scilab/modules/elementary_functions/help/fr_FR/insertion.xml

   1 <?xml version="1.0" encoding="UTF-8"?>
   2 <refentry xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" xmlns:scilab="http://www.scilab.org" xml:lang="fr" xml:id="insertion">
   3     <refnamediv>
   4         <refname>insertion</refname>
   5         <refpurpose>insertion/modification dans une
   6             variable
   7         </refpurpose>
   8     </refnamediv>
   9     <refnamediv xml:id="affectation">
  10         <refname>affectation</refname>
  11         <refpurpose>affectation partielle d'une variable  </refpurpose>
  12     </refnamediv>
  13     <refsynopsisdiv>
  14         <title>Séquence d'appel</title>
  15         <synopsis>x(i,j)=a
  16             x(i)=a
  17             l(i)=a
  18             l(k1)...(kn)(i)=a ou l(list(k1,...,kn,i))=a
  19             l(k1)...(kn)(i,j)=a ou l(list(k1,...,kn,list(i,j))=a
  20         </synopsis>
  21     </refsynopsisdiv>
  22     <refsection>
  23         <title>Paramètres</title>
  24         <variablelist>
  25             <varlistentry>
  26                 <term>x  </term>
  27                 <listitem>
  28                     <para>matrice de tout type
  29                     </para>
  30                 </listitem>
  31             </varlistentry>
  32             <varlistentry>
  33                 <term>l  </term>
  34                 <listitem>
  35                     <para>liste
  36                     </para>
  37                 </listitem>
  38             </varlistentry>
  39             <varlistentry>
  40                 <term>i,j  </term>
  41                 <listitem>
  42                     <para>indices
  43                     </para>
  44                 </listitem>
  45             </varlistentry>
  46             <varlistentry>
  47                 <term>k1,...kn  </term>
  48                 <listitem>
  49                     <para>indices à valeurs entières
  50                     </para>
  51                 </listitem>
  52             </varlistentry>
  53             <varlistentry>
  54                 <term>a  </term>
  55                 <listitem>
  56                     <para>nouvelles valeurs des termes
  57                     </para>
  58                 </listitem>
  59             </varlistentry>
  60         </variablelist>
  61     </refsection>
  62     <refsection>
  63         <title>Description</title>
  64         <variablelist>
  65             <varlistentry>
  66                 <term>CAS DES MATRICES</term>
  67                 <listitem>
  68                     <para/>
  69                     <para>
  70                         Si  <literal>x</literal> est un tableau <literal>i</literal> et <literal>j</literal> peuvent être :
  71                     </para>
  72                     <variablelist>
  73                         <varlistentry>
  74                             <term>Des scalaires, vecteurs ou matrices</term>
  75                             <listitem>
  76                                 <para>Dans ce cas, les valeurs données en
  77                                     indices doivent être strictement positives. Seules les parties
  78                                     entières sont prises en compte.
  79                                 </para>
  80                                 <itemizedlist>
  81                                     <listitem>
  82                                         <para>
  83                                             Si <literal>a</literal> est une matrice de dimensions
  84                                             <literal>(size(i,'*'),size(j,'*'))</literal>
  85                                             <literal>x(i,j)=a</literal> renvoie une nouvelle matrice
  86                                             <literal>x</literal> telle que <literal>x(int(i(l)),int(j(k)))=a(l,k)
  87                                             </literal>
  88                                             pour <literal>l</literal> variant de 1 à
  89                                             <literal>size(i,'*')</literal> et <literal>k</literal> variant de
  90                                             1 à <literal>size(j,'*')</literal>, les autres composantes
  91
  92                                             initiales de <literal>x</literal> sont inchangées.
  93                                         </para>
  94                                     </listitem>
  95                                     <listitem>
  96                                         <para>
  97                                             Si <literal>a</literal> est un scalaire
  98                                             <literal>x(i,j)=a</literal> renvoie une nouvelle matrice
  99                                             <literal>x</literal> telle que <literal>x(int(i(l)),int(j(k)))=a </literal>
 100                                             pour <literal>l</literal> variant de 1 à
 101                                             <literal>size(i,'*')</literal> et <literal>k</literal> variant de
 102                                             1 à <literal>size(j,'*')</literal>, les autres composantes
 103                                             initiales de <literal>x</literal> sont inchangées.
 104                                         </para>
 105                                     </listitem>
 106                                     <listitem>
 107                                         <para>
 108                                             Si la valeur maximum de <literal>i</literal> ou
 109                                             <literal>j</literal> dépasse la dimension correspondante de
 110                                             <literal>x</literal>, alors <literal>x</literal> est au préalable agrandie
 111                                             aux dimensions adéquates en stockant des zéros pour les matrices
 112                                             standard, des chaînes vides pour les matrices de chaînes de
 113                                             caractères ou la valeur %F pour les matrices booléennes.
 114                                         </para>
 115                                     </listitem>
 116                                     <listitem>
 117                                         <para>
 118                                             <literal>x(i,j)=[]</literal> détruit les lignes
 119                                             spécifiées par <literal>i</literal> si <literal>j</literal> désigne toutes
 120                                             les colonnes de <literal>x</literal> ou détruit les colonnes
 121                                             spécifiées par <literal>j</literal> si <literal>i</literal> désigne toutes
 122                                             les lignes de <literal>x</literal>. Dans tous les autres cas
 123                                             <literal>x(i,j)=[]</literal> produit une erreur.
 124                                         </para>
 125                                     </listitem>
 126                                     <listitem>
 127                                         <para>
 128                                             <literal>x(i)=a</literal> où <literal>a</literal> est un
 129                                             vecteur renvoie une nouvelle matrice <literal>x</literal> telle que
 130                                             <literal>x(int(i(l)))=a(l)</literal> pour <literal>l</literal> variant de 1
 131                                             à <literal>size(i,'*')</literal> , les autres composantes
 132                                             initiales de <literal>x</literal> sont inchangées.
 133                                         </para>
 134                                     </listitem>
 135                                     <listitem>
 136                                         <para>
 137                                             <literal>x(i)=a</literal> où <literal>a</literal> est un
 138                                             scalaire, renvoie une nouvelle matrice <literal>x</literal> telle que
 139                                             <literal>x(int(i(l)))=a</literal> pour <literal>l</literal> variant de 1 à
 140                                             <literal>size(i,'*')</literal> , les autres composantes
 141                                             initiales de <literal>x</literal> sont inchangées.
 142                                         </para>
 143                                         <para>
 144                                             Si la valeur maximum de <literal>i</literal> dépasse
 145                                             <literal>size(x,1)</literal>, <literal>x</literal> est au préalable agrandie
 146                                             aux dimensions adéquates en stockant des zéros pour les matrices
 147                                             standard, des chaînes vides pour les matrices de chaînes de
 148                                             caractères ou la valeur %F pour les matrices booléennes.
 149                                         </para>
 150                                         <variablelist>
 151                                             <varlistentry>
 152                                                 <term>Si</term>
 153                                                 <listitem>
 154                                                     <para>
 155                                                         <literal>x</literal> est une matrice 1 x 1 <literal>a</literal> peut
 156                                                         être un vecteur ligne (resp. colonne) de dimension
 157                                                         <literal>size(i,'*')</literal>. La matrice
 158                                                         <literal>x</literal> obtenue est un vecteur ligne
 159                                                         (resp. colonne)
 160                                                     </para>
 161                                                 </listitem>
 162                                             </varlistentry>
 163                                             <varlistentry>
 164                                                 <term>Si</term>
 165                                                 <listitem>
 166                                                     <para>
 167                                                         <literal>x</literal> est un vecteur
 168                                                         ligne (resp. colonne) <literal>a</literal> doit être un vecteur
 169                                                         ligne (resp. colonne) de dimension
 170                                                         <literal>size(i,'*')</literal>
 171                                                     </para>
 172                                                 </listitem>
 173                                             </varlistentry>
 174                                             <varlistentry>
 175                                                 <term>Si</term>
 176                                                 <listitem>
 177                                                     <para>
 178                                                         <literal>x</literal> est une matrice
 179                                                         en général <literal>a</literal> doit être un vecteur ligne ou
 180                                                         colonne de dimension <literal>size(i,'*')</literal> et
 181                                                         la valeur maximum de<literal>i</literal> ne peut dépasser
 182                                                         <literal>size(x,'*')</literal>,
 183                                                     </para>
 184                                                 </listitem>
 185                                             </varlistentry>
 186                                         </variablelist>
 187                                     </listitem>
 188                                     <listitem>
 189                                         <para>
 190                                             <literal>x(i)=[]</literal> supprime les termes
 191
 192
 193                                             spécifiés par <literal>i</literal>.
 194                                         </para>
 195                                     </listitem>
 196                                 </itemizedlist>
 197                             </listitem>
 198                         </varlistentry>
 199                         <varlistentry>
 200                             <term>Le : symbole</term>
 201                             <listitem>
 202                                 <para>
 203                                     Le symbole <literal> : </literal> signifiant "tous les éléments".
 204                                 </para>
 205                                 <itemizedlist>
 206                                     <listitem>
 207                                         <para>
 208                                             <literal>x(i,:)=a</literal> est interprété comme
 209
 210                                             <literal>x(i,1:size(x,2))=a</literal>
 211                                         </para>
 212                                     </listitem>
 213                                     <listitem>
 214                                         <para>
 215                                             <literal>x(:,j)=a</literal> est interprété comme
 216                                             <literal>x(1:size(x,1),j)=a</literal>
 217                                         </para>
 218                                     </listitem>
 219                                     <listitem>
 220                                         <para>
 221                                             <literal>x(:)=a</literal> renvoie dans
 222                                             <literal>x</literal> la matrice <literal>a</literal> remise en forme en
 223                                             accord avec les dimensions de
 224                                             x. <literal>size(x,'*')</literal> doit être égal
 225                                             à<literal>size(a,'*')</literal>
 226                                         </para>
 227                                     </listitem>
 228                                 </itemizedlist>
 229                             </listitem>
 230                         </varlistentry>
 231                         <varlistentry>
 232                             <term>Vecteurs de booléens</term>
 233                             <listitem>
 234                                 <para>  Si un indice
 235
 236                                     (<literal>i</literal> ou <literal>j</literal> ) est un vecteur de booléens, il
 237                                     est interprété comme <literal>find(i)</literal> ou <literal>find(j)</literal>,
 238                                     respectivement.
 239                                 </para>
 240                             </listitem>
 241                         </varlistentry>
 242                         <varlistentry>
 243                             <term>Polynomes</term>
 244                             <listitem>
 245                                 <para>
 246                                     Si un indice (<literal>i</literal> ou
 247                                     <literal>j</literal> ) est un vecteur de polynômes ou de polynômes
 248                                     implicites, il est interprété comme <literal>horner(i,m)</literal> ou
 249                                     <literal>horner(j,n)</literal>, respectivement, où <literal>m</literal> et
 250                                     <literal>n</literal> sont les dimensions de <literal>x</literal> associées.
 251                                     Même si cette fonctionnalité marche pour tous les polynômes, il
 252                                     est recommandé d'utiliser des polynômes dans <literal>$</literal>
 253                                     par souci de lisibilité.
 254                                 </para>
 255                             </listitem>
 256                         </varlistentry>
 257                     </variablelist>
 258                 </listitem>
 259             </varlistentry>
 260             <varlistentry>
 261                 <term>CAS DES LISTES</term>
 262                 <listitem>
 263                     <itemizedlist>
 264                         <listitem>
 265                             <para>
 266                                 S'ils sont présents les <literal>ki</literal> donnent le chemin
 267                                 vers un terme d'une sous-liste de la liste
 268                                 <literal>l</literal>. Ils permettent de faire une insertion récursive
 269                                 directe sans utiliser de variable intermédiaire.  Les instructions
 270                                 <literal>l(k1)...(kn)(i)=a</literal> et
 271                                 <literal>l(list(k1,...,kn,i)=a)</literal> sont interprétées comme :
 272                             </para>
 273                             <para>
 274                                 <literal>lk1 = l(k1)</literal>
 275                                 <literal> ..  = ..  </literal>
 276                             </para>
 277                             <para>
 278                                 <literal>lkn =   lkn-1(kn)</literal>
 279                             </para>
 280                             <para>
 281                                 <literal>lkn(i) = a</literal>
 282                                 <literal>lkn-1(kn) =lkn</literal>
 283                                 <literal> ..  = ..</literal>
 284                             </para>
 285                             <para>
 286                                 les instructions<literal>l(k1)...(kn)(i,j)=a</literal> et
 287                                 <literal>l(list(k1,...,kn,list(i,j))=a</literal> sont interprétées
 288                                 comme:
 289                             </para>
 290                             <para>
 291                                 <literal>lk1 = l(k1)</literal>
 292                                 <literal> ..  = ..  </literal>
 293                             </para>
 294                             <para>
 295                                 <literal>lkn =lkn-1(kn)</literal>
 296                                 <literal>lkn(i,j) = a</literal>
 297                             </para>
 298                             <para>
 299                                 <literal>lkn-1(kn) = lkn</literal>
 300                                 <literal> ..  = ..  </literal>
 301                             </para>
 302                             <para>
 303                                 <literal>l(k1) = lk1</literal>
 304                             </para>
 305                         </listitem>
 306                         <listitem>
 307                             <para>
 308                                 <literal>i</literal> peut être :
 309                             </para>
 310                             <itemizedlist>
 311                                 <listitem>
 312                                     <para>un scalaire réel positif (seule sa partie entière est prise en compte).
 313                                         <literal>l(0)=a</literal> ajoute un terme "à gauche"
 314                                         de la liste <literal>l(i)=a</literal> affecte <literal>a</literal> au
 315                                         terme <literal>i</literal> de la liste <literal>l</literal>. Si
 316                                         <literal>i&gt;size(l)</literal>, <literal>l</literal> est
 317                                         préalablement agrandie et les termes créés sont de type
 318                                         non-défini.  <literal>l(i)=null()</literal> supprime le terme
 319                                         <literal>i</literal>th de la liste.
 320                                     </para>
 321                                 </listitem>
 322                                 <listitem>
 323                                     <para>
 324                                         un polynôme. Si <literal>i</literal> est un
 325
 326                                         vecteur de polynômes ou de polynômes implicites il est
 327                                         interprété comme <literal>horner(i,m)</literal> où
 328                                         <literal>m=size(l)</literal>. Même si cette fonctionnalité marche
 329                                         pour tous les polynômes, il est recommandé d'utiliser
 330                                         des polynômes dans <literal>$</literal> par souci de lisibilité.
 331                                     </para>
 332                                 </listitem>
 333                             </itemizedlist>
 334                         </listitem>
 335                         <listitem>
 336                             <para>
 337                                 <literal>k1,..kn</literal> peuvent être :
 338                             </para>
 339                             <itemizedlist>
 340                                 <listitem>
 341                                     <para>un polynôme, interprété comme
 342                                         <literal>horner(ki,m)</literal> ou <literal>m</literal> est la taille de
 343                                         la sous-liste correspondante.
 344                                     </para>
 345                                 </listitem>
 346                                 <listitem>
 347                                     <para>une chaîne de caractères associée à un nom
 348
 349                                         d'entrée de sous-liste.
 350                                     </para>
 351                                 </listitem>
 352                             </itemizedlist>
 353                         </listitem>
 354                     </itemizedlist>
 355                 </listitem>
 356             </varlistentry>
 357         </variablelist>
 358     </refsection>
 359     <refsection>
 360         <title>Remarque</title>
 361         <para>
 362             Pour les matrices rationnelles et les systèmes dynamiques
 363             linéaires stockés sous forme de représentation d'état, la
 364             syntaxe <literal>x(i)</literal> ne doit pas être utilisée pour
 365             l'insertion des éléments d'un vecteur, à cause de la
 366             confusion possible avec l'insertion des éléments de liste. La
 367             syntaxe <literal>x(1,j)</literal> où <literal>x(i,1)</literal> doit être
 368             utilisée dans ce cas.
 369         </para>
 370     </refsection>
 371     <refsection>
 372         <title>Exemples</title>
 373         <programlisting role="example"><![CDATA[
 374 // CAS DES MATRICES
 375 a=[1 2 3;4 5 6]
 376 a(1,2)=10
 377 a([1 1],2)=[-1;-2]
 378 a(:,1)=[8;5]
 379 a(1,3:-1:1)=[77 44 99]
 380 a(1)=%s
 381 a(6)=%s+1
 382 a(:)=1:6
 383 a([%t %f],1)=33
 384 a(1:2,$-1)=[2;4]
 385 a($:-1:1,1)=[8;7]
 386 a($)=123
 387 a(1,%pi)=1 //équivalent à a(1,3)=1
 388 //
 389 x='test'
 390 x([4 5])=['4','5']
 391 //
 392 b=[1/%s,(%s+1)/(%s-1)]
 393 b(1,1)=0
 394 b(1,$)=b(1,$)+1
 395 b(2)=[1 2] // le numérateur
 396 // CAS des LISTES (types LIST et TLIST)
 397 l=list(1,'qwerw',%s)
 398 l(1)='Changed'
 399 l(0)='Added'
 400 l(%pi)=1 //équivalent à l(3)=1
 401 l(6)=['one more';'added']
 402 //
 403 //
 404 dts=list(1,tlist(['x';'a';'b'],10,[2 3]));
 405 dts(2)('a')=33
 406 dts(2)('b')(1,2)=-100
 407  ]]></programlisting>
 408     </refsection>
 409     <refsection role="see also">
 410         <title>Voir aussi</title>
 411         <simplelist type="inline">
 412             <member>
 413                 <link linkend="find">find</link>
 414             </member>
 415             <member>
 416                 <link linkend="horner">horner</link>
 417             </member>
 418             <member>
 419                 <link linkend="parentheses">parentheses</link>
 420             </member>
 421             <member>
 422                 <link linkend="extraction">extraction</link>
 423             </member>
 424         </simplelist>
 425     </refsection>
 426 </refentry>