numpy:变形的数组行为异常

结果发现我的整形操作并没有像我想象的那样操纵数组。以下函数将我的原始数组x重新整形为扁平形式(有两个轴),然后正确地恢复为非扁平形式(有三个轴)。我添加了评论和测试,以确保一切都如预期的那样:

from math import floor

def flatten(df, run_tests=True):
  '''
  df is a numpy array with the following three axes:
    df.shape[0] = the index of a vertex
    df.shape[1] = the index of a time stamp
    df.shape[2] = the index of a dimension (x, y, z)
  So df[1][0][2] is the value for the 1st vertex (0-based) at time 0 in dimension 2 (z).
  To flatten this dataframe will mean to push the data into shape:
    flattened.shape[0] = time index
    flattened.shape[1] = [vertex_index*3] + dimension_vertex
  So flattened[1][3] will be the 3rd dimension of the 1st index (0-based) at time 1. 
  '''
  if run_tests:
    assert df.shape == X.shape and np.all(df == X)

  # reshape X such that flattened.shape = time, [x0, y0, z0, x1, y1, z1, ... xn-1, yn-1, zn-1]
  flattened = X.swapaxes(0, 1).reshape( (df.shape[1], df.shape[0] * df.shape[2]), order='C' )

  if run_tests: # switch to false to skip tests
    for idx, i in enumerate(df):
      for jdx, j in enumerate(df[idx]):
        for kdx, k in enumerate(df[idx][jdx]):
          assert flattened[jdx][ (idx*df.shape[2]) + kdx ] == df[idx][jdx][kdx]

  return flattened

并解开扁平数据:

def unflatten(df, run_tests=True):
  '''
  df is a numpy array with the following two axes:
    df.shape[0] = time index
    df.shape[1] = [vertex_index*3] + dimension_vertex

  To unflatten this dataframe will mean to push the data into shape:
    unflattened.shape[0] = the index of a vertex
    unflattened.shape[1] = the index of a time stamp
    unflattened.shape[2] = the index of a dimension (x, y, z)

  So df[2][4] == unflattened[1][2][0]
  '''
  if run_tests:
    assert (len(df.shape) == 2) and (df.shape[1] == X.shape[0] * X.shape[2])

  unflattened = np.zeros(( X.shape[0], df.shape[0], X.shape[2] ))

  for idx, i in enumerate(df):
    for jdx, j in enumerate(df[idx]):
      kdx = floor(jdx / 3)
      ldx = jdx % 3
      unflattened[kdx][idx][ldx] = df[idx][jdx]

  if run_tests: # set to false to skip tests
    for idx, i in enumerate(unflattened):
      for jdx, j in enumerate(unflattened[idx]):
        for kdx, k in enumerate(unflattened[idx][jdx]):
          assert( unflattened[idx][jdx][kdx] == X[idx][jdx][kdx] )

  return unflattened

然后可视化:

import mpl_toolkits.mplot3d.axes3d as p3
from mpl_toolkits.mplot3d.art3d import juggle_axes
import matplotlib.pyplot as plt
from IPython.display import HTML
from matplotlib import animation
import matplotlib

# ask matplotlib to plot up to 2^128 frames in animations
matplotlib.rcParams['animation.embed_limit'] = 2**128

def update_points(time, points, df):
  points._offsets3d = juggle_axes(df[:,time,0], df[:,time,1], df[:,time,2], 'z')

def get_plot(df, lim=1, frames=200, duration=45):
  if len(df.shape) == 2: df = unflatten(df)
  fig = plt.figure()
  ax = p3.Axes3D(fig)
  ax.set_xlim(-lim, lim)
  ax.set_ylim(-lim, lim)
  ax.set_zlim(-lim, lim)
  points = ax.scatter(df[:,0,0], df[:,0,1], df[:,0,2], depthshade=False) # x,y,z vals
  return animation.FuncAnimation(fig,
    update_points,
    frames,
    interval=duration,
    fargs=(points, df),
    blit=False  
  ).to_jshtml()

HTML(get_plot(unflat, frames=200))

这使我可以毫无问题地切割时间轴:

flat = flatten(X)
unflat = unflatten(flat)

HTML(get_plot(unflat, frames=200))
HTML(get_plot(flat[:20], frames=20))
HTML(get_plot(unflat[:,:20,:], frames=20))