如何计算 python 中两个二面角（周期性）角分布之间的距离？
How to calculate distance between two dihedral (periodic) angles distributions in python?
在计算二面角的两个分布之间的地球移动距离（EMD：https://en.wikipedia.org/wiki/Earth_mover%27s_distance）（也称为 Wasserstein 度量）时，我正在寻找处理周期性的正确和最直接的方法。
根据 IUPAC 二面角定义，我得到的二面角范围是 [-180, 180]。
我不确定如何修改输入以使 EMD/Wasserstein 有意义。我觉得我可以在几个不同的修改输入和 select 最小值上计算 EMD，以避免周期性边界问题。您能提出一些想法吗？
以下是我的一些输入示例。对于它们中的每一个，我想使用一个单一的过程来获得真实的、最小的 EMD 距离
成对分布。
提前感谢您提出的任何意见:)
这是我目前使用的代码
from pyemd import emd
from scipy.stats import wasserstein_distance
from scipy.spatial.distance import cdist
bw = 2 # bandwidth used to prepare the data (Y1 .. Yn)
# Wasserstein distance that is independent of bandwidth choice but does not actually work with frequencies ?
wass_dist = bw * wasserstein_distance(Y1, Y2)
# EMD distance that is independent of bandwidth choice but does not take periodic boundaries into account
bins_dihedrals_reshape = np.array(X).reshape(-1,1)
bins_dihedrals_dist_matrix = cdist(bins_dihedrals_reshape, bins_dihedrals_reshape)
emd_dist = bw * emd(Y1, Y2, bins_dihedrals_dist_matrix)
示例：比较蓝色和橙色（Y1 和 Y2）
X= [-179.0,-177.0,-175.0,-173.0,-171.0,-169.0,-167.0,-165.0,-163.0,-161.0,-159.0,-157.0,-155.0,-153.0,-151.0,-149.0,-147.0,-145.0,-143.0,-141.0,-139.0,-137.0,-135.0,-133.0,-131.0,-129.0,-127.0,-125.0,-123.0,-121.0,-119.0,-117.0,-115.0,-113.0,-111.0,-109.0,-107.0,-105.0,-103.0,-101.0,-99.0,-97.0,-95.0,-93.0,-91.0,-89.0,-87.0,-85.0,-83.0,-81.0,-79.0,-77.0,-75.0,-73.0,-71.0,-69.0,-67.0,-65.0,-63.0,-61.0,-59.0,-57.0,-55.0,-53.0,-51.0,-49.0,-47.0,-45.0,-43.0,-41.0,-39.0,-37.0,-35.0,-33.0,-31.0,-29.0,-27.0,-25.0,-23.0,-21.0,-19.0,-17.0,-15.0,-13.0,-11.0,-9.0,-7.0,-5.0,-3.0,-1.0,1.0,3.0,5.0,7.0,9.0,11.0,13.0,15.0,17.0,19.0,21.0,23.0,25.0,27.0,29.0,31.0,33.0,35.0,37.0,39.0,41.0,43.0,45.0,47.0,49.0,51.0,53.0,55.0,57.0,59.0,61.0,63.0,65.0,67.0,69.0,71.0,73.0,75.0,77.0,79.0,81.0,83.0,85.0,87.0,89.0,91.0,93.0,95.0,97.0,99.0,101.0,103.0,105.0,107.0,109.0,111.0,113.0,115.0,117.0,119.0,121.0,123.0,125.0,127.0,129.0,131.0,133.0,135.0,137.0,139.0,141.0,143.0,145.0,147.0,149.0,151.0,153.0,155.0,157.0,159.0,161.0,163.0,165.0,167.0,169.0,171.0,173.0,175.0,177.0,179.0]
Y1= [0.00639872025594881,0.006998600279944011,0.010597880423915218,0.011097780443911218,0.015096980603879224,0.017096580683863227,0.021195760847830435,0.021695660867826434,0.02449510097980404,0.021495700859828035,0.01999600079984003,0.022895420915816835,0.01879624075184963,0.016996600679864027,0.015396920615876825,0.016896620675864827,0.013897220555888823,0.009998000399920015,0.008298340331933614,0.00599880023995201,0.004499100179964007,0.0028994201159768048,0.0016996600679864027,0.0008998200359928015,0.0005998800239952009,0.0003999200159968006,0.0,0.0,0.0001999600079984003,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,9.998000399920016e-05,0.0001999600079984003,0.00029994001199760045,0.0006998600279944011,0.001299740051989602,0.0023995200959808036,0.001999600079984003,0.0034993001399720057,0.0030993801239752048,0.006998600279944011,0.00629874025194961,0.007798440311937612,0.008798240351929614,0.009898020395920816,0.011297740451909618,0.01269746050789842,0.011897620475904818,0.015596880623875225,0.01269746050789842,0.009398120375924815,0.010497900419916016,0.009498100379924015,0.008098380323935212,0.007298540291941612,0.008098380323935212,0.006898620275944811,0.00609878024395121]
Y2= [0.006998600279944011,0.007198560287942412,0.007598480303939212,0.009398120375924815,0.009798040391921616,0.010997800439912017,0.011197760447910418,0.01289742051589682,0.013697260547890422,0.015396920615876825,0.01259748050389922,0.010797840431913617,0.010497900419916016,0.009898020395920816,0.008198360327934412,0.007098580283943211,0.007198560287942412,0.0057988402319536095,0.004599080183963208,0.002999400119976005,0.001899620075984803,0.0016996600679864027,0.0008998200359928015,0.0006998600279944011,0.0005998800239952009,0.0003999200159968006,0.00029994001199760045,9.998000399920016e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,9.998000399920016e-05,0.0,9.998000399920016e-05,9.998000399920016e-05,0.00029994001199760045,0.0001999600079984003,0.0004999000199960008,0.0009998000399920016,0.0015996800639872025,0.0021995600879824036,0.0030993801239752048,0.005298940211957609,0.008698260347930415,0.008998200359928014,0.011397720455908818,0.013197360527894421,0.014997000599880024,0.022295540891821636,0.021795640871825634,0.023495300939812037,0.01969606078784243,0.022695460907818436,0.022395520895820836,0.021595680863827234,0.016596680663867228,0.016796640671865627,0.016196760647870425,0.011897620475904818,0.010697860427914417,0.010597880423915218]
考虑使用 scipy.stats.wasserstein_distance
https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.wasserstein_distance.html
从上页给出的功能描述：
scipy.stats.wasserstein_distance(u_values, v_values, u_weights=None, v_weights=None):
Compute the first Wasserstein distance between two 1D distributions.
This distance is also known as the earth mover’s distance since it
can be seen as the minimum amount of “work” required to transform u
into v, where “work” is measured as the amount of distribution
weight that must be moved, multiplied by the distance it has to be
moved.
现在可以了。我使用 pyemd 并创建了一个周期性距离矩阵。
from pyemd import emd
from scipy.stats import wasserstein_distance
from scipy.spatial.distance import cdist
X= [-179.0,-177.0,-175.0,-173.0,-171.0,-169.0,-167.0,-165.0,-163.0,-161.0,-159.0,-157.0,-155.0,-153.0,-151.0,-149.0,-147.0,-145.0,-143.0,-141.0,-139.0,-137.0,-135.0,-133.0,-131.0,-129.0,-127.0,-125.0,-123.0,-121.0,-119.0,-117.0,-115.0,-113.0,-111.0,-109.0,-107.0,-105.0,-103.0,-101.0,-99.0,-97.0,-95.0,-93.0,-91.0,-89.0,-87.0,-85.0,-83.0,-81.0,-79.0,-77.0,-75.0,-73.0,-71.0,-69.0,-67.0,-65.0,-63.0,-61.0,-59.0,-57.0,-55.0,-53.0,-51.0,-49.0,-47.0,-45.0,-43.0,-41.0,-39.0,-37.0,-35.0,-33.0,-31.0,-29.0,-27.0,-25.0,-23.0,-21.0,-19.0,-17.0,-15.0,-13.0,-11.0,-9.0,-7.0,-5.0,-3.0,-1.0,1.0,3.0,5.0,7.0,9.0,11.0,13.0,15.0,17.0,19.0,21.0,23.0,25.0,27.0,29.0,31.0,33.0,35.0,37.0,39.0,41.0,43.0,45.0,47.0,49.0,51.0,53.0,55.0,57.0,59.0,61.0,63.0,65.0,67.0,69.0,71.0,73.0,75.0,77.0,79.0,81.0,83.0,85.0,87.0,89.0,91.0,93.0,95.0,97.0,99.0,101.0,103.0,105.0,107.0,109.0,111.0,113.0,115.0,117.0,119.0,121.0,123.0,125.0,127.0,129.0,131.0,133.0,135.0,137.0,139.0,141.0,143.0,145.0,147.0,149.0,151.0,153.0,155.0,157.0,159.0,161.0,163.0,165.0,167.0,169.0,171.0,173.0,175.0,177.0,179.0]
Y1= [0.00639872025594881,0.006998600279944011,0.010597880423915218,0.011097780443911218,0.015096980603879224,0.017096580683863227,0.021195760847830435,0.021695660867826434,0.02449510097980404,0.021495700859828035,0.01999600079984003,0.022895420915816835,0.01879624075184963,0.016996600679864027,0.015396920615876825,0.016896620675864827,0.013897220555888823,0.009998000399920015,0.008298340331933614,0.00599880023995201,0.004499100179964007,0.0028994201159768048,0.0016996600679864027,0.0008998200359928015,0.0005998800239952009,0.0003999200159968006,0.0,0.0,0.0001999600079984003,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,9.998000399920016e-05,0.0001999600079984003,0.00029994001199760045,0.0006998600279944011,0.001299740051989602,0.0023995200959808036,0.001999600079984003,0.0034993001399720057,0.0030993801239752048,0.006998600279944011,0.00629874025194961,0.007798440311937612,0.008798240351929614,0.009898020395920816,0.011297740451909618,0.01269746050789842,0.011897620475904818,0.015596880623875225,0.01269746050789842,0.009398120375924815,0.010497900419916016,0.009498100379924015,0.008098380323935212,0.007298540291941612,0.008098380323935212,0.006898620275944811,0.00609878024395121]
Y2= [0.006998600279944011,0.007198560287942412,0.007598480303939212,0.009398120375924815,0.009798040391921616,0.010997800439912017,0.011197760447910418,0.01289742051589682,0.013697260547890422,0.015396920615876825,0.01259748050389922,0.010797840431913617,0.010497900419916016,0.009898020395920816,0.008198360327934412,0.007098580283943211,0.007198560287942412,0.0057988402319536095,0.004599080183963208,0.002999400119976005,0.001899620075984803,0.0016996600679864027,0.0008998200359928015,0.0006998600279944011,0.0005998800239952009,0.0003999200159968006,0.00029994001199760045,9.998000399920016e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,9.998000399920016e-05,0.0,9.998000399920016e-05,9.998000399920016e-05,0.00029994001199760045,0.0001999600079984003,0.0004999000199960008,0.0009998000399920016,0.0015996800639872025,0.0021995600879824036,0.0030993801239752048,0.005298940211957609,0.008698260347930415,0.008998200359928014,0.011397720455908818,0.013197360527894421,0.014997000599880024,0.022295540891821636,0.021795640871825634,0.023495300939812037,0.01969606078784243,0.022695460907818436,0.022395520895820836,0.021595680863827234,0.016596680663867228,0.016796640671865627,0.016196760647870425,0.011897620475904818,0.010697860427914417,0.010597880423915218]
bw = 2 # bandwidth used to prepare the data (Y1 .. Yn)
bins_dihedrals = np.arange(-180, 180+bw_dihedrals, bw_dihedrals)
bins_dihedrals_reshape = np.array(bins_dihedrals).reshape(-1,1)
bins_dihedrals_dist_matrix = cdist(bins_dihedrals_reshape, bins_dihedrals_reshape) # 'classical' distance matrix
bins_dihedrals_dist_matrix_periodoc = np.where(bins_dihedrals_dist_matrix > max(bins_dihedrals_dist_matrix[0])/2, max(bins_dihedrals_dist_matrix[0])-bins_dihedrals_dist_matrix, bins_dihedrals_dist_matrix) # modify distance matrix for periodicity
emd_dist = bw * emd(Y1, Y2, bins_dihedrals_dist_matrix_periodic)
在计算二面角的两个分布之间的地球移动距离（EMD：https://en.wikipedia.org/wiki/Earth_mover%27s_distance）（也称为 Wasserstein 度量）时，我正在寻找处理周期性的正确和最直接的方法。
根据 IUPAC 二面角定义，我得到的二面角范围是 [-180, 180]。
我不确定如何修改输入以使 EMD/Wasserstein 有意义。我觉得我可以在几个不同的修改输入和 select 最小值上计算 EMD，以避免周期性边界问题。您能提出一些想法吗？
以下是我的一些输入示例。对于它们中的每一个，我想使用一个单一的过程来获得真实的、最小的 EMD 距离 成对分布。
提前感谢您提出的任何意见:)
这是我目前使用的代码
from pyemd import emd
from scipy.stats import wasserstein_distance
from scipy.spatial.distance import cdist
bw = 2 # bandwidth used to prepare the data (Y1 .. Yn)
# Wasserstein distance that is independent of bandwidth choice but does not actually work with frequencies ?
wass_dist = bw * wasserstein_distance(Y1, Y2)
# EMD distance that is independent of bandwidth choice but does not take periodic boundaries into account
bins_dihedrals_reshape = np.array(X).reshape(-1,1)
bins_dihedrals_dist_matrix = cdist(bins_dihedrals_reshape, bins_dihedrals_reshape)
emd_dist = bw * emd(Y1, Y2, bins_dihedrals_dist_matrix)
示例：比较蓝色和橙色（Y1 和 Y2）
X= [-179.0,-177.0,-175.0,-173.0,-171.0,-169.0,-167.0,-165.0,-163.0,-161.0,-159.0,-157.0,-155.0,-153.0,-151.0,-149.0,-147.0,-145.0,-143.0,-141.0,-139.0,-137.0,-135.0,-133.0,-131.0,-129.0,-127.0,-125.0,-123.0,-121.0,-119.0,-117.0,-115.0,-113.0,-111.0,-109.0,-107.0,-105.0,-103.0,-101.0,-99.0,-97.0,-95.0,-93.0,-91.0,-89.0,-87.0,-85.0,-83.0,-81.0,-79.0,-77.0,-75.0,-73.0,-71.0,-69.0,-67.0,-65.0,-63.0,-61.0,-59.0,-57.0,-55.0,-53.0,-51.0,-49.0,-47.0,-45.0,-43.0,-41.0,-39.0,-37.0,-35.0,-33.0,-31.0,-29.0,-27.0,-25.0,-23.0,-21.0,-19.0,-17.0,-15.0,-13.0,-11.0,-9.0,-7.0,-5.0,-3.0,-1.0,1.0,3.0,5.0,7.0,9.0,11.0,13.0,15.0,17.0,19.0,21.0,23.0,25.0,27.0,29.0,31.0,33.0,35.0,37.0,39.0,41.0,43.0,45.0,47.0,49.0,51.0,53.0,55.0,57.0,59.0,61.0,63.0,65.0,67.0,69.0,71.0,73.0,75.0,77.0,79.0,81.0,83.0,85.0,87.0,89.0,91.0,93.0,95.0,97.0,99.0,101.0,103.0,105.0,107.0,109.0,111.0,113.0,115.0,117.0,119.0,121.0,123.0,125.0,127.0,129.0,131.0,133.0,135.0,137.0,139.0,141.0,143.0,145.0,147.0,149.0,151.0,153.0,155.0,157.0,159.0,161.0,163.0,165.0,167.0,169.0,171.0,173.0,175.0,177.0,179.0]
Y1= [0.00639872025594881,0.006998600279944011,0.010597880423915218,0.011097780443911218,0.015096980603879224,0.017096580683863227,0.021195760847830435,0.021695660867826434,0.02449510097980404,0.021495700859828035,0.01999600079984003,0.022895420915816835,0.01879624075184963,0.016996600679864027,0.015396920615876825,0.016896620675864827,0.013897220555888823,0.009998000399920015,0.008298340331933614,0.00599880023995201,0.004499100179964007,0.0028994201159768048,0.0016996600679864027,0.0008998200359928015,0.0005998800239952009,0.0003999200159968006,0.0,0.0,0.0001999600079984003,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,9.998000399920016e-05,0.0001999600079984003,0.00029994001199760045,0.0006998600279944011,0.001299740051989602,0.0023995200959808036,0.001999600079984003,0.0034993001399720057,0.0030993801239752048,0.006998600279944011,0.00629874025194961,0.007798440311937612,0.008798240351929614,0.009898020395920816,0.011297740451909618,0.01269746050789842,0.011897620475904818,0.015596880623875225,0.01269746050789842,0.009398120375924815,0.010497900419916016,0.009498100379924015,0.008098380323935212,0.007298540291941612,0.008098380323935212,0.006898620275944811,0.00609878024395121]
Y2= [0.006998600279944011,0.007198560287942412,0.007598480303939212,0.009398120375924815,0.009798040391921616,0.010997800439912017,0.011197760447910418,0.01289742051589682,0.013697260547890422,0.015396920615876825,0.01259748050389922,0.010797840431913617,0.010497900419916016,0.009898020395920816,0.008198360327934412,0.007098580283943211,0.007198560287942412,0.0057988402319536095,0.004599080183963208,0.002999400119976005,0.001899620075984803,0.0016996600679864027,0.0008998200359928015,0.0006998600279944011,0.0005998800239952009,0.0003999200159968006,0.00029994001199760045,9.998000399920016e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,9.998000399920016e-05,0.0,9.998000399920016e-05,9.998000399920016e-05,0.00029994001199760045,0.0001999600079984003,0.0004999000199960008,0.0009998000399920016,0.0015996800639872025,0.0021995600879824036,0.0030993801239752048,0.005298940211957609,0.008698260347930415,0.008998200359928014,0.011397720455908818,0.013197360527894421,0.014997000599880024,0.022295540891821636,0.021795640871825634,0.023495300939812037,0.01969606078784243,0.022695460907818436,0.022395520895820836,0.021595680863827234,0.016596680663867228,0.016796640671865627,0.016196760647870425,0.011897620475904818,0.010697860427914417,0.010597880423915218]
考虑使用 scipy.stats.wasserstein_distance
https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.wasserstein_distance.html
从上页给出的功能描述：
scipy.stats.wasserstein_distance(u_values, v_values, u_weights=None, v_weights=None):Compute the first Wasserstein distance between two 1D distributions.
This distance is also known as the earth mover’s distance since it can be seen as the minimum amount of “work” required to transform u into v, where “work” is measured as the amount of distribution weight that must be moved, multiplied by the distance it has to be moved.
现在可以了。我使用 pyemd 并创建了一个周期性距离矩阵。
from pyemd import emd
from scipy.stats import wasserstein_distance
from scipy.spatial.distance import cdist
X= [-179.0,-177.0,-175.0,-173.0,-171.0,-169.0,-167.0,-165.0,-163.0,-161.0,-159.0,-157.0,-155.0,-153.0,-151.0,-149.0,-147.0,-145.0,-143.0,-141.0,-139.0,-137.0,-135.0,-133.0,-131.0,-129.0,-127.0,-125.0,-123.0,-121.0,-119.0,-117.0,-115.0,-113.0,-111.0,-109.0,-107.0,-105.0,-103.0,-101.0,-99.0,-97.0,-95.0,-93.0,-91.0,-89.0,-87.0,-85.0,-83.0,-81.0,-79.0,-77.0,-75.0,-73.0,-71.0,-69.0,-67.0,-65.0,-63.0,-61.0,-59.0,-57.0,-55.0,-53.0,-51.0,-49.0,-47.0,-45.0,-43.0,-41.0,-39.0,-37.0,-35.0,-33.0,-31.0,-29.0,-27.0,-25.0,-23.0,-21.0,-19.0,-17.0,-15.0,-13.0,-11.0,-9.0,-7.0,-5.0,-3.0,-1.0,1.0,3.0,5.0,7.0,9.0,11.0,13.0,15.0,17.0,19.0,21.0,23.0,25.0,27.0,29.0,31.0,33.0,35.0,37.0,39.0,41.0,43.0,45.0,47.0,49.0,51.0,53.0,55.0,57.0,59.0,61.0,63.0,65.0,67.0,69.0,71.0,73.0,75.0,77.0,79.0,81.0,83.0,85.0,87.0,89.0,91.0,93.0,95.0,97.0,99.0,101.0,103.0,105.0,107.0,109.0,111.0,113.0,115.0,117.0,119.0,121.0,123.0,125.0,127.0,129.0,131.0,133.0,135.0,137.0,139.0,141.0,143.0,145.0,147.0,149.0,151.0,153.0,155.0,157.0,159.0,161.0,163.0,165.0,167.0,169.0,171.0,173.0,175.0,177.0,179.0]
Y1= [0.00639872025594881,0.006998600279944011,0.010597880423915218,0.011097780443911218,0.015096980603879224,0.017096580683863227,0.021195760847830435,0.021695660867826434,0.02449510097980404,0.021495700859828035,0.01999600079984003,0.022895420915816835,0.01879624075184963,0.016996600679864027,0.015396920615876825,0.016896620675864827,0.013897220555888823,0.009998000399920015,0.008298340331933614,0.00599880023995201,0.004499100179964007,0.0028994201159768048,0.0016996600679864027,0.0008998200359928015,0.0005998800239952009,0.0003999200159968006,0.0,0.0,0.0001999600079984003,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,9.998000399920016e-05,0.0001999600079984003,0.00029994001199760045,0.0006998600279944011,0.001299740051989602,0.0023995200959808036,0.001999600079984003,0.0034993001399720057,0.0030993801239752048,0.006998600279944011,0.00629874025194961,0.007798440311937612,0.008798240351929614,0.009898020395920816,0.011297740451909618,0.01269746050789842,0.011897620475904818,0.015596880623875225,0.01269746050789842,0.009398120375924815,0.010497900419916016,0.009498100379924015,0.008098380323935212,0.007298540291941612,0.008098380323935212,0.006898620275944811,0.00609878024395121]
Y2= [0.006998600279944011,0.007198560287942412,0.007598480303939212,0.009398120375924815,0.009798040391921616,0.010997800439912017,0.011197760447910418,0.01289742051589682,0.013697260547890422,0.015396920615876825,0.01259748050389922,0.010797840431913617,0.010497900419916016,0.009898020395920816,0.008198360327934412,0.007098580283943211,0.007198560287942412,0.0057988402319536095,0.004599080183963208,0.002999400119976005,0.001899620075984803,0.0016996600679864027,0.0008998200359928015,0.0006998600279944011,0.0005998800239952009,0.0003999200159968006,0.00029994001199760045,9.998000399920016e-05,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,9.998000399920016e-05,0.0,9.998000399920016e-05,9.998000399920016e-05,0.00029994001199760045,0.0001999600079984003,0.0004999000199960008,0.0009998000399920016,0.0015996800639872025,0.0021995600879824036,0.0030993801239752048,0.005298940211957609,0.008698260347930415,0.008998200359928014,0.011397720455908818,0.013197360527894421,0.014997000599880024,0.022295540891821636,0.021795640871825634,0.023495300939812037,0.01969606078784243,0.022695460907818436,0.022395520895820836,0.021595680863827234,0.016596680663867228,0.016796640671865627,0.016196760647870425,0.011897620475904818,0.010697860427914417,0.010597880423915218]
bw = 2 # bandwidth used to prepare the data (Y1 .. Yn)
bins_dihedrals = np.arange(-180, 180+bw_dihedrals, bw_dihedrals)
bins_dihedrals_reshape = np.array(bins_dihedrals).reshape(-1,1)
bins_dihedrals_dist_matrix = cdist(bins_dihedrals_reshape, bins_dihedrals_reshape) # 'classical' distance matrix
bins_dihedrals_dist_matrix_periodoc = np.where(bins_dihedrals_dist_matrix > max(bins_dihedrals_dist_matrix[0])/2, max(bins_dihedrals_dist_matrix[0])-bins_dihedrals_dist_matrix, bins_dihedrals_dist_matrix) # modify distance matrix for periodicity
emd_dist = bw * emd(Y1, Y2, bins_dihedrals_dist_matrix_periodic)