public static int Main(string[] args)
{
double[] x = new double[0];
double[] y = new double[0];
double[,] ytbl = new double[0, 0];
double eps = 0;
double h = 0;
int m = 0;
int i = 0;
odesolver.odesolverstate state = new odesolver.odesolverstate();
odesolver.odesolverreport rep = new odesolver.odesolverreport();
//
// ODESolver unit is used to solve simple ODE:
// y'' = -y, y(0) = 0, y'(0)=1.
//
// This ODE may be written as first-order system:
// y' = z
// z' = -y
//
// Its solution is well known in academic circles :)
//
// Three intermediate values are calculated,
// plus starting and final points.
//
y = new double[2];
y[0] = 0;
y[1] = 1;
x = new double[5];
x[0] = Math.PI * 0 / 4;
x[1] = Math.PI * 1 / 4;
x[2] = Math.PI * 2 / 4;
x[3] = Math.PI * 3 / 4;
x[4] = Math.PI * 4 / 4;
eps = 1.0E-8;
h = 0.01;
odesolver.odesolverrkck(ref y, 2, ref x, 5, eps, h, ref state);
while (odesolver.odesolveriteration(ref state))
{
state.dy[0] = state.y[1];
state.dy[1] = -state.y[0];
}
odesolver.odesolverresults(ref state, ref m, ref x, ref ytbl, ref rep);
System.Console.Write(" X Y(X) Error");
System.Console.WriteLine();
for (i = 0; i <= m - 1; i++)
{
System.Console.Write("{0,6:F3}", x[i]);
System.Console.Write(" ");
System.Console.Write("{0,6:F3}", ytbl[i, 0]);
System.Console.Write(" ");
System.Console.Write("{0,8:E1}", Math.Abs(ytbl[i, 0] - Math.Sin(x[i])));
System.Console.WriteLine();
}
return(0);
}
public static int Main(string[] args)
{
double[] x = new double[0];
double[] y = new double[0];
double[,] ytbl = new double[0,0];
double eps = 0;
double h = 0;
int m = 0;
int i = 0;
odesolver.odesolverstate state = new odesolver.odesolverstate();
odesolver.odesolverreport rep = new odesolver.odesolverreport();
//
// ODESolver unit is used to solve simple ODE:
// y'' = -y, y(0) = 0, y'(0)=1.
//
// This ODE may be written as first-order system:
// y' = z
// z' = -y
//
// Its solution is well known in academic circles :)
//
// Three intermediate values are calculated,
// plus starting and final points.
//
y = new double[2];
y[0] = 0;
y[1] = 1;
x = new double[5];
x[0] = Math.PI*0/4;
x[1] = Math.PI*1/4;
x[2] = Math.PI*2/4;
x[3] = Math.PI*3/4;
x[4] = Math.PI*4/4;
eps = 1.0E-8;
h = 0.01;
odesolver.odesolverrkck(ref y, 2, ref x, 5, eps, h, ref state);
while( odesolver.odesolveriteration(ref state) )
{
state.dy[0] = state.y[1];
state.dy[1] = -state.y[0];
}
odesolver.odesolverresults(ref state, ref m, ref x, ref ytbl, ref rep);
System.Console.Write(" X Y(X) Error");
System.Console.WriteLine();
for(i=0; i<=m-1; i++)
{
System.Console.Write("{0,6:F3}",x[i]);
System.Console.Write(" ");
System.Console.Write("{0,6:F3}",ytbl[i,0]);
System.Console.Write(" ");
System.Console.Write("{0,8:E1}",Math.Abs(ytbl[i,0]-Math.Sin(x[i])));
System.Console.WriteLine();
}
return 0;
}
public static int Main(string[] args)
{
double[] x = new double[0];
double[] y = new double[0];
double[,] ytbl = new double[0, 0];
double eps = 0;
double h = 0;
int m = 0;
int i = 0;
odesolver.odesolverstate state = new odesolver.odesolverstate();
odesolver.odesolverreport rep = new odesolver.odesolverreport();
//
// ODESolver unit is used to solve simple ODE:
// y' = y, y(0) = 1.
//
// Its solution is well known in academic circles :)
//
// No intermediate values are calculated,
// just starting and final points.
//
y = new double[1];
y[0] = 1;
x = new double[2];
x[0] = 0;
x[1] = 1;
eps = 1.0E-4;
h = 0.01;
odesolver.odesolverrkck(ref y, 1, ref x, 2, eps, h, ref state);
while (odesolver.odesolveriteration(ref state))
{
state.dy[0] = state.y[0];
}
odesolver.odesolverresults(ref state, ref m, ref x, ref ytbl, ref rep);
System.Console.Write(" X Y(X)");
System.Console.WriteLine();
for (i = 0; i <= m - 1; i++)
{
System.Console.Write("{0,5:F3}", x[i]);
System.Console.Write(" ");
System.Console.Write("{0,5:F3}", ytbl[i, 0]);
System.Console.WriteLine();
}
return(0);
}
public static int Main(string[] args)
{
double[] x = new double[0];
double[] y = new double[0];
double[,] ytbl = new double[0,0];
double eps = 0;
double h = 0;
int m = 0;
int i = 0;
odesolver.odesolverstate state = new odesolver.odesolverstate();
odesolver.odesolverreport rep = new odesolver.odesolverreport();
//
// ODESolver unit is used to solve simple ODE:
// y' = y, y(0) = 1.
//
// Its solution is well known in academic circles :)
//
// No intermediate values are calculated,
// just starting and final points.
//
y = new double[1];
y[0] = 1;
x = new double[2];
x[0] = 0;
x[1] = 1;
eps = 1.0E-4;
h = 0.01;
odesolver.odesolverrkck(ref y, 1, ref x, 2, eps, h, ref state);
while( odesolver.odesolveriteration(ref state) )
{
state.dy[0] = state.y[0];
}
odesolver.odesolverresults(ref state, ref m, ref x, ref ytbl, ref rep);
System.Console.Write(" X Y(X)");
System.Console.WriteLine();
for(i=0; i<=m-1; i++)
{
System.Console.Write("{0,5:F3}",x[i]);
System.Console.Write(" ");
System.Console.Write("{0,5:F3}",ytbl[i,0]);
System.Console.WriteLine();
}
return 0;
}
public odesolverstate(odesolver.odesolverstate obj)
{
_innerobj = obj;
}
public odesolverstate()
{
_innerobj = new odesolver.odesolverstate();
}
public odesolverstate(odesolver.odesolverstate obj)
{
_innerobj = obj;
}
public odesolverstate()
{
_innerobj = new odesolver.odesolverstate();
}
/*************************************************************************
Test
*************************************************************************/
public static bool testodesolver(bool silent)
{
bool result = new bool();
int passcount = 0;
bool curerrors = new bool();
bool rkckerrors = new bool();
bool waserrors = new bool();
double[] xtbl = new double[0];
double[,] ytbl = new double[0,0];
odesolver.odesolverreport rep = new odesolver.odesolverreport();
double[] xg = new double[0];
double[] y = new double[0];
double h = 0;
double eps = 0;
int solver = 0;
int pass = 0;
int mynfev = 0;
double v = 0;
int m = 0;
int m2 = 0;
int i = 0;
double err = 0;
odesolver.odesolverstate state = new odesolver.odesolverstate();
int i_ = 0;
rkckerrors = false;
waserrors = false;
passcount = 10;
//
// simple test: just A*sin(x)+B*cos(x)
//
ap.assert(passcount>=2);
for(pass=0; pass<=passcount-1; pass++)
{
for(solver=0; solver<=0; solver++)
{
//
// prepare
//
h = 1.0E-2;
eps = 1.0E-5;
if( pass%2==0 )
{
eps = -eps;
}
y = new double[2];
for(i=0; i<=1; i++)
{
y[i] = 2*math.randomreal()-1;
}
m = 2+math.randominteger(10);
xg = new double[m];
xg[0] = (m-1)*math.randomreal();
for(i=1; i<=m-1; i++)
{
xg[i] = xg[i-1]+math.randomreal();
}
v = 2*Math.PI/(xg[m-1]-xg[0]);
for(i_=0; i_<=m-1;i_++)
{
xg[i_] = v*xg[i_];
}
if( (double)(math.randomreal())>(double)(0.5) )
{
for(i_=0; i_<=m-1;i_++)
{
xg[i_] = -1*xg[i_];
}
}
mynfev = 0;
//
// choose solver
//
if( solver==0 )
{
odesolver.odesolverrkck(y, 2, xg, m, eps, h, state);
}
//
// solve
//
while( odesolver.odesolveriteration(state) )
{
state.dy[0] = state.y[1];
state.dy[1] = -state.y[0];
mynfev = mynfev+1;
}
odesolver.odesolverresults(state, ref m2, ref xtbl, ref ytbl, rep);
//
// check results
//
curerrors = false;
if( rep.terminationtype<=0 )
{
curerrors = true;
}
else
{
curerrors = curerrors | m2!=m;
err = 0;
for(i=0; i<=m-1; i++)
{
err = Math.Max(err, Math.Abs(ytbl[i,0]-(y[0]*Math.Cos(xtbl[i]-xtbl[0])+y[1]*Math.Sin(xtbl[i]-xtbl[0]))));
err = Math.Max(err, Math.Abs(ytbl[i,1]-(-(y[0]*Math.Sin(xtbl[i]-xtbl[0]))+y[1]*Math.Cos(xtbl[i]-xtbl[0]))));
}
curerrors = curerrors | (double)(err)>(double)(10*Math.Abs(eps));
curerrors = curerrors | mynfev!=rep.nfev;
}
if( solver==0 )
{
rkckerrors = rkckerrors | curerrors;
}
}
}
//
// another test:
//
// y(0) = 0
// dy/dx = f(x,y)
// f(x,y) = 0, x<1
// x-1, x>=1
//
// with BOTH absolute and fractional tolerances.
// Starting from zero will be real challenge for
// fractional tolerance.
//
ap.assert(passcount>=2);
for(pass=0; pass<=passcount-1; pass++)
{
h = 1.0E-4;
eps = 1.0E-4;
if( pass%2==0 )
{
eps = -eps;
}
y = new double[1];
y[0] = 0;
m = 21;
xg = new double[m];
for(i=0; i<=m-1; i++)
{
xg[i] = (double)(2*i)/(double)(m-1);
}
mynfev = 0;
odesolver.odesolverrkck(y, 1, xg, m, eps, h, state);
while( odesolver.odesolveriteration(state) )
{
state.dy[0] = Math.Max(state.x-1, 0);
mynfev = mynfev+1;
}
odesolver.odesolverresults(state, ref m2, ref xtbl, ref ytbl, rep);
if( rep.terminationtype<=0 )
{
rkckerrors = true;
}
else
{
rkckerrors = rkckerrors | m2!=m;
err = 0;
for(i=0; i<=m-1; i++)
{
err = Math.Max(err, Math.Abs(ytbl[i,0]-math.sqr(Math.Max(xg[i]-1, 0))/2));
}
rkckerrors = rkckerrors | (double)(err)>(double)(Math.Abs(eps));
rkckerrors = rkckerrors | mynfev!=rep.nfev;
}
}
//
// end
//
waserrors = rkckerrors;
if( !silent )
{
System.Console.Write("TESTING ODE SOLVER");
System.Console.WriteLine();
System.Console.Write("* RK CASH-KARP: ");
if( rkckerrors )
{
System.Console.Write("FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("OK");
System.Console.WriteLine();
}
if( waserrors )
{
System.Console.Write("TEST FAILED");
System.Console.WriteLine();
}
else
{
System.Console.Write("TEST PASSED");
System.Console.WriteLine();
}
}
result = !waserrors;
return result;
}