e j e j f d d d! d � Z6 f d d" d# � Z7 d$ d% � Z8 d& d' � Z9 d( d) � Z: f d* d+ d, d- d � Z; d S).� )�division�print_function�absolute_importN� )�_minpack)� atleast_1d�dot�take�triu�shape�eye� transpose�zeros�product�greater�array�all�where�isscalar�asarray�inf�abs�finfo�inexact� issubdtype�dtype)�svd)�_asarray_validated� _lazywhere)�OptimizeResult�_check_unknown_options�OptimizeWarning)� least_squares)�make_strictly_feasible)�prepare_bounds�fsolve�leastsq� fixed_point� curve_fitc C s t | | d | � f | � � } | d k r� t | � | k r� | d d k r� t | � d k r} | d d k r} t | � Sd | | f } t | d d � } | r� | d | 7} n | d 7} | d | t | � f 7} t | � � t | j t � r| j } n t t � } t | � | f S)Nr r zO%s: there is a mismatch between the input and output shape of the '%s' argument�__name__z '%s'.�.z Shape should be %s but it is %s.) r r �len�getattr� TypeErrorr r r �float) ZcheckerZargnameZthefunc�x0�argsZ numinputsZ output_shape�res�msg� func_nameZdt� r4 � /minpack.py� _check_func s$ # r6 gJ�� P>�d c s d | d | d | d | d | d | d | i } t | | | d | | �� | r� � d } t � f d d � d D� � } � d | d <| | � d � d f S� d } � d } | d k r� t | � � n: | d k r� n+ | d k r� t j | t � n t | � � � d Sd S) a� Find the roots of a function. Return the roots of the (non-linear) equations defined by ``func(x) = 0`` given a starting estimate. Parameters ---------- func : callable ``f(x, *args)`` A function that takes at least one (possibly vector) argument. x0 : ndarray The starting estimate for the roots of ``func(x) = 0``. args : tuple, optional Any extra arguments to `func`. fprime : callable(x), optional A function to compute the Jacobian of `func` with derivatives across the rows. By default, the Jacobian will be estimated. full_output : bool, optional If True, return optional outputs. col_deriv : bool, optional Specify whether the Jacobian function computes derivatives down the columns (faster, because there is no transpose operation). xtol : float, optional The calculation will terminate if the relative error between two consecutive iterates is at most `xtol`. maxfev : int, optional The maximum number of calls to the function. If zero, then ``100*(N+1)`` is the maximum where N is the number of elements in `x0`. band : tuple, optional If set to a two-sequence containing the number of sub- and super-diagonals within the band of the Jacobi matrix, the Jacobi matrix is considered banded (only for ``fprime=None``). epsfcn : float, optional A suitable step length for the forward-difference approximation of the Jacobian (for ``fprime=None``). If `epsfcn` is less than the machine precision, it is assumed that the relative errors in the functions are of the order of the machine precision. factor : float, optional A parameter determining the initial step bound (``factor * || diag * x||``). Should be in the interval ``(0.1, 100)``. diag : sequence, optional N positive entries that serve as a scale factors for the variables. Returns ------- x : ndarray The solution (or the result of the last iteration for an unsuccessful call). infodict : dict A dictionary of optional outputs with the keys: ``nfev`` number of function calls ``njev`` number of Jacobian calls ``fvec`` function evaluated at the output ``fjac`` the orthogonal matrix, q, produced by the QR factorization of the final approximate Jacobian matrix, stored column wise ``r`` upper triangular matrix produced by QR factorization of the same matrix ``qtf`` the vector ``(transpose(q) * fvec)`` ier : int An integer flag. Set to 1 if a solution was found, otherwise refer to `mesg` for more information. mesg : str If no solution is found, `mesg` details the cause of failure. See Also -------- root : Interface to root finding algorithms for multivariate functions. See the 'hybr' `method` in particular. Notes ----- ``fsolve`` is a wrapper around MINPACK's hybrd and hybrj algorithms. � col_deriv�xtol�maxfev�band�eps�factor�diag�jac�xc 3 s0 | ]& } | � k r | � j | � f Vq d S)N)�get)�.0�k)r1 r4 r5 � <genexpr>� s zfsolve.<locals>.<genexpr>�nfev�njev�fjac�r�qtf�fun�fvec�status�messager r � � � � N)rE rF rG rH rI )rN rO rP rQ )� _root_hybr�dictr- �warnings�warn�RuntimeWarning)�funcr/ r0 �fprime� full_outputr8 r9 r: r; �epsfcnr= r> Zoptionsr@ �inforL r2 r4 )r1 r5 r% 0 s0 Z c K sL t | � | } t | � j � } t | � } t | t � sF | f } t d d | | | | | f � \ } } | d k r� t | � j } | } | d k r| d k r� d \ } } n | d d � \ } } | d k r� d | d } t j | | | d | | | | | | | � } nf t d d | | | | | | f � | d k rQd | d } t j | | | | d | | | | | � } | d | d } } d d d d d d | d d | d d d d d d i } | d } | j d � | d <t d | d | d k d | � } | j | � y | | | d <Wn t k rG| d | d <Yn X| S) a� Find the roots of a multivariate function using MINPACK's hybrd and hybrj routines (modified Powell method). Options ------- col_deriv : bool Specify whether the Jacobian function computes derivatives down the columns (faster, because there is no transpose operation). xtol : float The calculation will terminate if the relative error between two consecutive iterates is at most `xtol`. maxfev : int The maximum number of calls to the function. If zero, then ``100*(N+1)`` is the maximum where N is the number of elements in `x0`. band : tuple If set to a two-sequence containing the number of sub- and super-diagonals within the band of the Jacobi matrix, the Jacobi matrix is considered banded (only for ``fprime=None``). eps : float A suitable step length for the forward-difference approximation of the Jacobian (for ``fprime=None``). If `eps` is less than the machine precision, it is assumed that the relative errors in the functions are of the order of the machine precision. factor : float A parameter determining the initial step bound (``factor * || diag * x||``). Should be in the interval ``(0.1, 100)``. diag : sequence N positive entries that serve as a scale factors for the variables. r% rW N� rN r �� r rX r7 z'Improper input parameters were entered.zThe solution converged.z8The number of calls to function has reached maxfev = %d.rO zWxtol=%f is too small, no further improvement in the approximate solution is possible.rP zuThe iteration is not making good progress, as measured by the improvement from the last five Jacobian evaluations.rQ zjThe iteration is not making good progress, as measured by the improvement from the last ten iterations.�unknownzAn error occurred.rK rJ r@ �successrL rM ������)r` ra ���)r r �flattenr+ � isinstance�tupler6 r r< r Z_hybrdZ_hybrj�popr �update�KeyError)rW r/ r0 r? r8 r9 r: r; r< r= r> Zunknown_optionsrZ �nr r �DfunZml�mu�retvalr@ rL �errorsr[ Zsolr4 r4 r5 rR � sT & ' " ! rR g c C s� t | � j � } t | � } t | t � s6 | f } t d d | | | | � \ } } | d } | | k r� t d | | f � � | d k r� t | � j } | d k r� | d k r� d | d } t j | | | | | | | | | | | � } n� | r t d d | | | | | | f � n" t d d | | | | | | f � | d k r[d | d } t j | | | | | | | | | | | | � } d d t g d d | d g d d | d g d d | | f d g d d | d g d d | t g d d | t g d d | t g d d | t g d d t g i } | d } | d! k r�| r�| d" k rst j | | d t � nQ y | | d | | d � � Wn. t k r�| d d | d d � � Yn X| | d } | r�d } | d# k r�d d l m } d d l m } t t | � | d d d d � } t t | d d � d | � d d � f � } t | | � } y | t t | � | � � } Wn | t f k r�Yn X| d | f | d d$ � | | f S| d | f Sd S)%a" Minimize the sum of squares of a set of equations. :: x = arg min(sum(func(y)**2,axis=0)) y Parameters ---------- func : callable should take at least one (possibly length N vector) argument and returns M floating point numbers. It must not return NaNs or fitting might fail. x0 : ndarray The starting estimate for the minimization. args : tuple, optional Any extra arguments to func are placed in this tuple. Dfun : callable, optional A function or method to compute the Jacobian of func with derivatives across the rows. If this is None, the Jacobian will be estimated. full_output : bool, optional non-zero to return all optional outputs. col_deriv : bool, optional non-zero to specify that the Jacobian function computes derivatives down the columns (faster, because there is no transpose operation). ftol : float, optional Relative error desired in the sum of squares. xtol : float, optional Relative error desired in the approximate solution. gtol : float, optional Orthogonality desired between the function vector and the columns of the Jacobian. maxfev : int, optional The maximum number of calls to the function. If `Dfun` is provided then the default `maxfev` is 100*(N+1) where N is the number of elements in x0, otherwise the default `maxfev` is 200*(N+1). epsfcn : float, optional A variable used in determining a suitable step length for the forward- difference approximation of the Jacobian (for Dfun=None). Normally the actual step length will be sqrt(epsfcn)*x If epsfcn is less than the machine precision, it is assumed that the relative errors are of the order of the machine precision. factor : float, optional A parameter determining the initial step bound (``factor * || diag * x||``). Should be in interval ``(0.1, 100)``. diag : sequence, optional N positive entries that serve as a scale factors for the variables. Returns ------- x : ndarray The solution (or the result of the last iteration for an unsuccessful call). cov_x : ndarray Uses the fjac and ipvt optional outputs to construct an estimate of the jacobian around the solution. None if a singular matrix encountered (indicates very flat curvature in some direction). This matrix must be multiplied by the residual variance to get the covariance of the parameter estimates -- see curve_fit. infodict : dict a dictionary of optional outputs with the key s: ``nfev`` The number of function calls ``fvec`` The function evaluated at the output ``fjac`` A permutation of the R matrix of a QR factorization of the final approximate Jacobian matrix, stored column wise. Together with ipvt, the covariance of the estimate can be approximated. ``ipvt`` An integer array of length N which defines a permutation matrix, p, such that fjac*p = q*r, where r is upper triangular with diagonal elements of nonincreasing magnitude. Column j of p is column ipvt(j) of the identity matrix. ``qtf`` The vector (transpose(q) * fvec). mesg : str A string message giving information about the cause of failure. ier : int An integer flag. If it is equal to 1, 2, 3 or 4, the solution was found. Otherwise, the solution was not found. In either case, the optional output variable 'mesg' gives more information. Notes ----- "leastsq" is a wrapper around MINPACK's lmdif and lmder algorithms. cov_x is a Jacobian approximation to the Hessian of the least squares objective function. This approximation assumes that the objective function is based on the difference between some observed target data (ydata) and a (non-linear) function of the parameters `f(xdata, params)` :: func(params) = ydata - f(xdata, params) so that the objective function is :: min sum((ydata - f(xdata, params))**2, axis=0) params r& rW r z)Improper input: N=%s must not exceed M=%sNr] r rj r7 zImproper input parameters.zTBoth actual and predicted relative reductions in the sum of squares are at most %frN zAThe relative error between two consecutive iterates is at most %frO z�Both actual and predicted relative reductions in the sum of squares are at most %f and the relative error between two consecutive iterates is at most %frP zhThe cosine of the angle between func(x) and any column of the Jacobian is at most %f in absolute valuerQ z4Number of calls to function has reached maxfev = %d.� zOftol=%f is too small, no further reduction in the sum of squares is possible.� zWxtol=%f is too small, no further improvement in the approximate solution is possible.� zbgtol=%f is too small, func(x) is orthogonal to the columns of the Jacobian to machine precision.r^ zUnknown error.)�inv)� LinAlgErrorZipvtrG rb )r rN rO rP )rQ rn ro rp )r rN rO rP rb )r rc r+ rd re r6 r- r r< r Z_lmdifZ_lmder� ValueErrorrT rU rV rh Z numpy.dualrq Z numpy.linalgrr r r r r r )rW r/ r0 rj rY r8 Zftolr9 Zgtolr: rZ r= r> ri r r �mrl rm r[ ZmesgZcov_xrq rr ZpermrH �Rr4 r4 r5 r& s� p ! %" ! $0 &c sF � d k r' � � � f d d � } n � � � � f d d � } | S)Nc s � � | � � S)Nr4 )�params)rW �xdata�ydatar4 r5 � func_wrapped� s z _wrap_func.<locals>.func_wrappedc s � � � | � � S)Nr4 )rv )rW �weightsrw rx r4 r5 ry � s r4 )rW rw rx rz ry r4 )rW rz rw rx r5 � _wrap_func� s r{ c s@ � d k r$ � � f d d � } n � � � f d d � } | S)Nc s � � | � S)Nr4 )rv )r? rw r4 r5 � jac_wrapped� s z _wrap_jac.<locals>.jac_wrappedc s- � d d � t j f t j � � | � � S)N)�npZnewaxisr )rv )r? rz rw r4 r5 r| � s r4 )r? rw rz r| r4 )r? rz rw r5 � _wrap_jac� s r~ c C s� t j | � } t j | � } t j | � } | | @} d | | | | | | <| | @} | | d | | <| | @} | | d | | <| S)Ng �?r )r} Z ones_like�isfinite)�lb�ub�p0Z lb_finiteZ ub_finite�maskr4 r4 r5 �_initialize_feasible� s r� FTc $ K s4 | d k re d d l m } | | � \ } } } } t | � d k rR t d � � t | � d } n t j | � } | j } t | | � \ } } | d k r� t | | � } t j | t j k | t j k B� } | d k r� | r� d } n d } | d k r| rt d � � | r*t j | � } n t j | � } t | t t t j f � r{| rlt j | � } n t j | � } | d k r�d t | � n d } t | | | | � } t | � r�t | | | � } n | d k r�| d k r�d } | d k rx| j d d � } t | | d | d d | �} | \ } } } } } t j | d d � } | d k r\t d | � � n� t | | d | d | d | | �} | j s�t d | j � � d | j } | j } t | j d d �\ } } } t j t � j! t" | j j# � | d }! | | |! k } | d | j � } t j$ | j% | d | � } d } d }" | d k r�t& t | � t | � f d t �} | j' t � d }" nL | s�| j | j k r�| | j | j }# | |# } n | j' t � d }" |" r t( j) d d t* �| r&| | | | | f S| | f Sd S) a( Use non-linear least squares to fit a function, f, to data. Assumes ``ydata = f(xdata, *params) + eps`` Parameters ---------- f : callable The model function, f(x, ...). It must take the independent variable as the first argument and the parameters to fit as separate remaining arguments. xdata : An M-length sequence or an (k,M)-shaped array for functions with k predictors. The independent variable where the data is measured. ydata : M-length sequence The dependent data --- nominally f(xdata, ...) p0 : None, scalar, or N-length sequence, optional Initial guess for the parameters. If None, then the initial values will all be 1 (if the number of parameters for the function can be determined using introspection, otherwise a ValueError is raised). sigma : None or M-length sequence, optional If not None, the uncertainties in the ydata array. These are used as weights in the least-squares problem i.e. minimising ``np.sum( ((f(xdata, *popt) - ydata) / sigma)**2 )`` If None, the uncertainties are assumed to be 1. absolute_sigma : bool, optional If False, `sigma` denotes relative weights of the data points. The returned covariance matrix `pcov` is based on *estimated* errors in the data, and is not affected by the overall magnitude of the values in `sigma`. Only the relative magnitudes of the `sigma` values matter. If True, `sigma` describes one standard deviation errors of the input data points. The estimated covariance in `pcov` is based on these values. check_finite : bool, optional If True, check that the input arrays do not contain nans of infs, and raise a ValueError if they do. Setting this parameter to False may silently produce nonsensical results if the input arrays do contain nans. Default is True. bounds : 2-tuple of array_like, optional Lower and upper bounds on independent variables. Defaults to no bounds. Each element of the tuple must be either an array with the length equal to the number of parameters, or a scalar (in which case the bound is taken to be the same for all parameters.) Use ``np.inf`` with an appropriate sign to disable bounds on all or some parameters. .. versionadded:: 0.17 method : {'lm', 'trf', 'dogbox'}, optional Method to use for optimization. See `least_squares` for more details. Default is 'lm' for unconstrained problems and 'trf' if `bounds` are provided. The method 'lm' won't work when the number of observations is less than the number of variables, use 'trf' or 'dogbox' in this case. .. versionadded:: 0.17 jac : callable, string or None, optional Function with signature ``jac(x, ...)`` which computes the Jacobian matrix of the model function with respect to parameters as a dense array_like structure. It will be scaled according to provided `sigma`. If None (default), the Jacobian will be estimated numerically. String keywords for 'trf' and 'dogbox' methods can be used to select a finite difference scheme, see `least_squares`. .. versionadded:: 0.18 kwargs Keyword arguments passed to `leastsq` for ``method='lm'`` or `least_squares` otherwise. Returns ------- popt : array Optimal values for the parameters so that the sum of the squared error of ``f(xdata, *popt) - ydata`` is minimized pcov : 2d array The estimated covariance of popt. The diagonals provide the variance of the parameter estimate. To compute one standard deviation errors on the parameters use ``perr = np.sqrt(np.diag(pcov))``. How the `sigma` parameter affects the estimated covariance depends on `absolute_sigma` argument, as described above. If the Jacobian matrix at the solution doesn't have a full rank, then 'lm' method returns a matrix filled with ``np.inf``, on the other hand 'trf' and 'dogbox' methods use Moore-Penrose pseudoinverse to compute the covariance matrix. Raises ------ ValueError if either `ydata` or `xdata` contain NaNs, or if incompatible options are used. RuntimeError if the least-squares minimization fails. OptimizeWarning if covariance of the parameters can not be estimated. See Also -------- least_squares : Minimize the sum of squares of nonlinear functions. stats.linregress : Calculate a linear least squares regression for two sets of measurements. Notes ----- With ``method='lm'``, the algorithm uses the Levenberg-Marquardt algorithm through `leastsq`. Note that this algorithm can only deal with unconstrained problems. Box constraints can be handled by methods 'trf' and 'dogbox'. Refer to the docstring of `least_squares` for more information. Examples -------- >>> import numpy as np >>> from scipy.optimize import curve_fit >>> def func(x, a, b, c): ... return a * np.exp(-b * x) + c >>> xdata = np.linspace(0, 4, 50) >>> y = func(xdata, 2.5, 1.3, 0.5) >>> ydata = y + 0.2 * np.random.normal(size=len(xdata)) >>> popt, pcov = curve_fit(func, xdata, ydata) Constrain the optimization to the region of ``0 < a < 3``, ``0 < b < 2`` and ``0 < c < 1``: >>> popt, pcov = curve_fit(func, xdata, ydata, bounds=(0, [3., 2., 1.])) Nr )�getargspec_no_selfrN z-Unable to determine number of fit parameters.r ZtrfZlmzQMethod 'lm' only works for unconstrained problems. Use 'trf' or 'dogbox' instead.g �?z2-pointrY Frj rK rO rP z Optimal parameters not found: r? �bounds�methodZ full_matricesr Tz3Covariance of the parameters could not be estimated�category)r rN rO rP )+�scipy._lib._utilr� r+ rs r} r �sizer$ r� �anyr Zasarray_chkfiniter rd �listre Zndarrayr{ �callabler~ rf r& �sum� RuntimeErrorr" r_ rM �costr@ r r? r r. r< �maxr r �Tr ZfillrT rU r! )$�frw rx r� �sigmaZabsolute_sigmaZ check_finiter� r� r? �kwargsZ _getargspecr0 ZvarargsZvarkwZdefaultsri r� r� Zbounded_problemrz rW Z return_fullr1 ZpoptZpcovZinfodict�errmsgZierr� �_�sZVTZ thresholdZwarn_covZs_sqr4 r4 r5 r( � s� � & " * $ c C sk t | � } t | � } | j | f � } t | | | � � } t | � } | j | f � } | } t | | | � � } | j | | f � } | d k r� t | � } t | f t � } t | f t � } d } t j | | | | | | | | d | � t | | | � � } | j | f � } t j | | | | | | | | d | � t t | d � d d �} | | f S)z=Perform a simple check on the gradient for correctness. r Nr rN g �?Zaxis) r r+ Zreshaper r r. r Z_chkderr r )ZfcnZDfcnr/ r0 r8 r@ ri rK rt ZldfjacrG Zxp�errZfvecpZgoodr4 r4 r5 �check_gradient� s( ((r� c C s | t j | | � | S)N)r} Zsquare)r� �p1�dr4 r4 r5 �_del2� s r� c C s | | | S)Nr4 )�actualZdesiredr4 r4 r5 �_relerr� s r� c C s� | } x� t | � D]� } | | | � } | r| | | | � } | d | | } t | d k | | | f d t d | �} n | } t | d k | | f d t d | �} t j t j | � | k � r� | S| } q Wd | | f } t | � � d S)Ng @r r� � fillvaluez3Failed to converge after %d iterations, value is %s)�ranger r� r� r} r r r� )rW r/ r0 r9 �maxiter� use_accelr� �ir� Zp2r� �pZrelerrr2 r4 r4 r5 �_fixed_point_helper� s -' r� g:�0�yE>i� �del2c C sA d d d d i | } t | d d �} t | | | | | | � S)a Find a fixed point of the function. Given a function of one or more variables and a starting point, find a fixed-point of the function: i.e. where ``func(x0) == x0``. Parameters ---------- func : function Function to evaluate. x0 : array_like Fixed point of function. args : tuple, optional Extra arguments to `func`. xtol : float, optional Convergence tolerance, defaults to 1e-08. maxiter : int, optional Maximum number of iterations, defaults to 500. method : {"del2", "iteration"}, optional Method of finding the fixed-point, defaults to "del2" which uses Steffensen's Method with Aitken's ``Del^2`` convergence acceleration [1]_. The "iteration" method simply iterates the function until convergence is detected, without attempting to accelerate the convergence. References ---------- .. [1] Burden, Faires, "Numerical Analysis", 5th edition, pg. 80 Examples -------- >>> from scipy import optimize >>> def func(x, c1, c2): ... return np.sqrt(c1/(x+c2)) >>> c1 = np.array([10,12.]) >>> c2 = np.array([3, 5.]) >>> optimize.fixed_point(func, [1.2, 1.3], args=(c1,c2)) array([ 1.4920333 , 1.37228132]) r� TZ iterationFZ as_inexact)r r� )rW r/ r0 r9 r� r� r� r4 r4 r5 r' s ))<Z __future__r r r rT � r Znumpyr} r r r r r r r r r r r r r r r r r r r r r Z scipy.linalgr r� r r �optimizer r r! Z_lsqr" Z _lsq.commonr# Z_lsq.least_squaresr$ �error�__all__r6 r% rR r& r{ r~ r� r( r� r� r� r� r' r4 r4 r4 r5 �<module> sB � u\ � �
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_basinhopping.cpython-35.opt-1.pyc
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_trustregion_dogleg.cpython-35.opt-1.pyc
3735 bytes
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_trustregion_dogleg.cpython-35.pyc
3735 bytes
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_trustregion_ncg.cpython-35.opt-1.pyc
3464 bytes
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_trustregion_ncg.cpython-35.pyc
3464 bytes
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_tstutils.cpython-35.opt-1.pyc
1995 bytes
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_tstutils.cpython-35.pyc
1995 bytes
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cobyla.cpython-35.opt-1.pyc
9239 bytes
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cobyla.cpython-35.pyc
9239 bytes
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lbfgsb.cpython-35.opt-1.pyc
15952 bytes
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lbfgsb.cpython-35.pyc
15952 bytes
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linesearch.cpython-35.opt-1.pyc
18967 bytes
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linesearch.cpython-35.pyc
18967 bytes
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minpack.cpython-35.opt-1.pyc
28403 bytes
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minpack.cpython-35.pyc
28403 bytes
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nnls.cpython-35.opt-1.pyc
1659 bytes
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nnls.cpython-35.pyc
1659 bytes
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nonlin.cpython-35.opt-1.pyc
47479 bytes
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nonlin.cpython-35.pyc
47545 bytes
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optimize.cpython-35.opt-1.pyc
83901 bytes
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optimize.cpython-35.pyc
83901 bytes
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setup.cpython-35.opt-1.pyc
2801 bytes
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setup.cpython-35.pyc
2801 bytes
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slsqp.cpython-35.opt-1.pyc
15484 bytes
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slsqp.cpython-35.pyc
15484 bytes
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tnc.cpython-35.opt-1.pyc
13998 bytes
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tnc.cpython-35.pyc
13998 bytes
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zeros.cpython-35.opt-1.pyc
19335 bytes
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zeros.cpython-35.pyc
19335 bytes
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N4ST4R_ID | Naxtarrr
