/// <summary>
/// Returns the elements of a Matrix<T> using the Matrix<T> Index object
/// </summary>
/// <param name="rows"></param>
/// <param name="cols"></param>
/// <returns></returns>
public Matrix <T> this[MatrixIndex rows, MatrixIndex cols]
{
get
{
Matrix <T> C = new Matrix <T>(rows.Length, cols.Length);
for (int r = 1; r <= rows.Length; r++)
{
for (int c = 1; c <= cols.Length; c++)
{
C[r, c] = this[rows[r], cols[c]];
}
}
return(C);
}
set
{
for (int r = 1; r <= rows.Length; r++)
{
for (int c = 1; c <= cols.Length; c++)
{
this[rows[r], cols[c]] = value[r, c];
}
}
}
}
public Matrix <T> this[MatrixIndex r, string c]
{
get
{
if (c.ToUpper() == "ALL" || c.ToUpper() == ":")
{
return(this[r, new MatrixIndex(1, NumCols)]);
}
else
{
throw new IndexOutOfRangeException("Column - No column selected");
}
}
set
{
if (r.Length == value.NumRows)
{
if (c.ToUpper() == "ALL" || c.ToUpper() == ":")
{
this[r, new MatrixIndex(1, NumCols)] = value;
}
else
{
throw new IndexOutOfRangeException("Row - No Row Selected");
}
}
else
{
throw new IndexOutOfRangeException("Column - Number of rows in Matrix<T> is not the same as new column");
}
}
}
/// <summary>
/// Returns the elements of a Matrix using the Matrix Index object
/// </summary>
/// <param name="rows"></param>
/// <param name="cols"></param>
/// <returns></returns>
///
public Vector this[MatrixIndex rows]
{
get
{
Vector C = new Vector(rows.Length);
for (int r = 1; r <= rows.Length; r++)
{
C[r] = this[rows[r]];
}
return(C);
}
set
{
for (int r = 1; r <= rows.Length; r++)
{
this[rows[r]] = value[r];
}
}
}
private static Matrix <double> RK45Helper(EOMS dynamics, Matrix <double> timeSpanData, Matrix <double> initialState, IntegratorOptions options, IntegratorParameters param)
{
// Make timeSpanData and initialState Column vectors
if (timeSpanData.NumRows < timeSpanData.NumCols)
{
timeSpanData = Matrix <double> .Transpose(timeSpanData);
}
if (initialState.NumRows < initialState.NumCols)
{
initialState = Matrix <double> .Transpose(initialState);
}
int nsteps = 0;
int nfailed = 0;
int nfevals = 0;
int refine = 4;
int nout = 0;
int nout_old = 0;
int nout_new = 0;
int neq = initialState.Length;
Matrix <double> S = new Matrix <double>(new double[, ] {
{ 1.0, 2.0, 3.0 }
}) / refine;
double t0 = timeSpanData[1, 1];
double tFinal = timeSpanData[2, 1];
double tSpan = tFinal - t0;
Matrix <double> tref = new Matrix <double>(1, 1);
Matrix <double> tout_new = new Matrix <double>(1, refine);
double t = t0;
Matrix <double> y = initialState;
Matrix <double> yout_new = new Matrix <double>(neq, 1);
MatrixIndex idx = new MatrixIndex();
int chunk = (int)System.Math.Min(System.Math.Max(100, 50 * refine), refine + System.Math.Floor(System.Math.Pow(2, 13) / neq));
Matrix <double> tout = new Matrix <double>(1, chunk);
Matrix <double> yout = new Matrix <double>(neq, chunk);
nout = 1;
tout[nout] = t;
yout[":", nout] = y;
double expon = 1.0 / 5.0;
double temph = 0.0;
Matrix <double> A = new Matrix <double>(new double[, ] {
{ 1.0 / 5.0, 3.0 / 10.0, 4.0 / 5.0, 8.0 / 9.0, 1.0, 1.0 }
}); // 1x6
Matrix <double> B = new Matrix <double>(new double[, ] {
{ 1.0 / 5.0, 3.0 / 40.0, 44.0 / 45.0, 19372.0 / 6561.0, 9017.0 / 3168.0, 35.0 / 384.0 }, //7x6
{ 0.0, 9.0 / 40.0, -56.0 / 15.0, -25360.0 / 2187.0, -355.0 / 33.0, 0.0 },
{ 0.0, 0.0, 32.0 / 9.0, 64448.0 / 6561.0, 46732.0 / 5247.0, 500.0 / 1113.0 },
{ 0.0, 0.0, 0.0, -212.0 / 729.0, 49.0 / 176.0, 125.0 / 192.0 },
{ 0.0, 0.0, 0.0, 0.0, -5103.0 / 18656.0, -2187.0 / 6784.0 },
{ 0.0, 0.0, 0.0, 0.0, 0.0, 11.0 / 84.0 },
{ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 }
});
Matrix <double> hA = new Matrix <double>(A.Size[1], A.Size[2]);
Matrix <double> hB = new Matrix <double>(B.Size[1], B.Size[2]);
Matrix <double> E = new Matrix <double>(new double[, ] {
{ 71.0 / 57600.0 }, { 0.0 }, { -71.0 / 16695.0 }, { 71.0 / 1920.0 }, { -17253.0 / 339200.0 }, { 22.0 / 525.0 }, { -1.0 / 40.0 }
}); // 7x1
Matrix <double> f = new Matrix <double>(neq, 7);
double htSpan = System.Math.Abs(tSpan);
double hmax = System.Math.Min(htSpan, 0.1 * htSpan);
double hmin = 16 * options.eps;
double absh = System.Math.Min(hmax, htSpan);
double rtol = options.rtol;
double atol = options.atol;
int tdir = 1;
double threshold = atol / rtol;
int next = 2;
if ((tFinal - t0) > 0)
{
tdir = 1;
}
else
{
tdir = -1;
}
// Compute an initial step size h using y'(t).
Matrix <double> f0 = dynamics[t0, initialState, param];
Matrix <double> temp = Matrix <double> .Max(Matrix <double> .Abs(initialState), threshold);
// TODO: Assert and throw expection if fo and temp are not the same size (or force f0 and temp to be the same size)
double tempSingle = (double)Matrix <double> .Max(Matrix <double> .Abs(f0 / temp));
double rh = tempSingle / (0.8 * System.Math.Pow(rtol, expon));
if (absh * rh > 1)
{
absh = 1 / rh;
}
absh = System.Math.Max(absh, hmin);
//f.setColumn(1,f0);
f[":", 1] = f0;
// THE MAIN RK45 LOOP
Matrix <double> ynew = y;
double tnew = t;
bool done = false;
bool nofailed = true;
int nStep = 1;
double err = 0.0;
double h;
while (!done)
{
// By default, hmin is a small number such that t+hmin is only slightly
// different than t. It might be 0 if t is 0.
hmin = 16 * options.eps;
//hmin = args.getParam("h");
absh = System.Math.Min(hmax, System.Math.Max(hmin, absh));
//absh = min(hmax, max(hmin, absh));
h = tdir * absh;
// Stretch the step if within 10% of tfinal-t.
//if (1.1*absh >= fabs(tFinal - t)){
if (1.1 * absh >= System.Math.Abs(tFinal - t))
{
h = tFinal - t;
absh = System.Math.Abs(h);
//absh = fabs(h);
done = true;
}
// LOOP FOR ADVANCING ONE STEP.
nofailed = true; // no failed attempts
while (true)
{
hA = h * A;
hB = h * B;
for (int i = 1; i < 6; i++)
{
f[":", i + 1] = dynamics[t + hA[1, i], y + f * hB[":", i], param];
}
tnew = t + hA[1, 6];
if (done)
{
tnew = tFinal; // Hit end point exactly.
}
h = tnew - t; // Purify h
ynew = y + f * hB[":", 6];
f[":", 7] = dynamics[tnew, ynew, param];
nfevals = nfevals + 6;
//err = absh * norm( (f * E) ./ max (max ( abs(y), abs(ynew)), threshold),inf);
err = (double)Matrix <double> .Max(Matrix <double> .Abs((f * E) / Matrix <double> .Max(Matrix <double> .Max(Matrix <double> .Abs(y), Matrix <double> .Abs(ynew)), threshold)));
err = absh * err;
// % Accept the solution only if the weighted error is no more than the
// % tolerance rtol. Estimate an h that will yield an error of rtol on
// % the next step or the next try at taking this step, as the case may be,
// % and use 0.8 of this value to avoid failures.
if (err > rtol)
{ // Failed Step
nfailed++;
// if (absh <= hmin)
// return;
// end
if (nofailed)
{
nofailed = false;
absh = System.Math.Max(hmin, absh * System.Math.Max(0.1, 0.8 * System.Math.Pow(rtol / err, expon)));
}
else
{
absh = System.Math.Max(hmin, 0.5 * absh);
}
h = tdir * absh;
done = false;
}
else // Successful step
{
break;
}
}
nsteps++;
tref = t + (tnew - t) * S;
nout_new = refine;
tout_new = Matrix <double> .Horzcat(tref, tnew);
yout_new = Matrix <double> .Horzcat(ntrp45(tref, t, y, h, f), ynew);
if (nout_new > 0)
{
nout_old = nout;
nout += nout_new;
if (nout > tout.Length)
{
tout = Matrix <double> .Horzcat(tout, new Matrix <double>(1, chunk));
yout = Matrix <double> .Horzcat(yout, new Matrix <double>(neq, chunk));
}
idx = new MatrixIndex(nout_old + 1, nout);
tout[1, idx] = tout_new;
yout[":", idx] = yout_new;
}
if (nofailed)
{
// Note that absh may shrink by 0.8, and that err may be 0.
temph = 1.25 * System.Math.Pow(err / rtol, expon);
if (temph > 0.2)
{
absh = absh / temph;
}
else
{
absh = 5.0 * absh;
}
}
t = tnew;
y = ynew;
f[":", 1] = f[":", 7];
}
Matrix <double> SolverReturnMatrix = new Matrix <double>(neq + 1, nout);
SolverReturnMatrix[1, ":"] = tout[1, new MatrixIndex(1, nout)];
SolverReturnMatrix[new MatrixIndex(2, neq + 1), ":"] = yout[":", new MatrixIndex(1, nout)];
return(SolverReturnMatrix);
}
private static Matrix<double> RK45Helper(EOMS dynamics, Matrix<double> timeSpanData, Matrix<double> initialState, IntegratorOptions options)
{
// Make timeSpanData and initialState Column vectors
if (timeSpanData.NumRows < timeSpanData.NumCols)
timeSpanData = Matrix<double>.Transpose(timeSpanData);
if (initialState.NumRows < initialState.NumCols)
initialState = Matrix<double>.Transpose(initialState);
int nsteps = 0;
int nfailed = 0;
int nfevals = 0;
int refine = 4;
int nout = 0;
int nout_old = 0;
int nout_new = 0;
int neq = initialState.Length;
Matrix<double> S = new Matrix<double>(new double[,] { { 1.0, 2.0, 3.0 } }) / refine;
double t0 = timeSpanData[1, 1];
double tFinal = timeSpanData[2, 1];
double tSpan = tFinal - t0;
Matrix<double> tref = new Matrix<double>(1, 1);
Matrix<double> tout_new = new Matrix<double>(1, refine);
double t = t0;
Matrix<double> y = initialState;
Matrix<double> yout_new = new Matrix<double>(neq, 1);
MatrixIndex idx = new MatrixIndex();
int chunk = (int)System.Math.Min(System.Math.Max(100, 50 * refine), refine + System.Math.Floor(System.Math.Pow(2, 13) / neq));
Matrix<double> tout = new Matrix<double>(1, chunk);
Matrix<double> yout = new Matrix<double>(neq, chunk);
nout = 1;
tout[nout] = t;
yout[":", nout] = y;
double expon = 1.0 / 5.0;
double temph = 0.0;
Matrix<double> A = new Matrix<double>(new double[,] { { 1.0 / 5.0, 3.0 / 10.0, 4.0 / 5.0, 8.0 / 9.0, 1.0, 1.0 } }); // 1x6
Matrix<double> B = new Matrix<double>(new double[,] { {1.0/5.0, 3.0/40.0, 44.0/45.0, 19372.0/6561.0, 9017.0/3168.0, 35.0/384.0}, //7x6
{0.0, 9.0/40.0, -56.0/15.0, -25360.0/2187.0, -355.0/33.0, 0.0},
{0.0, 0.0, 32.0/9.0, 64448.0/6561.0, 46732.0/5247.0, 500.0/1113.0},
{0.0, 0.0, 0.0, -212.0/729.0, 49.0/176.0, 125.0/192.0},
{0.0, 0.0, 0.0, 0.0, -5103.0/18656.0, -2187.0/6784.0},
{0.0, 0.0, 0.0, 0.0, 0.0, 11.0/84.0},
{0.0, 0.0, 0.0, 0.0, 0.0, 0.0}});
Matrix<double> hA = new Matrix<double>(A.Size[1], A.Size[2]);
Matrix<double> hB = new Matrix<double>(B.Size[1], B.Size[2]);
Matrix<double> E = new Matrix<double>(new double[,] { { 71.0 / 57600.0 }, { 0.0 }, { -71.0 / 16695.0 }, { 71.0 / 1920.0 }, { -17253.0 / 339200.0 }, { 22.0 / 525.0 }, { -1.0 / 40.0 } }); // 7x1
Matrix<double> f = new Matrix<double>(neq, 7);
double htSpan = System.Math.Abs(tSpan);
double hmax = System.Math.Min(htSpan, 0.1 * htSpan);
double hmin = 16*options.eps;
double absh = System.Math.Min(hmax, htSpan);
double rtol = options.rtol;
double atol = options.atol;
int tdir = 1;
double threshold = atol / rtol;
int next = 2;
if ((tFinal - t0) > 0)
tdir = 1;
else
tdir = -1;
// Compute an initial step size h using y'(t).
Matrix<double> f0 = dynamics[t0, initialState];
Matrix<double> temp = Matrix<double>.Max(Matrix<double>.Abs(initialState), threshold);
// TODO: Assert and throw expection if fo and temp are not the same size (or force f0 and temp to be the same size)
double tempSingle = (double)Matrix<double>.Max(Matrix<double>.Abs(f0 / temp));
double rh = tempSingle / (0.8 * System.Math.Pow(rtol, expon));
if (absh * rh > 1)
absh = 1 / rh;
absh = System.Math.Max(absh, hmin);
//f.setColumn(1,f0);
f[":", 1] = f0;
// THE MAIN RK45 LOOP
Matrix<double> ynew = y;
double tnew = t;
bool done = false;
bool nofailed = true;
int nStep = 1;
double err = 0.0;
double h;
while (!done)
{
// By default, hmin is a small number such that t+hmin is only slightly
// different than t. It might be 0 if t is 0.
hmin = 16*options.eps;
//hmin = args.getParam("h");
absh = System.Math.Min(hmax, System.Math.Max(hmin, absh));
//absh = min(hmax, max(hmin, absh));
h = tdir * absh;
// Stretch the step if within 10% of tfinal-t.
//if (1.1*absh >= fabs(tFinal - t)){
if (1.1 * absh >= System.Math.Abs(tFinal - t))
{
h = tFinal - t;
absh = System.Math.Abs(h);
//absh = fabs(h);
done = true;
}
// LOOP FOR ADVANCING ONE STEP.
nofailed = true; // no failed attempts
while (true)
{
hA = h * A;
hB = h * B;
for (int i = 1; i < 6; i++)
f[":", i + 1] = dynamics[t + hA[1, i], y + f * hB[":", i]];
tnew = t + hA[1, 6];
if (done)
tnew = tFinal; // Hit end point exactly.
h = tnew - t; // Purify h
ynew = y + f * hB[":", 6];
f[":", 7] = dynamics[tnew, ynew];
nfevals = nfevals + 6;
//err = absh * norm( (f * E) ./ max (max ( abs(y), abs(ynew)), threshold),inf);
err =(double) Matrix<double>.Max(Matrix<double>.Abs((f * E) / Matrix<double>.Max(Matrix<double>.Max(Matrix<double>.Abs(y), Matrix<double>.Abs(ynew)), threshold)));
err = absh * err;
// % Accept the solution only if the weighted error is no more than the
// % tolerance rtol. Estimate an h that will yield an error of rtol on
// % the next step or the next try at taking this step, as the case may be,
// % and use 0.8 of this value to avoid failures.
if (err > rtol)
{ // Failed Step
nfailed++;
// if (absh <= hmin)
// return;
// end
if (nofailed)
{
nofailed = false;
absh = System.Math.Max(hmin, absh * System.Math.Max(0.1, 0.8 * System.Math.Pow(rtol / err, expon)));
}
else
absh = System.Math.Max(hmin, 0.5 * absh);
h = tdir * absh;
done = false;
}
else // Successful step
{
break;
}
}
nsteps++;
tref = t + (tnew - t) * S;
nout_new = refine;
tout_new = Matrix<double>.Horzcat(tref, tnew);
yout_new = Matrix<double>.Horzcat(ntrp45(tref, t, y, h, f), ynew);
if (nout_new > 0)
{
nout_old = nout;
nout += nout_new;
if (nout > tout.Length)
{
tout = Matrix<double>.Horzcat(tout, new Matrix<double>(1, chunk));
yout = Matrix<double>.Horzcat(yout, new Matrix<double>(neq, chunk));
}
idx = new MatrixIndex(nout_old + 1, nout);
tout[1, idx] = tout_new;
yout[":", idx] = yout_new;
}
if (nofailed)
{
// Note that absh may shrink by 0.8, and that err may be 0.
temph = 1.25 * System.Math.Pow(err / rtol, expon);
if (temph > 0.2)
absh = absh / temph;
else
absh = 5.0 * absh;
}
t = tnew;
y = ynew;
f[":", 1] = f[":", 7];
}
Matrix<double> SolverReturnMatrix = new Matrix<double>(neq + 1, nout);
SolverReturnMatrix[1, ":"] = tout[1, new MatrixIndex(1, nout)];
SolverReturnMatrix[new MatrixIndex(2, neq + 1), ":"] = yout[":", new MatrixIndex(1, nout)];
return SolverReturnMatrix;
}