public static NCGrid_Distribution from_file(string title, bool using_full_path)
{
string path = Paths.DistributionRepo + "\\" + title + ".dist";
if (using_full_path)
{
path = title;
}
string[] contents = File.ReadAllLines(path);
int length = contents.Length;
RBounds2D new_bounds = RBounds2D.fromstring(contents[0]);
string[] numbers = contents[1].Split(':');
int nx, ny;
if (!(int.TryParse(numbers[1], out nx) && int.TryParse(numbers[3], out ny)))
{
throw new Exception("File format error");
}
NCGrid_Distribution created = new NCGrid_Distribution(new_bounds, nx, ny);
for (int q = additional_file_lines; q < contents.Length; q++)
{
int qprime = q - additional_file_lines;
int i = qprime % nx;
int j = (qprime - i) / nx;
created[i, j] = NCAMRNode.fromstring(contents[q]);
}
return(created);
}
public static NCGrid_Distribution NiceFunction(string vb_syntax_eval, RBounds2D bounds, int xcount, int ycount, bool keepfile, string title)
{
ExactFunctionGeneratorVB2D.GenerateFunction(vb_syntax_eval, bounds, xcount, ycount, title);
NCGrid_Distribution n = NCGrid_Distribution.from_file(title, false);
return(n);
}
private static double area_of_influence_region(NCGrid_Distribution A, int i, int j)
{
int imax = A.Xcount - 1;
int jmax = A.Ycount - 1;
double[] x = new double[4];
double[] y = new double[4];
NCAMRNode[] grid =
{
A.GetFake(i - 1, j + 1),
A.GetFake(i, j + 1),
A.GetFake(i + 1, j + 1),
A.GetFake(i - 1, j),
A.GetFake(i, j),
A.GetFake(i + 1, j),
A.GetFake(i - 1, j - 1),
A.GetFake(i, j - 1),
A.GetFake(i + 1, j - 1)
};
NCAMRNode[] poly =
{
xyavg(grid[3], grid[4], grid[6], grid[7]),
xyavg(grid[4], grid[5], grid[7], grid[8]),
xyavg(grid[1], grid[2], grid[4], grid[5]),
xyavg(grid[0], grid[1], grid[3], grid[4])
};
for (int z = 0; z < poly.Length; z++)
{
x[z] = poly[z].X;
y[z] = poly[z].Y;
}
return(quad_area(x, y));
}
public BVPLinear2D(BoundaryConditions _conditions, LinearOperatorOrder2 _operator, NCGrid_Distribution _discretization)
{
lin_operator = _operator;
discretization = _discretization;
boundary_conditions = _conditions;
bool[] all_necessary_compatibility_conditions =
{
boundary_conditions.Bounds.Xmax == discretization.Bounds.Xmax,
boundary_conditions.Bounds.Xmin == discretization.Bounds.Xmin,
boundary_conditions.Bounds.Ymax == discretization.Bounds.Ymax,
boundary_conditions.Bounds.Ymin == discretization.Bounds.Ymin,
boundary_conditions.Xcount == discretization.Xcount,
boundary_conditions.Ycount == discretization.Ycount
};
bool compatible = true;
foreach (bool i in all_necessary_compatibility_conditions)
{
compatible = compatible && i;
}
if (!compatible)
{
throw new Exception("Error: Boundary conditions and initial discretization are incompatible.");
}
}
public static double NormDifference(NCGrid_Distribution A, NCGrid_Distribution B)
{
NCGrid_Distribution newgrid = new NCGrid_Distribution(A.Bounds, A.Xcount + 1, A.Ycount + 1);
int n = newgrid.Ycount;
int m = newgrid.Xcount;
double xmin = newgrid.Xmin;
double xmax = newgrid.Xmax;
double ymin = newgrid.Ymin;
double ymax = newgrid.Ymax;
NCAMRNode ll = new NCAMRNode(xmin, ymin, 0);
NCAMRNode lr = new NCAMRNode(xmax, ymin, 0);
NCAMRNode ul = new NCAMRNode(xmin, ymax, 0);
NCAMRNode ur = new NCAMRNode(xmax, ymax, 0);
newgrid[0, 0] = ll;
newgrid[0, n - 1] = ul;
newgrid[m - 1, 0] = lr;
newgrid[m - 1, n - 1] = ur;
for (int i = 0; i < A.Xcount - 1; i++)
{
newgrid[i + 1, 0] = xyavg(A[i, 0], A[i + 1, 0]);
newgrid[i + 1, A.Ycount] = xyavg(A[i, A.Ycount - 1], A[i + 1, A.Ycount - 1]);
}
for (int j = 0; j < A.Ycount - 1; j++)
{
newgrid[0, j + 1] = xyavg(A[0, j], A[0, j + 1]);
newgrid[A.Xcount, j + 1] = xyavg(A[A.Xcount - 1, j], A[A.Xcount - 1, j + 1]);
}
for (int i = 0; i < A.Xcount - 1; i++)
{
for (int j = 0; j < A.Ycount - 1; j++)
{
newgrid[i + 1, j + 1] = xyavg(A[i, j], A[i + 1, j], A[i, j + 1], A[i + 1, j + 1]);
}
}
double accumulator = 0;
for (int i = 0; i < m - 1; i++)
{
for (int j = 0; j < n - 1; j++)
{
NCAMRNode[] nodes =
{
newgrid[i, j],
newgrid[i + 1, j],
newgrid[i + 1, j + 1],
newgrid[i, j + 1]
};
double[] x = new double[nodes.Length];
double[] y = new double[nodes.Length];
for (int z = 0; z < nodes.Length; z++)
{
x[z] = nodes[z].X;
y[z] = nodes[z].Y;
}
accumulator += quad_area(x, y) * (A[i, j].Value - B[i, j].Value) * (A[i, j].Value - B[i, j].Value);
}
}
return(Math.Sqrt(accumulator));
}
public DistributionSketch2D(NCGrid_Distribution _subject, DistributionSketchSettings S)
{
settings = S;
subject = _subject;
canvas = new Bitmap(S.ImageWidth, S.ImageHeight);
x_pixel_count = canvas.Width;
y_pixel_count = canvas.Height;
get_positions();
}
public static NCGrid_Distribution NiceFunction(string vb_syntax_eval, RBounds2D bounds, int xcount, int ycount)
{
ExactFunctionGeneratorVB2D.GenerateFunction(vb_syntax_eval, bounds, xcount, ycount, "temp");
NCGrid_Distribution n = NCGrid_Distribution.from_file("temp", false);
string to_delete = Paths.DistributionRepo + "\\temp.dist";
File.Delete(to_delete);
return(n);
}
public static NCGrid_Distribution GenerateFunctionToGrid(string vb_eval, NCGrid_Distribution discretization)
{
string absolute_temp_path = Paths.DistributionRepo + "\\temp.dist";
GenerateFunction(vb_eval, discretization, "temp");
NCGrid_Distribution output = NCGrid_Distribution.from_file("temp", false);
File.Delete(absolute_temp_path);
return(output);
}
public void MimicMorph(NCGrid_Distribution template)
{
for (int i = 0; i < x_node_count; i++)
{
for (int j = 0; j < y_node_count; j++)
{
this[i, j].X = template[i, j].X;
this[i, j].Y = template[i, j].Y;
}
}
}
static void run_presentation_transient(int numframes)
{
double t = 0;
double dt = 0.1;
int n = 25;
double L = 10;
double H = 10;
RBounds2D domain = new RBounds2D(0, L, 0, H);
NCGrid_Distribution soln = new NCGrid_Distribution(domain, n, n);
double max1 = 4;
double max2 = 3;
double max3 = 5;
double max4 = 2;
double omega1 = 1;
double omega2 = 0.6;
double omega3 = 0.2;
double omega4 = 1.2;
double phi1 = -0.4;
double phi2 = -0.9;
double phi3 = 1.3;
double phi4 = 0.2;
double dx = L / (n - 1);
double dy = H / (n - 1);
double refinestep = 0.1;
int refinecount = 3;
for (int i = 0; i < numframes; i++)
{
BoundaryConditions cond = new BoundaryConditions(soln, BoundaryConditions.BoundaryConditionType.Dirichlet);
t += dt;
for (int q = 0; q < n; q++)
{
double x = q * dx;
double y = q * dy;
cond[q, BoundaryConditions.Direction.Negative_X] = max1 * Math.Sin(4 * Math.PI * x / L) * Math.Sin(omega1 * t - phi1);
cond[q, BoundaryConditions.Direction.Negative_Y] = max2 * Math.Sin(2 * Math.PI * y / L) * Math.Sin(omega2 * t - phi2);
cond[q, BoundaryConditions.Direction.Positive_X] = max3 * Math.Sin(3 * Math.PI * x / L) * Math.Sin(omega3 * t - phi3);
cond[q, BoundaryConditions.Direction.Positive_Y] = max4 * Math.Sin(5 * Math.PI * y / L) * Math.Sin(omega4 * t - phi4);
}
BVPLinear2D problem = new BVPLinear2D(cond, LinearOperatorOrder2.Laplace, soln);
NCGrid_Distribution sol = problem.SolveKaczMarzExt(100, 10, 20);
sol.ApplyMeshMorphGA(refinestep);
for (int z = 0; z < refinecount - 1; z++)
{
problem = new BVPLinear2D(cond, LinearOperatorOrder2.Laplace, soln);
sol = problem.Solve(Matrix.SystemSolvingScheme.Kaczmarz);
sol.ApplyMeshMorphGA(refinestep);
}
sol.WriteToFile("longtransient_" + i.ToString());
sol.QuickSketch("sol_" + bufferint(i, 4));
}
}
public NCGrid_Distribution solve_iterative_morph(int max_morph_count, double size)
{
NCGrid_Distribution soln = Solve();
for (int i = 0; i < max_morph_count - 1; i++)
{
soln.QuickSketch("soln-" + i.ToString());
soln.ApplyMeshMorphGA(size);
discretization = soln.Clone();
soln = Solve();
}
return(soln);
}
public static NCGrid_Distribution operator *(double scale, NCGrid_Distribution A)
{
NCGrid_Distribution output = A.Clone();
for (int i = 0; i < A.Xcount; i++)
{
for (int j = 0; j < A.Ycount; j++)
{
output.assign_value_at(i, j, scale * A[i, j].Value);
}
}
return(output);
}
public static NCGrid_Distribution CompareNiceClean(NCGrid_Distribution test, string vbs_test_function)
{
string title = "temp";
string path = Paths.DistributionRepo + "\\" + title + ".dist";
ExactFunctionGeneratorVB2D.GenerateFunction(vbs_test_function, test, title);
NCGrid_Distribution true_dist = NCGrid_Distribution.from_file(title, false);
File.Delete(path);
NCGrid_Distribution dif = test - true_dist;
dif.force_extrema_update();
return(dif);
}
public NCGrid_Distribution Clone()
{
NCGrid_Distribution n = new NCGrid_Distribution(bounds, x_node_count, y_node_count);
for (int i = 0; i < x_node_count; i++)
{
for (int j = 0; j < y_node_count; j++)
{
n.assign_value_at(i, j, this[i, j].Value);
n[i, j].X = this[i, j].X;
n[i, j].Y = this[i, j].Y;
}
}
return(n);
}
public NavierStokesTransient(int timesteps, NCGrid_Distribution u_initial, NCGrid_Distribution v_initial, BoundaryConditions p, BoundaryConditions u, BoundaryConditions v, FluidProperties props, double dt)
{
deltat = dt;
properties = props;
current_ustar = new NCGrid_Distribution(u_initial.Bounds, u_initial.Xcount, u_initial.Ycount);
current_vstar = new NCGrid_Distribution(v_initial.Bounds, v_initial.Xcount, v_initial.Ycount);
current_ustar.SetConstant(1);
current_vstar.SetConstant(1);
time_steps = timesteps;
p_boundary = p;
u_boundary = u;
v_boundary = v;
initial_u = u_initial;
initial_v = v_initial;
}
static void Main(string[] args)
{
NCGrid_Distribution funcp = new NCGrid_Distribution(new RBounds2D(0, 10, 0, 10), 400, 400);
NCGrid_Distribution func = ExactFunctionGeneratorVB2D.GenerateFunctionToGrid("(-1*x) + (2*y)", funcp);
DistributionSketchSettings settings = DistributionSketchSettings.Fancy();
int n = 10;
settings.XLabelCount = n;
settings.YLabelCount = n;
settings.XGridlineCount = n;
settings.YGridlineCount = n;
DistributionSketch2D sktch = new DistributionSketch2D(func, settings);
sktch.CreateSketch(true);
sktch.SaveImage(@"C:\Users\Will\Desktop\output.png", true);
}
public static NCGrid_Distribution MakeMagnitude(NCGrid_Distribution A, NCGrid_Distribution B)
{
NCGrid_Distribution output = A.Clone();
for (int i = 0; i < A.Xcount; i++)
{
for (int j = 0; j < B.Ycount; j++)
{
double x = A[i, j].Value;
double y = B[i, j].Value;
output.assign_value_at(i, j, Math.Sqrt((x * x) + (y * y)));
}
}
output.force_extrema_update();
return(output);
}
public void WriteAllDerivs(string title, bool enable_console_output, bool using_full_path, bool allow_overwrite)
{
DateTime Then = DateTime.Now;
NCGrid_Distribution this_x = new NCGrid_Distribution(bounds, this.Xcount, this.Ycount);
NCGrid_Distribution this_y = new NCGrid_Distribution(bounds, this.Xcount, this.Ycount);
NCGrid_Distribution this_xx = new NCGrid_Distribution(bounds, this.Xcount, this.Ycount);
NCGrid_Distribution this_yy = new NCGrid_Distribution(bounds, this.Xcount, this.Ycount);
NCGrid_Distribution this_xy = new NCGrid_Distribution(bounds, this.Xcount, this.Ycount);
for (int i = 1; i < this.Xcount - 1; i++)
{
for (int j = 1; j < this.Ycount - 1; j++)
{
Matrix xi = EstimateSecondDerivs(i, j, SurplusNodeAccessingMode.UPPER_RIGHT);
this_x[i, j].Value = xi[0];
this_y[i, j].Value = xi[1];
this_xx[i, j].Value = xi[2];
this_yy[i, j].Value = xi[3];
this_xy[i, j].Value = xi[4];
}
}
DateTime Now = DateTime.Now;
string title_x = title + "_x";
string title_y = title + "_y";
string title_xx = title + "_xx";
string title_yy = title + "_yy";
string title_xy = title + "_xy";
if (using_full_path)
{
string basestring = title.Split('.')[0];
title_x = basestring + "_x.dist";
title_y = basestring + "_y.dist";
title_xx = basestring + "_xx.dist";
title_yy = basestring + "_yy.dist";
title_xy = basestring + "_xy.dist";
}
this_x.WriteToFile(title_x, enable_console_output, allow_overwrite, using_full_path);
this_y.WriteToFile(title_y, enable_console_output, allow_overwrite, using_full_path);
this_xx.WriteToFile(title_xx, enable_console_output, allow_overwrite, using_full_path);
this_yy.WriteToFile(title_yy, enable_console_output, allow_overwrite, using_full_path);
this_xy.WriteToFile(title_xy, enable_console_output, allow_overwrite, using_full_path);
if (enable_console_output)
{
Console.WriteLine((Now - Then).TotalMilliseconds);
}
}
public static void quickPlot(string vb_eval, string title, RBounds2D bounds)
{
int n = 100;
GenerateFunction(vb_eval, bounds, n, n, title);
NCGrid_Distribution p = NCGrid_Distribution.from_file(title, false);
File.Delete(Paths.DistributionRepo + "\\" + title + ".dist");
DistributionSketchSettings S = DistributionSketchSettings.Fancy();
S.HasHeatmap = true;
S.HasInfo = false;
S.Mode = SketchMode.DISTRIBUTION_ONLY;
DistributionSketch2D sk = new DistributionSketch2D(p, S);
sk.CreateSketch(false);
sk.SaveImage(title, false);
}
public static void GenerateFunction(string vb_syntax_eval, NCGrid_Distribution discretization, string name)
{
discretization.WriteToFile(@"C:\Users\Will\Desktop\Folders\MATH435\repo\visual-basic-templates\TEMPORARY.dist", false, true, true);
string[] vbsraw = File.ReadAllLines(script_disc_template);
int fileconst = discretization.Xcount * discretization.Ycount + 2;
vbsraw[0] = String.Format(vbsraw[0], discretization.Ycount);
vbsraw[1] = String.Format(vbsraw[1], discretization.Xcount);
vbsraw[16] = String.Format(vbsraw[16], fileconst);
vbsraw[13] = String.Format(vbsraw[13], fileconst);
vbsraw[2] = String.Format(vbsraw[2], name);
vbsraw[28] = String.Format(vbsraw[28], vb_syntax_eval);
string newname = @"C:\Users\Will\Desktop\Folders\MATH435\repo\visual-basic-templates\TEMPORARY.vbs";
File.WriteAllLines(newname, vbsraw);
run_script(newname);
File.Delete(@"C:\Users\Will\Desktop\Folders\MATH435\repo\visual-basic-templates\TEMPORARY.dist");
}
public NCGrid_Distribution SolveSRDD()
{
Matrix system_matrix, RHS;
NCGrid_Distribution dist = discretization.Clone();
dist.ApplyBoundary(boundary_conditions);
buildsystem(out system_matrix, out RHS);
Matrix results = RunExteriorSolve(system_matrix, RHS);
for (int i = 0; i < RHS.Rows; i++)
{
int offset = discretization.Ycount - 2;
int J = i % offset;
int I = (i - J) / offset;
dist.assign_value_at(I + 1, J + 1, results[i]);
}
return(dist);
}
public static bool check_compatibility(BoundaryConditions B, NCGrid_Distribution C)
{
bool[] stuff =
{
B.Bounds.Xmax == C.Xmax,
B.Bounds.Xmin == C.Xmin,
B.Bounds.Ymax == C.Ymax,
B.Bounds.Ymin == C.Ymin,
B.Ycount == C.Ycount,
B.Xcount == C.Xcount
};
bool valid = true;
foreach (bool i in stuff)
{
valid = valid && i;
}
return(valid);
}
public static NCGrid_Distribution operator /(NCGrid_Distribution A, NCGrid_Distribution B)
{
if (A.Xcount == B.Xcount && A.Ycount == B.Ycount)
{
NCGrid_Distribution C = new NCGrid_Distribution(A.Bounds, A.Xcount, B.Ycount);
for (int i = 0; i < A.Xcount; i++)
{
for (int j = 0; j < A.Ycount; j++)
{
C[i, j] = A[i, j].Clone();
C[i, j].Value = A[i, j].Value / B[i, j].Value;
}
}
return(C);
}
else
{
throw new Exception("Dimensions do not agree.");
}
}
public BoundaryConditions(NCGrid_Distribution boundary_of, BoundaryConditionType _type)
{
bounds = boundary_of.Bounds;
SetAllBoundaryConditionTypes(_type);
xcount = boundary_of.Xcount;
ycount = boundary_of.Ycount;
positive_x_vals = new double[xcount];
positive_y_vals = new double[xcount];
negative_x_vals = new double[ycount];
negative_y_vals = new double[ycount];
for (int i = 0; i < xcount; i++)
{
positive_x_vals[i] = boundary_of[i, ycount - 1].Value;
negative_x_vals[i] = boundary_of[i, 0].Value;
}
for (int j = 0; j < ycount; j++)
{
positive_y_vals[j] = boundary_of[xcount - 1, j].Value;
negative_y_vals[j] = boundary_of[0, j].Value;
}
}
public DistributionSketch3DBasic(NCGrid_Distribution sub)
{
subject = sub;
output = new Bitmap(2000, 2000);
}
public NCGrid_Distribution SolveSlow()
{
int m = discretization.Xcount;
int n = discretization.Ycount;
int total_nodes = (m - 2) * (n - 2);
//NCGrid_Distribution dist = new NCGrid_Distribution(boundary_conditions.Bounds, discretization.Xcount, discretization.Ycount);
NCGrid_Distribution dist = discretization.Clone();
dist.ApplyBoundary(boundary_conditions);
Matrix system_matrix = new Matrix(total_nodes, total_nodes);
Matrix RHS = new Matrix(total_nodes, 1);
int neg_y = 0;
int pos_y = 0;
int neg_x = 0;
int pos_x = 0;
int body = 0;
int ll_corner = 0;
int lr_corner = 0;
int ur_corner = 0;
int ul_corner = 0;
List <string> indices = new List <string>();
if (console_output)
{
Console.WriteLine("Populating linear system...");
}
for (int i = 1; i < m - 1; i++)
{
if (console_output && i % (m - 1) / 13 == 0)
{
Console.WriteLine((100 * i / (m - 1)).ToString() + "%");
}
for (int j = 1; j < n - 1; j++)
{
double rhs_here = 0;
indices.Add(i.ToString() + "," + j.ToString());
//for now, assume zero forcing function.
BoundaryCase _case;
bool interior = !isCloseToBoundary(i, j, m, n, out _case);
int surplusi = 1;
int surplusj = 1;
Matrix b = dist.GetTaylorSystemCoeffs(i, j, surplusi, surplusj);
double uijterm = 0;
double ui1jterm = 0;
double uij1term = 0;
double ui_1jterm = 0;
double uij_1term = 0;
double usurplusterm = 0;
int row = (m - 2) * (i - 1) + j - 1;
for (int h = 0; h < 5; h++)
{
ui1jterm += b[h, 0] * lin_operator[h];
uij1term += b[h, 1] * lin_operator[h];
ui_1jterm += b[h, 2] * lin_operator[h];
uij_1term += b[h, 3] * lin_operator[h];
usurplusterm += b[h, 4] * lin_operator[h];
double temp_ij = 0;
for (int k = 0; k < 5; k++)
{
temp_ij += b[h, k];
}
uijterm += lin_operator[h] * temp_ij;
}
switch (_case)
{
case BoundaryCase.NegativeYBoundary:
{
rhs_here -= dist[i, j - 1].Value * uij_1term;
uij_1term = 0;
neg_y++;
break;
}
case BoundaryCase.PositiveYBoundary:
{
rhs_here -= dist[i, j + 1].Value * uij1term;
rhs_here -= dist[i + surplusi, j + surplusj].Value * usurplusterm;
usurplusterm = 0;
uij1term = 0;
pos_y++;
break;
}
case BoundaryCase.NegativeXBoundary:
{
rhs_here -= dist[i - 1, j].Value * ui_1jterm;
ui_1jterm = 0;
neg_x++;
break;
}
case BoundaryCase.PositiveXBoundary:
{
rhs_here -= dist[i + 1, j].Value * ui1jterm;
rhs_here -= dist[i + surplusi, j + surplusj].Value * usurplusterm;
usurplusterm = 0;
ui1jterm = 0;
pos_x++;
break;
}
case BoundaryCase.ULCorner:
{
rhs_here -= dist[i, j + 1].Value * uij1term;
rhs_here -= dist[i - 1, j].Value * ui_1jterm;
rhs_here -= dist[i + surplusi, j + surplusj].Value * usurplusterm;
uij1term = 0;
ui_1jterm = 0;
usurplusterm = 0;
ul_corner++;
break;
}
case BoundaryCase.LLCorner:
{
rhs_here -= dist[i - 1, j].Value * ui_1jterm;
rhs_here -= dist[i, j - 1].Value * uij_1term;
ui_1jterm = 0;
uij_1term = 0;
ll_corner++;
break;
}
case BoundaryCase.URCorner:
{
rhs_here -= dist[i + 1, j].Value * ui1jterm;
rhs_here -= dist[i, j + 1].Value * uij1term;
rhs_here -= dist[i + surplusi, j + surplusj].Value * usurplusterm;
ui1jterm = 0;
uij1term = 0;
usurplusterm = 0;
ur_corner++;
break;
}
case BoundaryCase.LRCorner:
{
rhs_here -= dist[i, j - 1].Value * uij_1term;
rhs_here -= dist[i + 1, j].Value * ui1jterm;
rhs_here -= dist[i + surplusj, j + surplusj].Value * usurplusterm;
uij_1term = 0;
ui1jterm = 0;
usurplusterm = 0;
lr_corner++;
break;
}
case BoundaryCase.Body:
{
body++;
break;
}
}
system_matrix[row, map2Dto1D(i - 1, j - 1, m - 1, n - 1)] = -1 * uijterm;
if (ui1jterm != 0)
{
system_matrix[row, map2Dto1D(i, j - 1, m - 1, n - 1)] = ui1jterm;
}
if (uij1term != 0)
{
system_matrix[row, map2Dto1D(i - 1, j, m - 1, n - 1)] = uij1term;
}
if (ui_1jterm != 0)
{
system_matrix[row, map2Dto1D(i - 2, j - 1, m - 1, n - 1)] = ui_1jterm;
}
if (uij_1term != 0)
{
system_matrix[row, map2Dto1D(i - 1, j - 2, m - 1, n - 1)] = uij_1term;
}
if (usurplusterm != 0)
{
system_matrix[row, map2Dto1D(i - 1 + surplusi, j - 1 + surplusj, m - 1, n - 1)] = usurplusterm;
}
RHS[row] = rhs_here;
}
}
if (console_output)
{
Console.WriteLine("System populated.");
}
Matrix results = Matrix.solve_system(system_matrix, RHS, Matrix.SystemSolvingScheme.Basic, true, true);
for (int i = 0; i < total_nodes; i++)
{
int offset = n - 2;
int J = i % offset;
int I = (i - J) / offset;
dist.assign_value_at(I + 1, J + 1, results[i]);
}
return(dist);
}
public HybridDistributionSketch2D(NCGrid_Distribution subject, DistributionSketchSettings S) : base(subject, S)
{
has_superimposed = false;
}
public void set_superimposed_grid(NCGrid_Distribution _super)
{
has_superimposed = true;
superimpose_grid = _super;
}
private void buildsystem(out Matrix system_matrix, out Matrix RHS)
{
int m = discretization.Xcount;
int n = discretization.Ycount;
int total_nodes = (m - 2) * (n - 2);
NCGrid_Distribution dist = discretization.Clone();
dist.ApplyBoundary(boundary_conditions);
system_matrix = new Matrix(total_nodes, total_nodes);
RHS = new Matrix(total_nodes, 1);
int neg_y = 0;
int pos_y = 0;
int neg_x = 0;
int pos_x = 0;
int body = 0;
int ll_corner = 0;
int lr_corner = 0;
int ur_corner = 0;
int ul_corner = 0;
if (console_output)
{
Console.WriteLine("Populating linear system...");
}
for (int i = 1; i < m - 1; i++)
{
if (console_output && i % (m - 1) / 13 == 0)
{
Console.WriteLine((100 * i / (m - 1)).ToString() + "%");
}
for (int j = 1; j < n - 1; j++)
{
double rhs_here = 0;
//for now, assume zero forcing function.
BoundaryCase _case;
bool interior = !isCloseToBoundary(i, j, m, n, out _case);
int surplusi = 1;
int surplusj = 1;
Matrix b = dist.GetTaylorSystemCoeffs(i, j, surplusi, surplusj);
double uijterm = 0;
double ui1jterm = 0;
double uij1term = 0;
double ui_1jterm = 0;
double uij_1term = 0;
double usurplusterm = 0;
int row = (m - 2) * (i - 1) + j - 1;
for (int h = 0; h < 5; h++)
{
ui1jterm += b[h, 0] * lin_operator[h];
uij1term += b[h, 1] * lin_operator[h];
ui_1jterm += b[h, 2] * lin_operator[h];
uij_1term += b[h, 3] * lin_operator[h];
usurplusterm += b[h, 4] * lin_operator[h];
double temp_ij = 0;
for (int k = 0; k < 5; k++)
{
temp_ij += b[h, k];
}
uijterm += lin_operator[h] * temp_ij;
}
switch (_case)
{
case BoundaryCase.NegativeYBoundary:
{
rhs_here -= dist[i, j - 1].Value * uij_1term;
uij_1term = 0;
neg_y++;
break;
}
case BoundaryCase.PositiveYBoundary:
{
rhs_here -= dist[i, j + 1].Value * uij1term;
rhs_here -= dist[i + surplusi, j + surplusj].Value * usurplusterm;
usurplusterm = 0;
uij1term = 0;
pos_y++;
break;
}
case BoundaryCase.NegativeXBoundary:
{
rhs_here -= dist[i - 1, j].Value * ui_1jterm;
ui_1jterm = 0;
neg_x++;
break;
}
case BoundaryCase.PositiveXBoundary:
{
rhs_here -= dist[i + 1, j].Value * ui1jterm;
rhs_here -= dist[i + surplusi, j + surplusj].Value * usurplusterm;
usurplusterm = 0;
ui1jterm = 0;
pos_x++;
break;
}
case BoundaryCase.ULCorner:
{
rhs_here -= dist[i, j + 1].Value * uij1term;
rhs_here -= dist[i - 1, j].Value * ui_1jterm;
rhs_here -= dist[i + surplusi, j + surplusj].Value * usurplusterm;
uij1term = 0;
ui_1jterm = 0;
usurplusterm = 0;
ul_corner++;
break;
}
case BoundaryCase.LLCorner:
{
rhs_here -= dist[i - 1, j].Value * ui_1jterm;
rhs_here -= dist[i, j - 1].Value * uij_1term;
ui_1jterm = 0;
uij_1term = 0;
ll_corner++;
break;
}
case BoundaryCase.URCorner:
{
rhs_here -= dist[i + 1, j].Value * ui1jterm;
rhs_here -= dist[i, j + 1].Value * uij1term;
rhs_here -= dist[i + surplusi, j + surplusj].Value * usurplusterm;
ui1jterm = 0;
uij1term = 0;
usurplusterm = 0;
ur_corner++;
break;
}
case BoundaryCase.LRCorner:
{
rhs_here -= dist[i, j - 1].Value * uij_1term;
rhs_here -= dist[i + 1, j].Value * ui1jterm;
rhs_here -= dist[i + surplusj, j + surplusj].Value * usurplusterm;
uij_1term = 0;
ui1jterm = 0;
usurplusterm = 0;
lr_corner++;
break;
}
case BoundaryCase.Body:
{
body++;
break;
}
}
system_matrix[row, map2Dto1D(i - 1, j - 1, m - 1, n - 1)] = -1 * uijterm;
if (ui1jterm != 0)
{
system_matrix[row, map2Dto1D(i, j - 1, m - 1, n - 1)] = ui1jterm;
}
if (uij1term != 0)
{
system_matrix[row, map2Dto1D(i - 1, j, m - 1, n - 1)] = uij1term;
}
if (ui_1jterm != 0)
{
system_matrix[row, map2Dto1D(i - 2, j - 1, m - 1, n - 1)] = ui_1jterm;
}
if (uij_1term != 0)
{
system_matrix[row, map2Dto1D(i - 1, j - 2, m - 1, n - 1)] = uij_1term;
}
if (usurplusterm != 0)
{
system_matrix[row, map2Dto1D(i - 1 + surplusi, j - 1 + surplusj, m - 1, n - 1)] = usurplusterm;
}
RHS[row] = rhs_here;
}
}
if (console_output)
{
Console.WriteLine("System populated.");
}
}
public override void create_animation(string output_title, bool enable_console_output, bool using_full_path, bool allow_overwrite, bool use_floating_color_scale, DistributionSketchSettings S)
{
string absolute_video_output_path = video_default_repo + "\\" + output_title + ".avi";
if (using_full_path)
{
absolute_video_output_path = output_title;
}
if (File.Exists(absolute_video_output_path) && !allow_overwrite)
{
throw new Exception("Error: File exists and overwrite permission not granted.");
}
Directory.CreateDirectory(AbsoluteDataSetLocation + "\\images");
string[] allfiles = Directory.GetFiles(absolute_set_location);
List <string> distrib_files = new List <string>();
int q = 0;
foreach (string i in allfiles)
{
if (i.EndsWith(".dist"))
{
distrib_files.Add(i);
NCGrid_Distribution n = NCGrid_Distribution.from_file(i, true);
NCGrid_Distribution following_grid = new NCGrid_Distribution(n.Bounds, n.Xcount, n.Ycount);
int border = 1;
for (int ii = border; ii < following_grid.Xcount - border; ii++)
{
for (int jj = border; jj < following_grid.Ycount - border; jj++)
{
double deltax = (n.Xmax - n.Xmin) / (n.Xcount - 1);
double deltay = (n.Ymax - n.Ymin) / (n.Ycount - 1);
double[] stencil =
{
n[ii - 1, jj - 1].Value,
n[ii, jj - 1].Value,
n[ii + 1, jj - 1].Value,
n[ii - 1, jj].Value,
n[ii, jj].Value,
n[ii + 1, jj].Value,
n[ii - 1, jj + 1].Value,
n[ii, jj + 1].Value,
n[ii + 1, jj + 1].Value,
};
double ux = (stencil[5] - stencil[3]) / (2 * deltax);
double uy = (stencil[7] - stencil[1]) / (2 * deltay);
double uxx = (stencil[5] + stencil[3] - (2 * stencil[4])) / (deltax * deltax);
double uyy = (stencil[7] + stencil[1] - (2 * stencil[4])) / (deltay * deltay);
double uxy = (stencil[8] + stencil[0] - stencil[6] - stencil[2]) / (4 * deltax * deltay);
double dx = 0.06 * ((uxx * ux) + (uxy * uy));
double dy = 0.06 * ((uyy * uy) + (ux * uxy));
Vector3 move = new Vector3(dx, dy, 0);
while ((following_grid[ii, jj] + move).X > n.Bounds.Xmax || (following_grid[ii, jj] + move).X <n.Bounds.Xmin || (following_grid[ii, jj] + move).Y> n.Bounds.Ymax || (following_grid[ii, jj] + move).Y < n.Bounds.Ymin)
{
dx = 0.5 * dx;
dy = 0.5 * dy;
move = new Vector3(dx, dy, 0);
}
following_grid[ii, jj] = following_grid[ii, jj] + move;
}
}
HybridDistributionSketch2D sk = new HybridDistributionSketch2D(n, S);
if (!use_floating_color_scale)
{
sk.override_colormap_limits(info);
}
sk.set_superimposed_grid(following_grid);
sk.CreateSketch(true);
sk.SaveImage(AbsoluteDataSetLocation + "\\images\\render" + bufferint(q++, 5) + ".bmp", true);
}
}
AVIWriter V = new AVIWriter("wmv3");
string[] filenames = Directory.GetFiles(AbsoluteDataSetLocation + "\\images");
List <string> bmpnames = new List <string>();
foreach (string i in filenames)
{
if (i.EndsWith(".bmp"))
{
bmpnames.Add(i);
}
}
if (bmpnames.Count != 0)
{
Bitmap first = (Bitmap)Bitmap.FromFile(bmpnames[0]);
V.Open(absolute_video_output_path, first.Width, first.Height);
V.FrameRate = 50;
V.AddFrame(first);
int ct = bmpnames.Count;
for (int i = 1; i < bmpnames.Count; i++)
{
Bitmap butt = (Bitmap)Bitmap.FromFile(bmpnames[i]);
if (enable_console_output)
{
Console.WriteLine(i.ToString() + " of " + ct.ToString() + " frames stacked" + "(" + (i * 100 / ct).ToString() + "%)");
}
V.AddFrame(butt);
butt.Dispose();
}
V.Close();
first.Dispose();
if (enable_console_output)
{
Console.WriteLine("AVI successfully created on " + DateTime.Now.ToString() + " in directory " + absolute_video_output_path);
}
string[] imagenames = Directory.GetFiles(AbsoluteDataSetLocation + "\\images");
foreach (string g in imagenames)
{
File.Delete(g);
}
Directory.Delete(AbsoluteDataSetLocation + "\\images");
}
else
{
Console.WriteLine("No bitmap images found in the current directory.");
}
}
