
    tKgL                         d Z ddlZddlmZ ddlmZ dgZg dZ	 G d d	      Z
	 	 	 	 	 dd
Zd Zd Zd Zd Zd Zd Zd Zd Zy)z
Unified interfaces to root finding algorithms for real or complex
scalar functions.

Functions
---------
- root : find a root of a scalar function.
    N   )	_zeros_pyapprox_derivativeroot_scalar)bisectbrentqbrenthriddertoms748newtonsecanthalleyc                   .    e Zd ZdZd Zd Zd Zd Zd Zy)
MemoizeDera  Decorator that caches the value and derivative(s) of function each
    time it is called.

    This is a simplistic memoizer that calls and caches a single value
    of `f(x, *args)`.
    It assumes that `args` does not change between invocations.
    It supports the use case of a root-finder where `args` is fixed,
    `x` changes, and only rarely, if at all, does x assume the same value
    more than once.c                 <    || _         d | _        d | _        d| _        y )Nr   )funvalsxn_calls)selfr   s     _/home/alanp/www/video.onchill/myenv/lib/python3.12/site-packages/scipy/optimize/_root_scalar.py__init__zMemoizeDer.__init__   s    	    c                     | j                   || j                  k7  r9 | j                  |g| }|| _        | xj                  dz  c_        |dd | _         | j                   d   S )z,Calculate f or use cached value if availableNr   r   )r   r   r   r   )r   r   argsfgs       r   __call__zMemoizeDer.__call__$   s[     99TVV!#d#BDFLLAL1DIyy|r   c                 h    | j                   || j                  k7  r	 | |g|  | j                   d   S )z/Calculate f' or use a cached value if availabler   r   r   r   r   r   s      r   fprimezMemoizeDer.fprime.   /    99TVVNTNyy|r   c                 h    | j                   || j                  k7  r	 | |g|  | j                   d   S )z0Calculate f'' or use a cached value if available   r    r!   s      r   fprime2zMemoizeDer.fprime24   r#   r   c                     | j                   S )N)r   )r   s    r   ncallszMemoizeDer.ncalls:   s    ||r   N)	__name__
__module____qualname____doc__r   r   r"   r&   r(    r   r   r   r      s     r   r   c           	      :    t        |t              s|f}|i }d}|>t        |      s3t        |      r&t	                d} j
                  } j                  }nd}|2t        |      s't        |      rt	                d} j                  }nd}i }dD ]#  }t               j                  |      }||||<   % |r|j                  |       |j                  dd       |s|rd}n||r|rd}n
d}n|d	}nd}|st        d
      |j                         }ddd}	 t        t        |j                  ||            }|dv rMt        |t        t        t         j"                  f      st        d|z        |dd \  }}	  | ||fd|i|\  }}n|dv r;|t        d|z        d|v r|j1                  d      |d<    | |f|dd|d|\  }}n|dv rA|t        d|z        |s fd}d|v r|j1                  d      |d<    | |f||dd|\  }}nl|dv rZ|t        d|z        |st        d|z        |st        d|z        d|v r|j1                  d      |d<    | |f|||d|\  }}nt        d|z        |r j2                  }||_        |S # t        $ r}t        d|z        |d}~ww xY w# t        $ r]}t%        |d      rFt        j&                  |j(                  t         j*                  |j,                  t/        |      |      }n Y d}~d}~ww xY w)aV  
    Find a root of a scalar function.

    Parameters
    ----------
    f : callable
        A function to find a root of.
    args : tuple, optional
        Extra arguments passed to the objective function and its derivative(s).
    method : str, optional
        Type of solver.  Should be one of

            - 'bisect'    :ref:`(see here) <optimize.root_scalar-bisect>`
            - 'brentq'    :ref:`(see here) <optimize.root_scalar-brentq>`
            - 'brenth'    :ref:`(see here) <optimize.root_scalar-brenth>`
            - 'ridder'    :ref:`(see here) <optimize.root_scalar-ridder>`
            - 'toms748'    :ref:`(see here) <optimize.root_scalar-toms748>`
            - 'newton'    :ref:`(see here) <optimize.root_scalar-newton>`
            - 'secant'    :ref:`(see here) <optimize.root_scalar-secant>`
            - 'halley'    :ref:`(see here) <optimize.root_scalar-halley>`

    bracket: A sequence of 2 floats, optional
        An interval bracketing a root.  `f(x, *args)` must have different
        signs at the two endpoints.
    x0 : float, optional
        Initial guess.
    x1 : float, optional
        A second guess.
    fprime : bool or callable, optional
        If `fprime` is a boolean and is True, `f` is assumed to return the
        value of the objective function and of the derivative.
        `fprime` can also be a callable returning the derivative of `f`. In
        this case, it must accept the same arguments as `f`.
    fprime2 : bool or callable, optional
        If `fprime2` is a boolean and is True, `f` is assumed to return the
        value of the objective function and of the
        first and second derivatives.
        `fprime2` can also be a callable returning the second derivative of `f`.
        In this case, it must accept the same arguments as `f`.
    xtol : float, optional
        Tolerance (absolute) for termination.
    rtol : float, optional
        Tolerance (relative) for termination.
    maxiter : int, optional
        Maximum number of iterations.
    options : dict, optional
        A dictionary of solver options. E.g., ``k``, see
        :obj:`show_options()` for details.

    Returns
    -------
    sol : RootResults
        The solution represented as a ``RootResults`` object.
        Important attributes are: ``root`` the solution , ``converged`` a
        boolean flag indicating if the algorithm exited successfully and
        ``flag`` which describes the cause of the termination. See
        `RootResults` for a description of other attributes.

    See also
    --------
    show_options : Additional options accepted by the solvers
    root : Find a root of a vector function.

    Notes
    -----
    This section describes the available solvers that can be selected by the
    'method' parameter.

    The default is to use the best method available for the situation
    presented.
    If a bracket is provided, it may use one of the bracketing methods.
    If a derivative and an initial value are specified, it may
    select one of the derivative-based methods.
    If no method is judged applicable, it will raise an Exception.

    Arguments for each method are as follows (x=required, o=optional).

    +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+
    |                    method                     | f | args | bracket | x0 | x1 | fprime | fprime2 | xtol | rtol | maxiter | options |
    +===============================================+===+======+=========+====+====+========+=========+======+======+=========+=========+
    | :ref:`bisect <optimize.root_scalar-bisect>`   | x |  o   |    x    |    |    |        |         |  o   |  o   |    o    |   o     |
    +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+
    | :ref:`brentq <optimize.root_scalar-brentq>`   | x |  o   |    x    |    |    |        |         |  o   |  o   |    o    |   o     |
    +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+
    | :ref:`brenth <optimize.root_scalar-brenth>`   | x |  o   |    x    |    |    |        |         |  o   |  o   |    o    |   o     |
    +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+
    | :ref:`ridder <optimize.root_scalar-ridder>`   | x |  o   |    x    |    |    |        |         |  o   |  o   |    o    |   o     |
    +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+
    | :ref:`toms748 <optimize.root_scalar-toms748>` | x |  o   |    x    |    |    |        |         |  o   |  o   |    o    |   o     |
    +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+
    | :ref:`secant <optimize.root_scalar-secant>`   | x |  o   |         | x  | o  |        |         |  o   |  o   |    o    |   o     |
    +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+
    | :ref:`newton <optimize.root_scalar-newton>`   | x |  o   |         | x  |    |   o    |         |  o   |  o   |    o    |   o     |
    +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+
    | :ref:`halley <optimize.root_scalar-halley>`   | x |  o   |         | x  |    |   x    |    x    |  o   |  o   |    o    |   o     |
    +-----------------------------------------------+---+------+---------+----+----+--------+---------+------+------+---------+---------+

    Examples
    --------

    Find the root of a simple cubic

    >>> from scipy import optimize
    >>> def f(x):
    ...     return (x**3 - 1)  # only one real root at x = 1

    >>> def fprime(x):
    ...     return 3*x**2

    The `brentq` method takes as input a bracket

    >>> sol = optimize.root_scalar(f, bracket=[0, 3], method='brentq')
    >>> sol.root, sol.iterations, sol.function_calls
    (1.0, 10, 11)

    The `newton` method takes as input a single point and uses the
    derivative(s).

    >>> sol = optimize.root_scalar(f, x0=0.2, fprime=fprime, method='newton')
    >>> sol.root, sol.iterations, sol.function_calls
    (1.0, 11, 22)

    The function can provide the value and derivative(s) in a single call.

    >>> def f_p_pp(x):
    ...     return (x**3 - 1), 3*x**2, 6*x

    >>> sol = optimize.root_scalar(
    ...     f_p_pp, x0=0.2, fprime=True, method='newton'
    ... )
    >>> sol.root, sol.iterations, sol.function_calls
    (1.0, 11, 11)

    >>> sol = optimize.root_scalar(
    ...     f_p_pp, x0=0.2, fprime=True, fprime2=True, method='halley'
    ... )
    >>> sol.root, sol.iterations, sol.function_calls
    (1.0, 7, 8)


    NFT)xtolrtolmaxiter)full_outputdispr	   r   r   r   zIUnable to select a solver as neither bracket nor starting point provided.)r   r   zUnknown solver %s)r   r   r	   r
   r   zBracket needed for %sr%   r   _x)root
iterationsfunction_callsflagmethod)r   zx0 must not be None for %sr/   tol)r   r"   r&   x1)r   c                 (    t        | d|      d   S )Nz2-point)r9   r   r   r   )r   r   fs     r   r"   zroot_scalar.<locals>.fprime2  s    
 )AidKANNr   )r   r"   r&   )r   zfprime must be specified for %sz fprime2 must be specified for %s)
isinstancetuplecallableboolr   r&   r"   localsgetupdate
ValueErrorlowergetattroptzerosAttributeErrorlistnpndarrayhasattrRootResultsr4   nan_function_callsstrpopr   r7   )r=   r   r9   bracketr"   r&   x0r;   r/   r0   r1   optionsis_memoizedkwargskvmethmap2underlyingmethodceabrsolr   s   `                        r   r   r   >   s   d dE"w K8G#4=1AKiiGXXFG(6"2<1AKXXFF F(HLLO=F1I ) g MMdM/ F^%F%F!! 8 9 	9 <<>D (H=N<(N$6$6tT$BC BB'D%#<=4v=>>r{1	Q1:4:6:FAs 
	:9FBCCV"JJv.F5MB *T$*"(*3		:9FBCCO V"JJv.F5MB #T&$ #!#3		:9FBCC>GHH?&HIIV"JJv.F5MBTT&'TVT3,v566 ))$JE  <,t34!;<  	
 q$**68ff:;:K:K03AvG
  	s1    J <J4 	J1J,,J14	L=ALLc                       y)a?  
    Options
    -------
    args : tuple, optional
        Extra arguments passed to the objective function.
    bracket: A sequence of 2 floats, optional
        An interval bracketing a root.  `f(x, *args)` must have different
        signs at the two endpoints.
    xtol : float, optional
        Tolerance (absolute) for termination.
    rtol : float, optional
        Tolerance (relative) for termination.
    maxiter : int, optional
        Maximum number of iterations.
    options: dict, optional
        Specifies any method-specific options not covered above

    Nr-   r-   r   r   _root_scalar_brentq_docrc   S      & 	r   c                       ya@  
    Options
    -------
    args : tuple, optional
        Extra arguments passed to the objective function.
    bracket: A sequence of 2 floats, optional
        An interval bracketing a root.  `f(x, *args)` must have different
        signs at the two endpoints.
    xtol : float, optional
        Tolerance (absolute) for termination.
    rtol : float, optional
        Tolerance (relative) for termination.
    maxiter : int, optional
        Maximum number of iterations.
    options: dict, optional
        Specifies any method-specific options not covered above.

    Nr-   r-   r   r   _root_scalar_brenth_docrg   i  rd   r   c                       yrf   r-   r-   r   r   _root_scalar_toms748_docri   ~  rd   r   c                       y)a  
    Options
    -------
    args : tuple, optional
        Extra arguments passed to the objective function.
    xtol : float, optional
        Tolerance (absolute) for termination.
    rtol : float, optional
        Tolerance (relative) for termination.
    maxiter : int, optional
        Maximum number of iterations.
    x0 : float, required
        Initial guess.
    x1 : float, required
        A second guess.
    options: dict, optional
        Specifies any method-specific options not covered above.

    Nr-   r-   r   r   _root_scalar_secant_docrk     s    ( 	r   c                       y)a"  
    Options
    -------
    args : tuple, optional
        Extra arguments passed to the objective function and its derivative.
    xtol : float, optional
        Tolerance (absolute) for termination.
    rtol : float, optional
        Tolerance (relative) for termination.
    maxiter : int, optional
        Maximum number of iterations.
    x0 : float, required
        Initial guess.
    fprime : bool or callable, optional
        If `fprime` is a boolean and is True, `f` is assumed to return the
        value of derivative along with the objective function.
        `fprime` can also be a callable returning the derivative of `f`. In
        this case, it must accept the same arguments as `f`.
    options: dict, optional
        Specifies any method-specific options not covered above.

    Nr-   r-   r   r   _root_scalar_newton_docrm     s    . 	r   c                       y)ar  
    Options
    -------
    args : tuple, optional
        Extra arguments passed to the objective function and its derivatives.
    xtol : float, optional
        Tolerance (absolute) for termination.
    rtol : float, optional
        Tolerance (relative) for termination.
    maxiter : int, optional
        Maximum number of iterations.
    x0 : float, required
        Initial guess.
    fprime : bool or callable, required
        If `fprime` is a boolean and is True, `f` is assumed to return the
        value of derivative along with the objective function.
        `fprime` can also be a callable returning the derivative of `f`. In
        this case, it must accept the same arguments as `f`.
    fprime2 : bool or callable, required
        If `fprime2` is a boolean and is True, `f` is assumed to return the
        value of 1st and 2nd derivatives along with the objective function.
        `fprime2` can also be a callable returning the 2nd derivative of `f`.
        In this case, it must accept the same arguments as `f`.
    options: dict, optional
        Specifies any method-specific options not covered above.

    Nr-   r-   r   r   _root_scalar_halley_docro     s    8 	r   c                       yrf   r-   r-   r   r   _root_scalar_ridder_docrq     rd   r   c                       yrf   r-   r-   r   r   _root_scalar_bisect_docrs     rd   r   )r-   NNNNNNNNNN)r,   numpyrK    r   rH   _numdiffr   __all__ROOT_SCALAR_METHODSr   r   rc   rg   ri   rk   rm   ro   rq   rs   r-   r   r   <module>ry      so     # '/5 ' 'T 26%) .2	Rj	,	*	,	.	4	>	,	r   