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@ÿÿ"@ÿÿC@ÿÿd@ÿÿóÿÿüòÿÿóòÿÿêòÿÿáòÿÿØòÿÿ`ôÿÿ°óÿÿÑóÿÿXôÿÿôÿÿstatsmodels.nonparametric._smoothers_lowessFormat string allocated too short.statsmodels/nonparametric/_smoothers_lowess.pyxnumpy.core.umath failed to importndarray is not Fortran contiguouslowess(endog, exog, frac=2.0/3.0, it=3, delta=0.0)
    LOWESS (Locally Weighted Scatterplot Smoothing)

    A lowess function that outs smoothed estimates of endog
    at the given exog values from points (exog, endog)

    Parameters
    ----------
    endog: 1-D numpy array
        The y-values of the observed points
    exog: 1-D numpy array
        The x-values of the observed points. exog has to be increasing.
    frac: float
        Between 0 and 1. The fraction of the data used
        when estimating each y-value.
    it: int
        The number of residual-based reweightings
        to perform.
    delta: float
        Distance within which to use linear-interpolation
        instead of weighted regression.

    Returns
    -------
    out: numpy array
        A numpy array with two columns. The first column
        is the sorted x values and the second column the
        associated estimated y-values.

    Notes
    -----
    This lowess function implements the algorithm given in the
    reference below using local linear estimates.

    Suppose the input data has N points. The algorithm works by
    estimating the `smooth` y_i by taking the frac*N closest points
    to (x_i,y_i) based on their x values and estimating y_i
    using a weighted linear regression. The weight for (x_j,y_j)
    is tricube function applied to |x_i-x_j|.

    If it > 1, then further weighted local linear regressions
    are performed, where the weights are the same as above
    times the _lowess_bisquare function of the residuals. Each iteration
    takes approximately the same amount of time as the original fit,
    so these iterations are expensive. They are most useful when
    the noise has extremely heavy tails, such as Cauchy noise.
    Noise with less heavy-tails, such as t-distributions with df>2,
    are less problematic. The weights downgrade the influence of
    points with large residuals. In the extreme case, points whose
    residuals are larger than 6 times the median absolute residual
    are given weight 0.

    delta can be used to save computations. For each x_i, regressions
    are skipped for points closer than delta. The next regression is
    fit for the farthest point within delta of x_i and all points in
    between are estimated by linearly interpolating between the two
    regression fits.

    Judicious choice of delta can cut computation time considerably
    for large data (N > 5000). A good choice is delta = 0.01 *
    range(exog).

    Some experimentation is likely required to find a good
    choice of frac and iter for a particular dataset.

    References
    ----------
    Cleveland, W.S. (1979) "Robust Locally Weighted Regression
    and Smoothing Scatterplots". Journal of the American Statistical
    Association 74 (368): 829-836.

    Examples
    --------
    The below allows a comparison between how different the fits from
    lowess for different values of frac can be.

    >>> import numpy as np
    >>> import statsmodels.api as sm
    >>> lowess = sm.nonparametric.lowess
    >>> x = np.random.uniform(low = -2*np.pi, high = 2*np.pi, size=500)
    >>> y = np.sin(x) + np.random.normal(size=len(x))
    >>> z = lowess(y, x)
    >>> w = lowess(y, x, frac=1./3)

    This gives a similar comparison for when it is 0 vs not.

    >>> import numpy as np
    >>> import scipy.stats as stats
    >>> import statsmodels.api as sm
    >>> lowess = sm.nonparametric.lowess
    >>> x = np.random.uniform(low = -2*np.pi, high = 2*np.pi, size=500)
    >>> y = np.sin(x) + stats.cauchy.rvs(size=len(x))
    >>> z = lowess(y, x, frac= 1./3, it=0)
    >>> w = lowess(y, x, frac=1./3)

    Non-native byte order not supportedLowess `frac` must be in the range [0,1]!Format string allocated too short, see comment in numpy.pxdunknown dtype code in numpy.pxd (%d)numpy.core.multiarray failed to import
Univariate lowess function, like in R.

References
----------
Hastie, Tibshirani, Friedman. (2009) The Elements of Statistical Learning: Data
Mining, Inference, and Prediction, Second Edition: Chapter 6.

Cleveland, W.S. (1979) "Robust Locally Weighted Regression and Smoothing
Scatterplots". Journal of the American Statistical Association 74 (368): 829-836.
ndarray is not C contiguouscalculate_residual_weightsupdate_neighborhoodcline_in_tracebackupdate_indiceslowess (line 28)resid_weightsRuntimeErrorImportErrorlast_fit_iValueErrorstd_residright_endnegativeleft_endcutpointbisquareweightsrobiterxrangereg_okradiusmedianlowess__import__doublezerosy_fitrangenumpyendogdtypedeltaarrayDTYPE__test____name____main__fracexogsumabsnpityxnkiTBuffer dtype mismatch, expected %s%s%s but got %sBuffer dtype mismatch, expected '%s' but got %s in '%s.%s'%.200s.%.200s is not a type object%.200s.%.200s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObject%s.%s size changed, may indicate binary incompatibility. Expected %zd from C header, got %zd from PyObjectDoes not understand character buffer dtype format string ('%c')too many values to unpack (expected %zd)statsmodels/nonparametric/_smoothers_lowess.c%s() got multiple values for keyword argument '%U'%.200s() keywords must be strings%s() got an unexpected keyword argument '%U'__int__ returned non-int (type %.200s).  The ability to return an instance of a strict subclass of int is deprecated, and may be removed in a future version of Python.__%.4s__ returned non-%.4s (type %.200s)value too large to convert to intUnexpected format string character: '%c'Expected a dimension of size %zu, got %zuExpected %d dimensions, got %dPython does not define a standard format string size for long double ('g')..Buffer dtype mismatch; next field is at offset %zd but %zd expectedBig-endian buffer not supported on little-endian compilerBuffer acquisition: Expected '{' after 'T'Cannot handle repeated arrays in format stringExpected a dimension of size %zu, got %dExpected a comma in format string, got '%c'Expected %d dimension(s), got %dUnexpected end of format string, expected ')'Buffer has wrong number of dimensions (expected %d, got %d)Item size of buffer (%zd byte%s) does not match size of '%s' (%zd byte%s)statsmodels/nonparametric/_smoothers_lowess.pyxstatsmodels.nonparametric._smoothers_lowess.update_neighborhoodstatsmodels.nonparametric._smoothers_lowess.update_indicesstatsmodels.nonparametric._smoothers_lowess.bisquareArgument '%.200s' has incorrect type (expected %.200s, got %.200s)%.200s() takes %.8s %zd positional argument%.1s (%zd given)statsmodels.nonparametric._smoothers_lowess.calculate_residual_weightsCannot convert %.200s to %.200sBuffer acquisition failed on assignment; and then reacquiring the old buffer failed too!statsmodels.nonparametric._smoothers_lowess.fast_array_cubestatsmodels.nonparametric._smoothers_lowess.tricubestatsmodels.nonparametric._smoothers_lowess.calculate_weightscalling %R should have returned an instance of BaseException, not %Rraise: exception class must be a subclass of BaseExceptionneed more than %zd value%.1s to unpackstatsmodels.nonparametric._smoothers_lowess.calculate_y_fitstatsmodels.nonparametric._smoothers_lowess.interpolate_skipped_fitsstatsmodels.nonparametric._smoothers_lowess.lowessstatsmodels.nonparametric._smoothers_lowesscompiletime version %s of module '%.100s' does not match runtime version %sinit statsmodels.nonparametric._smoothers_lowessà?ð¿ð?»½×Ùß|Û=@UUUUUUå?
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    The bi-square function (1 - x**2)**2.

    Used to weight the residuals in the `robustifying`
    iterations. Called by the calculate_residual_weights function.

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    x: 1-D numpy array
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        6 times the median absolute residual.

    Returns
    -------
    A 1-D numpy array of residual weights.
    
    Calculate residual weights for the next `robustifying` iteration.

    Parameters
    ----------
    y: 1-D numpy array
        The vector of actual input y-values.
    y_fit: 1-D numpy array
        The vector of fitted y-values from the current
        iteration.

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    -------
    resid_weights: 1-D numpy array
        The vector of residual weights, to be used in the
        next iteration of regressions.
    
    Update the counters of the local regression.

    Parameters
    ----------
    x: 1-D numpy array
        The vector of input x-values.
    y_fit: 1-D numpy array
        The vector of fitted y-values
    delta: float
        Indicates the range of x values within which linear
        interpolation should be used to estimate y_fit instead
        of weighted regression.
    i: indexing integer
        The index of the current point being fit.
    n: indexing integer
        The length of the input vectors, x and y.
    last_fit_i: indexing integer
        The last point at which y_fit was calculated.

    Returns
    -------
    i: indexing integer
        The next point at which to run a weighted regression.
    last_fit_i: indexing integer
        The updated last point at which y_fit was calculated

    Notes
    -----
    The relationship between the outputs is s.t. x[i+1] >
    x[last_fit_i] + delta.

    
    Find the indices bounding the k-nearest-neighbors of the current point.

    Parameters
    ----------
    x: 1-D numpy array
        The input x-values
    i: indexing integer
        The index of the point currently being fit.
    n: indexing integer
        The length of the input vectors, x and y.
    left_end: indexing integer
        The index of the left-most point in the neighborhood
        of x[i-1] (the previously-fit point).
    right_end: indexing integer
        The index of the right-most point in the neighborhood
        of x[i-1]. Non-inclusive, s.t. the neighborhood is
        x[left_end] <= x < x[right_end].
    radius: float
        The radius of the current neighborhood. The larger of
        distances between x[i] and its left-most or right-most
        neighbor.

    Returns
    -------
    left_end: indexing integer
        The index of the left-most point in the neighborhood
              of x[i] (the current point).
    right_end: indexing integer
        The index of the right-most point in the neighborhood
               of x[i]. Non-inclusive, s.t. the neighborhood is
               x[left_end] <= x < x[right_end].
    radius: float
        The radius of the current neighborhood. The larger of
        distances between x[i] and its left-most or right-most
        neighbor.
    lowess(endog, exog, frac=2.0/3.0, it=3, delta=0.0)
    LOWESS (Locally Weighted Scatterplot Smoothing)

    A lowess function that outs smoothed estimates of endog
    at the given exog values from points (exog, endog)

    Parameters
    ----------
    endog: 1-D numpy array
        The y-values of the observed points
    exog: 1-D numpy array
        The x-values of the observed points. exog has to be increasing.
    frac: float
        Between 0 and 1. The fraction of the data used
        when estimating each y-value.
    it: int
        The number of residual-based reweightings
        to perform.
    delta: float
        Distance within which to use linear-interpolation
        instead of weighted regression.

    Returns
    -------
    out: numpy array
        A numpy array with two columns. The first column
        is the sorted x values and the second column the
        associated estimated y-values.

    Notes
    -----
    This lowess function implements the algorithm given in the
    reference below using local linear estimates.

    Suppose the input data has N points. The algorithm works by
    estimating the `smooth` y_i by taking the frac*N closest points
    to (x_i,y_i) based on their x values and estimating y_i
    using a weighted linear regression. The weight for (x_j,y_j)
    is tricube function applied to |x_i-x_j|.

    If it > 1, then further weighted local linear regressions
    are performed, where the weights are the same as above
    times the _lowess_bisquare function of the residuals. Each iteration
    takes approximately the same amount of time as the original fit,
    so these iterations are expensive. They are most useful when
    the noise has extremely heavy tails, such as Cauchy noise.
    Noise with less heavy-tails, such as t-distributions with df>2,
    are less problematic. The weights downgrade the influence of
    points with large residuals. In the extreme case, points whose
    residuals are larger than 6 times the median absolute residual
    are given weight 0.

    delta can be used to save computations. For each x_i, regressions
    are skipped for points closer than delta. The next regression is
    fit for the farthest point within delta of x_i and all points in
    between are estimated by linearly interpolating between the two
    regression fits.

    Judicious choice of delta can cut computation time considerably
    for large data (N > 5000). A good choice is delta = 0.01 *
    range(exog).

    Some experimentation is likely required to find a good
    choice of frac and iter for a particular dataset.

    References
    ----------
    Cleveland, W.S. (1979) "Robust Locally Weighted Regression
    and Smoothing Scatterplots". Journal of the American Statistical
    Association 74 (368): 829-836.

    Examples
    --------
    The below allows a comparison between how different the fits from
    lowess for different values of frac can be.

    >>> import numpy as np
    >>> import statsmodels.api as sm
    >>> lowess = sm.nonparametric.lowess
    >>> x = np.random.uniform(low = -2*np.pi, high = 2*np.pi, size=500)
    >>> y = np.sin(x) + np.random.normal(size=len(x))
    >>> z = lowess(y, x)
    >>> w = lowess(y, x, frac=1./3)

    This gives a similar comparison for when it is 0 vs not.

    >>> import numpy as np
    >>> import scipy.stats as stats
    >>> import statsmodels.api as sm
    >>> lowess = sm.nonparametric.lowess
    >>> x = np.random.uniform(low = -2*np.pi, high = 2*np.pi, size=500)
    >>> y = np.sin(x) + stats.cauchy.rvs(size=len(x))
    >>> z = lowess(y, x, frac= 1./3, it=0)
    >>> w = lowess(y, x, frac=1./3)

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