public void SetupSolver()
{
depth = parameter_names.Count;
width = (int)Mathf.Pow(PARTICLE_COUNT, 1f / (float)depth);
for (int i = 0; i < depth; i++)
{
string name = parameter_names[i];
indexedParam[i] = name;
parameterMin[name] = (float)solver.EvaluateExpression(parameter_min[name]);
parameterMax[name] = (float)solver.EvaluateExpression(parameter_max[name]);
solver.SetGlobalVariable(name, 0);
}
expr1 = solver.SymbolicateExpression(expression1);
expr2 = solver.SymbolicateExpression(expression2);
expr3 = solver.SymbolicateExpression(expression3);
for (int i = 0; i < depth; i++)
{
string name = parameter_names[i];
AK.Variable var = solver.GetGlobalVariable(name);
//vars.Add(var);
vars[name] = var;
}
}
// Evaluate all equations for a given x (called by a thread), and popluate arrays with the results
void ThreadedEvaluate(float x_temp, int inOrderCount)
{
AK.ExpressionSolver subSolver = new AK.ExpressionSolver();
AK.Expression subExp = new AK.Expression();
subSolver.SetGlobalVariable("x", 0);
subSolver.SetGlobalVariable("y", 0);
subSolver.SetGlobalVariable("z", 0);
AK.Variable subX = subSolver.GetGlobalVariable("x");
AK.Variable subY = subSolver.GetGlobalVariable("y");
AK.Variable subZ = subSolver.GetGlobalVariable("z");
subExp = subSolver.SymbolicateExpression(es.expressions["X"].expression);
for (float y_temp = ymin; y_temp < ymax; y_temp += delta)
{
for (float z_temp = zmin; z_temp < zmax; z_temp += delta)
{
if ((int)((z_temp - zmin) / delta) % sleepInterval == 0)
{
Thread.Sleep(1);
}
subX.value = x_temp;
subY.value = z_temp;
subZ.value = y_temp;
float x = (float)subExp.Evaluate();
//Mathf.Clamp(x, -Mathf.Exp(20), Mathf.Exp(20));
//float y = (float)expY.Evaluate();
//Mathf.Clamp(y, -Mathf.Exp(20), Mathf.Exp(20));
//float z = (float)expZ.Evaluate();
//Mathf.Clamp(z, -Mathf.Exp(20), Mathf.Exp(20));
Vector3 target = new Vector3(x_temp, y_temp, z_temp);
Vector3 result = new Vector3(x, 0, 0);
if (float.IsNaN(x)
// || float.IsNaN(y)
// || float.IsNaN(z)
||
Mathf.Abs(x) == 0)
{
result = new Vector3(0, 0, 0);
}
//Vector3 direction = result.normalized;
lock (lck)
{
max_magnitude = (Mathf.Abs(x) > max_magnitude) ? Mathf.Abs(x) : max_magnitude;
}
startPts[inOrderCount] = target;
offsets[inOrderCount] = result;
inOrderCount++;
}
}
// numComplete++;
}
// Use this for initialization
void Start()
{
vectors = new List <Transform>();
startPts = new List <Vector3>();
offsets = new List <Vector3>();
solver = new AK.ExpressionSolver();
expX = new AK.Expression(); expY = new AK.Expression(); expZ = new AK.Expression();
solver.SetGlobalVariable("x", 0); solver.SetGlobalVariable("y", 0); solver.SetGlobalVariable("z", 0);
varX = solver.GetGlobalVariable("x"); varY = solver.GetGlobalVariable("y"); varZ = solver.GetGlobalVariable("z");
max_magnitude = 0f;
//CalculateVectors();
//DrawVectorField();
}
void ThreadedEvaluate(int TID, int chunkSize, int extra)
{
AK.ExpressionSolver solver_ = new AK.ExpressionSolver();
AK.Variable u_ = solver_.SetGlobalVariable("theta", 0);
AK.Variable v_ = solver_.SetGlobalVariable("phi", 0);
AK.Expression exp_ = solver_.SymbolicateExpression(expr);
float umin = (float)solver_.EvaluateExpression(uminExpr);
float umax = (float)solver_.EvaluateExpression(umaxExpr);
float vmin = (float)solver_.EvaluateExpression(vminExpr);
float vmax = (float)solver_.EvaluateExpression(vmaxExpr);
System.Random rand = new System.Random();
for (int i = 0; i < chunkSize + extra; i++)
{
float u = (float)(chunkSize * TID + i) / (resolution - 1);
u_.value = umin + (umax - umin) * u;
for (int j = 0; j < resolution; j++)
{
float v = (float)j / (resolution - 1);
v_.value = vmin + (vmax - vmin) * v;
float result = (float)exp_.Evaluate();
Vector3 spherical = new Vector3((float)u_.value, (float)v_.value, result);
Vector3 cartesian = SphericalToCartesian(spherical);
Vector3 vel = new Vector3(
(float)rand.NextDouble(),
(float)rand.NextDouble(),
(float)rand.NextDouble());
vel = vel.normalized * 0.1f;
float sqrt2 = Mathf.Sqrt(2.0f);
Color c = Color.cyan * Mathf.Sqrt(u * u + v * v) / sqrt2
+ Color.yellow * (1.0f - Mathf.Sqrt(u * u + v * v) / sqrt2)
+ Color.red * Mathf.Sqrt(u * u + (1 - v) * (1 - v)) / sqrt2
+ Color.green * (1.0f - Mathf.Sqrt(u * u + (1 - v) * (1 - v)) / sqrt2);
Vector3 pos = new Vector3(cartesian.x, cartesian.z, cartesian.y);
Particle p = new Particle()
{
position = pos,
velocity = vel,
color = c
};
lock (insert_lck)
{
results.Add(p);
}
}
}
}
public Variable SetVariable(string name, string value)
{
Variable v;
if (constants.TryGetValue(name,out v))
{
if (v.stringValue == null)
{
throw new ESParameterTypeChangedException("Can not change type of existing parameter " + name);
}
v.stringValue = value;
return v;
}
v = new Variable(name,value);
constants.Add(name,v);
return v;
}
Vector3 ThreadedRK4(int TID, Vector3 v0, float dt)
{
AK.Variable varX_ = solvers[TID].GetGlobalVariable("x");
AK.Variable varY_ = solvers[TID].GetGlobalVariable("y");
AK.Variable varZ_ = solvers[TID].GetGlobalVariable("z");
varX_.value = v0.x; varY_.value = v0.z; varZ_.value = v0.y;
Vector3 m1 = new Vector3((float)expXs[TID].Evaluate(), (float)expZs[TID].Evaluate(), (float)expYs[TID].Evaluate()).normalized;
varX_.value = v0.x + m1.x * dt / 2.0f; varY_.value = v0.z + m1.z * dt / 2.0f; varZ_.value = v0.y + m1.y * dt / 2.0f;
Vector3 m2 = new Vector3((float)expXs[TID].Evaluate(), (float)expZs[TID].Evaluate(), (float)expYs[TID].Evaluate()).normalized;
varX_.value = v0.x + m2.x * dt / 2.0f; varY_.value = v0.z + m2.z * dt / 2.0f; varZ_.value = v0.y + m2.y * dt / 2.0f;
Vector3 m3 = new Vector3((float)expXs[TID].Evaluate(), (float)expZs[TID].Evaluate(), (float)expYs[TID].Evaluate()).normalized;
varX_.value = v0.x + m3.x * dt; varY_.value = v0.z + m3.z * dt; varZ_.value = v0.y + m3.y * dt;
Vector3 m4 = new Vector3((float)expXs[TID].Evaluate(), (float)expZs[TID].Evaluate(), (float)expYs[TID].Evaluate()).normalized;
Vector3 m = (m1 + m2 * 2.0f + m3 * 2.0f + m4) / 6.0f;
return(v0 + m * dt);
}
internal void ThreadedEvaluate(List <int[]> samples, ExpressionSet expressionSet, int TID)
{
Dictionary <string, AK.Variable> vars = new Dictionary <string, AK.Variable>();
int depth = expressionSet.ranges.Count;
int width = (int)Mathf.Pow(particlesPerES, 1f / (float)depth);
System.Random rand = new System.Random();
ThreadHelper threadHelper = SetupSolver(expressionSet);
Dictionary <int, string> indexedParam = new Dictionary <int, string>();
int k = 0;
foreach (string name in expressionSet.ranges.Keys)
{
AK.Variable var = threadHelper.solver.GetGlobalVariable(name);
indexedParam.Add(k, name);
vars[name] = var;
k++;
}
int iterations = Math.Min(particlesPerES - samples.Count * TID, samples.Count);
Particle[] particles = new Particle[iterations];
for (int i = 0; i < iterations; i++)
{
int[] arr = samples[i];
for (int j = 0; j < depth; j++)
{
int val = arr[j];
string name = indexedParam[j];
AK.Variable var = vars[name];
var.value = threadHelper.parameterMin[name] + (float)val / (width - 1) * (threadHelper.parameterMax[name] - threadHelper.parameterMin[name]);
}
float x = (float)threadHelper.expressionList[0].Evaluate();
float z = (float)threadHelper.expressionList[1].Evaluate();
float y = (float)threadHelper.expressionList[2].Evaluate();
lock (lck)
{
maxRange = (Mathf.Abs(x) > maxRange) ? Mathf.Abs(x) : maxRange;
maxRange = (Mathf.Abs(y) > maxRange) ? Mathf.Abs(y) : maxRange;
maxRange = (Mathf.Abs(z) > maxRange) ? Mathf.Abs(z) : maxRange;
}
particles[i] = new Particle();
particles[i].position = new Vector3(x, y, z);
Vector3 vel = new Vector3();
vel.x = 0.5f - (float)rand.NextDouble();
vel.y = 0.5f - (float)rand.NextDouble();
vel.z = 0.5f - (float)rand.NextDouble();
vel = 0.1f * Vector3.Normalize(vel);
particles[i].velocity = vel;
}
lock (lck)
{
threadResults.Add(particles);
}
}
public Symbol(Variable ptrToConstValue)
{
type = ptrToConstValue.stringValue != null ? SymbolType.StringVariable : SymbolType.RealValue;
variable = ptrToConstValue;
}
void SamplePoints()
{
Vector3 start = referencePoint.lastLocalPos;
//lck = new object();
//thread_num = SystemInfo.processorCount;
//thread_num = 1;
//thread_num = (thread_num > 2) ? 2 : thread_num;
tmin = (float)solver.EvaluateExpression(t_min);
tmin = (tmin > 0) ? 0 : tmin;
tmax = (float)solver.EvaluateExpression(t_max);
tmax = (tmax < 0) ? 0 : tmax;
currLocalPos = referencePoint.lastLocalPos;
currExpX = vectorField.expressionX;
currExpY = vectorField.expressionY;
currExpZ = vectorField.expressionZ;
int lastCount = positions.Count;
positions.Clear();
solver = new AK.ExpressionSolver();
solver.SetGlobalVariable("x", referencePoint.lastLocalPos.x);
solver.SetGlobalVariable("y", referencePoint.lastLocalPos.y);
solver.SetGlobalVariable("z", referencePoint.lastLocalPos.z);
expX = solver.SymbolicateExpression(vectorField.es.expressions[ExpressionSet.ExpOptions.X].expression);
expY = solver.SymbolicateExpression(vectorField.es.expressions[ExpressionSet.ExpOptions.Y].expression);
expZ = solver.SymbolicateExpression(vectorField.es.expressions[ExpressionSet.ExpOptions.Z].expression);
varX = solver.GetGlobalVariable("x");
varY = solver.GetGlobalVariable("y");
varZ = solver.GetGlobalVariable("z");
//solvers = new AK.ExpressionSolver[thread_num];
//expXs = new AK.Expression[thread_num];
//expYs = new AK.Expression[thread_num];
//expZs = new AK.Expression[thread_num];
//for(int i = 0; i < thread_num; i++)
//{
// solvers[i] = new AK.ExpressionSolver();
// solvers[i].SetGlobalVariable("x", 0);
// solvers[i].SetGlobalVariable("y", 0);
// solvers[i].SetGlobalVariable("z", 0);
// expXs[i] = solvers[i].SymbolicateExpression(vectorField.es.expressions[ExpressionSet.ExpOptions.X].expression);
// expYs[i] = solvers[i].SymbolicateExpression(vectorField.es.expressions[ExpressionSet.ExpOptions.Y].expression);
// expZs[i] = solvers[i].SymbolicateExpression(vectorField.es.expressions[ExpressionSet.ExpOptions.Z].expression);
//}
//Thread[] threads = new Thread[thread_num];
float positiveCount = tmax / time_step;
positiveCount = (positiveCount > 50000) ? 50000 : positiveCount;
float negativeCount = -tmin / time_step;
negativeCount = (negativeCount > 50000) ? 50000 : negativeCount;
//Vector3[] startPts = new Vector3[thread_num];
//startPts[0] = referencePoint.lastLocalPos;
//for(int i = 1; i < thread_num; i++)
//{
// startPts[i] = RK4(startPts[i - 1], time_step);
//}
//for(int i = 0; i < thread_num; i++)
//{
// int index = i;
// threads[i] = new Thread(() => ThreadedSampling(index, startPts[index], time_step * thread_num, positiveCount / thread_num,
// negativeCount / thread_num));
// threads[i].Start();
//}
////for (int i = 0; i < 5; i++)
////{
//// yield return null;
////}
//for (int i = 0; i < thread_num; i++)
//{
// threads[i].Join();
//}
Vector3 curr = start;
for (int i = 0; i < positiveCount; i++)
{
curr = RK4(curr, time_step);
positions.Add(i + 1, curr);
}
curr = start;
for (int i = 0; i < negativeCount; i++)
{
curr = RK4(curr, -time_step);
positions.Add(-i, curr);
}
if (positions.Count != lastCount)
{
InitializeParticleSystem();
}
//RenderParticles();
currHighlight = 0;
thread_finished = true;
}
public void SetParamValue(string name, float ratio)
{
AK.Variable var = vars[name];
var.value = parameterMin[name] + ratio * (parameterMax[name] - parameterMin[name]);
}
Symbol SymbolicateValue(string formula, int begin, int end, Expression exp)
{
if (formula[begin] == '+')
{
begin++;
}
// Check for string value
if (formula[begin] == '\'' && formula[end - 1] == '\'')
{
var svalue = formula.Substring(begin+1,end-begin-2).Replace("\\'","'");
return new Symbol(svalue);
}
int depth=0;
for (int k = begin; k < end; k++)
{
if (formula[k]=='(')
depth++;
else if (formula[k]==')')
depth--;
else if (depth == 0 && formula[k] == '^')
{
// Check for small integer powers: they will be done using multiplication instead!
Symbol lhs = Symbolicate(formula,begin,k,exp);
Symbol rhs = Symbolicate(formula,k+1,end,exp);
var newSubExpression = new SymbolList();
if (end-k-1 == 1 && lhs.type == SymbolType.RealValue && formula.Substring(k+1,end-k-1)=="2")
{
// Second power found
newSubExpression.Append(lhs);
newSubExpression.Append(lhs);
}
else if (end-k-1 == 1 && lhs.type == SymbolType.RealValue && formula.Substring(k+1,end-k-1)=="3")
{
// Second power found
newSubExpression.Append(lhs);
newSubExpression.Append(lhs);
newSubExpression.Append(lhs);
}
else
{
newSubExpression.Append(new Symbol(SymbolType.Pow));
newSubExpression.Append(lhs);
newSubExpression.Append(rhs);
}
Symbol newSymbol = new Symbol(SymbolType.SubExpression);
newSymbol.subExpression = newSubExpression;
return newSymbol;
}
}
if (formula[begin] == '(' && formula[end - 1] == ')')
{
var s = Symbolicate(formula, begin + 1, end - 1,exp);
s.Simplify();
return s;
}
double valueAsRealNumber;
if (double.TryParse(formula.Substring(begin,end-begin),out valueAsRealNumber))
{
return new Symbol(valueAsRealNumber);
}
// Check if the value is transformed by a function
if (formula[end-1]==')') {
int i = begin;
while (i < end-1) {
if (formula[i]=='(') {
break;
}
i++;
}
string funcName = formula.Substring(begin,i-begin);
CustomFunction customFunc;
if (customFuncs.TryGetValue(funcName,out customFunc))
{
int requiredParameterCount = customFunc.paramCount;
int foundParameterCount = SolverTools.CountParameters(formula,begin,end);
if (requiredParameterCount == foundParameterCount) {
if (requiredParameterCount == 1) {
SymbolList newSubExpression = new SymbolList();
newSubExpression.Append(new Symbol(customFunc));
newSubExpression.Append(Symbolicate(formula,i+1,end-1,exp));
return new Symbol(newSubExpression);
}
else {
List<SolverTools.IntPair> parameters = SolverTools.ParseParameters(formula,i,end);
SymbolList newSubExpression = new SymbolList();
newSubExpression.Append(new Symbol(customFunc));
for (int k=0;k<requiredParameterCount;k++) {
Symbol p = Symbolicate(formula,parameters[k].first,parameters[k].second,exp);
newSubExpression.Append(p);
}
Symbol newSymbol = new Symbol(SymbolType.SubExpression);
newSymbol.subExpression = newSubExpression;
return newSymbol;
}
}
else
{
throw new ESInvalidParametersException(customFunc.name + " expects " + requiredParameterCount + " parameters, " + foundParameterCount + " given.");
}
}
else
{
throw new ESInvalidFunctionNameException(funcName);
}
}
var valueName = formula.Substring(begin,end-begin);
// Then a local constant specific to our expression
Variable variable;
if (exp.constants.TryGetValue(valueName,out variable)) {
return new Symbol(variable);
}
// Non immutable globals
if (globalConstants.TryGetValue(valueName,out variable)) {
return new Symbol(variable);
}
// Immutable globals
double constDouble;
if (immutableGlobalConstants.TryGetValue(valueName, out constDouble))
{
return new Symbol(constDouble);
}
// Found an unknown value name. Check policy to see what to do.
Variable v = null;
switch (undefinedVariablePolicy)
{
case UndefinedVariablePolicy.DefineExpressionLocalVariable:
v = new Variable(valueName,0);
exp.constants.Add(valueName,v);
return new Symbol(v);
case UndefinedVariablePolicy.DefineGlobalVariable:
v = new Variable(valueName,0);
globalConstants.Add(valueName,v);
return new Symbol(v);
default:
throw new ESUnknownExpressionException(valueName);
}
}
public Variable SetGlobalVariable(string name, string value)
{
if (value == null)
{
throw new System.ArgumentException("Null is not acceptable string parameter value.");
}
Variable variable;
if (globalConstants.TryGetValue(name, out variable))
{
if (variable.stringValue == null)
{
throw new ESParameterTypeChangedException("Can not change type of existing parameter " + name);
}
variable.stringValue = value;
return variable;
}
else
{
Variable v = new Variable(name,value);
globalConstants.Add (name,v);
return v;
}
}
public Variable SetGlobalVariable(string name, double value)
{
Variable variable;
if (globalConstants.TryGetValue(name, out variable))
{
if (variable.stringValue != null)
{
throw new ESParameterTypeChangedException("Can not change type of existing parameter " + name);
}
variable.value = value;
return variable;
}
else
{
Variable v = new Variable(name,value);
globalConstants.Add (name,v);
return v;
}
}