创建固定宽度和标准的高斯

如何解决创建固定宽度和标准的高斯

我试图使 25.2 以上的每个点成为 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。

解决方法

关于如何为任意数量的轴和数量的中心位置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 表示维数（轴）。
• fwhm full width half maximum（估计高斯分布的宽度。）
• centers 一个 np.array 或 list 个索引，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,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,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,c=[0,1],cmap=mpl_cm.get_cmap('jet'))
        img.set_visible = False
        fig.colorbar(img)

        ax.scatter(x,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，下一行将崩溃。为了获得 2 的宽度，值 fwhm 被设置为 2，但您可以更改它直到获得您想要的宽度，或者使用 Finding the full width half maximum of a peak。