Python 查找曲线上坡度变化的位置
我有数据点的时间和电压,创造曲线如下所示Python 查找曲线上坡度变化的位置,python,pandas,numpy,scipy,Python,Pandas,Numpy,Scipy,我有数据点的时间和电压,创造曲线如下所示 时间数据为 array([ 0.10810811, 0.75675676, 1.62162162, 2.59459459, 3.56756757, 4.21621622, 4.97297297, 4.97297297, 4.97297297, 4.97297297, 4.97297297, 4.97297297, 4.97297297, 4.97297297,
时间
数据为
array([ 0.10810811, 0.75675676, 1.62162162, 2.59459459,
3.56756757, 4.21621622, 4.97297297, 4.97297297,
4.97297297, 4.97297297, 4.97297297, 4.97297297,
4.97297297, 4.97297297, 5.08108108, 5.18918919,
5.2972973 , 5.51351351, 5.72972973, 5.94594595,
6.27027027, 6.59459459, 7.13513514, 7.67567568,
8.32432432, 9.18918919, 10.05405405, 10.91891892,
11.78378378, 12.64864865, 13.51351351, 14.37837838,
15.35135135, 16.32432432, 17.08108108, 18.16216216,
19.02702703, 20. , 20. , 20. ,
20. , 20. , 20. , 20. ,
20.10810811, 20.21621622, 20.43243243, 20.64864865,
20.97297297, 21.40540541, 22.05405405, 22.91891892,
23.78378378, 24.86486486, 25.83783784, 26.7027027 ,
27.56756757, 28.54054054, 29.51351351, 30.48648649,
31.56756757, 32.64864865, 33.62162162, 34.59459459,
35.67567568, 36.64864865, 37.62162162, 38.59459459,
39.67567568, 40.75675676, 41.83783784, 42.81081081,
43.89189189, 44.97297297, 46.05405405, 47.02702703,
48.10810811, 49.18918919, 50.27027027, 51.35135135,
52.43243243, 53.51351351, 54.48648649, 55.56756757,
56.75675676, 57.72972973, 58.81081081, 59.89189189])
array([ 4.11041056, 4.11041056, 4.11041056, 4.11041056, 4.11041056,
4.11041056, 4.11041056, 4.10454545, 4.09794721, 4.09208211,
4.08621701, 4.07961877, 4.07228739, 4.06568915, 4.05909091,
4.05175953, 4.04516129, 4.03782991, 4.03123167, 4.02463343,
4.01803519, 4.01217009, 4.00557185, 3.99970674, 3.99384164,
3.98797654, 3.98284457, 3.97771261, 3.97331378, 3.96891496,
3.96451613, 3.96085044, 3.95645161, 3.95205279, 3.9483871 ,
3.94398827, 3.94032258, 3.93665689, 3.94325513, 3.94985337,
3.95645161, 3.96378299, 3.97038123, 3.97624633, 3.98284457,
3.98944282, 3.99604106, 4.0026393 , 4.00923754, 4.01510264,
4.02096774, 4.02609971, 4.02903226, 4.03196481, 4.03416422,
4.0356305 , 4.03709677, 4.03856305, 4.03929619, 4.04002933,
4.04076246, 4.04222874, 4.04296188, 4.04296188, 4.04369501,
4.04442815, 4.04516129, 4.04516129, 4.04589443, 4.04589443,
4.04662757, 4.04662757, 4.0473607 , 4.0473607 , 4.04809384,
4.04809384, 4.04809384, 4.04882698, 4.04882698, 4.04882698,
4.04956012, 4.04956012, 4.04956012, 4.04956012, 4.05029326,
4.05029326, 4.05029326, 4.05029326])
并且volts
数据为
array([ 0.10810811, 0.75675676, 1.62162162, 2.59459459,
3.56756757, 4.21621622, 4.97297297, 4.97297297,
4.97297297, 4.97297297, 4.97297297, 4.97297297,
4.97297297, 4.97297297, 5.08108108, 5.18918919,
5.2972973 , 5.51351351, 5.72972973, 5.94594595,
6.27027027, 6.59459459, 7.13513514, 7.67567568,
8.32432432, 9.18918919, 10.05405405, 10.91891892,
11.78378378, 12.64864865, 13.51351351, 14.37837838,
15.35135135, 16.32432432, 17.08108108, 18.16216216,
19.02702703, 20. , 20. , 20. ,
20. , 20. , 20. , 20. ,
20.10810811, 20.21621622, 20.43243243, 20.64864865,
20.97297297, 21.40540541, 22.05405405, 22.91891892,
23.78378378, 24.86486486, 25.83783784, 26.7027027 ,
27.56756757, 28.54054054, 29.51351351, 30.48648649,
31.56756757, 32.64864865, 33.62162162, 34.59459459,
35.67567568, 36.64864865, 37.62162162, 38.59459459,
39.67567568, 40.75675676, 41.83783784, 42.81081081,
43.89189189, 44.97297297, 46.05405405, 47.02702703,
48.10810811, 49.18918919, 50.27027027, 51.35135135,
52.43243243, 53.51351351, 54.48648649, 55.56756757,
56.75675676, 57.72972973, 58.81081081, 59.89189189])
array([ 4.11041056, 4.11041056, 4.11041056, 4.11041056, 4.11041056,
4.11041056, 4.11041056, 4.10454545, 4.09794721, 4.09208211,
4.08621701, 4.07961877, 4.07228739, 4.06568915, 4.05909091,
4.05175953, 4.04516129, 4.03782991, 4.03123167, 4.02463343,
4.01803519, 4.01217009, 4.00557185, 3.99970674, 3.99384164,
3.98797654, 3.98284457, 3.97771261, 3.97331378, 3.96891496,
3.96451613, 3.96085044, 3.95645161, 3.95205279, 3.9483871 ,
3.94398827, 3.94032258, 3.93665689, 3.94325513, 3.94985337,
3.95645161, 3.96378299, 3.97038123, 3.97624633, 3.98284457,
3.98944282, 3.99604106, 4.0026393 , 4.00923754, 4.01510264,
4.02096774, 4.02609971, 4.02903226, 4.03196481, 4.03416422,
4.0356305 , 4.03709677, 4.03856305, 4.03929619, 4.04002933,
4.04076246, 4.04222874, 4.04296188, 4.04296188, 4.04369501,
4.04442815, 4.04516129, 4.04516129, 4.04589443, 4.04589443,
4.04662757, 4.04662757, 4.0473607 , 4.0473607 , 4.04809384,
4.04809384, 4.04809384, 4.04882698, 4.04882698, 4.04882698,
4.04956012, 4.04956012, 4.04956012, 4.04956012, 4.05029326,
4.05029326, 4.05029326, 4.05029326])
我想确定标记为A、B、C、D和E的点的位置。点A是斜率从零到未定义的第一个位置。点B是直线不再垂直的位置。点C是曲线的最小值。点D是曲线不再垂直的位置。点E是斜率再次接近零的位置。下面的Python代码确定点A和C的位置
tdiff = np.diff(time)
vdiff = np.diff(volts)
# point A
idxA = np.where(vdiff < 0)[0][0]
timeA = time[idxA]
voltA = volts[idxA]
# point C
idxC = volts.idxmin()
timeC = time[idxC]
voltC = volts[idxC]
tdiff=np.diff(时间)
vdiff=np.差值(伏特)
#A点
idxA=np.where(vdiff<0)[0][0]
timeA=时间[idxA]
伏特=伏特[idxA]
#C点
idxC=volts.idxmin()
timeC=时间[idxC]
伏特c=伏特[idxC]
如何确定曲线上由点B、D和E表示的其他位置?您正在查找标记坡度变为零或无穷大的任何位置的点。实际上,我们不需要在任何地方计算斜率:
yn-yn-1==0
和yn+1-yn!=0
,反之亦然,或与x
相同
我们可以取x
的差值。如果两个连续元素中的一个为零,则该点处的差异将为差异或负差异。所以我们只想找到并标记diff(x)=diff(diff(x))
和diff(x)!=0
,当然,针对阵列之间的大小差异进行了适当调整。我们还需要y
中相同的所有点
用numpy术语来说,这可以写成如下
def masks(vec):
d = np.diff(vec)
dd = np.diff(d)
# Mask of locations where graph goes to vertical or horizontal, depending on vec
to_mask = ((d[:-1] != 0) & (d[:-1] == -dd))
# Mask of locations where graph comes from vertical or horizontal, depending on vec
from_mask = ((d[1:] != 0) & (d[1:] == dd))
return to_mask, from_mask
to_vert_mask, from_vert_mask = masks(time)
to_horiz_mask, from_horiz_mask = masks(volts)
请记住,掩码是根据二阶差计算的,因此它们比输入短两个元素。掩码中的元素对应于输入数组中的元素,其前缘和后缘上有一个元素边框(因此下面的索引[1:-1]
)。可以使用将遮罩转换为索引,也可以直接使用遮罩作为索引来获取x值和y值:
def apply_mask(mask, x, y):
return x[1:-1][mask], y[1:-1][mask]
to_vert_t, to_vert_v = apply_mask(to_vert_mask, time, volts)
from_vert_t, from_vert_v = apply_mask(from_vert_mask, time, volts)
to_horiz_t, to_horiz_v = apply_mask(to_horiz_mask, time, volts)
from_horiz_t, from_horiz_v = apply_mask(from_horiz_mask, time, volts)
plt.plot(time, volts, 'b-')
plt.plot(to_vert_t, to_vert_v, 'r^', label='Plot goes vertical')
plt.plot(from_vert_t, from_vert_v, 'kv', label='Plot stops being vertical')
plt.plot(to_horiz_t, to_horiz_v, 'r>', label='Plot goes horizontal')
plt.plot(from_horiz_t, from_horiz_v, 'k<', label='Plot stops being horizontal')
plt.legend()
plt.show()
我将此用作展示apply\u mask
结果的星形扩展。结果图为:
这正是你要找的情节。从_horiz中丢弃,
也会使“点A”仅被标识为垂直下降,这很好
正如
至_horiz
中的多个值所示,该方法对数据中的噪声非常敏感。您的数据非常平滑,但这种方法不太可能适用于未经过滤的原始测量值。是什么决定了这些点?您既没有提供数据,也没有明确定义要做什么。如果你不能清楚地定义你真正想要的东西,那么使用“拐点”这个词是没有任何帮助的。这些点当然不像数学上的拐点。当你们来到熊猫社区时,别忘了带一些数据。数据决定答案。那么这些点有什么特别之处呢?请把它编辑成一个非常详细的问题。如果你做对了,你可能会回答你自己的问题。仅仅实现数学定义有什么错:二阶导数在哪里改变符号?@Bharath。垂直的字面意思是共享相同的时间值。谢谢你的深入回答。@wigging。很高兴你喜欢它。我更新了图片,让它看起来更干净。