从 pandas 文件中绘制多个高斯 [英] Ploting multiple Gaussians from pandas file

问题描述

我正在尝试从这种类型的数据框在一个具有不同高度，宽度和中心的绘图上绘制多个高斯:

<身体>

高(y)	fwhM(width)	中心(x)
24.122348	1.827472	98
24.828252	4.333549	186
26.810812	1.728494	276
25.997897	1.882424	373
24.503944	2.222210	471
27.488572	1.750039	604
31.556823	3.844592	683
27.920951	0.891394	792
27.009054	1.917744	897

有什么想法吗?

解决方案

我们将重复使用

中定义的高斯绘图仪

• ---

  编辑

  由于问题现在要求使用不同的分布，因此可以使用以下方法在 create (和 create )方法中调整代码，以获取不同类型的分布:

    def create(self，dim = 1，fwhm = 3，center = None):"在一定宽度的中心上生成高斯分布."中心=中心，如果中心不是其他则self.center [:dim]distance = sum((ax_center的ax(ax -ax_center)，zip中的ax(center，self.axis))分布= sps.beta.pdf(距离/最大(距离)，a = 3，b = 100)收益分配 

  sps.beta 来自 import scipy.stats as sps ，并且也可以通过伽马分布进行更改.例如 distribution = sps.gamma.pdf(distance，10，40).

  请注意，距离不再是平方，并且可以将参数 fwhm 替换为分布所需的参数.

  I am trying to plot multiple gaussians on one plot with different heights, widths and centers from this type of dataframe:

  hight(y)	fwhM(width)	centers(x)
  24.122348	1.827472	98
  24.828252	4.333549	186
  26.810812	1.728494	276
  25.997897	1.882424	373
  24.503944	2.222210	471
  27.488572	1.750039	604
  31.556823	3.844592	683
  27.920951	0.891394	792
  27.009054	1.917744	897

  Any idea on how to go about it?

  解决方案

  We will reuse the Gaussian plotter as defined in

  • Creating gaussians of fixed width and std

  (The code is repeated here)

  Data

  The following code generates the above dataframe.

  data = [
      (24.122348, 1.827472, 98),
      (24.828252, 4.333549, 186),
      (26.810812, 1.728494, 276),
      (25.997897, 1.882424, 373),
      (24.503944, 2.222210, 471),
      (27.488572, 1.750039, 604),
      (31.556823, 3.844592, 683),
      (27.920951, 0.891394, 792),
      (27.009054, 1.917744, 897),
  ]
  
  df = pd.DataFrame(data, columns=["height", "fwhm", "center"])
  

  Gaussian

  Taken from the reference post above.

  
  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 or np.array([self.center]).T).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)
          ax.plot(distribution)
  
          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
  

  Solution

  Since it is unclear to me how you want to the Gaussian distributions to interact when they are in part of multiple widths, I will assume that you want the maximum value.

  Then the main logic is that we can now generate a unique Gaussian distribution for every center with given full width half maximum (fwhm), and take the maximum of all the distrubutions.

  distribution = np.zeros((1200,))
  
  df = pd.DataFrame(data, columns=["height", "fwhm", "center"])
  gaussian = Gaussian(size=distribution.shape)
  
  for idx, row in df.iterrows():
      distribution = np.maximum(distribution, gaussian.create(fwhm=row.fwhm, center=[row.center]))
  
  gaussian.plot(distribution, show=True)
  

  Result

  ---

  Edit

  Since the question now asks for a different distribution, you can adjust the code in the create (and creates) method with the following to get different types of distributions:

  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) for ax_center, ax in zip(center, self.axis))
      distribution = sps.beta.pdf(distance / max(distance), a=3, b=100)
      return distribution
  

  Where sps.beta comes from import scipy.stats as sps, and can be changed with a gamma distribution as well. e.g. distribution = sps.gamma.pdf(distance, 10, 40).

  Note that the distance is no longer squared, and that the argument fwhm, could be replaced by the parameters required for the distribution.

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