如何绘制不连接所有点的样条

Question

我正在尝试用样条曲线通过点绘制大量数据，它应该看起来像这样。

但是当我尝试用情节来做到这一点时，样条曲线坚持要遍历所有像这样的点

当第一张图片只是数据点，第二张是样条线时。

我尝试的代码是

dates = [dates_arr]
x = dates.strftime("%Y-%m-%d")
y = [data_points]
xy_data = go.Scatter(x=x, y=y, mode='markers', marker=dict(size=4), 
name='AAPL')

mov_avg = go.Scatter(x=x, y=y, name="spline",text= 
["spline"],hoverinfo='text+name',line_shape='spline', line_smoothing = 1.3)    

data = [xy_data, mov_avg]  

py.iplot(data, filename='Spline fit')

#################################
first_plot_url = py.plot(data, filename='apple stock moving average', 
auto_open=True, )

有人知道吗？

Answer 1

在您的第一张图片中，样条曲线是所有数据点的近似值。在您的 sn-p 中，spline 是一个属性，设置为您的行 数据点的图形表示。这些是非常不同的事情。为了完成您的任务，您应该仔细查看用户 np8 和 Matthew Drury 在 other SO posts 和 github 上的贡献。您还应该仔细查看如何计算不同的样条曲线。下图估计了natural cubic spline，由下面名为Snippet 2: The whole thing 的代码示例生成。它相当大，但这主要是因为来自Python natural smoothing splines 的函数get_natural_cubic_spline_model。情节部分简单地遵循这个逻辑：

片段 1：只关注情节部分

# data points
points = go.Scatter(
    x = x,
    y = y,
    mode = 'markers',
    name = 'iris')

# spline
line = go.Scatter(
    x = df_spline['x'],
    y = df_spline['y_est'],
    mode = 'lines',
    name = 'spline')

# gather data
data=[points, line]

# build figure
fig=go.Figure(data)

# plot
fig.show()

剧情：

片段 2： 整件事

# imports
import plotly.express as px
import plotly.graph_objs as go
import numpy as np
import pandas as pd
from sklearn.base import BaseEstimator, TransformerMixin
from sklearn.linear_model import LinearRegression
from sklearn.pipeline import Pipeline

# sample data set
iris = px.data.iris() # iris is a pandas DataFrame
x=iris['sepal_length']
y=iris['sepal_width']

# spline using function from https://stackoverflow.com/questions/51321100/python-natural-smoothing-splines

def get_natural_cubic_spline_model(x, y, minval=None, maxval=None, n_knots=None, knots=None):
    """
    Get a natural cubic spline model for the data.

    For the knots, give (a) `knots` (as an array) or (b) minval, maxval and n_knots.

    If the knots are not directly specified, the resulting knots are equally
    space within the *interior* of (max, min).  That is, the endpoints are
    *not* included as knots.

    Parameters
    ----------
    x: np.array of float
        The input data
    y: np.array of float
        The outpur data
    minval: float 
        Minimum of interval containing the knots.
    maxval: float 
        Maximum of the interval containing the knots.
    n_knots: positive integer 
        The number of knots to create.
    knots: array or list of floats 
        The knots.

    Returns
    --------
    model: a model object
        The returned model will have following method:
        - predict(x):
            x is a numpy array. This will return the predicted y-values.
    """

    if knots:
        spline = NaturalCubicSpline(knots=knots)
    else:
        spline = NaturalCubicSpline(max=maxval, min=minval, n_knots=n_knots)

    p = Pipeline([
        ('nat_cubic', spline),
        ('regression', LinearRegression(fit_intercept=True))
    ])

    p.fit(x, y)

    return p


class AbstractSpline(BaseEstimator, TransformerMixin):
    """Base class for all spline basis expansions."""

    def __init__(self, max=None, min=None, n_knots=None, n_params=None, knots=None):
        if knots is None:
            if not n_knots:
                n_knots = self._compute_n_knots(n_params)
            knots = np.linspace(min, max, num=(n_knots + 2))[1:-1]
            max, min = np.max(knots), np.min(knots)
        self.knots = np.asarray(knots)

    @property
    def n_knots(self):
        return len(self.knots)

    def fit(self, *args, **kwargs):
        return self


class NaturalCubicSpline(AbstractSpline):
    """Apply a natural cubic basis expansion to an array.
    The features created with this basis expansion can be used to fit a
    piecewise cubic function under the constraint that the fitted curve is
    linear *outside* the range of the knots..  The fitted curve is continuously
    differentiable to the second order at all of the knots.
    This transformer can be created in two ways:
      - By specifying the maximum, minimum, and number of knots.
      - By specifying the cutpoints directly.  

    If the knots are not directly specified, the resulting knots are equally
    space within the *interior* of (max, min).  That is, the endpoints are
    *not* included as knots.
    Parameters
    ----------
    min: float 
        Minimum of interval containing the knots.
    max: float 
        Maximum of the interval containing the knots.
    n_knots: positive integer 
        The number of knots to create.
    knots: array or list of floats 
        The knots.
    """

    def _compute_n_knots(self, n_params):
        return n_params

    @property
    def n_params(self):
        return self.n_knots - 1

    def transform(self, X, **transform_params):
        X_spl = self._transform_array(X)
        if isinstance(X, pd.Series):
            col_names = self._make_names(X)
            X_spl = pd.DataFrame(X_spl, columns=col_names, index=X.index)
        return X_spl

    def _make_names(self, X):
        first_name = "{}_spline_linear".format(X.name)
        rest_names = ["{}_spline_{}".format(X.name, idx)
                      for idx in range(self.n_knots - 2)]
        return [first_name] + rest_names

    def _transform_array(self, X, **transform_params):
        X = X.squeeze()
        try:
            X_spl = np.zeros((X.shape[0], self.n_knots - 1))
        except IndexError: # For arrays with only one element
            X_spl = np.zeros((1, self.n_knots - 1))
        X_spl[:, 0] = X.squeeze()

        def d(knot_idx, x):
            def ppart(t): return np.maximum(0, t)

            def cube(t): return t*t*t
            numerator = (cube(ppart(x - self.knots[knot_idx]))
                         - cube(ppart(x - self.knots[self.n_knots - 1])))
            denominator = self.knots[self.n_knots - 1] - self.knots[knot_idx]
            return numerator / denominator

        for i in range(0, self.n_knots - 2):
            X_spl[:, i+1] = (d(i, X) - d(self.n_knots - 2, X)).squeeze()
        return X_spl

# spline calculations
m1=get_natural_cubic_spline_model(x, y, minval=min(x), maxval=max(x), n_knots=6)
y_est_m1=m1.predict(x)

# gather results and sort them so that the line is not messed up
df_spline=pd.DataFrame({'x':x,
                       'y':y,
                       'y_est':m1.predict(x)})
df_spline=df_spline.sort_values(by=['x'])

### PLOTLY ###
# data source
points = go.Scatter(
    x = x,
    y = y,
    mode = 'markers',
    name = 'iris')

# spline
line = go.Scatter(
    x = df_spline['x'],
    y = df_spline['y_est'],
    mode = 'lines',
    name = 'spline')

# gather data
data=[points, line]

# build figure
fig=go.Figure(data)

# plot
fig.show()