OpenXM/src/asir-contrib/packages/src/la_solution_guide.rr - diff

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Diff for /OpenXM/src/asir-contrib/packages/src/la_solution_guide.rr between version 1.4 and 1.5

-version 1.4, 2003/05/07 02:22:07
+version 1.5, 2003/05/08 03:45:37
 Line 1
 Line 1
 Line 1
- /* $OpenXM: OpenXM/src/asir-contrib/packages/src/la_solution_guide.rr,v 1.3 2002/08/11 11:20:36 takayama Exp $ */
+ /* $OpenXM: OpenXM/src/asir-contrib/packages/src/la_solution_guide.rr,v 1.4 2003/05/07 02:22:07 takayama Exp $ */
  /* The file name should be la_solution_guide.rr (la = linear algebra) */
  /* Suffix should be  lasg_ */
 Line 333  def lasg_copy_matrix(A) {
 Line 333  def lasg_copy_matrix(A) {
 Line 333  def lasg_copy_matrix(A) {
   example: lasg_reduced_form(newmat(2,3,[[2,3,8],[1,2,5]]));
   end:
  */
+ Lasg_test_data_1=newmat(3,5,[[0,0,0,1,1],[0,0,1,0,-2],[1,3,0,0,2]]) $
  def lasg_reduced_form(A) {
    Ans = [ ];
    M = size(A)[0];
    N = size(A)[1];
    AA = A;
+   Pivot = 0;
+   J = 0;
+   while (J < N) {
+     I = Pivot;
+     AllZero = 1;
+     while (I < M) {
+       if (AA[I][J] != 0) {
+        AllZero = 0;
+        if (AA[I][J] != 1) {
+          Msg = "Multiplying the "+rtostr(I+1)+"th row by "+
+                rtostr(1/AA[I][J]);
+          B = lasg_copy_matrix(AA);
+          for (JJ=0; JJ<N; JJ++) {
+            B[I][JJ] = AA[I][JJ]/AA[I][J];
+          }
+          Ans = append(Ans,[[Msg,B]]);
+          AA = B;
+        }
+        if (I != Pivot) {
+          Msg = "Exchanging the "+rtostr(I+1)+"th row and "+rtostr(Pivot+1)+
+                "th row";
+          B = lasg_copy_matrix(AA);
+          for (JJ=0; JJ<N; JJ++) {
+            B[I][JJ] = AA[Pivot][JJ];
+            B[Pivot][JJ] = AA[I][JJ];
+          }
+          Ans = append(Ans,[[Msg,B]]);
+          AA = B;
+        }
+        Msg = "Eliminating the "+rtostr(J+1)+"th column by "+
+                "("+rtostr(I+1)+","+rtostr(J+1)+")th entry" ;
+        B = lasg_copy_matrix(AA);
+        print(B); print("----------------");
+        Changed = 0;
+        for (II = 0; II<M; II++) {
+          if (II != Pivot && B[II][J] != 0) {
+            C = B[II][J];  Changed = 1;
+            for (JJ=0; JJ<N; JJ++) {
+              B[II][JJ] = B[II][JJ] - B[Pivot][JJ]*C;
+            }
+          }
+        }
+        if (Changed) {
+          Ans = append(Ans,[[Msg,B]]);
+          print(B); print("---------------");
+        }
+        AA = B;
+        break; /* break J loop */
+       }
+       I++;
+     }
+     if (!AllZero) Pivot++;
+     J++;
+   }
+   return(Ans);
+ }
+ def lasg_reduced_form_old(A) {
+   Ans = [ ];
+   M = size(A)[0];
+   N = size(A)[1];
+   AA = A;
    I = 0;
    while (I < M) {
      J = 0;
-Line 559  def lasg_gen_reduced_matrix(PP) {
+Line 622  def lasg_gen_reduced_matrix(PP) {
 Line 559  def lasg_gen_reduced_matrix(PP) {
 Line 622  def lasg_gen_reduced_matrix(PP) {
       S = "% problem. \n";
       S += "\\noindent $\\bullet$ Make elementary transformations for \n"+
            "$$ A = "+taka_tex_form(PP) + "$$\n";
-      S += "to generate the reduced expression$.\n \\medbreak \\noindent Answer:\n";
+      S += "to generate the reduced expression.\n \\medbreak \\noindent Answer:\n";
       A = lasg_reduced_form(PP);
       M = length(A);
       for (J=0; J<M; J++) {
         S += A[J][0]+", we get \\\\ \n";
         S += "$$ "+taka_tex_form(A[J][1])+" $$\n";
       }
-      S += "BUG: the coding has not yet been completed.";
       S += "\n\n";
       return S;
  }

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