找到最陡坡的起点和终点

问题描述

我必须在数据集中找到最陡坡的起点和终点.数据集显示实验期间的温度变化.冷却开始大约 420 帧，结束大约 500 帧.有人可以帮我计算这些分数吗?

<预类= 郎吡prettyprint-越权"> <代码> Y = [308.09262874940794，308.1216944088393，308.2620809214068，308.2185299674233，308.0441705852154，308.06355616177564，307.9374947672655，308.15075314506964，308.0684020743851，307.9859953521339，308.0974735069697，308.1265380121872，308.09262874940794，308.0780933219296，307.9859953521339，308.0247819257457，308.0005417638036，308.1555955950364，308.09262874940794，308.0780933219296，308.17496347364175，308.2185299674233，308.20400953030344，308.2378878644666，308.2524042737181，308.22336972940053，308.3056163523782，308.3829743977657，308.34913627709466，308.08778379939605，308.3636394757246，308.3636394757246，308.3636394757246，308.4844326170746，308.4361296746482，308.5375438416535，308.460283529643，308.5761557193945，308.64852019740135，308.69673945106905，308.53271650065454308.691918372092685,308.6858520198686,686,689,686,689,689,686,689,689,6686,686,686,689,689,686,688，308.68.688，308.68，308.68，308.68，308.68，308.68，308.68，308.68，308.68，308.68，308.68，308.68227566668，但308.735301202496，308.8364681549037，308.77866868368494，308.7690327906589，308.8075718225567，308.8701719464355，308.75939614063134，308.8172046893795，308.69673945106905，308.88942710227735，308.9952765331329，308.88942710227735，309.1634857265685，308.9375517868669，308.9423632184057，309.00489468840124，308.9760379640753，308.9423632184057，309.0289367843301，309.0385523062737，308.9231163613786，309.18269499806115，308.9231163613786，309.0000857048534，309.20190127232803，309.07700687606655，309.0193205102312，309.19709998467357，308.9952765331329，309.09142424016557，309.05297417928875，309.0577810944096，309.20190127232803，309.105839914524，309.04816707624076，309.11544942564836，309.18749684756233，309.1586829402123，309.38900566395995，309.31227925555163，309.2690996495939，309.2978877349221，309.2211045507886，309.283494533135，309.2786964255123，309.2115032859454，309.1634857265685，309.3362613889812，309.3602388569431，309.2786964255123，309.29309018781777, 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307.2662035835691,307.32959980418053，307.24181158431395，307.30522056810406，307.23205340877587，307.3003441322015，307.3003441322015，307.22229444675827，307.1100097932646，307.23205340877587，307.2466903772131，307.2613255767183，307.3247243493438，307.8889748630513，307.30522056810406，307.3978355878861，307.40758042253736，307.2857136466891，307.2515689735642，307.19301283991086，307.3393501254531，307.2857136466891，307.38808997000365，307.4027081031038，307.38808997000365，307.3442249919368，307.33447506287564，307.4319390837782，307.40758042253736，307.28083642550376，307.2857136466891，307.3149728511503，307.3832168672912，307.36372249741055，307.3490996623505，307.31984869834173，307.4124525462108，307.47090276965224，307.48064173613346，307.3003441322015，307.41732447414785，307.5147219648439，307.45629285398684，307.45629285398684，307.3832168672912，307.5147219648439，307.6120413603623，307.5682572845433，307.50985394664536，307.57798844340505，307.3978355878861，307.4027081031038, 307.36372249741055，307.5390591277433，307.45629285398684，307.4270677429077，307.4952487203862，307.48064173613346，307.45142249108505，307.3978355878861，307.62176901196995，307.5390591277433，307.6606718315838，307.5001173244402，307.5147219648439，307.6801185719411，307.6314958847072，307.573122961451，307.52932484810736，307.50985394664536，307.573122961451，307.63635902905844，307.57798844340505，307.6266325456856，307.5828537304289，307.7044226227817，307.68497977088464，307.62176901196995，307.65094729432553，307.5390591277433，307.60231292969553，307.50498573318544，307.573122961451，307.62176901196995，307.7821629546704，307.6120413603623，307.5828537304289，307.50985394664536，307.6120413603623，307.48064173613346，307.48064173613346，307.48064173613346，307.33447506287564，307.4416811786191，307.5536590838609，307.5682572845433，307.65094729432553，307.77244813033496，307.50498573318544，307.5147219648439，307.69956220134196，307.60717724242306，307.646084733844, 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3070.84529041194054，307.82101449623093，307.91323723153334，307.92294082559295，307.7432990008586，307.8307254436129，307.65094729432553，307.81130277383306，307.9471964290412，307.8938277235077，307.75787443886094，307.85014501407795，307.7530161536168，307.90838514455027，307.72872181569426，307.84529041194054]

在我的第一次尝试中，我使用了最大累积:

i = np.argmax(np.maximum.accumulate(y) - y)j = np.argmax(y[:i])plt.plot(y)plt.plot([i, j], [y[i], y[j]], 'o', color='Red', markersize=10)

它找到了最大百分比下降，但不是最陡的

解决方案

当我听到斜率时，我想到了导数，所以我想要一个函数.我通过使用样条插值得到一个.如果您不熟悉样条曲线，它们基本上是拼接在一起以形成平滑函数的多项式.

从 scipy.interpolate 导入 UnivariateSplinex = np.arange(len(y))f = UnivariateSpline(x, y, s=7)plt.plot(x,f(x))

在玩弄了 s 参数后，我得到了这个

现在我想在现在的斜坡上找到一个突然的跳跃来切断.所以我绘制了有序的负斜率，而忽略了前 50 个值.

dy = np.sort(f.derivative()(x[50:]))plt.plot(dy[dy<0])

在我看来，这看起来像是在 -0.01 左右突然跳跃.因此，让我们尝试将所有坡度标记为更陡峭(即小于该坡度)，同时仍然忽略前 50 个值.

idx = np.argwhere((f.derivative()(x) <-0.01) & (x > 50))点 = x[idx]plt.plot(x,f(x))plt.scatter(points,f(points), c='r')

我们还可以打印区域开始和结束的 x 坐标

idx.min(), idx.max()

给我们

(403, 496)

I have to find start and endpoint of steepest slope in dataset. Dataset shows temperature changes during experiment. Cooling down start about 420 frame and ends around 500 frame. Could someone help me how I can calculate this points?

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In my first attempt I used maximum accumulate:

i = np.argmax(np.maximum.accumulate(y) - y)
j = np.argmax(y[:i])
plt.plot(y)
plt.plot([i, j], [y[i], y[j]], 'o', color='Red', markersize=10)

It found maximum percentage drop, but not the steepest one

解决方案

When I hear slope I think of derivative so I want a function having one. I get one by using a spline interpolation. If you're not familiar with splines they are basically polynomials stitched together to make a smooth function.

from scipy.interpolate import UnivariateSpline
x = np.arange(len(y))
f = UnivariateSpline(x, y, s=7)
plt.plot(x,f(x))

After playing around with the s parameter I got this

Now I want to find a sudden jump in the slopes present to cut off. So I plot the ordered negative slopes while ignoring the first 50 values.

dy = np.sort(f.derivative()(x[50:]))
plt.plot(dy[dy<0])

To me this looks like there is a sudden jump at around -0.01. So lets try to mark all slopes being steeper i.e. smaller than that while stil ignoring the first 50 values.

idx = np.argwhere((f.derivative()(x) < -0.01) & (x > 50))
points = x[idx]
plt.plot(x,f(x))
plt.scatter(points,f(points), c='r')

And while we are at it we can also print the x coordinates of the beginning and end of the region

idx.min(), idx.max()

giving us

(403, 496)