
samayam warp edittu dooram

samayathinte 'ilaasthikatha' yumayi poruthappedunna vyathirikthamaya samaya shreniyude samaanathayude (allengil vyathyaasathinte) alavaanu time warp edittu dooram (twed). mattu dooraparidhikalumaayi thaarathamyappeduthumbol, (udha.jii. dtw (dynamic time warping) allengil lcs (ettavum dairkhyameriya saadhaarana thudarprashnam), twed oru metrik aanu. athinte computational samaya sankeernnatha formula _ 1 aanu, ennaal thirayal idam kuraykkunnathinu oru idanaazhi upayogichu chila prathyeka saahacharyangalil ganyamaayi kuraykkaan kazhiyum. athinte memory space sankeernnatha formula _ 2 aayi kuraykkaam. ithu 2009 ll pii aanu aadyamaayi nirddeshichathu.-eph. martio.
nirvachanam.
soothravaakyam _ 3 evideyengilum
formula _ 4
soothravaakyam _ 5
soothravaakyam _ 6
athesamayam aavarthanam
soothravaakyam _ 7
inipparayunna reethiyil aarambikkunnu
soothravaakyam _ 8
formula _ 9
soothravaakyam _ 10
koode
soothravaakyam _ 11
nadappaakkal.
paitthan rapper upayogichu sii yill twed algoritam nadappaakkunnathu ivide labhyamaan 
ivide labhyamaya time seerees sequence serch paitthan paakkejilum (churukkatthil tssearch) twed nadappilaakkunnu.
twedinte nadappaakkal traminerilekku samyojippichirikkunnu, khananathinulla oru aarr paakkej, avasthakaludeyo sambhavangaludeyo sequenceukal vivarikkukayum drishyavalkkarikkukayum cheyyuka, kooduthal saadhaaranayaayi vyathirikthamaya sequence daatta.
koodaathe, jii kaaranam mechappetta algoritam upayogikkunna twedinte oru cuda-accelered nadappakkalaanu katt vedu. raitt (2020). eee reethi memmariyil rekheeyavum valia samaantharavumaanu. cutwade kuda sii/sii + + ll ezhuthappettirikkunnu, paitthan bindingukalodeyaanu varunnath, koodaathe maarttuvinte reference sii nadappakkunnathinulla paitthan bindingukalum ulppedunnu.
paitthan.
nupy enna peril import cheyyuka
dii. eph. dii. ell. pii (eiii, bii, pii = 2):
 chelavu = enn. pii.thuka (enn. pii.power (enn. pii.abs (eiii-bii), pii))
 enn. pii. thirike nalkuka.vaidyuthi (chelavu, 1/pii)
def twed (eiii, timesa, bii, times bii, nyoo, _ lamda):
 #[dooram, dipi] = twed (eiii, timesa, bii, times bii, lamda, nyoo)
 #eiii, bii ennee samaya shrenikalude samayaparidhi kanakkukoottuka.
 #a: = samaya shreni a (e.jii. [10 2 30 4])
 #timesa = time seerees eiii (iii.jii. 1: 4)
 #bii = samaya shreni bii
 #times bii = time seerees bii yude time staambu
 #lamda = illaathaakkal pravarthanatthinu pizha
 #nu: = ilaasthikatha paaraameettar-nu> = 0 dooram alakkaan aavasyamaanu
 #references
 #martue, pii.; eph. (2009). "time seerees poruthappedutthalinaayi kaadinyam krameekarichukondu samayam warp edittu dooram".
 #paatten vishakalanathilum mesheen intalijansilum edapaadukal. 31 (2): 306-318. arxiv: cs/0703033
 #HTTP:// aalukal.airisa.efr/piyari-francois.martio/
 #inputt aargyumentukal undo ennu parisodhikkuka
 lenne (eiii) aanenkil!= lenne (timesa):
 print ("a yude neelam timesayude thulya neelamalla")
 onnum thirike nalkaruth, onnumilla
 lenne (bii) aanenkil!= lenne (times bii):
 print ("b yude neelam times b yude thulya neelamalla")
 onnum thirike nalkaruth, onnumilla
 nyoo <0 aanenkil
 print ("nu is negative")
 onnum thirike nalkaruth, onnumilla
 #padding cherkkuka
 a = np.shreni ([0] + pattika (eiii))
 timesa = enn. pii.shreni ([0] + listt (timesa))
 b = np.shreni ([0] + pattika (bii))
 times bii = enpi.shreni ([0] + listt (times bii))
 n = lenne (a)
 m = lenne (bii)
 #dynamic prograaming
 dp = np.poojyangal ((n, m))
 #dipi matricks aarambikkukayum aadya variyum nirayum ananthathayilekku sajjamaakkukayum cheyyuka
 dp [0,:] = np.inf
 dp [:, 0] = np.inf
 dp [0,0] = 0
 #kuranja chelavu kanakkaakkuka
 shreniyile (1, n) i-nn
 J-nuu (1, m):
 #vividha pravartthanangalude chelavu kanakkaakkukayum laabhikkukayum cheyyuka
 sii = enpi.orennam ((3,1)) * enn. pii.inf
 #eiii yill illaathaakkuka
 sii [0] = (
 dipi [aii-1, jeey]
 + dii. ell. pii (a [i-1], a [i])
 + nu * (timesa [i]-timesa [i-1])
 + _ lambda
 #bii yill illaathaakkuka
 sii [1] = (
 dipi [aii, jeey-1]
 + dii. ell. pii (bii [jeey-1], bii [jeey])
 + nu * (times bii [jeey]-times bii [jeey-1])
 + _ lambda
 #rund samaya shrenikalilum dattaa pooyintukal sookshikkuka
 sii [2] = (
 dipi [aii-1, jeey-1]
 + dii. ell. pii (a [i], b [j])
 + dii. ell. pii (a [i-1], b [j-1])
 + nu * (ebbs (timesa [i]-times bii [jeey]) + ebbs (times bii [jeey-1]-times bii [jeey-1]))
 #kuranja chelavil pravartthanam thiranjedukkukayum dipi matricks update cheyyukayum cheyyuka
 dp [i, j] = np.minimum (sii)
 dooram = dipi [n-1, m-1]
 madakka dooram, dipi
ettavum chelavu kuranja paatha kandethunnathinu pinnott pookuka
def backtracking (dipi):
 #[bestt _ paathu] = back tracking (dipi)
 #ettavum chelavu kuranja paatha kanakkukoottuka
 #dipi = twed functionte dipi matricks
 x = np.aakruthi (dipi)
 i = x [0]-1
 jeey = x [1]-1
 #paathakalude soochikakal vipareeta dishayilaanu save cheiyunnathu.
 #paathu = enn. pii.(i + j, 2) * np.inf;
 mikacha _ paatha = []
 gattangal = 0
 njaan!= 0 allengil jeey!= 0:
 bestt _ paathu.kootticherkkuka ((i-1, j-1))
 sii = enpi.orennam ((3,1)) * enn. pii.inf
 #rund samaya shrenikalilum dattaa pooyintukal sookshikkuka
 c [0] = dp [i-1, j-1]
 #eiii yill illaathaakkuka
 c [1] = dp [i-1, j]
 #bii yill illaathaakkuka
 c [2] = dp [i, j-1]
 #ettavum kuranja chelavinte soochika kandethuka
 idx = enpi.aargman (sii)
 idx = = 0 aanenkil
 #rund samaya shrenikalilum dattaa pooyintukal sookshikkuka
 i = i-1
 jeey = jeey-1
 eliph idx = = 1:
 #eiii yill illaathaakkuka
 i = i-1
 jeey = jeey
 mattethu
 #bii yill illaathaakkuka
 i = i
 jeey = jeey-1
 gattangal = gattangal + 1
 bestt _ paathu.kootticherkkuka ((i-1, j-1))
 bestt _ paathu.nere thirichaanu ()
 mikacha paatha thirike nalkuka [1:]
maatt laab.
function [dooram, dp] = twed (a, timesa, b, times bii, lamda, nu)
 % [dooram, dp] = twed (a, timesa, b, times bii, lamda, nu)
 a, b ennee samaya shrenikalile dooram (twed) edittu cheyyaan% kanakkukoottunnu
 % a: = samaya shreni a (e.jii. [10 2 30 4])
 % timesa = samaya shreniyude samaya mudra a (e.jii. 1: 4)
 % b: = samayakramam b
 % times bii = time seerees bii yude time staambu
 % lamda = illaathaakkal pravarthanatthinu pizha
 % nu: = ilaasthikatha paaraameettar-nu> = 0 dooram alakkaan aavasyamaanu
 % coode baiah p.-eph. martue-HTTP:// aalukal.airisa.efr/piyari-francois.martio/
 inputt aargyumentukal undo ennu% parisodhikkuka
 neelam (eiii) ~ = neelam (timesa) aanenkil
 munnariyipp ('a yude neelam samayathinte thulya neelamalla')
 madanguka
 avasaanam
 neelam (bii) ~ = neelam (times bii) aanenkil
 munnariyipp ('bii yude neelam time bii yude thulya neelamalla')
 madanguka
 avasaanam
 nyoo <0 aanenkil
 munnariyipp ('nyoo negatteevu aanu')
 madanguka
 avasaanam
 % padding cherkkuka
 a = [0 a];
 timesa = [0 timesa];
 b = [0 b];
 times bii = [0 times bii];
 % chalanathmaka prograaming
 dp = poojyangal (neelam (a), neelam (b));
 % dipi matricks aarambikkukayum aadya variyum nirayum ananthathayilekku sajjamaakkukayum cheyyuka
 dp (1,:) = inf;
 dp (:, 1) = inf;
 dp (1,1) = 0;
 n = neelam (timesa);
 m = neelam (times bii);
 % kuranja chelavu kanakkakkunnu
 i = 2: n
 jeey = 2: emm
 chelavu = dii. ell. pii (eiii (aii), bii (jeey));
 % vividha pravartthanangalude chelavu kanakkaakkukayum laabhikkukayum cheiyunnu
 sii = orennam (3,1) * inf;
 % illaathaakkal a
 c (1) = dp (i-1, j) + dlp (a (i-1), a (i)) + nu * (timesa (i)-timesa (i-1)) + lamda;
 bii yill% illaathaakkal
 c (2) = dp (i, j-1) + dlp (b (j-1), b (j)) + nu * (timesb (j)-timesb (j-1)) + lamda;
 % rund samaya shrenikalilum dattaa pooyintukal sookshikkunnu
 c (3) = dp (i-1, j-1) + dlp (a (i), b (j)) + dlp (a (i-1), b (j-1)) +...
 nu * (abs (timesa (i)-times bii (jeey)) + abs (times bii (aii-1)-times bii (jeey-1)));
 % kuranja chelavil pravartthanam thiranjedukkukayum dipi matricks update cheyyukayum cheiyunnu
 dp (i, j) = minimum (c);
 avasaanam
 avasaanam
 dooram = dipi (enn, emm);
 euclidean dooram kanakkakkaan% function
 function [koost] = dii. ell. pii (eiii, bii)
 chelavu = chathurashra ((a-b).^ 2, 2));
 avasaanam
avasaanam
ettavum chelavu kuranja paatha kandethunnathinu pinnott pookuka
function [paathu] = backtracking (dipi)
 % [paathu] = back tracking (dipi)
 % ettavum chelavu kuranja paatha kanakkukoottuka
 % dp: = twed functionte dp matricks
 x = valippam (dipi);
 i = x (1);
 jeey = x (2);
 % paathakalude soochikakal vipareeta dishayilaanu save cheiyunnathu
 paatha = vansu (i + j, 2) * inf;
 gattangal = 1;
 athesamayam (i ~ = 1 || jeey ~ = 1)
 paatha (gattangal,:) = [i; j];
 sii = orennam (3,1) * inf;
 % rund samaya shrenikalilum dattaa pooyintukal sookshikkunnu
 c (1) = dp (i-1, j-1);
 % illaathaakkal a
 c (2) = dp (i-1, j);
 bii yill% illaathaakkal
 c (3) = dp (i, j-1);
 % ettavum kuranja chelavinte soochika kandethuka
 [~, idx] = minitt (sii);
 idx maattuka
 cases 1
 % rund samaya shrenikalilum dattaa pooyintukal sookshikkunnu
 i = i-1;
 jeey = jeey-1;
 cases 2
 % illaathaakkal a
 i = i-1;
 jeey = jeey;
 cases 3
 bii yill% illaathaakkal
 i = i;
 jeey = jeey-1;
 avasaanam
 gattangal = gattangal + 1;
 avasaanam
 paatha (gattangal,:) = [ij];
 % paathu vipareeta dishayilaanu kanakkaakkiyath.
 paatha = paatha (1: gattangal,:);
 paatha = paatha (avasaanam-1:1,:);
avasaanam

