创建固定宽度和标准的高斯

Question

我试图使高于 25.2 的每个点都成为 x 轴上宽度为 2 的高斯峰。 enter image description here

不太清楚如何在 python 中生成高斯曲线。

Answer 1

关于如何为任意数量的轴和中心位置数量生成高斯分布的完整示例。它需要包matplotlib、scipy 和numpy。

模块可以通过以下方式控制：

• dim 表示维度（轴）的数量。
• fwhmfull width half maximum（估计高斯分布的宽度。）
• centers 一个 np.array 或 list 的索引，它们是高斯​​分布的中心。

import matplotlib.cm as mpl_cm
import matplotlib.colors as mpl_colors
import matplotlib.pyplot as plt
import numpy as np

from scipy.spatial.distance import cdist


class Gaussian:
    def __init__(self, size):
        self.size = size
        self.center = np.array(self.size) / 2
        self.axis = self._calculate_axis()

    def _calculate_axis(self):
        """
            Generate a list of rows, columns over multiple axis.

            Example:
                Input: size=(5, 3)
                Output: [array([0, 1, 2, 3, 4]), array([[0], [1], [2]])]
        """
        axis = [np.arange(size).reshape(-1, *np.ones(idx, dtype=np.uint8))
                for idx, size in enumerate(self.size)]
        return axis

    def update_size(self, size):
        """ Update the size and calculate new centers and axis.  """
        self.size = size
        self.center = np.array(self.size) / 2
        self.axis = self._calculate_axis()

    def create(self, dim=1, fwhm=3, center=None):
        """ Generate a gaussian distribution on the center of a certain width.  """
        center = center if center is not None else self.center[:dim]
        distance = sum((ax - ax_center) ** 2 for ax_center, ax in zip(center, self.axis))
        distribution = np.exp(-4 * np.log(2) * distance / fwhm ** 2)
        return distribution

    def creates(self, dim=2, fwhm=3, centers: np.ndarray = (None,)):
        """ Combines multiple gaussian distributions based on multiple centers.  """
        centers = np.array(centers).T
        indices = np.indices(self.size).reshape(dim, -1).T

        distance = np.min(cdist(indices, centers, metric='euclidean'), axis=1)
        distance = np.power(distance.reshape(self.size), 2)

        distribution = np.exp(-4 * np.log(2) * distance / fwhm ** 2)
        return distribution

    @staticmethod
    def plot(distribution, show=True):
        """ Plotter, in case you do not know the dimensions of your distribution, or want the same interface.  """
        if len(distribution.shape) == 1:
            return Gaussian.plot1d(distribution, show)
        if len(distribution.shape) == 2:
            return Gaussian.plot2d(distribution, show)
        if len(distribution.shape) == 3:
            return Gaussian.plot3d(distribution, show)
        raise ValueError(f"Trying to plot {len(distribution.shape)}-dimensional data, "
                         f"Only 1D, 2D, and 3D distributions are valid.")

    @staticmethod
    def plot1d(distribution, show=True, vmin=None, vmax=None, cmap=None):
        norm = mpl_colors.Normalize(
                vmin=vmin if vmin is not None else distribution.min(),
                vmax=vmax if vmin is not None else distribution.max()
        )
        cmap = mpl_cm.ScalarMappable(norm=norm, cmap=cmap or mpl_cm.get_cmap('jet'))
        cmap.set_array(distribution)
        c = [cmap.to_rgba(value) for value in distribution]  # defines the color

        fig, ax = plt.subplots()
        ax.scatter(np.arange(len(distribution)), distribution, c=c)
        fig.colorbar(cmap)
        if show: plt.show()
        return fig

    @staticmethod
    def plot2d(distribution, show=True):
        fig, ax = plt.subplots()
        img = ax.imshow(distribution, cmap='jet')
        fig.colorbar(img)
        if show: plt.show()
        return fig

    @staticmethod
    def plot3d(distribution, show=True):
        m, n, c = distribution.shape
        x, y, z = np.mgrid[:m, :n, :c]
        out = np.column_stack((x.ravel(), y.ravel(), z.ravel(), distribution.ravel()))
        x, y, z, values = np.array(list(zip(*out)))

        fig = plt.figure()
        ax = fig.add_subplot(111, projection='3d')

        # Standalone colorbar, directly creating colorbar on fig results in strange artifacts.
        img = ax.scatter([0, 0], [0, 0], [0, 0], c=[0, 1], cmap=mpl_cm.get_cmap('jet'))
        img.set_visible = False
        fig.colorbar(img)

        ax.scatter(x, y, z, c=values, cmap=mpl_cm.get_cmap('jet'))
        if show: plt.show()
        return fig

示例

gaussian = Gaussian(size=(20,))
dist = gaussian.create(dim=1, centers=(1,)
gaussian.plot1d(dist, show=True)

你的问题

为了获得适合您问题的解决方案，以下代码将起作用：

import numpy as np

arr = np.random.randint(0, 28, (25,))

gaussian = Gaussian(size=arr.shape)
centers = np.where(arr > 25.2)

distribution = gaussian.creates(dim=len(arr.shape), fwhm=2, centers=centers)
gaussian.plot(distribution, show=True)

为此，中心由条件arr > 25.2 确定。请注意，如果没有值，则下一行将崩溃。为了获得 2 的宽度，将值 fwhm 设置为 2，但您可以更改它直到获得所需的宽度，或使用 Finding the full width half maximum of a peak。