From f440edda982fb47ae4ca7df5ad13243d6203f659 Mon Sep 17 00:00:00 2001 From: Audric Schiltknecht Date: Thu, 8 May 2014 18:53:25 +0200 Subject: Essaie reécriture du site avec pelican MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Suppression des anciens fichiers. Création architecture site pelican. Récupération des contenus statiques. --- content/static/TIPE_2007/Maple/TFD.mw | 472 ++++++++++++++++++++++++++++++++++ 1 file changed, 472 insertions(+) create mode 100644 content/static/TIPE_2007/Maple/TFD.mw (limited to 'content/static/TIPE_2007/Maple/TFD.mw') diff --git a/content/static/TIPE_2007/Maple/TFD.mw b/content/static/TIPE_2007/Maple/TFD.mw new file mode 100644 index 0000000..87d6772 --- /dev/null +++ b/content/static/TIPE_2007/Maple/TFD.mw @@ -0,0 +1,472 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +restart: + + +
+<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Calcul de la TFD par une proc\303\251dure "na\303\257ve"</Font></Text-field> +Cette proc\303\251dure calcule les coefficients de Fourier par une m\303\251thode dite "naive". + + +TFDSimple:=proc(x) + +local n,X: +n:=nops(x): + +X:=[seq(sum(x[j]*exp(-2*I*(j-1)*(k-1)*Pi/n),j=1..n),k=1..n)]; + +end proc: + + +
+
+<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Calcul de la TFD par une proc\303\251dure r\303\251cursive</Font></Text-field> +Cette proc\303\251dure prend en entr\303\251e une liste repr\303\251sentant les coefficients d'un polyn\303\264me dont on cherche \303\240 calculer les coefficients de Fourier. + + +TFDRecur:=proc(x) + +local N,CoefFFT,xp,xi,u,v,omega: +N:=nops(x): + +if N=1 then CoefFFT:=x: +else + +xp:=[seq(x[2*i],i=1..N/2)]: +xi:=[seq(x[2*i-1],i=1..N/2)]: +u:=TFDRecur(xp): +v:=TFDRecur(xi): + +omega:=exp(-2*I*Pi/N): + +CoefFFT:=[seq(omega^(k-1)*u[k]+v[k],k=1..N/2),seq(-omega^(k-1)*u[k]+v[k],k=1..N/2)]; +end if: +CoefFFT; + +end proc: + + +
+
+<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Calcul de la TFD par it\303\251ration</Font></Text-field> +On va utiliser l'\303\251criture des divers coefficients en binaire. + + + +TFDIter:=proc(x) +local n,i,j,k,a,b,p,l,z,w,h,m,tmp: +n:=nops(x): +l:=Array(1..n): +l:=Array(x): +p:=n/2:#p: puissance de 2 dans d\303\251composition. + +while p>=1 do + z:=1: #premi\303\250re valeur de omega. + w:=exp(-I*Pi/p): #c'est omega. + + for h from 1 to p do #Variable servant \303\240 la d\303\251composition + for m from 1 to n/(2*p) do + #On va calculer le signal xm + a:=h+2*(m-1)*p: #Premi\303\250re valeur du signal x_(m-1) + b:=a+p: #Seconde valeur du signal x_(m-1) + tmp:=(l[a]-l[b])*z: + l[a]:=l[a]+l[b]: #x_m(a) = x_(m-1)(a)+x_(m-1)(b) + l[b]:=tmp: #x_m(b) = (x_(m-1)(a)-x_(m-1)(b))*z + end do: + #On passe au signal m+1 -> w<-w^(m+1) + z:=z*w: + end do: + p:=p/2: +end do: + +#On a maintenant notre liste contenant les signaux x_r +#Il reste \303\240 remettre les signaux dans le bon ordre. +j:=1: +for i from 1 to n do + if j>i then tmp:=l[j]: + l[j]:=l[i]: + l[i]:=tmp: + end if: + p:=n/2: + while p>=2 and j>p do + j:=j-p: + p:=p/2: + end do: + j:=j+p: +end do: +l; +end proc: + + +
+
+<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Calcul de la Transform\303\251e Inverse.</Font></Text-field> +De m\303\252me, il est possible d'effectuer deux m\303\251thodes pour calculer la transform\303\251e inverse de Fourier : +
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">La m\303\251thode na\303\257ve</Font></Text-field> +En utilisant le m\303\252me algorithme, on obtient : + + +TFDISimple:=proc(X) + +local n,F: +n:=nops(X): + +F:=[seq((1/n)*sum(X[i]*exp(2*I*(j-1)*(i-1)*Pi/(n)),i=1..n),j=1..n)]; + +end proc: + + +
+
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">La m\303\251thode r\303\251cursive</Font></Text-field> +Attention : Pour que l'on puisse retrouver les valeurs initiales, +il ne faut pas oublier de diviser par le nombre de valeurs. + + +TFDIRecur:=proc(X) +local Coef,N,Xi,Xp,U,V,Omega,k; +N:=nops(X); + +if N=1 then Coef:=X: +else + Xi:=[seq(X[2*k-1],k=1..N/2)]; + Xp:=[seq(X[2*k],k=1..N/2)]; + U:=TFDIRecur(Xi); + V:=TFDIRecur(Xp); + Omega:=exp(2*I*Pi/N); + Coef:=[seq(U[k]+Omega^(k-1)*V[k],k=1..N/2),seq(U[k]-Omega^(k-1)*V[k],k=1..N/2)]: + end if; +Coef; +end proc: + + +
+
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">La m\303\251thode it\303\251rative</Font></Text-field> + + + +TFDIIter:=proc(x) +local n,i,j,k,a,b,p,l,z,w,h,m,tmp: +n:=nops(x): +l:=Array(1..n): +l:=Array(x): +p:=n/2: + +while p>=1 do + z:=1: + w:=exp(I*Pi/p); #C'est la diff\303\251rence + + for h from 1 to p do + for m from 1 to n/(2*p) do + a:=h+2*(m-1)*p: + b:=a+p: + tmp:=(l[a]-l[b])*z: + l[a]:=l[a]+l[b]: + l[b]:=tmp: + end do: + z:=z*w: + end do: + p:=p/2: +end do: + +j:=1: +for i from 1 to n do + if j>i then tmp:=l[j]: + l[j]:=l[i]: + l[i]:=tmp: + end if: + p:=n/2: + while p>=2 and j>p do + j:=j-p: + p:=p/2: + end do: + j:=j+p: +end do: +for i from 1 to n do + l[i]:=l[i]/n: +end do: +return l; +end proc: + + +
+
+
+<Text-field style="Heading 1" layout="Heading 1">Mesure du temps de calcul</Text-field> +On va ici s'int\303\251resser \303\240 la mesure du temps n\303\251cessaire pour calculer les coefficients de Fourier (Transform\303\251e Directe) pour n "grand", par exemple n=2^5, n=2^10,... . +Pour cela, on va d\303\251finir la liste de nos coefficients par une m\303\251thode "pseudo-al\303\251atoire" : + + + +with(RandomTools[MersenneTwister]): +A:=[seq(GenerateFloat(),i=1..2^8)]: + + +
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">M\303\251thode na\303\257ve</Font></Text-field> +On effectue le calcul pour la m\303\251thode na\303\257ve : + + +t:=time(): +TFDSimple(A): +Temps := time()-t; + + 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 + + +
+
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">M\303\251thode r\303\251cursive</Font></Text-field> +Calcul pour la m\303\251thode r\303\251cursive : + + +t:=time(): +TFDRecur(A): +Temps := time()-t; + + 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 + + +
+
+<Text-field style="Heading 2" layout="Heading 2"><Font encoding="UTF-8">M\303\251thode it\303\251rative</Font></Text-field> +Mesure pour la m\303\251thode it\303\251rative : + + +t:=time(): +TFDIter(A): +Temps:= time()-t; + + 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 + + +
+
+
+<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Multiplication de polyn\303\264mes</Font></Text-field> +
+<Text-field style="Heading 2" layout="Heading 2">Algorithme</Text-field> +On va prendre en entr\303\251e deux listes contenant les coefficients des deux polyn\303\264mes dont on cherche \303\240 calculer le produit. +Il faut prendre des pr\303\251cautions, car la proc\303\251dure ne v\303\251rifie pas si les deux polyn\303\264mes sont de m\303\252me degr\303\251, qui doit \303\252tre une puissance de 2, si l'on souhaite utiliser la m\303\251thode r\303\251cursive ou it\303\251rative. + + +Multiplication:=proc(P,Q) + +local n,N,R,A,B,i,j,k: + +n:=nops(P): +N:=2*n: + +#On cr\303\251e la liste des coefficients \303\251tendus \303\240 2n \303\251l\303\251ments. +A:=[seq(P[k],k=1..n),seq(0,k=n+1..N)]; +B:=[seq(Q[k],k=1..n),seq(0,k=n+1..N)]; + +#On calcule la TFD de chacune de ces listes. +A:=TFDIter(A): +B:=TFDIter(B): + +#On effectue les produits +R:=[seq(A[k]*B[k],k=1..N)]: + +#On r\303\251cup\303\250re les coefficients. +TFDIIter(R); + +end proc: + + +
+
+<Text-field style="Heading 2" layout="Heading 2">Exemple</Text-field> +On va poser 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 et 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 doncLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW9HRiQ2M1ExJkludmlzaWJsZVRpbWVzO0YnLyUlZm9ybUdRJmluZml4RicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjQvJSdsc3BhY2VHUS90aGlja21hdGhzcGFjZUYnLyUncnNwYWNlR0Y5LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShtYXhzaXplR1EpaW5maW5pdHlGJy8lKG1pbnNpemVHUSIxRicvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lMGZvbnRfc3R5bGVfbmFtZUdRKDJEfk1hdGhGJy8lJXNpemVHUSMxMkYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdRictSSNtaUdGJDY5USJuRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHRlEvJSVib2xkR0Y0LyUnaXRhbGljR1EldHJ1ZUYnLyUqdW5kZXJsaW5lR0Y0LyUqc3Vic2NyaXB0R0Y0LyUsc3VwZXJzY3JpcHRHRjQvJStmb3JlZ3JvdW5kR0ZULyUrYmFja2dyb3VuZEdGVy8lJ29wYXF1ZUdGNC8lK2V4ZWN1dGFibGVHRjQvJSlyZWFkb25seUdGNC8lKWNvbXBvc2VkR0Y0LyUqY29udmVydGVkR0Y0LyUraW1zZWxlY3RlZEdGNC8lLHBsYWNlaG9sZGVyR0Y0LyUwZm9udF9zdHlsZV9uYW1lR0ZOLyUqbWF0aGNvbG9yR0ZULyUvbWF0aGJhY2tncm91bmRHRlcvJStmb250ZmFtaWx5R0Zobi8lLG1hdGh2YXJpYW50R1EnaXRhbGljRicvJSltYXRoc2l6ZUdGUS1GLDYzUSI9RidGL0YyRjVGN0Y6RjxGPkZARkNGRkZIRkpGTEZPRlJGVS1JI21uR0YkNjlRIjhGJ0ZmbkZpbkZbby9GXm9GNEZgb0Zib0Zkb0Zmb0Zob0Zqb0ZccEZecEZgcEZicEZkcEZmcEZocEZqcEZccUZecS9GYXFRJ25vcm1hbEYnRmNxRmVxLUklbXN1cEdGJDYlLUZpcTY5USIyRidGZm5GaW5GW29GXHJGYG9GYm9GZG9GZm9GaG9Gam9GXHBGXnBGYHBGYnBGZHBGZnBGaHBGanBGXHFGXnFGXXJGY3EtRmlxNjlRIzMuRidGZm5GaW5GW29GXHJGYG9GYm9GZG9GZm9GaG9Gam9GXHBGXnBGYHBGYnBGZHBGZnBGaHBGanBGXHFGXnFGXXJGY3EvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUZZNjlRIUYnRmZuRmluRltvRl1vRmBvRmJvRmRvRmZvRmhvRmpvRlxwRl5wRmBwRmJwRmRwRmZwRmhwRmpwRlxxRl5xRmBxRmNx +
+<Text-field style="Heading 3" layout="Heading 3">Algo</Text-field> +On va demander la liste des coefficients du polyn\303\264me R=P*Q. Pour une lecture plus facile, nous en prendrons les valeurs arrondies. + + +P:=[seq(i,i=0..7)]: + + + + +Q:=[seq(i^i,i=0..7)]: + + + + +R:=evalf(Multiplication(P,Q)): + + + + +[seq(R[j],j=1..2*nops(P))]; + + 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 + + + + +R:=[seq(round(R[j]),j=1..2*nops(P))]; + + 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 + + +
+
+<Text-field style="Heading 3" layout="Heading 3">Maple</Text-field> +On va evaluer le polyn\303\264me P*Q : + + +P:=sum(i*X^i,i=0..7): + + + + +Q:=sum(i^i*X^i,i=0..7): + + + + +sort(expand(P*Q),X,ascending); + + 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 + + + + + + + +
+
+
+ \ No newline at end of file -- cgit v1.2.3-70-g09d2