Python six.callable函数代码示例

def _select_function(sort, typ):
    if typ in ['F', 'D']:
        if callable(sort):
            # assume the user knows what they're doing
            sfunction = sort
        elif sort == 'lhp':
            sfunction = lambda x, y: (np.real(x/y) < 0.0)
        elif sort == 'rhp':
            sfunction = lambda x, y: (np.real(x/y) >= 0.0)
        elif sort == 'iuc':
            sfunction = lambda x, y: (abs(x/y) <= 1.0)
        elif sort == 'ouc':
            sfunction = lambda x, y: (abs(x/y) > 1.0)
        else:
            raise ValueError("sort parameter must be None, a callable, or "
                "one of ('lhp','rhp','iuc','ouc')")
    elif typ in ['f', 'd']:
        if callable(sort):
            # assume the user knows what they're doing
            sfunction = sort
        elif sort == 'lhp':
            sfunction = lambda x, y, z: (np.real((x+y*1j)/z) < 0.0)
        elif sort == 'rhp':
            sfunction = lambda x, y, z: (np.real((x+y*1j)/z) >= 0.0)
        elif sort == 'iuc':
            sfunction = lambda x, y, z: (abs((x+y*1j)/z) <= 1.0)
        elif sort == 'ouc':
            sfunction = lambda x, y, z: (abs((x+y*1j)/z) > 1.0)
        else:
            raise ValueError("sort parameter must be None, a callable, or "
                "one of ('lhp','rhp','iuc','ouc')")
    else:  # to avoid an error later
        raise ValueError("dtype %s not understood" % typ)
    return sfunction

    def set_bandwidth(self, bw_method=None):
        """Compute the estimator bandwidth with given method.

        The new bandwidth calculated after a call to `set_bandwidth` is used
        for subsequent evaluations of the estimated density.

        Parameters
        ----------
        bw_method : str, scalar or callable, optional
            The method used to calculate the estimator bandwidth.  This can be
            'scott', 'silverman', a scalar constant or a callable.  If a
            scalar, this will be used directly as `kde.factor`.  If a callable,
            it should take a `gaussian_kde` instance as only parameter and
            return a scalar.  If None (default), nothing happens; the current
            `kde.covariance_factor` method is kept.

        Notes
        -----
        .. versionadded:: 0.11

        Examples
        --------
        >>> x1 = np.array([-7, -5, 1, 4, 5.])
        >>> kde = stats.gaussian_kde(x1)
        >>> xs = np.linspace(-10, 10, num=50)
        >>> y1 = kde(xs)
        >>> kde.set_bandwidth(bw_method='silverman')
        >>> y2 = kde(xs)
        >>> kde.set_bandwidth(bw_method=kde.factor / 3.)
        >>> y3 = kde(xs)

        >>> fig = plt.figure()
        >>> ax = fig.add_subplot(111)
        >>> ax.plot(x1, np.ones(x1.shape) / (4. * x1.size), 'bo',
        ...         label='Data points (rescaled)')
        >>> ax.plot(xs, y1, label='Scott (default)')
        >>> ax.plot(xs, y2, label='Silverman')
        >>> ax.plot(xs, y3, label='Const (1/3 * Silverman)')
        >>> ax.legend()
        >>> plt.show()

        """
        if bw_method is None:
            pass
        elif bw_method == 'scott':
            self.covariance_factor = self.scotts_factor
        elif bw_method == 'silverman':
            self.covariance_factor = self.silverman_factor
        elif np.isscalar(bw_method) and not isinstance(bw_method, string_types):
            self._bw_method = 'use constant'
            self.covariance_factor = lambda: bw_method
        elif callable(bw_method):
            self._bw_method = bw_method
            self.covariance_factor = lambda: self._bw_method(self)
        else:
            msg = "`bw_method` should be 'scott', 'silverman', a scalar " \
                  "or a callable."
            raise ValueError(msg)

        self._compute_covariance()

    def _init_function(self, r):
        if isinstance(self.function, str):
            self.function = self.function.lower()
            _mapped = {'inverse': 'inverse_multiquadric',
                       'inverse multiquadric': 'inverse_multiquadric',
                       'thin-plate': 'thin_plate'}
            if self.function in _mapped:
                self.function = _mapped[self.function]

            func_name = "_h_" + self.function
            if hasattr(self, func_name):
                self._function = getattr(self, func_name)
            else:
                functionlist = [x[3:] for x in dir(self)
                                if x.startswith('_h_')]
                raise ValueError("function must be a callable or one of " +
                                 ", ".join(functionlist))
            self._function = getattr(self, "_h_"+self.function)
        elif callable(self.function):
            allow_one = False
            if hasattr(self.function, 'func_code') or \
               hasattr(self.function, '__code__'):
                val = self.function
                allow_one = True
            elif hasattr(self.function, "im_func"):
                val = get_method_function(self.function)
            elif hasattr(self.function, "__call__"):
                val = get_method_function(self.function.__call__)
            else:
                raise ValueError("Cannot determine number of arguments to "
                                 "function")

            argcount = get_function_code(val).co_argcount
            if allow_one and argcount == 1:
                self._function = self.function
            elif argcount == 2:
                if sys.version_info[0] >= 3:
                    self._function = self.function.__get__(self, Rbf)
                else:
                    import new
                    self._function = new.instancemethod(self.function, self,
                                                        Rbf)
            else:
                raise ValueError("Function argument must take 1 or 2 "
                                 "arguments.")

        a0 = self._function(r)
        if a0.shape != r.shape:
            raise ValueError("Callable must take array and return array of "
                             "the same shape")
        return a0

def _select_function(sort):
    if callable(sort):
        # assume the user knows what they're doing
        sfunction = sort
    elif sort == 'lhp':
        sfunction = _lhp
    elif sort == 'rhp':
        sfunction = _rhp
    elif sort == 'iuc':
        sfunction = _iuc
    elif sort == 'ouc':
        sfunction = _ouc
    else:
        raise ValueError("sort parameter must be None, a callable, or "
                         "one of ('lhp','rhp','iuc','ouc')")

    return sfunction

def _select_function(sort):
    if callable(sort):
        # assume the user knows what they're doing
        sfunction = sort
    elif sort == 'lhp':
        sfunction = lambda x, y: (np.real(x/y) < 0.0)
    elif sort == 'rhp':
        sfunction = lambda x, y: (np.real(x/y) > 0.0)
    elif sort == 'iuc':
        sfunction = lambda x, y: (abs(x/y) < 1.0)
    elif sort == 'ouc':
        sfunction = lambda x, y: (abs(x/y) > 1.0)
    else:
        raise ValueError("sort parameter must be None, a callable, or "
                         "one of ('lhp','rhp','iuc','ouc')")

    return sfunction

def fmin_cobyla(func, x0, cons, args=(), consargs=None, rhobeg=1.0,
                rhoend=1e-4, iprint=1, maxfun=1000, disp=None, catol=2e-4):
    """
    Minimize a function using the Constrained Optimization BY Linear
    Approximation (COBYLA) method. This method wraps a FORTRAN
    implementation of the algorithm.

    Parameters
    ----------
    func : callable
        Function to minimize. In the form func(x, \\*args).
    x0 : ndarray
        Initial guess.
    cons : sequence
        Constraint functions; must all be ``>=0`` (a single function
        if only 1 constraint). Each function takes the parameters `x`
        as its first argument, and it can return either a single number or
        an array or list of numbers.
    args : tuple, optional
        Extra arguments to pass to function.
    consargs : tuple, optional
        Extra arguments to pass to constraint functions (default of None means
        use same extra arguments as those passed to func).
        Use ``()`` for no extra arguments.
    rhobeg : float, optional
        Reasonable initial changes to the variables.
    rhoend : float, optional
        Final accuracy in the optimization (not precisely guaranteed). This
        is a lower bound on the size of the trust region.
    iprint : {0, 1, 2, 3}, optional
        Controls the frequency of output; 0 implies no output.  Deprecated.
    disp : {0, 1, 2, 3}, optional
        Over-rides the iprint interface.  Preferred.
    maxfun : int, optional
        Maximum number of function evaluations.
    catol : float, optional
        Absolute tolerance for constraint violations.

    Returns
    -------
    x : ndarray
        The argument that minimises `f`.

    See also
    --------
    minimize: Interface to minimization algorithms for multivariate
        functions. See the 'COBYLA' `method` in particular.

    Notes
    -----
    This algorithm is based on linear approximations to the objective
    function and each constraint. We briefly describe the algorithm.

    Suppose the function is being minimized over k variables. At the
    jth iteration the algorithm has k+1 points v_1, ..., v_(k+1),
    an approximate solution x_j, and a radius RHO_j.
    (i.e. linear plus a constant) approximations to the objective
    function and constraint functions such that their function values
    agree with the linear approximation on the k+1 points v_1,.., v_(k+1).
    This gives a linear program to solve (where the linear approximations
    of the constraint functions are constrained to be non-negative).

    However the linear approximations are likely only good
    approximations near the current simplex, so the linear program is
    given the further requirement that the solution, which
    will become x_(j+1), must be within RHO_j from x_j. RHO_j only
    decreases, never increases. The initial RHO_j is rhobeg and the
    final RHO_j is rhoend. In this way COBYLA's iterations behave
    like a trust region algorithm.

    Additionally, the linear program may be inconsistent, or the
    approximation may give poor improvement. For details about
    how these issues are resolved, as well as how the points v_i are
    updated, refer to the source code or the references below.


    References
    ----------
    Powell M.J.D. (1994), "A direct search optimization method that models
    the objective and constraint functions by linear interpolation.", in
    Advances in Optimization and Numerical Analysis, eds. S. Gomez and
    J-P Hennart, Kluwer Academic (Dordrecht), pp. 51-67

    Powell M.J.D. (1998), "Direct search algorithms for optimization
    calculations", Acta Numerica 7, 287-336

    Powell M.J.D. (2007), "A view of algorithms for optimization without
    derivatives", Cambridge University Technical Report DAMTP 2007/NA03


    Examples
    --------
    Minimize the objective function f(x,y) = x*y subject
    to the constraints x**2 + y**2 < 1 and y > 0::

        >>> def objective(x):
        ...     return x[0]*x[1]
        ...
        >>> def constr1(x):
        ...     return 1 - (x[0]**2 + x[1]**2)
#.........这里部分代码省略.........

def binned_statistic_dd(sample, values, statistic='mean',
                        bins=10, range=None):
    """
    Compute a multidimensional binned statistic for a set of data.

    This is a generalization of a histogramdd function.  A histogram divides
    the space into bins, and returns the count of the number of points in
    each bin.  This function allows the computation of the sum, mean, median,
    or other statistic of the values within each bin.

    Parameters
    ----------
    sample : array_like
        Data to histogram passed as a sequence of D arrays of length N, or
        as an (N,D) array.
    values : array_like
        The values on which the statistic will be computed.  This must be
        the same shape as x.
    statistic : string or callable, optional
        The statistic to compute (default is 'mean').
        The following statistics are available:

          * 'mean' : compute the mean of values for points within each bin.
            Empty bins will be represented by NaN.
          * 'median' : compute the median of values for points within each
            bin. Empty bins will be represented by NaN.
          * 'count' : compute the count of points within each bin.  This is
            identical to an unweighted histogram.  `values` array is not
            referenced.
          * 'sum' : compute the sum of values for points within each bin.
            This is identical to a weighted histogram.
          * function : a user-defined function which takes a 1D array of
            values, and outputs a single numerical statistic. This function
            will be called on the values in each bin.  Empty bins will be
            represented by function([]), or NaN if this returns an error.

    bins : sequence or int, optional
        The bin specification:

          * A sequence of arrays describing the bin edges along each dimension.
          * The number of bins for each dimension (nx, ny, ... =bins)
          * The number of bins for all dimensions (nx=ny=...=bins).

    range : sequence, optional
        A sequence of lower and upper bin edges to be used if the edges are
        not given explicitely in `bins`. Defaults to the minimum and maximum
        values along each dimension.

    Returns
    -------
    statistic : ndarray, shape(nx1, nx2, nx3,...)
        The values of the selected statistic in each two-dimensional bin
    bin_edges : list of ndarrays
        A list of D arrays describing the (nxi + 1) bin edges for each
        dimension
    binnumber : 1-D ndarray of ints
        This assigns to each observation an integer that represents the bin
        in which this observation falls. Array has the same length as values.

    See Also
    --------
    np.histogramdd, binned_statistic, binned_statistic_2d

    Notes
    -----

    .. versionadded:: 0.11.0

    """
    known_stats = ['mean', 'median', 'count', 'sum', 'std']
    if not callable(statistic) and statistic not in known_stats:
        raise ValueError('invalid statistic %r' % (statistic,))

    # This code is based on np.histogramdd
    try:
        # Sample is an ND-array.
        N, D = sample.shape
    except (AttributeError, ValueError):
        # Sample is a sequence of 1D arrays.
        sample = np.atleast_2d(sample).T
        N, D = sample.shape

    nbin = np.empty(D, int)
    edges = D * [None]
    dedges = D * [None]

    try:
        M = len(bins)
        if M != D:
            raise AttributeError('The dimension of bins must be equal '
                                 'to the dimension of the sample x.')
    except TypeError:
        bins = D * [bins]

    # Select range for each dimension
    # Used only if number of bins is given.
    if range is None:
        smin = np.atleast_1d(np.array(sample.min(0), float))
        smax = np.atleast_1d(np.array(sample.max(0), float))
    else:
#.........这里部分代码省略.........

def minimize_scalar(fun, bracket=None, bounds=None, args=(),
                    method='brent', tol=None, options=None):
    """Minimization of scalar function of one variable.

    Parameters
    ----------
    fun : callable
        Objective function.
        Scalar function, must return a scalar.
    bracket : sequence, optional
        For methods 'brent' and 'golden', `bracket` defines the bracketing
        interval and can either have three items ``(a, b, c)`` so that
        ``a < b < c`` and ``fun(b) < fun(a), fun(c)`` or two items ``a`` and
        ``c`` which are assumed to be a starting interval for a downhill
        bracket search (see `bracket`); it doesn't always mean that the
        obtained solution will satisfy ``a <= x <= c``.
    bounds : sequence, optional
        For method 'bounded', `bounds` is mandatory and must have two items
        corresponding to the optimization bounds.
    args : tuple, optional
        Extra arguments passed to the objective function.
    method : str or callable, optional
        Type of solver.  Should be one of:

            - 'Brent'     :ref:`(see here) <optimize.minimize_scalar-brent>`
            - 'Bounded'   :ref:`(see here) <optimize.minimize_scalar-bounded>`
            - 'Golden'    :ref:`(see here) <optimize.minimize_scalar-golden>`
            - custom - a callable object (added in version 0.14.0), see below

    tol : float, optional
        Tolerance for termination. For detailed control, use solver-specific
        options.
    options : dict, optional
        A dictionary of solver options.

            maxiter : int
                Maximum number of iterations to perform.
            disp : bool
                Set to True to print convergence messages.

        See :func:`show_options()` for solver-specific options.

    Returns
    -------
    res : OptimizeResult
        The optimization result represented as a ``OptimizeResult`` object.
        Important attributes are: ``x`` the solution array, ``success`` a
        Boolean flag indicating if the optimizer exited successfully and
        ``message`` which describes the cause of the termination. See
        `OptimizeResult` for a description of other attributes.

    See also
    --------
    minimize : Interface to minimization algorithms for scalar multivariate
        functions
    show_options : Additional options accepted by the solvers

    Notes
    -----
    This section describes the available solvers that can be selected by the
    'method' parameter. The default method is *Brent*.

    Method :ref:`Brent <optimize.minimize_scalar-brent>` uses Brent's
    algorithm to find a local minimum.  The algorithm uses inverse
    parabolic interpolation when possible to speed up convergence of
    the golden section method.

    Method :ref:`Golden <optimize.minimize_scalar-golden>` uses the
    golden section search technique. It uses analog of the bisection
    method to decrease the bracketed interval. It is usually
    preferable to use the *Brent* method.

    Method :ref:`Bounded <optimize.minimize_scalar-bounded>` can
    perform bounded minimization. It uses the Brent method to find a
    local minimum in the interval x1 < xopt < x2.

    **Custom minimizers**

    It may be useful to pass a custom minimization method, for example
    when using some library frontend to minimize_scalar.  You can simply
    pass a callable as the ``method`` parameter.

    The callable is called as ``method(fun, args, **kwargs, **options)``
    where ``kwargs`` corresponds to any other parameters passed to `minimize`
    (such as `bracket`, `tol`, etc.), except the `options` dict, which has
    its contents also passed as `method` parameters pair by pair.  The method
    shall return an ``OptimizeResult`` object.

    The provided `method` callable must be able to accept (and possibly ignore)
    arbitrary parameters; the set of parameters accepted by `minimize` may
    expand in future versions and then these parameters will be passed to
    the method.  You can find an example in the scipy.optimize tutorial.

    .. versionadded:: 0.11.0

    Examples
    --------
    Consider the problem of minimizing the following function.

    >>> def f(x):
#.........这里部分代码省略.........

def minimize(fun, x0, args=(), method=None, jac=None, hess=None,
             hessp=None, bounds=None, constraints=(), tol=None,
             callback=None, options=None):
    """Minimization of scalar function of one or more variables.

    In general, the optimization problems are of the form::

        minimize f(x) subject to

        g_i(x) >= 0,  i = 1,...,m
        h_j(x)  = 0,  j = 1,...,p

    where x is a vector of one or more variables.
    ``g_i(x)`` are the inequality constraints.
    ``h_j(x)`` are the equality constrains.

    Optionally, the lower and upper bounds for each element in x can also be
    specified using the `bounds` argument.

    Parameters
    ----------
    fun : callable
        The objective function to be minimized. Must be in the form
        ``f(x, *args)``. The optimizing argument, ``x``, is a 1-D array
        of points, and ``args`` is a tuple of any additional fixed parameters
        needed to completely specify the function.
    x0 : ndarray
        Initial guess. ``len(x0)`` is the dimensionality of the minimization
        problem.
    args : tuple, optional
        Extra arguments passed to the objective function and its
        derivatives (Jacobian, Hessian).
    method : str or callable, optional
        Type of solver.  Should be one of

            - 'Nelder-Mead' :ref:`(see here) <optimize.minimize-neldermead>`
            - 'Powell'      :ref:`(see here) <optimize.minimize-powell>`
            - 'CG'          :ref:`(see here) <optimize.minimize-cg>`
            - 'BFGS'        :ref:`(see here) <optimize.minimize-bfgs>`
            - 'Newton-CG'   :ref:`(see here) <optimize.minimize-newtoncg>`
            - 'L-BFGS-B'    :ref:`(see here) <optimize.minimize-lbfgsb>`
            - 'TNC'         :ref:`(see here) <optimize.minimize-tnc>`
            - 'COBYLA'      :ref:`(see here) <optimize.minimize-cobyla>`
            - 'SLSQP'       :ref:`(see here) <optimize.minimize-slsqp>`
            - 'dogleg'      :ref:`(see here) <optimize.minimize-dogleg>`
            - 'trust-ncg'   :ref:`(see here) <optimize.minimize-trustncg>`
            - 'trust-exact' :ref:`(see here) <optimize.minimize-trustexact>`
            - custom - a callable object (added in version 0.14.0),
              see below for description.

        If not given, chosen to be one of ``BFGS``, ``L-BFGS-B``, ``SLSQP``,
        depending if the problem has constraints or bounds.
    jac : bool or callable, optional
        Jacobian (gradient) of objective function. Only for CG, BFGS,
        Newton-CG, L-BFGS-B, TNC, SLSQP, dogleg, trust-ncg.
        If `jac` is a Boolean and is True, `fun` is assumed to return the
        gradient along with the objective function. If False, the
        gradient will be estimated numerically.
        `jac` can also be a callable returning the gradient of the
        objective. In this case, it must accept the same arguments as `fun`.
    hess, hessp : callable, optional
        Hessian (matrix of second-order derivatives) of objective function or
        Hessian of objective function times an arbitrary vector p.  Only for
        Newton-CG, dogleg, trust-ncg.
        Only one of `hessp` or `hess` needs to be given.  If `hess` is
        provided, then `hessp` will be ignored.  If neither `hess` nor
        `hessp` is provided, then the Hessian product will be approximated
        using finite differences on `jac`. `hessp` must compute the Hessian
        times an arbitrary vector.
    bounds : sequence, optional
        Bounds for variables (only for L-BFGS-B, TNC and SLSQP).
        ``(min, max)`` pairs for each element in ``x``, defining
        the bounds on that parameter. Use None for one of ``min`` or
        ``max`` when there is no bound in that direction.
    constraints : dict or sequence of dict, optional
        Constraints definition (only for COBYLA and SLSQP).
        Each constraint is defined in a dictionary with fields:

            type : str
                Constraint type: 'eq' for equality, 'ineq' for inequality.
            fun : callable
                The function defining the constraint.
            jac : callable, optional
                The Jacobian of `fun` (only for SLSQP).
            args : sequence, optional
                Extra arguments to be passed to the function and Jacobian.

        Equality constraint means that the constraint function result is to
        be zero whereas inequality means that it is to be non-negative.
        Note that COBYLA only supports inequality constraints.
    tol : float, optional
        Tolerance for termination. For detailed control, use solver-specific
        options.
    options : dict, optional
        A dictionary of solver options. All methods accept the following
        generic options:

            maxiter : int
                Maximum number of iterations to perform.
            disp : bool
#.........这里部分代码省略.........

def minimize(fun, x0, args=(), method=None, jac=None, hess=None,
             hessp=None, bounds=None, constraints=(), tol=None,
             callback=None, options=None):
    """Minimization of scalar function of one or more variables.

    Parameters
    ----------
    fun : callable
        The objective function to be minimized.

            ``fun(x, *args) -> float``

        where x is an 1-D array with shape (n,) and `args`
        is a tuple of the fixed parameters needed to completely
        specify the function.
    x0 : ndarray, shape (n,)
        Initial guess. Array of real elements of size (n,),
        where 'n' is the number of independent variables.
    args : tuple, optional
        Extra arguments passed to the objective function and its
        derivatives (`fun`, `jac` and `hess` functions).
    method : str or callable, optional
        Type of solver.  Should be one of

            - 'Nelder-Mead' :ref:`(see here) <optimize.minimize-neldermead>`
            - 'Powell'      :ref:`(see here) <optimize.minimize-powell>`
            - 'CG'          :ref:`(see here) <optimize.minimize-cg>`
            - 'BFGS'        :ref:`(see here) <optimize.minimize-bfgs>`
            - 'Newton-CG'   :ref:`(see here) <optimize.minimize-newtoncg>`
            - 'L-BFGS-B'    :ref:`(see here) <optimize.minimize-lbfgsb>`
            - 'TNC'         :ref:`(see here) <optimize.minimize-tnc>`
            - 'COBYLA'      :ref:`(see here) <optimize.minimize-cobyla>`
            - 'SLSQP'       :ref:`(see here) <optimize.minimize-slsqp>`
            - 'trust-constr':ref:`(see here) <optimize.minimize-trustconstr>`
            - 'dogleg'      :ref:`(see here) <optimize.minimize-dogleg>`
            - 'trust-ncg'   :ref:`(see here) <optimize.minimize-trustncg>`
            - 'trust-exact' :ref:`(see here) <optimize.minimize-trustexact>`
            - 'trust-krylov' :ref:`(see here) <optimize.minimize-trustkrylov>`
            - custom - a callable object (added in version 0.14.0),
              see below for description.

        If not given, chosen to be one of ``BFGS``, ``L-BFGS-B``, ``SLSQP``,
        depending if the problem has constraints or bounds.
    jac : {callable,  '2-point', '3-point', 'cs', bool}, optional
        Method for computing the gradient vector. Only for CG, BFGS,
        Newton-CG, L-BFGS-B, TNC, SLSQP, dogleg, trust-ncg, trust-krylov,
        trust-exact and trust-constr. If it is a callable, it should be a
        function that returns the gradient vector:

            ``jac(x, *args) -> array_like, shape (n,)``

        where x is an array with shape (n,) and `args` is a tuple with
        the fixed parameters. Alternatively, the keywords
        {'2-point', '3-point', 'cs'} select a finite
        difference scheme for numerical estimation of the gradient. Options
        '3-point' and 'cs' are available only to 'trust-constr'.
        If `jac` is a Boolean and is True, `fun` is assumed to return the
        gradient along with the objective function. If False, the gradient
        will be estimated using '2-point' finite difference estimation.
    hess : {callable, '2-point', '3-point', 'cs', HessianUpdateStrategy},  optional
        Method for computing the Hessian matrix. Only for Newton-CG, dogleg,
        trust-ncg,  trust-krylov, trust-exact and trust-constr. If it is
        callable, it should return the  Hessian matrix:

            ``hess(x, *args) -> {LinearOperator, spmatrix, array}, (n, n)``

        where x is a (n,) ndarray and `args` is a tuple with the fixed
        parameters. LinearOperator and sparse matrix returns are
        allowed only for 'trust-constr' method. Alternatively, the keywords
        {'2-point', '3-point', 'cs'} select a finite difference scheme
        for numerical estimation. Or, objects implementing
        `HessianUpdateStrategy` interface can be used to approximate
        the Hessian. Available quasi-Newton methods implementing
        this interface are:

            - `BFGS`;
            - `SR1`.

        Whenever the gradient is estimated via finite-differences,
        the Hessian cannot be estimated with options
        {'2-point', '3-point', 'cs'} and needs to be
        estimated using one of the quasi-Newton strategies.
        Finite-difference options {'2-point', '3-point', 'cs'} and
        `HessianUpdateStrategy` are available only for 'trust-constr' method.
    hessp : callable, optional
        Hessian of objective function times an arbitrary vector p. Only for
        Newton-CG, trust-ncg, trust-krylov, trust-constr.
        Only one of `hessp` or `hess` needs to be given.  If `hess` is
        provided, then `hessp` will be ignored.  `hessp` must compute the
        Hessian times an arbitrary vector:

            ``hessp(x, p, *args) ->  ndarray shape (n,)``

        where x is a (n,) ndarray, p is an arbitrary vector with
        dimension (n,) and `args` is a tuple with the fixed
        parameters.
    bounds : sequence or `Bounds`, optional
        Bounds on variables for L-BFGS-B, TNC, SLSQP and
        trust-constr methods. There are two ways to specify the bounds:

#.........这里部分代码省略.........

def schur(a, output='real', lwork=None, overwrite_a=False, sort=None,
          check_finite=True):
    """
    Compute Schur decomposition of a matrix.

    The Schur decomposition is::

        A = Z T Z^H

    where Z is unitary and T is either upper-triangular, or for real
    Schur decomposition (output='real'), quasi-upper triangular.  In
    the quasi-triangular form, 2x2 blocks describing complex-valued
    eigenvalue pairs may extrude from the diagonal.

    Parameters
    ----------
    a : (M, M) array_like
        Matrix to decompose
    output : {'real', 'complex'}, optional
        Construct the real or complex Schur decomposition (for real matrices).
    lwork : int, optional
        Work array size. If None or -1, it is automatically computed.
    overwrite_a : bool, optional
        Whether to overwrite data in a (may improve performance).
    sort : {None, callable, 'lhp', 'rhp', 'iuc', 'ouc'}, optional
        Specifies whether the upper eigenvalues should be sorted.  A callable
        may be passed that, given a eigenvalue, returns a boolean denoting
        whether the eigenvalue should be sorted to the top-left (True).
        Alternatively, string parameters may be used::

            'lhp'   Left-hand plane (x.real < 0.0)
            'rhp'   Right-hand plane (x.real > 0.0)
            'iuc'   Inside the unit circle (x*x.conjugate() <= 1.0)
            'ouc'   Outside the unit circle (x*x.conjugate() > 1.0)

        Defaults to None (no sorting).
    check_finite : boolean, optional
        Whether to check that the input matrix contains only finite numbers.
        Disabling may give a performance gain, but may result in problems
        (crashes, non-termination) if the inputs do contain infinities or NaNs.

    Returns
    -------
    T : (M, M) ndarray
        Schur form of A. It is real-valued for the real Schur decomposition.
    Z : (M, M) ndarray
        An unitary Schur transformation matrix for A.
        It is real-valued for the real Schur decomposition.
    sdim : int
        If and only if sorting was requested, a third return value will
        contain the number of eigenvalues satisfying the sort condition.

    Raises
    ------
    LinAlgError
        Error raised under three conditions:

        1. The algorithm failed due to a failure of the QR algorithm to
           compute all eigenvalues
        2. If eigenvalue sorting was requested, the eigenvalues could not be
           reordered due to a failure to separate eigenvalues, usually because
           of poor conditioning
        3. If eigenvalue sorting was requested, roundoff errors caused the
           leading eigenvalues to no longer satisfy the sorting condition

    See also
    --------
    rsf2csf : Convert real Schur form to complex Schur form

    """
    if output not in ['real','complex','r','c']:
        raise ValueError("argument must be 'real', or 'complex'")
    if check_finite:
        a1 = asarray_chkfinite(a)
    else:
        a1 = asarray(a)
    if len(a1.shape) != 2 or (a1.shape[0] != a1.shape[1]):
        raise ValueError('expected square matrix')
    typ = a1.dtype.char
    if output in ['complex','c'] and typ not in ['F','D']:
        if typ in _double_precision:
            a1 = a1.astype('D')
            typ = 'D'
        else:
            a1 = a1.astype('F')
            typ = 'F'
    overwrite_a = overwrite_a or (_datacopied(a1, a))
    gees, = get_lapack_funcs(('gees',), (a1,))
    if lwork is None or lwork == -1:
        # get optimal work array
        result = gees(lambda x: None, a1, lwork=-1)
        lwork = result[-2][0].real.astype(numpy.int)

    if sort is None:
        sort_t = 0
        sfunction = lambda x: None
    else:
        sort_t = 1
        if callable(sort):
            sfunction = sort
#.........这里部分代码省略.........

def root(fun, x0, args=(), method='hybr', jac=None, tol=None, callback=None,
         options=None):
    """
    Find a root of a vector function.

    Parameters
    ----------
    fun : callable
        A vector function to find a root of.
    x0 : ndarray
        Initial guess.
    args : tuple, optional
        Extra arguments passed to the objective function and its Jacobian.
    method : str, optional
        Type of solver.  Should be one of

            - 'hybr'             :ref:`(see here) <optimize.root-hybr>`
            - 'lm'               :ref:`(see here) <optimize.root-lm>`
            - 'broyden1'         :ref:`(see here) <optimize.root-broyden1>`
            - 'broyden2'         :ref:`(see here) <optimize.root-broyden2>`
            - 'anderson'         :ref:`(see here) <optimize.root-anderson>`
            - 'linearmixing'     :ref:`(see here) <optimize.root-linearmixing>`
            - 'diagbroyden'      :ref:`(see here) <optimize.root-diagbroyden>`
            - 'excitingmixing'   :ref:`(see here) <optimize.root-excitingmixing>`
            - 'krylov'           :ref:`(see here) <optimize.root-krylov>`
            - 'df-sane'          :ref:`(see here) <optimize.root-dfsane>`

    jac : bool or callable, optional
        If `jac` is a Boolean and is True, `fun` is assumed to return the
        value of Jacobian along with the objective function. If False, the
        Jacobian will be estimated numerically.
        `jac` can also be a callable returning the Jacobian of `fun`. In
        this case, it must accept the same arguments as `fun`.
    tol : float, optional
        Tolerance for termination. For detailed control, use solver-specific
        options.
    callback : function, optional
        Optional callback function. It is called on every iteration as
        ``callback(x, f)`` where `x` is the current solution and `f`
        the corresponding residual. For all methods but 'hybr' and 'lm'.
    options : dict, optional
        A dictionary of solver options. E.g. `xtol` or `maxiter`, see
        :obj:`show_options()` for details.

    Returns
    -------
    sol : OptimizeResult
        The solution represented as a ``OptimizeResult`` object.
        Important attributes are: ``x`` the solution array, ``success`` a
        Boolean flag indicating if the algorithm exited successfully and
        ``message`` which describes the cause of the termination. See
        `OptimizeResult` for a description of other attributes.

    See also
    --------
    show_options : Additional options accepted by the solvers

    Notes
    -----
    This section describes the available solvers that can be selected by the
    'method' parameter. The default method is *hybr*.

    Method *hybr* uses a modification of the Powell hybrid method as
    implemented in MINPACK [1]_.

    Method *lm* solves the system of nonlinear equations in a least squares
    sense using a modification of the Levenberg-Marquardt algorithm as
    implemented in MINPACK [1]_.

    Method *df-sane* is a derivative-free spectral method. [3]_

    Methods *broyden1*, *broyden2*, *anderson*, *linearmixing*,
    *diagbroyden*, *excitingmixing*, *krylov* are inexact Newton methods,
    with backtracking or full line searches [2]_. Each method corresponds
    to a particular Jacobian approximations. See `nonlin` for details.

    - Method *broyden1* uses Broyden's first Jacobian approximation, it is
      known as Broyden's good method.
    - Method *broyden2* uses Broyden's second Jacobian approximation, it
      is known as Broyden's bad method.
    - Method *anderson* uses (extended) Anderson mixing.
    - Method *Krylov* uses Krylov approximation for inverse Jacobian. It
      is suitable for large-scale problem.
    - Method *diagbroyden* uses diagonal Broyden Jacobian approximation.
    - Method *linearmixing* uses a scalar Jacobian approximation.
    - Method *excitingmixing* uses a tuned diagonal Jacobian
      approximation.

    .. warning::

        The algorithms implemented for methods *diagbroyden*,
        *linearmixing* and *excitingmixing* may be useful for specific
        problems, but whether they will work may depend strongly on the
        problem.

    .. versionadded:: 0.11.0

    References
    ----------
    .. [1] More, Jorge J., Burton S. Garbow, and Kenneth E. Hillstrom.
#.........这里部分代码省略.........

def cdist(XA, XB, metric='euclidean', p=2, V=None, VI=None, w=None):
    timer = MyTimer.MyTimerCLS()
    timer.refresh('enter cidst')
    XA = np.asarray(XA, order='c')
    XB = np.asarray(XB, order='c')
    timer.refresh('asarray')
    # The C code doesn't do striding.
    XA = _copy_array_if_base_present(_convert_to_double(XA))
    XB = _copy_array_if_base_present(_convert_to_double(XB))
    timer.refresh('_copy_array_if_base_present')
    s = XA.shape
    sB = XB.shape
    timer.refresh('get shape')
    if len(s) != 2:
        raise ValueError('XA must be a 2-dimensional array.')
    if len(sB) != 2:
        raise ValueError('XB must be a 2-dimensional array.')
    if s[1] != sB[1]:
        raise ValueError('XA and XB must have the same number of columns '
                         '(i.e. feature dimension.)')
    timer.refresh('error check')
    mA = s[0]
    mB = sB[0]
    n = s[1]
    timer.refresh('get dim')
    dm = np.zeros((mA, mB), dtype=np.double)
    timer.refresh(' np.zeros ')
    if callable(metric):
        if metric == minkowski:
            for i in xrange(0, mA):
                for j in xrange(0, mB):
                    dm[i, j] = minkowski(XA[i, :], XB[j, :], p)
        elif metric == wminkowski:
            for i in xrange(0, mA):
                for j in xrange(0, mB):
                    dm[i, j] = wminkowski(XA[i, :], XB[j, :], p, w)
        elif metric == seuclidean:
            for i in xrange(0, mA):
                for j in xrange(0, mB):
                    dm[i, j] = seuclidean(XA[i, :], XB[j, :], V)
        elif metric == mahalanobis:
            for i in xrange(0, mA):
                for j in xrange(0, mB):
                    dm[i, j] = mahalanobis(XA[i, :], XB[j, :], V)
        else:
            for i in xrange(0, mA):
                for j in xrange(0, mB):
                    dm[i, j] = metric(XA[i, :], XB[j, :])
        timer.refresh(' if callable ')
        print 'cool'
    elif isinstance(metric, string_types):
        mstr = metric.lower()
        timer.refresh('else')
        try:
            validate, cdist_fn = _SIMPLE_CDIST[mstr]
            XA = validate(XA)
            XB = validate(XB)
            cdist_fn(XA, XB, dm)
            return dm
        except KeyError:
            pass
        timer.refresh(' try')
        if mstr in ['hamming', 'hamm', 'ha', 'h']:
            if XA.dtype == bool:
                XA = _convert_to_bool(XA)
                XB = _convert_to_bool(XB)
                _distance_wrap.cdist_hamming_bool_wrap(XA, XB, dm)
            else:
                XA = _convert_to_double(XA)
                XB = _convert_to_double(XB)
                _distance_wrap.cdist_hamming_wrap(XA, XB, dm)
        elif mstr in ['jaccard', 'jacc', 'ja', 'j']:
            if XA.dtype == bool:
                XA = _convert_to_bool(XA)
                XB = _convert_to_bool(XB)
                _distance_wrap.cdist_jaccard_bool_wrap(XA, XB, dm)
            else:
                XA = _convert_to_double(XA)
                XB = _convert_to_double(XB)
                _distance_wrap.cdist_jaccard_wrap(XA, XB, dm)
        elif mstr in ['minkowski', 'mi', 'm', 'pnorm']:
            timer.refresh('before _convert_to_double')
            XA = _convert_to_double(XA)
            XB = _convert_to_double(XB)
            timer.refresh('_convert_to_double')
            _distance_wrap.cdist_minkowski_wrap(XA, XB, dm, p)
            timer.refresh('after minkowski')
        elif mstr in ['wminkowski', 'wmi', 'wm', 'wpnorm']:
            timer.refresh('before _convert_to_double')
            XA = _convert_to_double(XA)
            XB = _convert_to_double(XB)
            timer.refresh('_convert_to_double')
            w = _convert_to_double(w)
            _distance_wrap.cdist_weighted_minkowski_wrap(XA, XB, dm, p, w)
        elif mstr in ['seuclidean', 'se', 's']:
            XA = _convert_to_double(XA)
            XB = _convert_to_double(XB)
            if V is not None:
                V = np.asarray(V, order='c')
                if V.dtype != np.double:
#.........这里部分代码省略.........

def root_scalar(f, args=(), method=None, bracket=None,
                fprime=None, fprime2=None,
                x0=None, x1=None,
                xtol=None, rtol=None, maxiter=None,
                options=None):
    """
    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.


    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)
#.........这里部分代码省略.........

def binned_statistic_dd(sample, values, statistic='mean',
                        bins=10, range=None, expand_binnumbers=False):
    """
    Compute a multidimensional binned statistic for a set of data.

    This is a generalization of a histogramdd function.  A histogram divides
    the space into bins, and returns the count of the number of points in
    each bin.  This function allows the computation of the sum, mean, median,
    or other statistic of the values within each bin.

    Parameters
    ----------
    sample : array_like
        Data to histogram passed as a sequence of D arrays of length N, or
        as an (N,D) array.
    values : (N,) array_like or list of (N,) array_like
        The data on which the statistic will be computed.  This must be
        the same shape as `x`, or a list of sequences - each with the same
        shape as `x`.  If `values` is such a list, the statistic will be
        computed on each independently.
    statistic : string or callable, optional
        The statistic to compute (default is 'mean').
        The following statistics are available:

          * 'mean' : compute the mean of values for points within each bin.
            Empty bins will be represented by NaN.
          * 'median' : compute the median of values for points within each
            bin. Empty bins will be represented by NaN.
          * 'count' : compute the count of points within each bin.  This is
            identical to an unweighted histogram.  `values` array is not
            referenced.
          * 'sum' : compute the sum of values for points within each bin.
            This is identical to a weighted histogram.
          * function : a user-defined function which takes a 1D array of
            values, and outputs a single numerical statistic. This function
            will be called on the values in each bin.  Empty bins will be
            represented by function([]), or NaN if this returns an error.

    bins : sequence or int, optional
        The bin specification must be in one of the following forms:

          * A sequence of arrays describing the bin edges along each dimension.
          * The number of bins for each dimension (nx, ny, ... = bins).
          * The number of bins for all dimensions (nx = ny = ... = bins).

    range : sequence, optional
        A sequence of lower and upper bin edges to be used if the edges are
        not given explicitely in `bins`. Defaults to the minimum and maximum
        values along each dimension.
    expand_binnumbers : bool, optional
        'False' (default): the returned `binnumber` is a shape (N,) array of
        linearized bin indices.
        'True': the returned `binnumber` is 'unraveled' into a shape (D,N)
        ndarray, where each row gives the bin numbers in the corresponding
        dimension.
        See the `binnumber` returned value, and the `Examples` section of
        `binned_statistic_2d`.

        .. versionadded:: 0.17.0

    Returns
    -------
    statistic : ndarray, shape(nx1, nx2, nx3,...)
        The values of the selected statistic in each two-dimensional bin.
    bin_edges : list of ndarrays
        A list of D arrays describing the (nxi + 1) bin edges for each
        dimension.
    binnumber : (N,) array of ints or (D,N) ndarray of ints
        This assigns to each element of `sample` an integer that represents the
        bin in which this observation falls.  The representation depends on the
        `expand_binnumbers` argument.  See `Notes` for details.


    See Also
    --------
    numpy.digitize, numpy.histogramdd, binned_statistic, binned_statistic_2d

    Notes
    -----
    Binedges:
    All but the last (righthand-most) bin is half-open in each dimension.  In
    other words, if `bins` is ``[1, 2, 3, 4]``, then the first bin is
    ``[1, 2)`` (including 1, but excluding 2) and the second ``[2, 3)``.  The
    last bin, however, is ``[3, 4]``, which *includes* 4.

    `binnumber`:
    This returned argument assigns to each element of `sample` an integer that
    represents the bin in which it belongs.  The representation depends on the
    `expand_binnumbers` argument. If 'False' (default): The returned
    `binnumber` is a shape (N,) array of linearized indices mapping each
    element of `sample` to its corresponding bin (using row-major ordering).
    If 'True': The returned `binnumber` is a shape (D,N) ndarray where
    each row indicates bin placements for each dimension respectively.  In each
    dimension, a binnumber of `i` means the corresponding value is between
    (bin_edges[D][i-1], bin_edges[D][i]), for each dimension 'D'.

    .. versionadded:: 0.11.0

    """
    known_stats = ['mean', 'median', 'count', 'sum', 'std']
#.........这里部分代码省略.........