public static int Solve(List <DoubleRefObject> originalData, ConstraintContainer cons, double isFine)
{
var xLength = originalData.Count;
//Save the original parameters for later.
var origSolution1 = new List <DoubleRefObject>();
foreach (var element in originalData)
{
var auxVal = new DoubleRefObject(element.Value);
origSolution1.Add(auxVal);
}
var convergence = isFine > 0 ? XconvergenceFine : XconvergenceRough;
//integer to keep track of how many times calc is called
var ftimes = 0;
//Calculate Function at the starting point:
var f0 = cons.Calc();
if (f0 < SmallF)
{
return(0);
}
ftimes++;
//Calculate the gradient at the starting point:
//Calculate the gradient
//gradF=x;
var grad = BuildSizedList <double>(xLength); //The gradient vector (1xn)
double first, second, temper; //The norm of the gradient vector
double f1;
double norm = 0;
var pert = f0 * PertMag;
for (var j = 0; j < xLength; j++)
{
temper = originalData[j].Value;
originalData[j].Value = temper - pert;
first = cons.Calc();
originalData[j].Value = temper + pert;
second = cons.Calc();
grad[j] = .5 * (second - first) / pert;
ftimes++;
originalData[j].Value = temper;
norm = norm + (grad[j] * grad[j]);
}
norm = Math.Sqrt(norm);
//Estimate the norm of N
//Initialize N and calculate s
var s = BuildSizedList <double>(xLength); //The current search direction
var n = BuildSizedList <List <double> >(xLength);
for (var i = 0; i < xLength; i++)
{
n[i] = BuildSizedList <double>(xLength);
}
for (var i = 0; i < xLength; i++)
{
for (var j = 0; j < xLength; j++)
{
if (i == j)
{
//N[i][j]=norm; //Calculate a scaled identity matrix as a Hessian inverse estimate
//N[i][j]=grad[i]/(norm+.001);
n[i][j] = 1;
s[i] = -grad[i]; //Calculate the initial search vector
}
else
{
n[i][j] = 0;
}
}
}
var fnew = f0 + 1;
double alpha = 1; //Initial search vector multiplier
var xold = new List <DoubleRefObject>(); //Storage for the previous design variables
foreach (var element in originalData)
{
var auxValue = new DoubleRefObject(element.Value);
xold.Add(auxValue);
}
///////////////////////////////////////////////////////
// Start of line search
///////////////////////////////////////////////////////
//Make the initial position alpha1
double alpha1 = 0;
f1 = f0;
//Take a step of alpha=1 as alpha2
double alpha2 = 1;
for (int i = 0; i < xLength; i++)
{
originalData[i].Value = xold[i].Value + alpha2 * s[i];//calculate the new x
}
var f2 = cons.Calc();
ftimes++;
//Take a step of alpha 3 that is 2*alpha2
var alpha3 = alpha * 2;
for (var i = 0; i < xLength; i++)
{
originalData[i].Value = xold[i].Value + alpha3 * s[i];//calculate the new x
}
var f3 = cons.Calc();
ftimes++;
//Now reduce or lengthen alpha2 and alpha3 until the minimum is
//Bracketed by the triplet f1>f2<f3
while (f2 > f1 || f2 > f3)
{
if (f2 > f1)
{
//If f2 is greater than f1 then we shorten alpha2 and alpha3 closer to f1
//Effectively both are shortened by a factor of two.
alpha3 = alpha2;
f3 = f2;
alpha2 = alpha2 / 2;
for (var i = 0; i < xLength; i++)
{
originalData[i].Value = xold[i].Value + alpha2 * s[i];//calculate the new x
}
f2 = cons.Calc();
ftimes++;
}
else if (f2 > f3)
{
//If f2 is greater than f3 then we length alpah2 and alpha3 closer to f1
//Effectively both are lengthened by a factor of two.
alpha2 = alpha3;
f2 = f3;
alpha3 = alpha3 * 2;
for (var i = 0; i < xLength; i++)
{
originalData[i].Value = xold[i].Value + alpha3 * s[i];//calculate the new x
}
f3 = cons.Calc();
ftimes++;
}
}
// get the alpha for the minimum f of the quadratic approximation
var alphaStar = alpha2 + ((alpha2 - alpha1) * (f1 - f3)) / (3 * (f1 - 2 * f2 + f3));
//Guarantee that the new alphaStar is within the bracket
if (alphaStar > alpha3 || alphaStar < alpha1)
{
alphaStar = alpha2;
}
// Set the values to alphaStar
for (var i = 0; i < xLength; i++)
{
originalData[i].Value = xold[i].Value + alphaStar * s[i];//calculate the new x
}
fnew = cons.Calc();
ftimes++;
var fold = fnew;
/////////////////////////////////////
// end of line search
/////////////////////////////////////
var deltaX = BuildSizedList <double>(xLength);
var gradnew = BuildSizedList <double>(xLength);
var gamma = BuildSizedList <double>(xLength);
var gammatDotN = BuildSizedList <double>(xLength);
var firstSecond = BuildSizedList <List <double> >(xLength);
var deltaXDotGammatDotN = BuildSizedList <List <double> >(xLength);;
var gammatDotDeltaXt = BuildSizedList <List <double> >(xLength);
var nDotGammaDotDeltaXt = BuildSizedList <List <double> >(xLength);
for (var i = 0; i < xLength; i++)
{
firstSecond[i] = BuildSizedList <double>(xLength);
deltaXDotGammatDotN[i] = BuildSizedList <double>(xLength);
gammatDotDeltaXt[i] = BuildSizedList <double>(xLength);
nDotGammaDotDeltaXt[i] = BuildSizedList <double>(xLength);
}
double deltaXnorm = 1;
var iterations = 1;
//Calculate deltaX
for (var i = 0; i < xLength; i++)
{
deltaX[i] = originalData[i].Value - xold[i].Value;//Calculate the difference in x for the Hessian update
}
double maxIterNumber = MaxIterations * xLength;
while (deltaXnorm > convergence && fnew > SmallF && iterations < maxIterNumber)
{
/////////////////////////////////////////////////////////////////////
//Start of main loop!!!!
/////////////////////////////////////////////////////////////////////
double bottom = 0;
double deltaXtDotGamma = 0;
pert = fnew * PertMag;
if (pert < PertMin)
{
pert = PertMin;
}
for (var i = 0; i < xLength; i++)
{
//Calculate the new gradient vector
temper = originalData[i].Value;
originalData[i].Value = temper - pert;
first = cons.Calc();
originalData[i].Value = temper + pert;
second = cons.Calc();
gradnew[i] = .5 * (second - first) / pert;
ftimes++;
originalData[i].Value = temper;
//Calculate the change in the gradient
gamma[i] = gradnew[i] - grad[i];
bottom += deltaX[i] * gamma[i];
deltaXtDotGamma += deltaX[i] * gamma[i];
}
//make sure that bottom is never 0
if (bottom == 0)
{
bottom = 1e-9;
}
//calculate all (1xn).(nxn)
for (var i = 0; i < xLength; i++)
{
gammatDotN[i] = 0;
for (var j = 0; j < xLength; j++)
{
gammatDotN[i] += gamma[j] * n[i][j]; //This is gammatDotN transpose
}
}
//calculate all (1xn).(nx1)
double gammatDotNDotGamma = 0;
for (var i = 0; i < xLength; i++)
{
gammatDotNDotGamma += gammatDotN[i] * gamma[i];
}
//Calculate the first term
var firstTerm = 1 + gammatDotNDotGamma / bottom;
//Calculate all (nx1).(1xn) matrices
for (var i = 0; i < xLength; i++)
{
for (var j = 0; j < xLength; j++)
{
firstSecond[i][j] = ((deltaX[j] * deltaX[i]) / bottom) * firstTerm;
deltaXDotGammatDotN[i][j] = deltaX[i] * gammatDotN[j];
gammatDotDeltaXt[i][j] = gamma[i] * deltaX[j];
}
}
//Calculate all (nxn).(nxn) matrices
for (var i = 0; i < xLength; i++)
{
for (var j = 0; j < xLength; j++)
{
nDotGammaDotDeltaXt[i][j] = 0;
for (var k = 0; k < xLength; k++)
{
nDotGammaDotDeltaXt[i][j] += n[i][k] * gammatDotDeltaXt[k][j];
}
}
}
//Now calculate the BFGS update on N
//cout<<"N:"<<endl;
for (var i = 0; i < xLength; i++)
{
for (var j = 0; j < xLength; j++)
{
n[i][j] = n[i][j] + firstSecond[i][j] -
(deltaXDotGammatDotN[i][j] + nDotGammaDotDeltaXt[i][j]) / bottom;
}
}
//Calculate s
for (var i = 0; i < xLength; i++)
{
s[i] = 0;
for (var j = 0; j < xLength; j++)
{
s[i] += -n[i][j] * gradnew[j];
}
}
alpha = 1; //Initial search vector multiplier
//copy newest values to the xold
xold.Clear();
foreach (var element in originalData)
{
var auxValue = new DoubleRefObject(element.Value);
xold.Add(auxValue);//Copy last values to xold
}
///////////////////////////////////////////////////////
// Start of line search
///////////////////////////////////////////////////////
//Make the initial position alpha1
alpha1 = 0;
f1 = fnew;
//Take a step of alpha=1 as alpha2
alpha2 = 1;
for (var i = 0; i < xLength; i++)
{
originalData[i].Value = xold[i].Value + alpha2 * s[i];//calculate the new x
}
f2 = cons.Calc();
ftimes++;
//Take a step of alpha 3 that is 2*alpha2
alpha3 = alpha2 * 2;
for (int i = 0; i < xLength; i++)
{
originalData[i].Value = xold[i].Value + alpha3 * s[i];//calculate the new x
}
f3 = cons.Calc();
ftimes++;
//Now reduce or lengthen alpha2 and alpha3 until the minimum is
//Bracketed by the triplet f1>f2<f3
var steps = 0;
while (f2 > f1 || f2 > f3)
{
if (f2 > f1)
{
//If f2 is greater than f1 then we shorten alpha2 and alpha3 closer to f1
//Effectively both are shortened by a factor of two.
alpha3 = alpha2;
f3 = f2;
alpha2 = alpha2 / 2;
for (int i = 0; i < xLength; i++)
{
originalData[i].Value = xold[i].Value + alpha2 * s[i];//calculate the new x
}
f2 = cons.Calc();
ftimes++;
}
else if (f2 > f3)
{
//If f2 is greater than f3 then we length alpah2 and alpha3 closer to f1
//Effectively both are lengthened by a factor of two.
alpha2 = alpha3;
f2 = f3;
alpha3 = alpha3 * 2;
for (int i = 0; i < xLength; i++)
{
originalData[i].Value = xold[i].Value + alpha3 * s[i];//calculate the new x
}
f3 = cons.Calc();
ftimes++;
}
steps = steps + 1;
}
// get the alpha for the minimum f of the quadratic approximation
alphaStar = alpha2 + ((alpha2 - alpha1) * (f1 - f3)) / (3 * (f1 - 2 * f2 + f3));
//Guarantee that the new alphaStar is within the bracket
if (alphaStar >= alpha3 || alphaStar <= alpha1)
{
alphaStar = alpha2;
}
// Set the values to alphaStar
for (var i = 0; i < xLength; i++)
{
originalData[i].Value = xold[i].Value + alphaStar * s[i];//calculate the new x
}
fnew = cons.Calc();
ftimes++;
/////////////////////////////////////
// end of line search
////////////////////////////////////
deltaXnorm = 0;
for (int i = 0; i < xLength; i++)
{
deltaX[i] = originalData[i].Value - xold[i].Value;//Calculate the difference in x for the hessian update
deltaXnorm += deltaX[i] * deltaX[i];
grad[i] = gradnew[i];
}
deltaXnorm = Math.Sqrt(deltaXnorm);
iterations++;
/////////////////////////////////////////////////////////////
// End of Main loop
/////////////////////////////////////////////////////////////
}
// End of function
double validSolution;
if (isFine == 1)
{
validSolution = ValidSolutionFine;
}
else
{
validSolution = ValidSoltuionRough;
}
if (fnew < validSolution)
{
return(0);
}
//Replace the bad numbers with the last result
for (var i = 0; i < xLength; i++)
{
originalData[i] = origSolution1[i];
}
return(1);
}
public static void derivatives(List <DoubleRefObject> original, List <int> x, List <double> gradF, int xLength, ConstraintContainer cons, int consLength)
{
int position;
for (int i = 0; i < consLength; i++)
{
var constraint = cons[i];
//////////////////////////////////////
//Point on Point Constraint derivative
//////////////////////////////////////
if (constraint is PointOnPoint)
{
// Derivative with respect to p1x
position = (int)(constraint.P1.X.Value - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += 2 * (constraint.P1.X.Value - constraint.P2.X.Value);
}
// Derivative with respect to p1y
position = (int)(constraint.P1.Y.Value - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += 2 * (constraint.P1.Y.Value - constraint.P2.Y.Value);
}
// Derivative with respect to p2x
position = (int)(constraint.P2.X.Value - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += -2 * (constraint.P1.X.Value - constraint.P2.X.Value);
}
// Derivative with respect to p2y
position = (int)(constraint.P2.Y.Value - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += -2 * (constraint.P1.Y.Value - constraint.P2.Y.Value);
}
}
//.........................................
// End Point On Point Constraint derivative
//.........................................
//////////////////////////////////////
//Point to Point Distance Constraint derivative
//////////////////////////////////////
if (constraint is P2PDistance)
{
// Derivative with respect to p1x
position = (int)(constraint.P1.X.Value - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += 2 * (constraint.P1.X.Value - constraint.P2.X.Value);
}
// Derivative with respect to p1y
position = (int)(constraint.P1.Y.Value - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += 2 * (constraint.P1.Y.Value - constraint.P2.Y.Value);
}
// Derivative with respect to p2x
position = (int)(constraint.P2.X.Value - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += -2 * (constraint.P1.X.Value - constraint.P2.X.Value);
}
// Derivative with respect to p2y
position = (int)(constraint.P2.Y.Value - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += -2 * (constraint.P1.Y.Value - constraint.P2.Y.Value);
}
// Derivative with respect to distance
position = (int)(constraint.Distance - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += -2 * constraint.Distance;
}
}
//..................................................
// End Point to Point distance Constraint derivative
//..................................................
//////////////////////////////////////
//Point to Point Distance Vert Constraint derivative
//////////////////////////////////////
if (constraint is P2PDistanceVert)
{
// Derivative with respect to p1y
position = (int)(constraint.P1.Y.Value - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += 2 * (constraint.P1.Y.Value - constraint.P2.Y.Value);
}
// Derivative with respect to p2y
position = (int)(constraint.P2.Y.Value - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += -2 * (constraint.P1.Y.Value - constraint.P2.Y.Value);
}
// Derivative with respect to distance
position = (int)(constraint.Distance - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += -2 * constraint.Distance;
}
}
//........................................................
// End Point to Point Vert distance Constraint derivative
//........................................................
//////////////////////////////////////
//Point to Point Horz Distance Constraint derivative
//////////////////////////////////////
if (constraint is P2PDistanceHorz)
{
// Derivative with respect to p1x
position = (int)(constraint.P1.X.Value - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += 2 * (constraint.P1.X.Value - constraint.P2.X.Value);
}
// Derivative with respect to p2x
position = (int)(constraint.P2.X.Value - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += -2 * (constraint.P1.X.Value - constraint.P2.X.Value);
}
// Derivative with respect to distance
position = (int)(constraint.Distance - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += -2 * constraint.Distance;
}
}
//.......................................................
// End Point to Point Horz distance Constraint derivative
//.......................................................
//////////////////////////////////////
//Point on line Constraint derivatives
//////////////////////////////////////
if (constraint is PointOnLine)
{
// Derivative with respect to p1x
position = (int)(constraint.P1.X.Value - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += 2 * (constraint.P1.X.Value - constraint.P2.X.Value);
}
// Derivative with respect to p2x
position = (int)(constraint.P2.X.Value - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += -2 * (constraint.P1.X.Value - constraint.P2.X.Value);
}
// Derivative with respect to distance
position = (int)(constraint.Distance - x[0]);
if (position >= 0 & position < xLength)
{
gradF[position] += -2 * constraint.Distance;
}
}
//.......................................................
// End Point to Point Horz distance Constraint derivative
//.......................................................
}
}
public void Run()
{
P = parameters;
Point origin;
constants[0] = 6;
constants[1] = 6;
constants[2] = 2;
constants[3] = Math.PI / 3;
constants[4] = 3;
points.Add(new Point(parameters[0], parameters[1]));
points.Add(new Point(parameters[2], parameters[3]));
points.Add(new Point(parameters[4], parameters[5]));
points.Add(new Point(parameters[6], parameters[7]));
points.Add(new Point(new DoubleRefObject(constants[0]), new DoubleRefObject(constants[1])));
lines[0].P1 = points[0];
lines[0].P2 = points[1];
lines[1].P1 = points[1];
lines[1].P2 = points[2];
var constraitns = new ConstraintContainer();
constraitns.AddConstraint(new Horizontal()
{
L1 = lines[0]
});
constraitns.AddConstraint(new Vertical()
{
L1 = lines[1]
});
constraitns.AddConstraint(new PointOnPoint()
{
P1 = points[2],
P2 = points[4]
});
constraitns.AddConstraint(new PointOnPoint()
{
P1 = points[3],
P2 = points[4]
});
for (int i = 0; i < 1; i++)
{
parameters[0].Value = 0; //1x
parameters[1].Value = 0; //y
parameters[2].Value = 5; //x
parameters[3].Value = 0; //y
parameters[4].Value = 6; //xstart
parameters[5].Value = 5; //y
parameters[6].Value = 6; //xend
parameters[7].Value = 5; //y
var pparameters = new List <int>();
for (var index = 0; index < 100; index++)
{
pparameters.Add(index);
}
var sol = SketchSolve.Solve(parameters, constraitns, Rough);
switch (sol)
{
case 0:
Console.WriteLine("A good Solution was found");
break;
case 1:
Console.WriteLine("No valid Solutions were found from this start point");
break;
}
DisplayPoints();
var hey = parameters[0].Value * parameters[2].Value + parameters[1].Value * parameters[3].Value;
Console.WriteLine("dot product: " + hey);
var gradF = new List <double>();
List <int> ggradF = new List <int>();
for (int index = 0; index < 20; index++)
{
gradF.Add(0);
ggradF.Add(index);
}
SketchDerivative.derivatives(parameters, pparameters, gradF, 4, constraitns, 3);
for (var index = 0; index < 4; index++)
{
Console.WriteLine("GradF[" + index + "]: " + gradF[ggradF[index]]);
}
}
}