From 29d1a88b3e0ff452262284515ee15a8f781d6c4c Mon Sep 17 00:00:00 2001 From: Denis Monnerat Date: Mon, 30 Mar 2026 18:40:09 +0200 Subject: [PATCH] tp1 --- scilab/README.md | 435 +++++++++++++++++++++++++++++++ scilab/Scilab_debutant_annot.pdf | Bin 0 -> 6223560 bytes scilab/img/img1.png | Bin 0 -> 16430 bytes scilab/img/img2.png | Bin 0 -> 15046 bytes scilab/img/img3.png | Bin 0 -> 10065 bytes scilab/img/img4.png | Bin 0 -> 10174 bytes 6 files changed, 435 insertions(+) create mode 100644 scilab/README.md create mode 100644 scilab/Scilab_debutant_annot.pdf create mode 100644 scilab/img/img1.png create mode 100644 scilab/img/img2.png create mode 100644 scilab/img/img3.png create mode 100644 scilab/img/img4.png diff --git a/scilab/README.md b/scilab/README.md new file mode 100644 index 0000000..16e96a9 --- /dev/null +++ b/scilab/README.md @@ -0,0 +1,435 @@ +## Avant de commencer +SCILAB est téléchargeable rapidement [http://www.scilab.org/](http://www.scilab.org/). + +Le logiciel est accompagné d'une documentation très complète. + +De nombreux TP sont présents sur le site de Scilab référencé ci-dessus. + + +Il faut savoir que scilab, comme matlab, est basé sur un noyau de +fonctions en Fortran ou en C déjà compilées donc rapides +d'utilisation. En revanche, tout ce que vous créerez vous-même sera +interprété ce qui ralentira l'exécution par rapport à d'autres +langages. De plus, la gestion des nombres n'est pas toujours optimale +car ils sont codés en complexes double précision ce qui peut être lourd. + +### Console + +La ligne de commande dans la console permet de taper des opérations +élémentaires, comme pour une calculatrice scientifique. Il faut taper tous les +opérateurs, et bien mettre des parenthèses autour de la formule. Une fois la +formule correctement entrée, appuyer sur la touche "entrée" affiche le résultat. +Par exemple : +``` +--> 1+1 +ans = + +2. +``` + +`ans` est l’abréviation de answer, il s’agit du nom +de la variable où la réponse est stockée. + +### Variables + +``` +--> x=9 +``` + +- `clear x` supprime `x` +- `clear` supprime toutes les variables et fonctions. + +Variables permanentes : + +| variable | valeur | +| :--------------- |:---------------| +| ans | dernière réponse | +|%t,%f | Constante booléenne Vrai,Faux | +|%e,%pi | $e$ , $\pi$ | +|%inf | infini | + +### Opérations de base +``` +--> 3+2 +``` + +Si on ajoute un `;` à la fin de la ligne, cell-ci est lue, mais le résultat n'est pas affiché : c'est le mode silencieux. + +``` +--> a=2; b=2;3*a+8*b^3 // le résultat de ce dernier calcul sera affiché +ans = + +70. +``` + +``` +1+sqrt(2) +``` + +On peut naviguer, comme dans le shell, dans l'historique des commandes avec les fléches directionnelles. + +``` +--> %e,%pi +--> log(%e^2) +``` + +On peut utiliser des variables : + +``` +--> a=3; +--> a^2 +--> clear a +``` + +### Objet de base : la matrice +Tout est matrice pour scilab + +Une **matrice ligne** (vecteur ligne) : + +``` +--> vl = [1 2 3 10 100*%pi] //espace ou virgule +vl = + + 1. 2. 3. 10. 314.15927 + +``` + +Une **matrice colonne** (vecteur colonne) : + +``` +--> w=[2;-3*%pi;7] // point virgule + w = + + 2. + -9.4247780 + 7. +``` + +Transposée : opérateur `'` +``` +--> vl' + ans = + + 1. + 2. + 3. + 10. + 314.15927 +``` + +#### Vecteur dont les éléments forment une suite arithmétique + +Syntaxe `v=a:r:b` premier terme `a`, raison `r`, ne dépassant pas `b` + +``` +--> w=[-3:1.5:14] + w = + + -3. -1.5 0. 1.5 3. 4.5 6. 7.5 9. 10.5 12. 13.5 +``` + +Lorsque le pas est 1, on peut l'omettre. + +``` +--> y=[0:9] + y = + + 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. + +``` + +Subdivision uniforme d'un intervalle avec `v=linspace(début, fin, nombre de valeurs)` + +``` +--> v=linspace(-5,8,6) + v = + + -5. -2.4 0.2 2.8 5.4 8. +``` + +#### Création de matrices +Avec la liste des coefficients + +``` +--> A=[1,2,3;4,5,6] + A = + + 1. 2. 3. + 4. 5. 6. + +--> A=[1:4;2:5;3:6] + A = + + 1. 2. 3. 4. + 2. 3. 4. 5. + 3. 4. 5. 6. + + +``` + +Matrices prédéfinies : + +| variable | valeur | +| :--------------- |:---------------| +| `ones(n,m)` | matrice nxm dont les éléments valent 1 | +| `zeros(n,m)` | matrice nxm dont les éléments valent 0 | +| `eye(n,m)` | matrice nxm dont les éléemnts diagonaux valent 1, et 0 ailleurs | + + +### Opérations sur les matrices +**Concaténation** +La concaténation permet de juxtaposer vecteurs et matrices dont les formats sont compatibles. +``` +--> u=1:3; v=[u,u,u] + v = + + 1. 2. 3. 1. 2. 3. 1. 2. 3. + +--> u=1:3; v=[u;u;u] + v = + + 1. 2. 3. + 1. 2. 3. + 1. 2. 3. + +``` + +**Opérations algébriques** + + +| Syntaxe | k*A | A+B | A-B | A*B | A^n | inv(A) ou A^(-1)| A' | +| --- | --- | --- | --- | --- | --- | --- | --- | +| Signification | $kA$ | $A+B$ | $A-B$ | $AB$ | $A^n$ | $A^{-1}$ | $^tA$ | + + + +**Opérations algébriques pointées** + +Ce sont des opérations élément par élément +| Syntaxe |A.*B | A./B | A.^n | +| --- | --- | --- | --- | +| Valeur | $(a_{ij}b_{ij})$ | $(a_{ij}/b_{ij})$ | $(a_{ij}^{n})$ | + + +``` +--> u.^2 + ans = + + 0. 4. 16. 36. 64. 100. +``` + + +**Fonctions matricielles** + +Si `A` est une matrice, et `f` une fonction connue de scilab, `f(A)` retourne la matrice sont les éléments sont les images des éléments de `A` par +`f`. + +``` +--> A=[1 2 3;4 5 6;7 8 9] + A = + + 1. 2. 3. + 4. 5. 6. + 7. 8. 9. + +--> sqrt(A+1) + ans = + + 1.4142136 1.7320508 2. + 2.236068 2.4494897 2.6457513 + 2.8284271 3. 3.1622777 + +``` + + + + + +**Accès à une partie** + +``` +--> A=[1 2 3;4 5 6]; + +--> A(1,2) = 10 + A = + + 1. 10. 3. + 4. 5. 6. + +--> u=[0 2 4 8 10]; + +--> u(3),u(1:3),u($) + ans = + + 4. + ans = + + 0. 2. 4. + ans = + + 10. + +``` + +On peut rechercher dans un vecteur + +``` +--> (A>2) + ans = + + F T T + T T T + + +--> find(u>2) + ans = + + 3. 4. 5. 6. + +``` + + +Pour extraire des lignes ou des colonnes ou des éléments particuliers : + +``` +--> A=[1,2,3;4,5,6;7,8,9]; +--> A(1,3) +--> A(1,:) +--> A(:,1) +--> A($,:) +--> A(1:2:$,:) +--> A($:-1:1,:) +``` +### Fonctions usuelles prédéfinies + +**Analyse** + +`exp,log,sin,abs,floor` + +``` +--> exp(3),log(2),sin(%pi/3),abs(-2),floor(2.178) + ans = + + 20.085537 + ans = + + 0.6931472 + ans = + + 0.8660254 + ans = + + 2. + ans = + + 2. + +``` + +**Matrice** + +`min,max,mean,median,sum,cumsum,size` + +``` +--> u=1:10, s=sum(u),cs = cumsum(u),m=mean(u), + u = + + 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. + s = + + 55. + cs = + + 1. 3. 6. 10. 15. 21. 28. 36. 45. 55. + m = + + 5.5 +``` + +### Graphiques +On commence par créer un vecteur de 10000 valeurs régulièrement espacées entre 0 et 100 : +``` +-->x=linspace(0,100,10000); +``` + +On aurait pu aussi bien poser : +``` +--> x=0:.01:100 +``` + +Nous voulons obtenir la représentation graphique de la fonction $x \rightarrow x\sin(x)$ sur $[0,100]$ : + +``` +--> plot(x,x .*sin(x)) +``` +
+ +
+ +Pour ajouter une autre courbe : +``` +--> plot(x,x); +``` + +Tout demander d'un coup + +``` +--> clf; plot(x,x .*sin(x),x,x,x,-x) +``` + +On peut modifier le style des courbes + +``` +--> X=linspace(-%pi,%pi,20); +--> clf;plot(X,sin(X),"+-b"); +``` + +
+ +
+ + +L'option **+-b** signifie qu'on représente chaque point par une croix (+) , qu'on les relie par un trait continue (-), en bleu (b) + +Regardez l'aide pour toutes les options. + +### Statistiques +La fonction `rand(l,c)` permet de générer une matrice de nombres réelles aléatoires (par défaut, distribution uniforme sur [0,1[) + +Par exemple, pour simuler 100 lancers d'un dé à six faces : + +``` +--> m=floor(6*rand(100,1)+1) +``` +On utilisera aussi la fonction `grand` (help grand) qui permet de simuler la plupart des lois classiques : binomiale, bernoulli, exponentielle, poisson, uniforme, normale, etc. + + +La fonction `tabul(mat)` est très pratique : elle renvoie une matrice de deux colonnes avec les valeurs prises +par les coefficients de mat sur la première colonne et leurs effectifs respectifs sur la deuxième. + +``` +--> t = tabul(m) +``` + +Pour obtenir une représentation graphique sous forme d’un diagramme en bâtons, +on utilise `bar(liste des abs,liste des ord)` : + +``` +--> bar(t(:,1),t(:,2)) +``` + +
+ +
+ +On peut aussi générer un camembert (une tarte en anglais :-)) + +``` +--> pie(t(:,2),t(:,1),string(t(:,1))) +``` + +
+ +
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