private static void fdjac(double[] x, double[] fvec, double[,] df, EquationSet objEquationSet)
{
const double EPS = 1E-08;
double h, temp;
int n = x.Length;
double[] f = new double[n];
for (int j = 0; j < n; j++)
{
temp = x[j];
h = EPS * Abs(temp);
if (h == 0)
{
h = EPS;
}
x[j] = temp + h;
h = x[j] - temp;
objEquationSet(x, f);
x[j] = temp;
for (int i = 0; i < n; i++)
{
df[i, j] = (f[i] - fvec[i]) / h;
}
}
}
public static bool[] FindRoot(double[] x, EquationSet objEquationSet)
{
bool Check = false;
bool timesUP = newt(x, objEquationSet, Check);
bool[] states = new bool[] { timesUP, Check };
return(states);
}
private static double fmin(double[] x, double[] fvec, EquationSet objEquationSet)
{
objEquationSet(x, fvec);
int n = x.Length;
double sum = 0.0;
for (int i = 0; i < n; i++)
{
sum = sum + fvec[i] * fvec[i];
}
return(0.5 * sum);
}
private void Update()
{
if (queue.Count != 0)
{
if (isRunning == false)
{
EquationSet es = queue.Dequeue();
var go = new GameObject("Mesh Visualizer" + meshVisuals.Count);
go.transform.SetParent(transform);
go.transform.localPosition = Vector3.zero;
go.transform.localRotation = Quaternion.identity;
var mrenderer = go.AddComponent <MeshRenderer>();
mrenderer.material = new Material(Shader.Find("Wireframe"));
MeshFilter meshVisual = go.AddComponent <MeshFilter>();
meshVisuals.Add(meshVisual);
uMin = es.uMin; uMax = es.uMax; vMin = es.vMin; vMax = es.vMax;
solver.SetGlobalVariable("u", uMin * Mathf.PI);
solver.SetGlobalVariable("v", vMin * Mathf.PI);
expX = solver.SymbolicateExpression(es.exprX);
expY = solver.SymbolicateExpression(es.exprY);
expZ = solver.SymbolicateExpression(es.exprZ);
varU = solver.GetGlobalVariable("u");
varV = solver.GetGlobalVariable("v");
meshVisual.transform.localScale = Vector3.one * es.scale;
positions.Clear();
normals.Clear();
faces.Clear();
uvs.Clear();
mappingCache = new Dictionary <Vector2, Vector3>();
Vector3 v0 = MapPoint01(0, 0);
Vector3 n0 = GetNormal01(0, 0);
positions.Add(v0); normals.Add(n0); uvs.Add(new Vector2(0, 0));
Vector3 v1 = MapPoint01(0, 1);
Vector3 n1 = GetNormal01(0, 1);
positions.Add(v1); normals.Add(n1); uvs.Add(new Vector2(0, 1));
Vector3 v2 = MapPoint01(1, 1);
Vector3 n2 = GetNormal01(1, 1);
positions.Add(v2); normals.Add(n2); uvs.Add(new Vector2(1, 1));
Vector3 v3 = MapPoint01(1, 0);
Vector3 n3 = GetNormal01(1, 0);
positions.Add(v3); normals.Add(n3); uvs.Add(new Vector2(1, 0));
Tessellate(ref meshVisual, 0, 1, 2, 3);
//tessel = StartCoroutine(Tessellate(0, 1, 2, 3));
}
}
}
private void Update()
{
if (queue.Count != 0)
{
if (isRunning == false)
{
EquationSet es = queue.Dequeue();
uMin = es.uMin; uMax = es.uMax; vMin = es.vMin; vMax = es.vMax;
solver.SetGlobalVariable("u", uMin * Mathf.PI);
solver.SetGlobalVariable("v", vMin * Mathf.PI);
expX = solver.SymbolicateExpression(es.exprX);
expY = solver.SymbolicateExpression(es.exprY);
expZ = solver.SymbolicateExpression(es.exprZ);
varU = solver.GetGlobalVariable("u");
varV = solver.GetGlobalVariable("v");
positions.Clear();
normals.Clear();
faces.Clear();
uvs.Clear();
mappingCache = new Dictionary <Vector2, Vector3>();
Vector3 v0 = MapPoint01(0, 0);
Vector3 n0 = GetNormal01(0, 0);
positions.Add(v0); normals.Add(n0); uvs.Add(new Vector2(0, 0));
Vector3 v1 = MapPoint01(0, 1);
Vector3 n1 = GetNormal01(0, 1);
positions.Add(v1); normals.Add(n1); uvs.Add(new Vector2(0, 1));
Vector3 v2 = MapPoint01(1, 1);
Vector3 n2 = GetNormal01(1, 1);
positions.Add(v2); normals.Add(n2); uvs.Add(new Vector2(1, 1));
Vector3 v3 = MapPoint01(1, 0);
Vector3 n3 = GetNormal01(1, 0);
positions.Add(v3); normals.Add(n3); uvs.Add(new Vector2(1, 0));
Tessellate(0, 1, 2, 3);
//tessel = StartCoroutine(Tessellate(0, 1, 2, 3));
}
}
}
private static bool newt(double[] x, EquationSet objEquationSet, bool Check)
{
const int MAXITS = 200;
const double TOLF = 1E-08;
const double TOLMIN = 1E-10;
const int STPMX = 100;
const double TOLX = 1E-11;
bool timsUP = false;
double den, f, fold, stpmax, sum, temp, test;
double d = 0;
int n = x.Length;
int[] indx = new int[n];
double[] g = new double[n];
double[] p = new double[n];
double[] xold = new double[n];
double[,] fjac = new double[n, n];
double[] fvec = new double[n];
f = fmin(x, fvec, objEquationSet);
test = 0.0;
for (int i = 0; i < n; i++)
{
if ((Abs(fvec[i]) > test))
{
test = Abs(fvec[i]);
}
}
if (test < 0.01 * TOLF)
{
Check = false;
return(timsUP);
}
sum = 0;
for (int i = 0; i < n; i++)
{
sum = sum + x[i] * x[i];
}
stpmax = STPMX * Max(Sqrt(sum), Convert.ToDouble(n));
for (int its = 0; its < MAXITS; its++)
{
fdjac(x, fvec, fjac, objEquationSet);
for (int i = 0; i < n; i++)
{
sum = 0;
for (int j = 0; j < n; j++)
{
sum = sum + fjac[j, i] * fvec[j];
}
g[i] = sum;
}
for (int i = 0; i < n; i++)
{
xold[i] = x[i];
}
fold = f;
for (int i = 0; i < n; i++)
{
p[i] = -fvec[i];
}
ludcmp(fjac, indx, d);
lubksb(fjac, indx, p);
timsUP = lnsrch(xold, fold, g, p, x, f, stpmax, Check, fvec, objEquationSet);
if (timsUP)
{
x[0] = 0;
return(timsUP);
}
test = 0.0;
for (int i = 0; i < n; i++)
{
if (Abs(fvec[i]) > test)
{
test = Abs(fvec[i]);
}
}
if (test < TOLF)
{
Check = false;
return(timsUP);
}
if (Check)
{
test = 0.0;
den = Max(f, 0.5 * n);
for (int i = 0; i < n; i++)
{
temp = Abs(g[i]) * Max(Abs(x[i]), 1.0) / den;
if (temp > test)
{
test = temp;
}
}
Check = (test < TOLMIN);
return(timsUP);
}
test = 0.0;
for (int i = 0; i < n; i++)
{
temp = (Abs(x[i] - xold[i])) / Max(Abs(x[i]), 1.0);
if (temp > test)
{
test = temp;
}
}
if (test < TOLX)
{
return(timsUP);
}
}
return(timsUP);
}
private static bool lnsrch(double[] xold, double fold, double[] g, double[] p, double[] x, double f, double stpmax, bool Check, double[] fvec, EquationSet objEquationSet)
{
const double ALF = 1E-08;
const double TOLX = 1E-11;
double a, alam, alam2 = 0.0, alamin, b, disc, f2 = 0.0;
double rhs1, rhs2, slope, sum, temp, test, tmplam;
int n = xold.Length;
Check = false;
sum = 0.0;
for (int i = 0; i < n; i++)
{
sum = sum + p[i] * p[i];
}
sum = Sqrt(sum);
if (sum > stpmax)
{
for (int i = 0; i < n; i++)
{
p[i] = p[i] * stpmax / sum;
}
}
slope = 0.0;
for (int i = 0; i < n; i++)
{
slope = slope + g[i] * p[i];
}
if (slope >= 0.0)
{
nError = "Roundoff problem in lnsrch.";
}
test = 0.0;
for (int i = 0; i < n; i++)
{
temp = Abs(p[i]) / Max(Abs(xold[i]), 1);
if (temp > test)
{
test = temp;
}
}
alamin = TOLX / test;
alam = 1.0;
DateTime startT = DateTime.Now;
int i_times = 0;
while (true)
{
if (i_times == 100)
{
i_times = 0;
if (DateTime.Now - startT > TimeSpanLimit)
{
Debug.WriteLine("NonLinear Find Root Overtime({0}s)", TimeSpanLimit.Seconds);
return(true);
}
}
for (int i = 0; i < n; i++)
{
x[i] = xold[i] + alam * p[i];
}
f = fmin(x, fvec, objEquationSet);
if (alam < alamin)
{
for (int i = 0; i < n; i++)
{
x[i] = xold[i];
}
Check = true;
return(false);
}
else if (f <= fold + ALF * alam * slope)
{
return(false);
}
else
{
if (alam == 1.0)
{
tmplam = -slope / (2.0 * (f - fold - slope));
}
else
{
rhs1 = f - fold - alam * slope;
rhs2 = f2 - fold - alam2 * slope;
a = (rhs1 / (alam * alam) - rhs2 / (alam2 * alam2)) / (alam - alam2);
b = (-alam2 * rhs1 / (alam * alam) + alam * rhs2 / (alam2 * alam2)) / (alam - alam2);
if (a == 0.0)
{
tmplam = -slope / (2.0 * b);
}
else
{
disc = b * b - 3.0 * a * slope;
if (disc < 0.0)
{
tmplam = 0.5 * alam;
}
else if (b <= 0.0)
{
tmplam = (-b + Sqrt(disc)) / (3.0 * a);
}
else
{
tmplam = -slope / (b + Sqrt(disc));
}
}
if (tmplam > 0.5 * alam)
{
tmplam = 0.5 * alam;
}
}
}
alam2 = alam;
f2 = f;
alam = Max(tmplam, 0.1 * alam);
i_times++;
}
}
