static public List <State> Split(List <State> states, int dim, int divs)
{
State[] result = new State[divs];
foreach (State s in states)
{
List <DoubleInterval[]> sec = new List <DoubleInterval[]>(divs);
double dimL = s.continuousState.axes[dim].left;
double dimR = s.continuousState.axes[dim].right;
var next = new DoubleInterval[s.continuousState.axes.Length];
for (int i = 0; i < s.continuousState.axes.Length; ++i)
{
next[i] = s.continuousState.axes[i];
}
double prevR = dimL;
for (int j = 1; j < divs; ++j)
{
double R = (dimR - dimL) * j / divs + dimL;
next[dim] = new DoubleInterval(prevR, R);
// intermix the results for faster coverage
int index = (j % 2 == 1) ? (j / 2 + 1) : (divs - j / 2);
result[index] = new State(s.step, s.continuousNames, new DoubleBoundingBox(next), s.discreteNames, s.discreteState);
prevR = R;
}
next[dim] = new DoubleInterval(prevR, dimR);
result[0] = new State(s.step, s.continuousNames, new DoubleBoundingBox(next), s.discreteNames, s.discreteState);
}
List <State> list = new List <State>(divs);
foreach (var s in result)
{
list.Add(s);
}
return(list);
}
static public Polynomial Expansion(List<TaylorStructure> fs, string[] variables, Dictionary<string, DoubleInterval> x0, int maxOrder)
{
Polynomial polynomial = new Polynomial();
int[] deg = new int[variables.Length];
foreach (TaylorStructure e in fs)
{
DoubleInterval fval = e.func.Eval(x0) / e.coeff;
// Constant: d^alphaF / alpha!
Polynomial p = new Polynomial(new Monomial(fval, variables.Length));
// Multiply by h^alpha = (x-a)^alpha (first var is time)
for (int i = 1; i < variables.Length; ++i)
{
DoubleInterval a = x0[variables[i]];
deg[i] = 1;
var mx = new Monomial(new DoubleInterval(1.0), deg);
var ma = new Monomial(a, deg.Length);
for (int j = 0; j < e.degrees[i]; ++j)
p *= (new Polynomial(mx) - new Polynomial(ma));
deg[i] = 0;
}
p.Cutoff();
polynomial += p;
}
return polynomial;
}
protected override void VerifiedSafeState(State q)
{
if (plotter == null || q.step > 0)
{
return;
}
if (!timeAxis && !searchIndexAxis)
{
return;
}
// Extract visualization data
double top = 0;
double bottom = 1;
double left = 0;
double right = 1;
Dictionary <string, DoubleInterval> currentValues = GetSystemState(q);
if (timeAxis && searchIndexAxis)
{
DoubleInterval current = axisValue[1].Eval(currentValues);
top = (current.left - axisInitialValue[1].left) / axisInitialValue[1].width;
bottom = (current.right - axisInitialValue[1].left) / axisInitialValue[1].width;
}
else if (timeAxis)
{
DoubleInterval currentY = axisValue[1].Eval(currentValues);
DoubleInterval currentZ = axisValue[2].Eval(currentValues);
if (axisInitialValue[1].width > 1E-6)
{
top = (currentY.left - axisInitialValue[1].left) / axisInitialValue[1].width;
bottom = (currentY.right - axisInitialValue[1].left) / axisInitialValue[1].width;
}
if (axisInitialValue[2].width > 1E-6)
{
left = (currentZ.left - axisInitialValue[2].left) / axisInitialValue[2].width;
right = (currentZ.right - axisInitialValue[2].left) / axisInitialValue[2].width;
}
}
else if (searchIndexAxis)
{
DoubleInterval currentX = axisValue[0].Eval(currentValues);
DoubleInterval currentY = axisValue[1].Eval(currentValues);
if (axisInitialValue[0].width > 1E-6)
{
top = (currentX.left - axisInitialValue[0].left) / axisInitialValue[0].width;
bottom = (currentX.right - axisInitialValue[0].left) / axisInitialValue[0].width;
}
if (axisInitialValue[1].width > 1E-6)
{
left = (currentY.left - axisInitialValue[1].left) / axisInitialValue[1].width;
right = (currentY.right - axisInitialValue[1].left) / axisInitialValue[1].width;
}
}
lock (plotter.plotDataLock)
{
verifiedRegions.Add(new RectangleF((float)left, (float)top, (float)(right - left), (float)(bottom - top)));
}
}
private double[] NormalizeAlongAxis(DoubleInterval value, int axis)
{
double[] result =
{
value.left, value.right
};
return(result);
}
public override AST Simplify()
{
var A = children[0].Simplify();
if (A.type == TYPE.REAL)
{
DoubleInterval value = ((REAL)A).value;
return new REAL(value.Sqrt());
}
return new SQRT(A);
}
public DoubleBoundingBox Eval()
{
IntPtr[] ival = new IntPtr[numVars];
EvalFlowpipe(this.ptr, ival);
DoubleInterval[] result = new DoubleInterval[numVars];
for (int i = 0; i < numVars; ++i)
{
result[i] = new DoubleInterval(ival[i]);
}
return(new DoubleBoundingBox(result));
}
public override DoubleInterval Eval(Dictionary<string,DoubleInterval> values)
{
DoubleInterval value = children[0].Eval(values);
DoubleInterval result = new DoubleInterval(1.0);
if (power > 0)
for (int k = 0; k < power; ++k)
result *= value;
else
for (int k = 0; k > power; --k)
result /= value;
return result;
}
public override AST Simplify()
{
var A = children[0].Simplify();
if (A.type == TYPE.REAL)
{
DoubleInterval value = ((REAL)A).value;
if (value.left == 0 && value.right == 0)
return A;
return new REAL(-value);
}
return new NEG(A);
}
protected FPIntegerInterval Measure(DoubleInterval d, uint bits, uint decimals)
{
double lower = d.left;
double upper = d.right;
for (int i = 0; i < decimals; ++i)
{
lower *= 2;
upper *= 2;
}
return(new FPIntegerInterval((int)lower, (int)(upper + 1), bits, decimals));
}
public Flowpipe(State state)
{
this.numVars = state.continuousNames.Length;
DoubleInterval[] domain = new DoubleInterval[numVars];
IntPtr[] domain_ptr = new IntPtr[numVars];
for (int i = 0; i < numVars; ++i)
{
domain[i] = state.continuousState.axes[i].Clone();
domain_ptr[i] = domain[i].ptr;
}
ptr = CreateFlowpipe(numVars, domain_ptr, new DoubleInterval(0.0).ptr);
}
public override AST GetDerivative(string dvar)
{
var A = children[0].GetDerivative(dvar).Simplify();
var B = children[1].GetDerivative(dvar).Simplify();
if (B.type == TYPE.REAL)
{
DoubleInterval value = ((REAL)B).value;
if (value.left == 0 && value.right == 0)
return new DIV(A, children[1]);
}
return
new DIV(
new SUB(
new MUL(A, children[1]),
new MUL(children[0], B)),
new MUL(children[1], children[1]));
}
public override AST Simplify()
{
var A = children[0].Simplify();
var B = children[1].Simplify();
if (A.type == TYPE.REAL)
{
DoubleInterval value = ((REAL)A).value;
if (value.left == 0 && value.right == 0)
return A;
}
if (B.type == TYPE.REAL)
{
DoubleInterval value = ((REAL)B).value;
if (value.left == 1 && value.right == 1)
return A;
}
return new DIV(A, B);
}
public override AST Simplify()
{
if (power == 0)
return new REAL(1);
var A = children[0].Simplify();
if (power == 1)
return A;
if (A.type == TYPE.REAL)
{
DoubleInterval value = ((REAL)A).value;
DoubleInterval v = value;
for (int i = 1; i < power; ++i)
v = value * v;
return new REAL(v);
}
return new POW(A, power);
}
/// <summary>
/// Returns true if this interval is subset of A
/// </summary>
/// <param name="A"></param>
/// <returns></returns>
public bool Subseteq(DoubleInterval A)
{
return(SubseteqInterval(this.ptr, A.ptr));
}
private List <VizData> GetStateRepresentation()
{
List <VizData> result = new List <VizData>();
bool allUnsafe = true;
for (int j = 0; j < plotData.Count; ++j)
{
if (plotData[j].type != PlotData.PlotType.UNSAFE)
{
allUnsafe = false;
break;
}
}
for (int j = 0; j < plotData.Count; ++j)
{
PlotData data = plotData[j];
if (data.q == null)
{
continue;
}
Dictionary <string, DoubleInterval> varValues = GetSystemState(data.q);
if (timeAxis)
{
PlotData datanext = j < plotData.Count - 1 ? plotData[j + 1] : null;
if (datanext == null || datanext.q == null || data.searchIndex != datanext.searchIndex)
{
continue;
}
Dictionary <string, DoubleInterval> varValuesNext = datanext != null?GetSystemState(datanext.q) : null;
// X is time
double time = NormalizeAlongAxis(data.q.step, 0);
double timenext = NormalizeAlongAxis(datanext.q.step, 0);
if (searchIndexAxis)
{
// Z is search index
double index = NormalizeAlongAxis(data.searchIndex, 2) * searchZDepth;
DoubleInterval value = axisValue[1].Eval(varValues);
DoubleInterval valueNext = axisValue[1].Eval(varValuesNext);
double[] nvalue = NormalizeAlongAxis(value, 1);
double[] nvalueNext = NormalizeAlongAxis(valueNext, 1);
VizData viz = new VizData();
viz.data = data;
viz.quad[0] = new Vector3d(time, nvalue[1], index);
viz.quad[1] = new Vector3d(time, nvalue[0], index);
viz.quad[2] = new Vector3d(timenext, nvalueNext[0], index);
viz.quad[3] = new Vector3d(timenext, nvalueNext[1], index);
result.Add(viz);
}
else
{
if (data.type == PlotData.PlotType.UNSAFE && !allUnsafe)
{
continue;
}
// Y-Z are variables
DoubleInterval valueY = axisValue[1].Eval(varValues);
DoubleInterval valueZ = axisValue[2].Eval(varValues);
DoubleInterval valueYnext = axisValue[1].Eval(varValuesNext);
DoubleInterval valueZnext = axisValue[2].Eval(varValuesNext);
double[] nvalueY = NormalizeAlongAxis(valueY, 1);
double[] nvalueZ = NormalizeAlongAxis(valueZ, 2);
double[] nvalueYnext = NormalizeAlongAxis(valueYnext, 1);
double[] nvalueZnext = NormalizeAlongAxis(valueZnext, 2);
VizData viz = new VizData();
viz.data = data;
viz.quad[0] = new Vector3d(time, nvalueY[1], nvalueZ[1]);
viz.quad[1] = new Vector3d(time, nvalueY[0], nvalueZ[1]);
viz.quad[2] = new Vector3d(timenext, nvalueYnext[0], nvalueZnext[1]);
viz.quad[3] = new Vector3d(timenext, nvalueYnext[1], nvalueZnext[1]);
result.Add(viz);
viz = new VizData();
viz.data = data;
viz.quad[0] = new Vector3d(time, nvalueY[1], nvalueZ[0]);
viz.quad[1] = new Vector3d(time, nvalueY[0], nvalueZ[0]);
viz.quad[2] = new Vector3d(timenext, nvalueYnext[0], nvalueZnext[0]);
viz.quad[3] = new Vector3d(timenext, nvalueYnext[1], nvalueZnext[0]);
result.Add(viz);
viz = new VizData();
viz.data = data;
viz.quad[0] = new Vector3d(time, nvalueY[1], nvalueZ[0]);
viz.quad[1] = new Vector3d(time, nvalueY[1], nvalueZ[1]);
viz.quad[2] = new Vector3d(timenext, nvalueYnext[1], nvalueZnext[1]);
viz.quad[3] = new Vector3d(timenext, nvalueYnext[1], nvalueZnext[0]);
result.Add(viz);
viz = new VizData();
viz.data = data;
viz.quad[0] = new Vector3d(time, nvalueY[0], nvalueZ[0]);
viz.quad[1] = new Vector3d(time, nvalueY[0], nvalueZ[1]);
viz.quad[2] = new Vector3d(timenext, nvalueYnext[0], nvalueZnext[1]);
viz.quad[3] = new Vector3d(timenext, nvalueYnext[0], nvalueZnext[0]);
result.Add(viz);
}
}
else
{
if (searchIndexAxis)
{
// X-Y are variables
double index = NormalizeAlongAxis(data.searchIndex, 2) * searchZDepth;
DoubleInterval valueX = axisValue[0].Eval(varValues);
DoubleInterval valueY = axisValue[1].Eval(varValues);
double[] nvalueX = NormalizeAlongAxis(valueX, 0);
double[] nvalueY = NormalizeAlongAxis(valueY, 1);
VizData viz = new VizData();
viz.data = data;
viz.quad[0] = new Vector3d(nvalueX[1], nvalueY[0], index);
viz.quad[1] = new Vector3d(nvalueX[0], nvalueY[0], index);
viz.quad[2] = new Vector3d(nvalueX[0], nvalueY[1], index);
viz.quad[3] = new Vector3d(nvalueX[1], nvalueY[1], index);
result.Add(viz);
}
}
}
return(result);
}
public FormulaSystem(string filename, Plot3d plotter)
: base()
{
axisValue[0] = new REAL(0.0);
axisValue[1] = new REAL(0.0);
axisValue[2] = new REAL(0.0);
Load(filename, "M");
string[] cNames = new string[cVariables.Count];
string[] dNames = new string[dVariables.Count];
DoubleInterval[] cInitial = new DoubleInterval[cVariables.Count];
FPIntegerInterval[] dInitial = new FPIntegerInterval[dVariables.Count];
int i = 0;
foreach (var kvp in cVariables)
{
cNames[i] = kvp.Key.name;
cInitial[i] = kvp.Value.Clone();
i++;
}
i = 0;
foreach (var kvp in dVariables)
{
dNames[i] = kvp.Key.Expr;
dInitial[i] = kvp.Value.Clone();
i++;
}
// build the ODEs
ode = new List <AST>();
foreach (var kvp in cVariables)
{
AST f;
if (odes.TryGetValue(kvp.Key.name, out f))
{
ode.Add(f);
}
}
Print(Log.Output);
Print(Log.Debug);
Initialize(cNames, cInitial, dNames, dInitial, order, period);
if (IsPolynomial)
{
Log.WriteLine("Using polynomial solver");
}
else if (ContainsSqrt)
{
Log.WriteLine("Using approximate Taylor expansion solver");
}
else
{
Log.WriteLine("Using non-polynomial Taylor model solver");
}
// look for lower and upper bounds
foreach (var kvp in dVariables)
{
FixedPointNumber fp = kvp.Key;
int lo = -(1 << ((int)fp.bits - 1));
int up = (1 << ((int)fp.bits - 1)) - 1;
var solver = ctx.MkSimpleSolver();
AddController(ctx, solver, kvp.Key.Expr);
lo = LowerBound(ctx, solver, fp.Expr, fp.bits, lo, up);
up = UpperBound(ctx, solver, fp.Expr, fp.bits, lo, up);
var ival = new FPIntegerInterval(lo, up, fp.bits, fp.decimals);
controlBounds.Add(fp.Expr, ival);
Log.Debug.WriteLine("Control variable '{0}' always in {1}", kvp.Key, ival);
}
Dictionary <string, DoubleInterval> initialValues = GetSystemState(initialState); // initialState.ToDictionary();
if (!timeAxis)
{
axisInitialValue[0] = axisValue[0].Eval(initialValues);
}
axisInitialValue[1] = axisValue[1].Eval(initialValues);
if (!searchIndexAxis)
{
axisInitialValue[2] = axisValue[2].Eval(initialValues);
}
this.plotter = plotter;
if (plotter != null)
{
plotter.SetMinMax(axisMin[0], axisMax[0], axisMin[1], axisMax[1], axisMin[2], axisMax[2]);
plotter.DefaultSettings();
plotter.DrawEvent += Draw;
}
}
public Monomial(DoubleInterval I, int[] degs)
{
ptr = CreateMonomial(I.ptr, degs.Length, degs);
}
public Monomial(DoubleInterval I, int numVars)
{
ptr = CreateConstantMonomial(I.ptr, numVars);
}
public REAL(double value)
{
this.type = TYPE.REAL;
this.value = new DoubleInterval(value);
}
public TaylorModel(Polynomial polynomial, DoubleInterval I)
{
ptr = CreateTaylorModel(polynomial.ptr, I.ptr);
}
public REAL(DoubleInterval value)
{
this.value = value;
}