ó î&]\c @`sãdZddlmZmZmZddlZddlmZddl m Z dgZ de fd „ƒYZdddddddddddd „ Zd „Zd „Zd „Zd„Zd„Zd„Zd„Zd„ZdS(s• Unified interfaces to root finding algorithms for real or complex scalar functions. Functions --------- - root : find a root of a scalar function. i(tdivisiontprint_functiontabsolute_importN(tcallablei(tzerost root_scalart MemoizeDercB`s;eZdZd„Zd„Zd„Zd„Zd„ZRS(sšDecorator 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.cC`s(||_d|_d|_d|_dS(Ni(tfuntNonetvalstxtn_calls(tselfR((s:lib/python2.7/site-packages/scipy/optimize/_root_scalar.pyt__init__s   cG`s`|jdks||jkrU|j||Œ}||_|jd7_||_n|jdS(s,Calculate f or use cached value if availableiiN(R RR RR (R R targstfg((s:lib/python2.7/site-packages/scipy/optimize/_root_scalar.pyt__call__#s   cG`s9|jdks||jkr.|||Œn|jdS(s/Calculate f' or use a cached value if availableiN(R RR (R R R((s:lib/python2.7/site-packages/scipy/optimize/_root_scalar.pytfprime-scG`s9|jdks||jkr.|||Œn|jdS(s0Calculate f'' or use a cached value if availableiN(R RR (R R R((s:lib/python2.7/site-packages/scipy/optimize/_root_scalar.pytfprime23scC`s|jS(N(R (R ((s:lib/python2.7/site-packages/scipy/optimize/_root_scalar.pytncalls9s(t__name__t __module__t__doc__R RRRR(((s:lib/python2.7/site-packages/scipy/optimize/_root_scalar.pyRs     c  C`sŒt|tƒs|f}n| dkr0i} nt} |dk r‹t|ƒ r‹t|ƒr‚t|ƒ}t} |j}|j }q‹d}n|dk r×t|ƒ r×t|ƒrÎt|ƒ}t} |j }q×d}ni} xBdddgD]1}t ƒj |ƒ}|dk rí|| |` - 'brentq' :ref:`(see here) ` - 'brenth' :ref:`(see here) ` - 'ridder' :ref:`(see here) ` - 'toms748' :ref:`(see here) ` - 'newton' :ref:`(see here) ` - 'secant' :ref:`(see here) ` - 'halley' :ref:`(see here) ` 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 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, optional 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`. 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. 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) txtoltrtoltmaxitert full_outputtdisptbrentqthalleytnewtontsecantsIUnable to select a solver as neither bracket nor starting point provided.sUnknown solver %stbisecttriddertbrenthttoms748sBracket needed for %siRsx0 must not be None for %ssx1 must not be None for %sttolRRtx1sfprime must be specified for %ss fprime2 must be specified for %sN(R R!RR"R#(R(R(R(t isinstancettupleRtFalseRtboolRtTrueRRtlocalstgettupdatet ValueErrortlowertgetattrtoptzerostAttributeErrortlisttnptndarraytpopR tfunction_calls(tfRtmethodtbracketRRtx0R%RRRtoptionst is_memoizedtkwargstktvtmethtmap2underlyingtmethodctatbtrtsolR ((s:lib/python2.7/site-packages/scipy/optimize/_root_scalar.pyR=s¢w                     $          -  cC`sdS(s£ 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. options: dict, optional Specifies any method-specific options not covered above N((((s:lib/python2.7/site-packages/scipy/optimize/_root_scalar.pyt_root_scalar_brentq_doc!scC`sdS(s£ 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. options: dict, optional Specifies any method-specific options not covered above N((((s:lib/python2.7/site-packages/scipy/optimize/_root_scalar.pyt_root_scalar_brenth_doc4scC`sdS(s£ 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. options: dict, optional Specifies any method-specific options not covered above N((((s:lib/python2.7/site-packages/scipy/optimize/_root_scalar.pyt_root_scalar_toms748_docFscC`sdS(s 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 N((((s:lib/python2.7/site-packages/scipy/optimize/_root_scalar.pyt_root_scalar_secant_docYscC`sdS(s! 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 N((((s:lib/python2.7/site-packages/scipy/optimize/_root_scalar.pyt_root_scalar_newton_docpscC`sdS(sq 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 N((((s:lib/python2.7/site-packages/scipy/optimize/_root_scalar.pyt_root_scalar_halley_docŠscC`sdS(s£ 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. options: dict, optional Specifies any method-specific options not covered above N((((s:lib/python2.7/site-packages/scipy/optimize/_root_scalar.pyt_root_scalar_ridder_doc©scC`sdS(s£ 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. options: dict, optional Specifies any method-specific options not covered above N((((s:lib/python2.7/site-packages/scipy/optimize/_root_scalar.pyt_root_scalar_bisect_doc¼s((Rt __future__RRRtnumpyR4tscipy._lib.sixRtRR1t__all__tobjectRRRRHRIRJRKRLRMRNRO(((s:lib/python2.7/site-packages/scipy/optimize/_root_scalar.pyts&  *   à