public MainPage()
{
InitializeComponent();
//An example of Gear method use
var rk1 = Ode.GearBDF(
0, // Initial time point
new Microsoft.Research.Oslo.Vector(1000.0), // Initial X vector
(t, x) => { return(new Vector(-0.01 * x[0])); }, // Right part
new Options {
MaxStep = 5.0d, NumberOfIterations = 4
});
var eds1 = rk1.AppendStep().SolveFromToStep(0, 2000, 0.1).ToArray();
var x11 = eds1.Select(p => new Point(p.T, p.X[0])).ToArray();
linegraph1.Plot(x11.Select(x => x.X).ToArray(), x11.Select(x => x.Y).ToArray());
//An example of RK method use
var rk2 = Ode.RK547M(
0, // Initial time point
new Microsoft.Research.Oslo.Vector(1000.0), // Initial X vector
(t, x) => { return(new Vector(-0.01 * x[0])); }); // Right part
var eds2 = rk2.AppendStep().SolveFromToStep(0, 2000, 0.1).ToArray();
var x12 = eds2.Select(p => new Point(p.T, p.X[0])).ToArray();
linegraph2.Plot(x12.Select(x => x.X).ToArray(),
x12.Select(x => 1000 * Math.Exp(-0.01d * x.X)).ToArray());
var err = x11.Max(x => Math.Abs(x.Y - 1000 * Math.Exp(-0.01d * x.X)));
}
private static void solveExternalExample(int option, ref List <double> tsim, ref List <double> xsim)
{
// Ode options and initial conditions, then solve
double onex = 50.0;
var treat = new double[] { 0.0, 0.1, 0.3, 1.0 };
var ks = new double[] { 4.91e-6, 2.22e-6, 1.72e-6 };
var ics = new double[] { 0.12, 0.25 };
var bad = 0.1;
var opts = new Options {
MaxStep = 3600.0, RelativeTolerance = 1e-3
};
var x0 = initialCondition(ics, onex);
x0[0] += treat[option] * onex * (1 - bad);
var sol = Ode.GearBDF(0.0, 20 * 3600.0, x0, (t, x) => derivs(t, x, ks));
// Write to variables
foreach (var sp in sol)
{
tsim.Add(sp.T);
xsim.Add(sp.X[3]);
}
}
public void JacobianGearTest()
{
var A = new Matrix(new double[, ] {
{ -1, 0.5 }, { 0, -1 }
});
var sol = new List <double>();
foreach (var sp in Ode.GearBDF(0,
new Vector(1, 1),
(t, x) => A * x).SolveFromToStep(0, 10, 0.1))
{
sol.Add(sp.X[0]);
}
var solJ = new List <double>();
foreach (var sp in Ode.GearBDF(0,
new Vector(1, 1),
(t, x) => A * x).SolveFromToStep(0, 10, 0.1))
{
solJ.Add(sp.X[0]);
}
for (int i = 0; i < sol.Count; i++)
{
Assert.IsTrue(Math.Abs(sol[i] - solJ[i]) < 1e-3);
}
}
public MainPage()
{
InitializeComponent();
var rk = Ode.GearBDF(
0, // Initial time point
new Vector(1, Math.E), // Initial X vector
Felberg, // Right part
new Options {
RelativeTolerance = 1e-5
}); // Set relative tolerance
// Append time step as extra vector component and solve from t = 0 to 5
//and output points with step 0.01
var ed = rk.AppendStep().SolveFromToStep(0, 5, 0.01).ToArray();
// Draw numeric solution
x1 = (LineGraph)plotter.FindName("x1");
x1.Plot(ed.Select(sp => sp.T), ed.Select(sp => sp.X[0]));
x2 = (LineGraph)plotter.FindName("x2");
x2.Plot(ed.Select(sp => sp.T), ed.Select(sp => sp.X[1]));
x1_1 = (LineGraph)plotter.FindName("x1_1");
x1_1.Plot(ed.Select(sp => sp.T), ed.Select(sp => Math.Exp(Math.Sin(sp.T * sp.T))));
x2_1 = (LineGraph)plotter.FindName("x2_1");
x2_1.Plot(ed.Select(sp => sp.T), ed.Select(sp => Math.Exp(Math.Cos(sp.T * sp.T))));
}
public void solve(ref List <double> tsim, ref List <double>[] xsim)
{
var plotLocs = new List <List <int> >();
plotLocs.Add(new List <int> {
76, 128, 143
});
plotLocs.Add(new List <int> {
44, 82, 97
});
plotLocs.Add(new List <int> {
40, 50, 56
});
double tfinal = 500000.0;
// Ode options and initial conditions, then solve
var opts = new Options {
RelativeTolerance = 1e-4
};
var x0 = oscillating_ics();
IEnumerable <SolPoint> sol;
sol = Ode.GearBDF(0.0, tfinal, x0, (t, x) => derivs(t, x), opts);
double dt;
// Write to variables
foreach (var sp in sol)
{
if (tsim.Count > 0)
{
dt = sp.T - tsim.Last();
}
else
{
dt = sp.T;
}
if (Double.IsNaN(sp.X[0]))
{
return;
}
//xsim[plotLocs.Count].Add(dt);
tsim.Add(sp.T);
for (int i = 0; i < plotLocs.Count; i++)
{
double x = 0.0;
foreach (int j in plotLocs[i])
{
x += sp.X[j];
}
xsim[i].Add(x);
}
}
}
public MainPage()
{
InitializeComponent();
var gear = Ode.GearBDF(
0, // Initial time point
new Vector(2.0, 0.0), // Initial X vector
VanDerPol, new Options {
MinStep = 1e-6, MaxStep = 1e-1
}); // Right part
var rk = Ode.RK547M(
0, // Initial time point
new Vector(2.0, 0.0), // Initial X vector
VanDerPol, new Options {
MinStep = 1e-6, MaxStep = 1e-1
}); // Right part
// Append time step as extra vector component and solve from t = 0 to 20 and output points with step 0.01
var edg = gear.AppendStep().SolveFromTo(0.0, 20.0).ToArray();
var edrk = rk.AppendStep().SolveFromTo(0.0, 20.0).ToArray();
// Draw numeric solution
x1 = (LineGraph)plotter.FindName("x1");
x1.PlotY(edrk.Select(sp => sp.X[0]));
x2 = (LineGraph)plotter.FindName("x2");
x2.PlotY(edrk.Select(sp => sp.X[1]));
x1_1 = (LineGraph)plotter.FindName("x1_1");
x1_1.PlotY(edg.Select(sp => sp.X[0]));
x2_1 = (LineGraph)plotter.FindName("x2_1");
x2_1.PlotY(edg.Select(sp => sp.X[1]));
}
public void ExponentSolveToGEarTest()
{
foreach (var sp in Ode.GearBDF(0,
1,
(t, x) => - x,
new Options {
RelativeTolerance = 1e-4
}).SolveTo(10))
{
Assert.IsTrue(Math.Abs(sp.X[0] - Math.Exp(-sp.T)) < 1e-3);
}
}
public MainPage()
{
InitializeComponent();
var gear = Ode.GearBDF(
0, // Initial time point
new Vector(1, 0, 0, 0, 0, 0, 0, 0.0057d), // Initial X vector
FloralMaterial, // Right part
new Options()
{
RelativeTolerance = 1e-4, AbsoluteTolerance = 1e-6, MaxStep = 0.7d
});
// Append time step as extra vector component and solve from t = 0 to 200 and output points with step 0.05
var ed = gear.AppendStep().SolveFromToStep(0, 200, 0.05).ToArray();
// Draw numeric solution
var x1data = ed.Select(p => new Point(p.T, p.X[0])).ToArray();
x1.Plot(x1data.Select(x => x.X).ToArray(), x1data.Select(x => x.Y).ToArray());
var x2data = ed.Select(p => new Point(p.T, p.X[1])).ToArray();
x2.Plot(x2data.Select(x => x.X).ToArray(), x2data.Select(x => x.Y).ToArray());
var x3data = ed.Select(p => new Point(p.T, p.X[2])).ToArray();
x3.Plot(x3data.Select(x => x.X).ToArray(), x3data.Select(x => x.Y).ToArray());
var x4data = ed.Select(p => new Point(p.T, p.X[3])).ToArray();
x4.Plot(x4data.Select(x => x.X).ToArray(), x4data.Select(x => x.Y).ToArray());
var x5data = ed.Select(p => new Point(p.T, p.X[4])).ToArray();
x5.Plot(x5data.Select(x => x.X).ToArray(), x5data.Select(x => x.Y).ToArray());
var x6data = ed.Select(p => new Point(p.T, p.X[5])).ToArray();
x6.Plot(x1data.Select(x => x.X).ToArray(), x6data.Select(x => x.Y).ToArray());
var x7data = ed.Select(p => new Point(p.T, p.X[6])).ToArray();
x7.Plot(x7data.Select(x => x.X).ToArray(), x7data.Select(x => x.Y).ToArray());
var x8data = ed.Select(p => new Point(p.T, p.X[7])).ToArray();
x8.Plot(x8data.Select(x => x.X).ToArray(), x8data.Select(x => x.Y).ToArray());
}
public static void lotkaExample()
{
var tfinal = 200000.0; // Final time for simulation
// Species names map to UnaryRx |-> [y2]{t^*}, UnaryLxLL_1 |-> {x^*}[i]:[y1l t^]<y1 x^>:[y1l t^]<y1 x^>, UnaryLxLL |-> {t^*}[y1 x^]<i y1l t^ y1l t^>, SpeciesR |-> <y2 t^ y2r>, sp_1 |-> [y2 t^]<y2r>, sp_0 |-> <y2>, SpeciesL |-> <y1l t^ y1 x^>, sp_3 |-> <y1l>[t^ y1 x^], sp_2 |-> <y1 x^ i y1l t^ y1l t^>, sp_5 |-> <y1>[x^ i y1l t^ y1l t^], sp_4 |-> <i>, BinaryLRxRR_1 |-> {x^*}[y2 i.1]:<y2>[t^ y2r]:<y2>[t^ y2r], BinaryLRxRR |-> {t^*}[y1 x^ y2]<i.1 t^ y2r t^ y2r>{t^*}, sp_7 |-> {t^*}[y1 x^ y2]<i.1 t^ y2r t^ y2r>:<y2>[t^]<y2r>, sp_9 |-> <y1l>[t^ y1 x^]:[y2 t^]<y2r>, sp_8 |-> <y1 x^ y2 i.1 t^ y2r t^ y2r>, sp_11 |-> <y1>[x^ y2 i.1 t^ y2r t^ y2r], sp_10 |-> <y2 i.1>, sp_6 |-> <y1l>[t^ y1 x^]:<y1 x^>[y2]<i.1 t^ y2r t^ y2r>{t^*}
var species = new string[] { "UnaryRx", "UnaryLxLL_1", "UnaryLxLL", "SpeciesR", "sp_1", "sp_0", "SpeciesL", "sp_3", "sp_2", "sp_5", "sp_4", "BinaryLRxRR_1", "BinaryLRxRR", "sp_7", "sp_9", "sp_8", "sp_11", "sp_10", "sp_6" }; //% The list of all species
int n = species.Length;
Vector x0 = Vector.Zeros(n);
// Assign initial conditions
var UnaryRx = x0[0] = 1000.0;
var UnaryLxLL_1 = x0[1] = 100000.0;
var UnaryLxLL = x0[2] = 1000.0;
var SpeciesR = x0[3] = 1000.0;
var SpeciesL = x0[6] = 1000.0;
var BinaryLRxRR_1 = x0[11] = 3000000.0;
var BinaryLRxRR = x0[12] = 30000.0;
var maxstep = 1.0;
var opts = new Options {
MaxStep = maxstep
};
// Solve the ODEs
Console.WriteLine("Time,SpeciesL,SpecieR");
var dataset = DataSet.OpenShared("msds:memory2");
// define variables
dataset.Add <double[]>("t", "t");
dataset.Add <double[]>("SpecieL", "t");
dataset.Add <double[]>("SpecieR", "t");
dataset.SpawnViewer("SpecieR(Time) Style:Polyline; Thickness:1; Visible:-6565.19579745115,21.3352279262563,219999.15388962,1004.11943342034;;SpecieL(Time) Style:Polyline; Thickness:1; Visible:-6565.19579745115,21.3352279262563,219999.15388962,1004.11943342034");
foreach (var sp in Ode.GearBDF(0.0, x0, f, opts).SolveTo(tfinal))
{
Console.WriteLine("Time={0}, SpeciesL={1}, SpecieR={2}",
sp.T.ToString(CultureInfo.InvariantCulture),
sp.X[3].ToString(CultureInfo.InvariantCulture),
sp.X[6].ToString(CultureInfo.InvariantCulture));
dataset.Append("t", sp.T);
dataset.Append("SpecieL", sp.X[3]);
dataset.Append("SpecieR", sp.X[6]);
}
Console.WriteLine("Waiting for the DataSet Viewer...");
}
public MainPage()
{
InitializeComponent();
//Try to solve ODE dx / dt = Sin(t), x(0) = 0
//An example of RK547M method use
var rk1 = Ode.RK547M(0, 20, new Microsoft.Research.Oslo.Vector(0),
(t, x) => { return(new Vector(Math.Cos(t))); }// Right part
);
//An example of Gear method use
var rk2 = Ode.GearBDF(0, 20, new Microsoft.Research.Oslo.Vector(0),
(t, x) => { return(new Vector(Math.Cos(t))); }// Right part
);
SinT.Plot(rk2.Select(x => x.T).ToArray(), rk2.Select(x => Math.Sin(x.T)).ToArray());
SinRK.Plot(rk1.Select(x => x.T).ToArray(), rk1.Select(x => x.X[0]).ToArray());
SinGear.Plot(rk2.Select(x => x.T).ToArray(), rk2.Select(x => x.X[0]).ToArray());
}
public static void lotkaExample()
{
var tfinal = 200000.0; // Final time for simulation
// Species names map to UnaryRx |-> [y2]{t^*}, UnaryLxLL_1 |-> {x^*}[i]:[y1l t^]<y1 x^>:[y1l t^]<y1 x^>, UnaryLxLL |-> {t^*}[y1 x^]<i y1l t^ y1l t^>, SpeciesR |-> <y2 t^ y2r>, sp_1 |-> [y2 t^]<y2r>, sp_0 |-> <y2>, SpeciesL |-> <y1l t^ y1 x^>, sp_3 |-> <y1l>[t^ y1 x^], sp_2 |-> <y1 x^ i y1l t^ y1l t^>, sp_5 |-> <y1>[x^ i y1l t^ y1l t^], sp_4 |-> <i>, BinaryLRxRR_1 |-> {x^*}[y2 i.1]:<y2>[t^ y2r]:<y2>[t^ y2r], BinaryLRxRR |-> {t^*}[y1 x^ y2]<i.1 t^ y2r t^ y2r>{t^*}, sp_7 |-> {t^*}[y1 x^ y2]<i.1 t^ y2r t^ y2r>:<y2>[t^]<y2r>, sp_9 |-> <y1l>[t^ y1 x^]:[y2 t^]<y2r>, sp_8 |-> <y1 x^ y2 i.1 t^ y2r t^ y2r>, sp_11 |-> <y1>[x^ y2 i.1 t^ y2r t^ y2r], sp_10 |-> <y2 i.1>, sp_6 |-> <y1l>[t^ y1 x^]:<y1 x^>[y2]<i.1 t^ y2r t^ y2r>{t^*}
var species = new string[] { "UnaryRx", "UnaryLxLL_1", "UnaryLxLL", "SpeciesR", "sp_1", "sp_0", "SpeciesL", "sp_3", "sp_2", "sp_5", "sp_4", "BinaryLRxRR_1", "BinaryLRxRR", "sp_7", "sp_9", "sp_8", "sp_11", "sp_10", "sp_6" }; //% The list of all species
int n = species.Length;
Vector x0 = Vector.Zeros(n);
// Assign initial conditions
var UnaryRx = x0[0] = 1000.0;
var UnaryLxLL_1 = x0[1] = 100000.0;
var UnaryLxLL = x0[2] = 1000.0;
var SpeciesR = x0[3] = 1000.0;
var SpeciesL = x0[6] = 1000.0;
var BinaryLRxRR_1 = x0[11] = 3000000.0;
var BinaryLRxRR = x0[12] = 30000.0;
var maxstep = 1.0;
var opts = new Options {
MaxStep = maxstep
};
// Solve the ODEs
var sw = new StreamWriter("lotka" + ((int)maxstep).ToString() + ".csv");
sw.WriteLine("Time,SpeciesL,SpecieR");
Console.WriteLine("Time,SpeciesL,SpecieR");
foreach (var sp in Ode.GearBDF(0.0, x0, f, opts).SolveTo(tfinal))
{
sw.WriteLine("{0},{1},{2}", sp.T.ToString(CultureInfo.InvariantCulture),
sp.X[3].ToString(CultureInfo.InvariantCulture),
sp.X[6].ToString(CultureInfo.InvariantCulture));
Console.WriteLine("Time={0}, SpeciesL={1}, SpecieR={2}",
sp.T.ToString(CultureInfo.InvariantCulture),
sp.X[3].ToString(CultureInfo.InvariantCulture),
sp.X[6].ToString(CultureInfo.InvariantCulture));
}
Console.WriteLine("Numerical solution has been saved in " + "lotka" + ((int)maxstep).ToString() + ".csv");
sw.Close();
}
public MainPage()
{
InitializeComponent();
var gear = Ode.GearBDF(
0, // Initial time point
new Vector(0.001d, 0.004d, 0.0002d), // Initial X vector
Oregonator // Right part
);
var ed = gear.SolveFromToStep(0.0d, 1000.0, 0.1d).ToArray();
// Draw numeric solution
x1 = (LineGraph)plotter.FindName("x1");
x1.Plot(ed.Select(sp => sp.T), ed.Select(sp => sp.X[0]));
x2 = (LineGraph)plotter.FindName("x2");
x2.Plot(ed.Select(sp => sp.T), ed.Select(sp => sp.X[1]));
x3 = (LineGraph)plotter.FindName("x3");
x3.Plot(ed.Select(sp => sp.T), ed.Select(sp => sp.X[2]));
}
public MainPage()
{
InitializeComponent();
var rk = Ode.GearBDF(
0, // Initial time point
new Microsoft.Research.Oslo.Vector(0.4, 0.13), // Initial X vector
Population); // Right part
var eds = rk.AppendStep().SolveFromToStep(0, 200, 0.1).ToArray();
var x1 = eds.Select(p => new Point(p.T, p.X[0])).ToArray();
var x2 = eds.Select(p => new Point(p.T, p.X[1])).ToArray();
//Draw 1st population dynamics graph
linegraph1.Plot(x1.Select(x => x.X).ToArray(), x1.Select(x => x.Y).ToArray());
//Draw 2nd population dynamics graph
linegraph2.Plot(x2.Select(x => x.X).ToArray(), x2.Select(x => x.Y).ToArray());
//Draw phase portrait for system
Portrait.Plot(x1.Select(x => x.Y).ToArray(), x2.Select(x => x.Y).ToArray());
}
private void SolveStiff(float c)
{
L = (double)c; //PLEASE FOR THE LOVE OF GOD DONT CHANGE THIS GOD DAMN ROW!
var sol = Ode.GearBDF(
0,
new Vector(Ap, Yp, Bp, m, S),
(t, x) => new Vector(
(1 / (1 + Math.Exp(N * (1 - x[3] / 2 + Math.Log((1 + L / Kaoff) / (1 + L / Kaon)))))) * kbar1 * (1 - x[0]) - kbar2 * x[0] * (1 - x[1]) - kbar3 * x[0] * (1 - x[2]), //a
alpha1 * kbar2 * x[0] * (1 - x[1]) - (kbar4 + kbar6) * x[1], //y
alpha2 * kbar3 * x[0] * (1 - x[2]) - kbar5 * x[2], //b
(gammaR * (1 - (1 / (1 + Math.Exp(N * (1 - x[3] / 2 + Math.Log((1 + L / Kaoff) / (1 + L / Kaon))))))) -
gammaB * Math.Pow(x[2], 2) * (1 / (1 + Math.Exp(N * (1 - x[3] / 2 + Math.Log((1 + L / Kaoff) / (1 + L / Kaon))))))), //m
h(x[1]) * (1 - x[4]) //S
)
);
var points = sol.SolveFromTo(0, tSpan).ToArray();
var result = points[points.Length - 1];
Ap = result.X[0];
Yp = result.X[1];
Bp = result.X[2];
m = result.X[3];
S = result.X[4];
}
public MainPage()
{
InitializeComponent();
var rk = Ode.GearBDF(
0, // Initial time point
Vector.Zeros(16), // Initial X vector
MHC, // Right part
new Options // Optional options
{
RelativeTolerance = 1e-3, AbsoluteTolerance = 1e-6
});
// Solve to t = 2.0 and store results in array
var ed = rk.SolveFromToStep(0, 1000, 0.05).ToArray();
// Draw numeric solution
x1 = (LineGraph)plotter.FindName("x1");
x1.PlotY(ed.Select(sp => sp.X[0]));
x2 = (LineGraph)plotter.FindName("x2");
x2.PlotY(ed.Select(sp => sp.X[1]));
x3 = (LineGraph)plotter.FindName("x3");
x3.PlotY(ed.Select(sp => sp.X[2]));
x4 = (LineGraph)plotter.FindName("x4");
x4.PlotY(ed.Select(sp => sp.X[3]));
x5 = (LineGraph)plotter.FindName("x5");
x5.PlotY(ed.Select(sp => sp.X[4]));
x6 = (LineGraph)plotter.FindName("x6");
x6.PlotY(ed.Select(sp => sp.X[5]));
x7 = (LineGraph)plotter.FindName("x7");
x7.PlotY(ed.Select(sp => sp.X[6]));
x8 = (LineGraph)plotter.FindName("x8");
x8.PlotY(ed.Select(sp => sp.X[7]));
x9 = (LineGraph)plotter.FindName("x9");
x9.PlotY(ed.Select(sp => sp.X[8]));
x10 = (LineGraph)plotter.FindName("x10");
x10.PlotY(ed.Select(sp => sp.X[9]));
x11 = (LineGraph)plotter.FindName("x11");
x11.PlotY(ed.Select(sp => sp.X[10]));
x12 = (LineGraph)plotter.FindName("x12");
x12.PlotY(ed.Select(sp => sp.X[11]));
x13 = (LineGraph)plotter.FindName("x13");
x13.PlotY(ed.Select(sp => sp.X[12]));
x14 = (LineGraph)plotter.FindName("x14");
x14.PlotY(ed.Select(sp => sp.X[13]));
x15 = (LineGraph)plotter.FindName("x15");
x15.PlotY(ed.Select(sp => sp.X[14]));
x16 = (LineGraph)plotter.FindName("x16");
x16.PlotY(ed.Select(sp => sp.X[15]));
}
public void SingleExecute(double windVel, double windDir)
{
// Generate instance
Dynamics dy = new Dynamics();
Initital init = new Initital();
// Postprocess setting
post.InitializePost();
post.SetListPair();
postPara.InitializePost();
postPara.SetListPair();
// Send rocket specification setting to Dynamics.
dy.GroupList = allParam;
dy.SetParam();
dy.SetWind(windVel, windDir);
// Define initial vector.
init.GroupList = allParam;
init.SetRailParam();
var initVec = init.GetInitVec();
// Define computational parameter.
var tinit = 0.0;
var tfinal = 100;
var maxStep = 0.01;
var opts = new Options {
};
opts.MaxStep = maxStep;
opts.AbsoluteTolerance = Math.Pow(10, -4);
// Trajectory calculation
foreach (var sol in Ode.GearBDF(tinit, initVec, dy.Func, opts).SolveTo(tfinal))
{
if (sol.X[2] >= -0.1)
{
post.AddResult(sol);
}
else
{
break;
}
}
// Save result of trajectory case
var mode = "Trajectory";
post.SaveResultCsv(mode, tempDir, windVel, windDir);
// Postprocess for Max value
post.CalcExtra();
post.CalcMaxValue();
// Deployment calculation
IsParaDeploy = true;
if (IsParaDeploy)
{
// Deploy 1st parachute calculation.
var deployTime = post.GetDeployInitTime();
var deployInitVec = post.GetDeployInitVec();
// Postprocess setting
postPara.InitializePost();
postPara.SetListPair();
foreach (var sol in Ode.GearBDF(deployTime, deployInitVec,
dy.DeployEq, opts).SolveTo(tfinal + deployTime))
{
if (sol.X[2] >= -0.1)
{
postPara.AddResult(sol);
}
else
{
break;
}
}
// Save result of deployment case
mode = "DeployPara";
postPara.SaveResultCsv(mode, tempDir, windVel, windDir);
}
}