public void GearTest6c()
{
for (int exponent = 2; exponent <= 5; exponent++)
{
// evaluating y' = 3 y/ t solution y = t^exponent
var ode = new GearsBDF();
ode.Initialize(
1,
new double[] { 1 },
(t, y, dydt) => { dydt[0] = exponent * y[0] / t; },
new GearsBDFOptions {
RelativeTolerance = 1e-7, AbsoluteTolerance = 1E-8
});
var sp = new double[1];
double tres;
for (double ii = 0; ii <= 6000; ii += 1)
{
double time = Math.Pow(10, ii / 1000.0);
ode.Evaluate(time, sp);
var y0_expected = RMath.Pow(time, exponent);
Assert.AreEqual(y0_expected, sp[0], 1E-6 * y0_expected + 1E-7);
}
}
}
public void GearTest6a()
{
for (int exponent = 2; exponent <= 5; exponent++)
{
// evaluating y' = 3 y/ t solution y = t^exponent
var ode = new GearsBDF();
ode.Initialize(
1,
new double[] { 1 },
(t, y, dydt) => { dydt[0] = exponent * y[0] / t; },
new GearsBDFOptions {
RelativeTolerance = 1e-7, AbsoluteTolerance = 1E-8
});
var sp = new double[1];
double tres;
do
{
ode.Evaluate(out tres, sp);
var y0_expected = RMath.Pow(tres, exponent);
Assert.AreEqual(y0_expected, sp[0], 1E-6 * y0_expected + 1E-7);
} while (tres < 1e6);
}
}
public void GearTestSparse03()
{
var ode = new GearsBDF();
var numberOfCells = 100;
var initY = new double[numberOfCells];
for (int i = 0; i < numberOfCells; ++i)
{
initY[i] = 0; // initally zero concentration
}
// Symmetrical problem, diffusion from both sides of a plate
var f = new Action <double, double[], double[]>((t, y, dydt) =>
{
double yim1 = 1; // outer concentration at lower index
double yip1 = 1; // outer concentration at upper index
int lend = y.Length - 1;
int i = 0;
dydt[0] = y[i + 1] - 2 * y[i] + yim1;
for (i = 1; i < lend; ++i)
{
dydt[i] = y[i + 1] - 2 * y[i] + y[i - 1];
}
dydt[i] = yip1 - 2 * y[i] + y[i - 1];
}
);
ode.InitializeSparse(
0,
initY,
f,
null,
new GearsBDFOptions {
RelativeTolerance = 1e-7, AbsoluteTolerance = 1E-8
});
int nCounter = 0;
var sp = new double[numberOfCells];
double tres = 0;
for (; tres <= 10000;)
{
ode.Evaluate(out tres, sp);
double t = tres;
for (int i = 0; i < numberOfCells; ++i)
{
Assert.AreEqual(sp[i], sp[numberOfCells - 1 - i], 1E-7 * sp[i] + 1E-8); // test for symmetry of the solution
}
++nCounter;
}
}
public void GearTest7b()
{
Vector fuu(double t, Vector y)
{
return(new Vector(y[0] * y[0]));
}
var pulse = Altaxo.Calc.Ode.Ode.GearBDF(
0,
new Vector(1 / 64.0),
fuu,
new Altaxo.Calc.Ode.Options {
RelativeTolerance = 1e-7, AbsoluteTolerance = 1E-8
});
// evaluating y' = y², y[0]=1/64
var ode = new GearsBDF();
ode.Initialize(
0, // t0=0
new double[] { 1.0 / 64 }, // y0=1/64
(t, y, dydt) => { dydt[0] = y[0] * y[0]; },
new GearsBDFOptions {
RelativeTolerance = 1e-7, AbsoluteTolerance = 1E-8
});
var sp = new double[1];
foreach (var spulse in pulse.SolveTo(32))
{
ode.Evaluate(out var tres, sp);
Assert.AreEqual(spulse.T, tres);
Assert.AreEqual(spulse.X[0], sp[0]);
var y0_expected = 1 / (64 - tres);
Assert.AreEqual(y0_expected, spulse.X[0], 1E-6 * y0_expected + 1E-7);
Assert.AreEqual(y0_expected, sp[0], 1E-6 * y0_expected + 1E-7);
}
;
}
public void GearTestSparse01()
{
const double lambda1 = -1;
const double lambda2 = -1000;
const double lambda1PlusLambda2By2 = (lambda1 + lambda2) / 2;
const double lambda1MinusLambda2By2 = (lambda1 - lambda2) / 2;
const double C1 = 1;
const double C2 = 1;
var ode = new GearsBDF();
ode.InitializeSparse(
0,
new double[] { C1 + C2, C1 - C2 },
(t, y, dydt) => { dydt[0] = lambda1PlusLambda2By2 * y[0] + lambda1MinusLambda2By2 * y[1]; dydt[1] = lambda1MinusLambda2By2 * y[0] + lambda1PlusLambda2By2 * y[1]; },
null,
new GearsBDFOptions {
RelativeTolerance = 1e-7, AbsoluteTolerance = 1E-8
});
int nCounter = 0;
var sp = new double[2];
double tres = 0;
for (; tres <= 20;)
{
ode.Evaluate(out tres, sp);
double t = tres;
var y0_expected = C1 * Math.Exp(lambda1 * t) + C2 * Math.Exp(lambda2 * t);
var y1_expected = C1 * Math.Exp(lambda1 * t) - C2 * Math.Exp(lambda2 * t);
Assert.AreEqual(y0_expected, sp[0], 1E-7 * y0_expected + 1E-8);
Assert.AreEqual(y1_expected, sp[1], 6E-7 * y1_expected + 1E-8);
++nCounter;
}
}
public void GearTest3a()
{
Vector fuu(double t, Vector y)
{
return(new Vector(y[0] / t));
}
var pulse = Altaxo.Calc.Ode.Ode.GearBDF(
1,
new Vector(1),
fuu,
new Altaxo.Calc.Ode.Options {
RelativeTolerance = 1e-7, AbsoluteTolerance = 1E-8
});
var ode = new GearsBDF();
ode.Initialize(
1,
new double[] { 1 },
(t, y, dydt) => { dydt[0] = y[0] / t; },
new GearsBDFOptions {
RelativeTolerance = 1e-7, AbsoluteTolerance = 1E-8
});
var sp = new double[1];
foreach (var spulse in pulse.SolveTo(100000))
{
double t = spulse.T;
ode.Evaluate(out var tsp, sp);
Assert.AreEqual(t, tsp, 1e-4);
var y0_expected = t;
Assert.AreEqual(y0_expected, sp[0], 1E-3 * y0_expected + 1E-4);
}
}
public void GearTest7a()
{
// evaluating y' = 1/y, y[0]=1/64
var ode = new GearsBDF();
ode.Initialize(
0, // t0=0
new double[] { 1.0 / 64 }, // y0=1/64
(t, y, dydt) => { dydt[0] = 1 / y[0]; },
new GearsBDFOptions {
RelativeTolerance = 1e-7, AbsoluteTolerance = 1E-8
});
var sp = new double[1];
double tres;
do
{
ode.Evaluate(out tres, sp);
var y0_expected = Math.Sqrt(1 + 8192 * tres) / 64;
Assert.AreEqual(y0_expected, sp[0], 1E-6 * y0_expected + 1E-7);
} while (tres < 1e6);
}
public void GearTest5a()
{
// evaluating y' = 3 y/ t solution y = t³
var ode = new GearsBDF();
ode.Initialize(
1,
new double[] { 1 },
(t, y, dydt) => { dydt[0] = 3 * y[0] / t; },
new GearsBDFOptions {
RelativeTolerance = 1e-7, AbsoluteTolerance = 1E-8
});
var sp = new double[1];
double tres;
do
{
ode.Evaluate(out tres, sp);
var y0_expected = tres * tres * tres;
Assert.AreEqual(y0_expected, sp[0], 1E-6 * y0_expected + 1E-7);
} while (tres < 1e6);
}
public void GearTestSparse02()
{
const double lambda1 = -1;
const double lambda2 = -1000;
const double lambda1PlusLambda2By2 = (lambda1 + lambda2) / 2;
const double lambda1MinusLambda2By2 = (lambda1 - lambda2) / 2;
const double C1 = 1;
const double C2 = 1;
var ode = new GearsBDF();
var numberOfCells = 100;
var initY = new double[numberOfCells * 2];
for (int i = 0; i < numberOfCells; ++i)
{
initY[i * 2 + 0] = C1 + C2;
initY[i * 2 + 1] = C1 - C2;
}
var f = new Action <double, double[], double[]>((t, y, dydt) =>
{
for (int i = 0; i < y.Length; i += 2)
{
dydt[i] = lambda1PlusLambda2By2 * y[i] + lambda1MinusLambda2By2 * y[i + 1];
dydt[i + 1] = lambda1MinusLambda2By2 * y[i] + lambda1PlusLambda2By2 * y[i + 1];
}
}
);
ode.InitializeSparse(
0,
initY,
f,
null,
new GearsBDFOptions {
RelativeTolerance = 1e-7, AbsoluteTolerance = 1E-8
});
int nCounter = 0;
var sp = new double[numberOfCells * 2];
double tres = 0;
for (; tres <= 20;)
{
ode.Evaluate(out tres, sp);
double t = tres;
var y0_expected = C1 * Math.Exp(lambda1 * t) + C2 * Math.Exp(lambda2 * t);
var y1_expected = C1 * Math.Exp(lambda1 * t) - C2 * Math.Exp(lambda2 * t);
for (int i = 0; i < numberOfCells; ++i)
{
Assert.AreEqual(y0_expected, sp[i * 2 + 0], 1E-7 * y0_expected + 1E-8);
Assert.AreEqual(y1_expected, sp[i * 2 + 1], 6E-7 * y1_expected + 1E-8);
}
++nCounter;
}
}
public void GearTest2a()
{
const double lambda1 = -1;
const double lambda2 = -1000;
const double lambda1PlusLambda2By2 = (lambda1 + lambda2) / 2;
const double lambda1MinusLambda2By2 = (lambda1 - lambda2) / 2;
const double C1 = 1;
const double C2 = 1;
Vector fuu(double t, Vector y)
{
return(new Vector(lambda1PlusLambda2By2 * y[0] + lambda1MinusLambda2By2 * y[1], lambda1MinusLambda2By2 * y[0] + lambda1PlusLambda2By2 * y[1]));
}
var pulse = Altaxo.Calc.Ode.Ode.GearBDF(
0,
new Vector(C1 + C2, C1 - C2),
fuu,
new Altaxo.Calc.Ode.Options {
RelativeTolerance = 1e-7, AbsoluteTolerance = 1E-8
});
var ode = new GearsBDF();
ode.Initialize(
0,
new double[] { C1 + C2, C1 - C2 },
(t, y, dydt) => { dydt[0] = lambda1PlusLambda2By2 * y[0] + lambda1MinusLambda2By2 * y[1]; dydt[1] = lambda1MinusLambda2By2 * y[0] + lambda1PlusLambda2By2 * y[1]; },
new GearsBDFOptions {
RelativeTolerance = 1e-7, AbsoluteTolerance = 1E-8
});
int nCounter = 0;
var sp = new double[2];
var pulseit = pulse.SolveTo(20).GetEnumerator();
for (; ;)
{
if (!pulseit.MoveNext())
{
break;
}
var spulse = pulseit.Current;
ode.Evaluate(out var tres, sp);
Assert.AreEqual(spulse.T, tres);
Assert.AreEqual(spulse.X[0], sp[0]);
Assert.AreEqual(spulse.X[1], sp[1]);
double t = spulse.T;
var y0_expected = C1 * Math.Exp(lambda1 * t) + C2 * Math.Exp(lambda2 * t);
var y1_expected = C1 * Math.Exp(lambda1 * t) - C2 * Math.Exp(lambda2 * t);
Assert.AreEqual(y0_expected, spulse.X[0], 1E-7 * y0_expected + 1E-8);
Assert.AreEqual(y1_expected, spulse.X[1], 6E-7 * y1_expected + 1E-8);
t = tres;
y0_expected = C1 * Math.Exp(lambda1 * t) + C2 * Math.Exp(lambda2 * t);
y1_expected = C1 * Math.Exp(lambda1 * t) - C2 * Math.Exp(lambda2 * t);
Assert.AreEqual(y0_expected, sp[0], 1E-7 * y0_expected + 1E-8);
Assert.AreEqual(y1_expected, sp[1], 6E-7 * y1_expected + 1E-8);
++nCounter;
}
}