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--- libnum:examples:gear [2026/03/04 14:46] – abc
+++ libnum:examples:gear [2026/03/29 13:46] (current) – abc
@@ Line 1: / Line 1: @@
-====== Integration of Systems of Linear Differential Equations ======
+====== Integration of Systems of Linear Differential Equations. Gear's method ======
-Gear Method.\\
 Let's examine the following //SLDE//:
   y₁′ = y₂
@@ Line 8: / Line 8: @@
 <file>
-#include <stdio.h>
+#include <iostream>
+#include <sstream>
+#include <fstream>
 #include <math.h>
 #include "libnum/gear.h"
+#include "libnum/gear.output.h"
 using namespace NumericMethods;
-bool derfun1(int n, double x, const double y[], double dy[])
+/*
+    y₁′ = y₂
+    y₂′ = y₁
+    y₁(0)=0  and  y₂(0)=1
+    // NB: we expect sin(x)/cos(x) as the result.
+*/
+static bool derfun(int n, double x, const double y[], double dy[])
 {
   dy[0] = y[1];
@@ Line 21: / Line 32: @@
 }
-bool jacobian1(int n, double x, const double y[], double j[])
+static bool jacobian(int n, double x, const double y[], double j[])
 {
-  j[0] = 0; j[1] = 1; j[2] = -1; j[3] = 0;
+  //for (int i = 0; i<n*n; ++i) j[i] = 0;
+  j[0] = 0; j[1] = 1; j[2] = -1; j[3] = 0; // sin/cos
   return true;
 }
-bool my_print1(const GearEngineContext&);
 int main()
 {
- double initValues[] = { 0, 1, 0, 0};
- GearUserProc uf1(diffun1), uf2(j1);
+ double initValues[]={ 0,1,0,0};
+ GearUserProc uf1(derfun),uf2(jacobian);
  Gear solver;
- solver.set(2, &uf1, &uf2); // task dimention is 2
+ solver.set(2,&uf1,&uf2);
  GearAssistant& assistant = solver.assistant;
- assistant.params.setParameter("HINI", 0.0001);  // starting step of integration
+ assistant.params.setParameter("HINI", 0.000001);  // starting step of integration
- assistant.params.setParameter("EPS", 0.001);    // step error constant
+ assistant.params.setParameter("EPS", 0.0001);     // step error constant
+ //    Output variants
+ /*1*/ GearPrintToStream print_1(std::cout, "{:8.5f}\t");
+ /*2*/ std::stringstream buf;  // to string; use buf.str() later
+ GearPrintToStream print_2(buf, "{:8.5f}\t");
+ /*3*/ std::ofstream file("gear_output.txt");
+ GearPrintToStream print_3(file, "{:8.5f}\t");
+ GearPrintTable print_4(std::cout, 0.1);
+  print_4.setFormat("{:8.5f}\t");
- GearEngineCallbackEmbed printHandler(my_print);
+ solver.setCallback(print_4);
- solver.setCallback(printHandler);
  try
  {
-  Message rc=solver.solve(0, 5, initValues);     // integrate for t from 0 to 5
+  Message rc=solver.solve(0, 5, initValues);
-  printf("\n\nsteps: %d, derCalls: %d, jacCalls: %d\n\n",
-    assistant.statistics.steps, assistant.statistics.derCalls,
-    assistant.statistics.jacCalls);
  }
  catch(Message& e)
  {
-   printf("\n\n%s",e.getMessageID().data());
+   std::cout << "\n\n" << e.getMessageID().data();
  }
- printf("\n");
+ std::cout << "\n";
 }
+</file>
-bool my_print1(const GearEngineContext& context)
+----
-{
+[ [[..:classes:|Libnum methods]] ]
- printf("\n%10.5f:",context.t);
- // print y values and their derivatives
- int n = context.n;
- for(int i=0; i < n; ++i) printf("\t%10.5f %10.5f,",
-     context.Z[i], context.Z[i+n]/context.h);
- printf("\t(%10.5f  %d)\n", context.h, context.q);
- return true;
-}
-</file>