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How to fit a series of datapoints using 3 piecewise linear fit lines
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I have the following datapoints:
xdata = [-4.09434456 -3.40119738 -2.99573227 -2.7080502 -2.48490665 -2.30258509 -2.14843441 -2.01490302 -1.89711998 -1.79175947 -1.69644929 -1.60943791 -1.5293952 -1.45528723 -1.38629436 -1.32175584 -1.26113122 -1.2039728 -1.14990558 -1.09861229 -1.04982212 -1.00330211 -0.95885035 -0.91629073 -0.87546874 -0.83624802 -0.7985077 -0.76214005 -0.72704873 -0.69314718 -0.66035736 -0.62860866 -0.597837 -0.56798404 -0.5389965 -0.51082562 -0.48342665 -0.4567584 -0.43078292 -0.40546511 -0.3807725 -0.35667494 -0.33314445 -0.31015493 -0.28768207 -0.26570317 -0.24419696 -0.22314355 -0.20252426 -0.18232156 -0.16251893 -0.14310084 -0.12405265 -0.10536052 -0.08701138 -0.06899287 -0.05129329 -0.03390155 -0.01680712 0. 0.0165293 0.03278982 0.04879016 0.06453852 0.08004271 0.09531018 0.11034806 0.12516314 0.13976194 0.15415068 0.16833531 0.18232156 0.19611488 0.20972053 0.22314355 0.23638878 0.24946086 0.26236426 0.27510329 0.28768207 0.30010459 0.31237469 0.32449605 0.33647224 0.34830669 0.36000273 0.37156356 0.38299225 0.39429181 0.40546511 0.41651494 0.42744401 0.43825493 0.44895022 0.45953233 0.47000363 0.48036642 0.49062292 0.50077529 0.51082562 0.52077595 0.53062825 0.54038443 0.55004634 0.55961579 0.56909453 0.57848427 0.58778666 0.59700332 0.6061358 0.61518564 0.62415431 0.63304326 0.64185389 0.65058757 0.65924563 0.66782937 0.67634006 0.68477893 0.69314718 0.70144598 0.70967648 0.71783979 0.725937 0.73396918 0.74193734 0.74984252 0.7576857 0.76546784 0.77318989 0.78085276 0.78845736 0.79600457 0.80349524 0.81093022 0.81831032 0.82563636 0.83290912 0.84012937 0.84729786 0.85441533 0.8614825 0.86850007 0.87546874 0.88238918 0.88926206 0.89608802 0.90286771 0.90960174 0.91629073 0.92293527 0.92953596 0.93609336 0.94260804 0.94908055 0.95551145 0.96190124 0.96825047 0.97455964 0.98082925 0.9870598 0.99325177 0.99940564 1.00552187 1.01160091 1.01764323 1.02364925 1.02961942 1.03555415 1.04145387 1.04731899 1.05314991 1.05894703 1.06471074 1.07044141 1.07613943 1.08180517 1.08743899 1.09304124 1.09861229 1.10415247 1.10966212 1.11514159 1.1205912 1.12601126 1.13140211 1.13676405 1.1420974 1.14740245 1.15267951 1.15792887 1.16315081 1.16834563 1.1735136 1.178655 1.1837701 1.18885917 1.19392247 1.19896026 1.2039728 1.20896035 1.21392314 1.21886142 1.22377543 1.22866542 1.23353161 1.23837423 1.24319352 1.24798969 1.25276297 1.25751357 1.26224171 1.2669476 1.27163145 1.27629347 1.28093385 1.28555279 1.2901505 1.29472717 1.29928298 1.30381814 1.30833282 1.31282721 1.31730149 1.32175584 1.32619044 1.33060546 1.33500107 1.33937744 1.34373475 1.34807315 1.35239281 1.35669389 1.36097655 1.36524095 1.36948724 1.37371558 1.37792611 1.38211899 1.38629436 1.39045237 1.39459316 1.39871688 1.40282366 1.40691365 1.41098697 1.41504377 1.41908418 1.42310833 1.42711636 1.43110838 1.43508453 1.43904493 1.4429897 1.44691898 1.45083288 1.45473152 1.45861502 1.4624835 1.46633707 1.47017585 1.47399994 1.47780947 1.48160454 1.48538526 1.48915175 1.4929041 1.49664242 1.50036682 1.5040774 1.50777426 1.5114575 1.51512723 1.51878354 1.52242654 1.5260563 1.52967294 1.53327655 1.53686722 1.54044504 1.54401011 1.54756251 1.55110234 1.55462968 1.55814462 1.56164725 1.56513765 1.56861592 1.57208213 1.57553636 1.5789787 1.58240924 1.58582805 1.58923521 1.59263079 1.59601489 1.59938758 1.60274892 1.60609901 1.60943791 1.6127657 1.61608246 1.61938824 1.62268314 1.62596721 1.62924054 1.63250319 1.63575522 1.63899671 1.64222774 1.64544835 1.64865863 1.65185863 1.65504842 1.65822808 1.66139765 1.66455721 1.66770682 1.67084654 1.67397643 1.67709656 1.68020698 1.68330776 1.68639895 1.68948062 1.69255282 1.69561561 1.69866905 1.70171319 1.70474809 1.70777381 1.71079041 1.71379793 1.71679643 1.71978597 1.7227666 1.72573837 1.72870133 1.73165555 1.73460106 1.73753792 1.74046617 1.74338588 1.7462971 1.74919985 1.75209421 1.75498022 1.75785792 1.76072736 1.76358859 1.76644166 1.76928661 1.77212349 1.77495235 1.77777323 1.78058617 1.78339122 1.78618842 1.78897783 1.79175947 1.7945334 1.79729965 1.80005827 1.80280931 1.80555279 1.80828877 1.81101729 1.81373838 1.81645208 1.81915844 1.8218575 1.82454929 1.82723386 1.82991124 1.83258146 1.83524458 1.83790063 1.84054963 1.84319164 1.84582669 1.84845481 1.85107605 1.85369043 1.85629799 1.85889877 1.86149281 1.86408013 1.86666078 1.86923478 1.87180218 1.874363 1.87691728 1.87946505 1.88200635 1.8845412 1.88706965 1.88959172 1.89210744 1.89461685 1.89711998 1.89961687 1.90210753 1.904592 1.90707032 1.9095425 1.9120086 1.91446862 1.91692261 1.91937059 1.9218126 1.92424865 1.92667879 1.92910303 1.93152141 1.93393396 1.9363407 1.93874166 1.94113687 1.94352636 1.94591015 1.94828827 1.95066075 1.95302762 1.95538889 1.95774461 1.96009478 1.96243945 1.96477863 1.96711236 1.96944065 1.97176353 1.97408103 1.97639317 1.97869997 1.98100147 1.98329768 1.98558863 1.98787435 1.99015485 1.99243016 1.99470031 1.99696532 1.99922521 2.00148 2.00372972 2.00597439 2.00821403 2.01044867 2.01267833 2.01490302 2.01712278 2.01933762 2.02154756 2.02375264 2.02595286 2.02814825 2.03033883 2.03252462 2.03470565 2.03688193 2.03905348 2.04122033 2.04338249 2.04553999 2.04769284 2.04984107 2.0519847 2.05412373 2.05625821 2.05838813 2.06051353 2.06263442 2.06475083 2.06686276 2.06897024 2.07107329 2.07317193 2.07526617 2.07735604 2.07944154 2.08152271 2.08359955 2.08567209 2.08774034 2.08980433 2.09186406 2.09391956 2.09597084 2.09801793 2.10006083 2.10209957 2.10413415 2.10616461 2.10819095 2.1102132 2.11223136 2.11424546 2.11625551 2.11826153 2.12026354 2.12226154 2.12425556 2.12624561 2.12823171 2.13021387 2.13219211 2.13416644 2.13613689 2.13810345 2.14006616 2.14202503 2.14398006 2.14593128 2.1478787 2.14982234 2.1517622 2.15369831 2.15563068 2.15755932 2.15948425 2.16140548 2.16332303 2.1652369 2.16714712 2.1690537 2.17095665 2.17285599 2.17475172 2.17664387 2.17853244 2.18041746 2.18229893 2.18417686 2.18605128 2.18792218 2.1897896 2.19165353 2.193514 2.19537101 2.19722458 2.19907472 2.20092144 2.20276476 2.20460468 2.20644123 2.20827441 2.21010424 2.21193072 2.21375388 2.21557372 2.21739025 2.21920348 2.22101344 2.22282012 2.22462355 2.22642373 2.22822068 2.2300144 2.23180491 2.23359222 2.23537634 2.23715729 2.23893507 2.24070969 2.24248117 2.24424952 2.24601474 2.24777686 2.24953587 2.2512918 2.25304465 2.25479443 2.25654115 2.25828483 2.26002548 2.2617631 2.2634977 2.26522931 2.26695792 2.26868354 2.27040619 2.27212589 2.27384262 2.27555642 2.27726729 2.27897523 2.28068026 2.28238239 2.28408162 2.28577797 2.28747146 2.28916207 2.29084984 2.29253476 2.29421684 2.2958961 2.29757255 2.29924619 2.30091704 2.30258509 2.30425037 2.30591288 2.30757263 2.30922964 2.3108839 2.31253542 2.31418423 2.31583032 2.31747371 2.31911439 2.3207524 2.32238772 2.32402037 2.32565037 2.32727771 2.3289024 2.33052446 2.3321439 2.33376071 2.33537492 2.33698652 2.33859553 2.34020196 2.34180581 2.34340709 2.34500581 2.34660198 2.3481956 2.34978669 2.35137526 2.3529613 2.35454483 2.35612586 2.35770439 2.35928044 2.360854 2.36242509 2.36399372 2.36555989 2.36712361 2.36868489 2.37024374 2.37180016 2.37335416 2.37490575 2.37645494 2.37800173 2.37954613 2.38108815 2.3826278 2.38416508 2.3857 2.38723257 2.38876279 2.39029067 2.39181623 2.39333946 2.39486037 2.39637897 2.39789527 2.39940928 2.40092099 2.40243043 2.40393759 2.40544248 2.40694511 2.40844548 2.40994361 2.4114395 2.41293315 2.41442457 2.41591378 2.41740077 2.41888555 2.42036813 2.42184851 2.42332671 2.42480273 2.42627657 2.42774824 2.42921774 2.4306851 2.4321503 2.43361336 2.43507428 2.43653307 2.43798973 2.43944428 2.44089671 2.44234704 2.44379526 2.44524139 2.44668544 2.4481274 2.44956728 2.4510051 2.45244085 2.45387454 2.45530618 2.45673577 2.45816332 2.45958884 2.46101233 2.46243379 2.46385324 2.46527068 2.4666861 2.46809953 2.46951096 2.47092041 2.47232787 2.47373335 2.47513686 2.4765384 2.47793798 2.4793356 2.48073128 2.48212501 2.4835168 2.48490665 2.48629458 2.48768058 2.48906466 2.49044683 2.49182709 2.49320545 2.49458192 2.49595649 2.49732917 2.49869997 2.5000689 2.50143595 2.50280114 2.50416447 2.50552594 2.50688556 2.50824333 2.50959926 2.51095336 2.51230562 2.51365606 2.51500468 2.51635148 2.51769647 2.51903966 2.52038104 2.52172062 2.52305842 2.52439442 2.52572864 2.52706109 2.52839176 2.52972067 2.53104781 2.53237319 2.53369681 2.53501869 2.53633882 2.53765722 2.53897387 2.5402888 2.54160199 2.54291347 2.54422323 2.54553127 2.54683761 2.54814224 2.54944517 2.55074641 2.55204595 2.55334381 2.55463999 2.55593449 2.55722731 2.55851847 2.55980796 2.56109579 2.56238196 2.56366648 2.56494936 2.56623059 2.56751018 2.56878813 2.57006446 2.57133916 2.57261223 2.57388369 2.57515353 2.57642176 2.57768838 2.57895341 2.58021683 2.58147866 2.5827389 2.58399755 2.58525462 2.58651012 2.58776404 2.58901638 2.59026717 2.59151638 2.59276405 2.59401015 2.59525471 2.59649772 2.59773918 2.59897911 2.6002175 2.60145435 2.60268969 2.60392349 2.60515578 2.60638655 2.6076158 2.60884355 2.61006979 2.61129453 2.61251777 2.61373952 2.61495978 2.61617855 2.61739583 2.61861164 2.61982597 2.62103882 2.62225021 2.62346013 2.62466859 2.62587559 2.62708114 2.62828523 2.62948788 2.63068908 2.63188884 2.63308716 2.63428405 2.63547951 2.63667354 2.63786614 2.63905733 2.6402471 2.64143545 2.6426224 2.64380793 2.64499207 2.6461748 2.64735613 2.64853607 2.64971462 2.65089179 2.65206757 2.65324196 2.65441499 2.65558663 2.65675691 2.65792581 2.65909336 2.66025954 2.66142436 2.66258783 2.66374994 2.66491071 2.66607013 2.66722821 2.66838494 2.66954035 2.67069441 2.67184715 2.67299856 2.67414865 2.67529741 2.67644486 2.67759099 2.67873581 2.67987932 2.68102153 2.68216243 2.68330203 2.68444034 2.68557735 2.68671306 2.68784749 2.68898064 2.6901125 2.69124308 2.69237239 2.69350042 2.69462718 2.69575267 2.6968769 2.69799987 2.69912157 2.70024202 2.70136121 2.70247916 2.70359585 2.7047113 2.70582551 2.70693847 2.7080502 2.7091607 2.71026996 2.71137799 2.7124848 2.71359038 2.71469474 2.71579789 2.71689982 2.71800053 2.71910004 2.72019834 2.72129543 2.72239132 2.72348601 2.7245795 2.7256718 2.72676291 2.72785283 2.72894156 2.73002911 2.73111547 2.73220066 2.73328467 2.73436751 2.73544918 2.73652967 2.737609 2.73868717 2.73976418 2.74084002 2.74191472 2.74298825 2.74406064 2.74513188 2.74620197 2.74727091 2.74833872 2.74940539 2.75047092 2.75153531 2.75259858 2.75366071 2.75472172 2.7557816 2.75684037 2.75789801 2.75895453 2.76000994 2.76106424 2.76211742 2.7631695 2.76422047 2.76527034 2.76631911 2.76736678 2.76841335 2.76945883 2.77050322 2.77154651 2.77258872 2.77362985 2.77466989 2.77570885 2.77674673 2.77778354 2.77881927 2.77985393 2.78088753 2.78192005 2.78295151 2.78398191 2.78501124 2.78603952 2.78706674 2.78809291 2.78911802 2.79014209 2.79116511 2.79218708 2.79320801 2.7942279 2.79524675 2.79626456 2.79728133 2.79829708 2.79931179 2.80032548 2.80133814 2.80234977 2.80336038 2.80436997 2.80537855 2.8063861 2.80739264 2.80839817 2.8094027 2.81040621 2.81140871 2.81241022 2.81341072 2.81441022 2.81540872 2.81640623 2.81740274 2.81839826 2.81939279 2.82038633 2.82137889 2.82237046 2.82336105 2.82435066 2.82533929 2.82632694 2.82731362 2.82829933 2.82928407 2.83026783 2.83125063 2.83223247 2.83321334 2.83419326 2.83517221 2.8361502 2.83712724 2.83810333 2.83907846 2.84005265 2.84102588 2.84199817 2.84296952 2.84393992 2.84490938 2.84587791 2.84684549 2.84781214 2.84877786 2.84974265 2.8507065 2.85166943 2.85263143 2.85359251 2.85455266 2.85551189 2.85647021 2.8574276 2.85838408 2.85933965 2.8602943 2.86124805 2.86220088 2.86315281 2.86410383 2.86505395 2.86600317 2.86695148 2.8678989 2.86884542 2.86979105 2.87073578 2.87167962 2.87262258 2.87356464 2.87450582 2.87544611 2.87638552 2.87732404 2.87826169 2.87919846 2.88013435 2.88106937 2.88200351 2.88293678 2.88386918 2.88480071 2.88573138 2.88666118 2.88759011 2.88851819 2.8894454 2.89037176 2.89129726 2.8922219 2.89314568 2.89406862 2.8949907 2.89591194 2.89683232 2.89775187 2.89867056 2.89958841 2.90050542 2.90142159 2.90233693 2.90325142 2.90416508 2.90507791 2.9059899 2.90690106 2.90781139 2.9087209 2.90962957 2.91053743 2.91144446 2.91235066 2.91325605 2.91416062 2.91506437 2.91596731 2.91686943 2.91777073 2.91867123 2.91957091 2.92046979 2.92136786 2.92226512 2.92316158 2.92405724 2.92495209 2.92584615 2.9267394 2.92763186 2.92852352 2.92941439 2.93030447 2.93119375 2.93208225 2.93296995 2.93385687 2.934743 2.93562835 2.93651291 2.9373967 2.9382797 2.93916192 2.94004337 2.94092404 2.94180393 2.94268305 2.9435614 2.94443898 2.94531579 2.94619183 2.9470671 2.94794161 2.94881535 2.94968834 2.95056055 2.95143201 2.95230272 2.95317266 2.95404185 2.95491028 2.95577796 2.95664488 2.95751106 2.95837649 2.95924116 2.9601051 2.96096828 2.96183072 2.96269242 2.96355338 2.96441359 2.96527307 2.9661318 2.9669898 2.96784707 2.9687036 2.9695594 2.97041447 2.9712688 2.97212241 2.97297529 2.97382744 2.97467886 2.97552957 2.97637955 2.9772288 2.97807734 2.97892516 2.97977225 2.98061864 2.9814643 2.98230925 2.98315349 2.98399702 2.98483983 2.98568194 2.98652333 2.98736402 2.98820401 2.98904329 2.98988186 2.99071973 2.9915569 2.99239337 2.99322914 2.99406422 2.99489859 2.99573227 2.99656526 2.99739755 2.99822915 2.99906006 2.99989028 3.00071982 3.00154866 3.00237682 3.00320429 3.00403108 3.00485718 3.0056826 3.00650735 3.00733141 3.00815479 3.0089775 3.00979953 3.01062089 3.01144157 3.01226158 3.01308091 3.01389958 3.01471757 3.0155349 3.01635156 3.01716755 3.01798288 3.01879755 3.01961155 3.02042489 3.02123756 3.02204958 3.02286094 3.02367164 3.02448169 3.02529108 3.02609981 3.02690789 3.02771532 3.0285221 3.02932822 3.0301337 3.03093853 3.03174271 3.03254625 3.03334914 3.03415138 3.03495299 3.03575395 3.03655427 3.03735395 3.03815299 3.03895139 3.03974916 3.04054629 3.04134278 3.04213865 3.04293388 3.04372847 3.04452244 3.04531577 3.04610848 3.04690056 3.04769201 3.04848284 3.04927304 3.05006262 3.05085157 3.05163991 3.05242762 3.05321471 3.05400118 3.05478704 3.05557227 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which would give a spectrum (as shown). I would like to fit it using 3 piecewise linear lines and also find the first 'break-point' (just after the first zero slope line). Can anyone help me with that?
Thanks
0 个评论
采纳的回答
Bruno Luong
2020-12-29
编辑:Bruno Luong
2020-12-29
Use this FEX
load data.mat % attached above
ydata(end) = []; % your xdata/ydata do not match in length !
slope0 = struct('p', 1, 'x', [min(xdata) max(xdata)], 'v', [0 0]);
% Download BSFK function here
% https://www.mathworks.com/matlabcentral/fileexchange/25872-free-knot-spline-approximation
pp = BSFK(xdata,ydata, 2, 3, [], struct('KnotRemoval', 'none', 'pntcon', slope0));
% Check
figure
xi = linspace(min(xdata),max(xdata));
yi = ppval(pp,xi)
plot(xdata,ydata,'b',xi,yi,'r');
for xb=pp.breaks
xline(xb);
end
grid on
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/473302/image.png)
12 个评论
Bruno Luong
2021-1-23
编辑:Bruno Luong
2021-1-23
Sorry but all that is the conclusion of your own eye and/or the data is too noisy at the left.
BSFK simply minimizes based on the least square; Meaning that the break it finds so as minimizes the l2 norm of the residual. To me the second figure fits better than then first figure, frankly.
If you enter the data less noisy I bet that BSFK gives the "right" break point.
If you want it as the first figure then just the do it manually, instead of the computer algorithm which is totally objective even if yo don't like it.
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