/// <summary>Create nodes that we use inside FemVisualization2d.nb and FemVisualization3d.nb</summary>
public static void CreateNodes()
{
var nodes = // 10 by 10 array of nodes on a regular lattice.
Enumerable.Range(0, 10).Select(row =>
Enumerable.Range(0, 10).Select(col =>
new double[] { -3.0 + col * (6.0 / 9), -3.0 + row * (6.0 / 9) }
).ToArray()
).ToArray();
FWriter.SetDirAndFile("Seminar/Mathematica/", nameof(nodes), ".txt");
FWriter.WriteLine(nodes);
var nodesM = // Only the mid 2 by 2 = 4 nodes on a regular lattice.
nodes.Take(7).Skip(3).Select(col =>
col.Take(7).Skip(3)
.ToArray()
).ToArray();
FWriter.WriteLine(nodesM, nameof(nodesM));
Rng.SetRange(-0.6, 0.6); // Set RNG range.
var nodesC = // Only corners of elements.
nodes.Where((row, i) => i % 3 == 0)
.Select(row =>
row.Where((col, j) => j % 3 == 0).ToArray()
).ToArray();
FWriter.WriteLine(nodesC, nameof(nodesC));
var transNodesCM = // C = element corner nodes (only nodes on corners of elements)
nodesC.Take(3).Skip(1).Select(row => // Pick only those nodes that we will be moving. Take 2 inner rows (3,6).
row.Take(3).Skip(1).Select(col => // Take 2 inner nodes from each row (3,6).
col.Select(coord => coord + Rng.Dbl).ToArray()
).ToArray()
).ToArray();
FWriter.WriteLine(transNodesCM, nameof(transNodesCM));
}
/// <summary>Once transformed nodes have been created, generate array combinations appropriate for Mathematica plotting.</summary>
public static void CreateDerivedData()
{
FReader.SetDirAndFile("Seminar/Mathematica", "transNodesCM", ".txt");
var transNodesCM = (double[][][])FReader.ReadArray <double>();
FReader.SetFile("nodesC", ".txt");
var nodesC = (double[][][])FReader.ReadArray <double>();
var transNodesC1 = // Reassemble the rows (including static nodes).
transNodesCM.Select((row, i) => // Take the newly created array.
new double[][] { nodesC[i + 1][0] }.Concat(row).Append(nodesC[i + 1][3]).ToArray() // Attach a static node to the left and a static node to the right of each row.
).ToArray();
FWriter.SetDirAndFile("Seminar/Mathematica/", nameof(transNodesC1), ".txt"); // Have to set dir for the first time.
FWriter.WriteLine(transNodesC1);
var transNodesC = transNodesC1.Prepend(nodesC[0]).Append(nodesC[3]).ToArray(); // Reassemble the array (including filtered static rows).
FWriter.WriteLine(transNodesC, nameof(transNodesC));
var transNodesCByElms = Enumerable.Range(0, 3).Select(row => // Groups of 4 corner nodes for each element.
Enumerable.Range(0, 3).Select(col =>
new double[][] {
(double[])transNodesC[row][col].Clone(),
(double[])transNodesC[row][col + 1].Clone(),
(double[])transNodesC[row + 1][col + 1].Clone(),
(double[])transNodesC[row + 1][col].Clone()
}
).ToArray()
).ToArray();
FWriter.WriteLine(transNodesCByElms, nameof(transNodesCByElms));
var transNodesByElms = transNodesCByElms.Select(row =>
row.Select(elm =>
new double[][][] {
new double[][] { elm[0], TrueCoords(new double[] { -1.0 / 3, -1 }, elm), TrueCoords(new double[] { 1.0 / 3, -1 }, elm), elm[1] },
new double[][] { TrueCoords(new double[] { -1, -1.0 / 3 }, elm), TrueCoords(new double[] { -1.0 / 3, -1.0 / 3 }, elm), TrueCoords(new double[] { 1.0 / 3, -1.0 / 3 }, elm), TrueCoords(new double[] { 1, -1.0 / 3 }, elm) },
new double[][] { TrueCoords(new double[] { -1, 1.0 / 3 }, elm), TrueCoords(new double[] { -1.0 / 3, 1.0 / 3 }, elm), TrueCoords(new double[] { 1.0 / 3, 1.0 / 3 }, elm), TrueCoords(new double[] { 1, 1.0 / 3 }, elm) },
new double[][] { elm[3], TrueCoords(new double[] { -1.0 / 3, 1 }, elm), TrueCoords(new double[] { 1.0 / 3, 1 }, elm), elm[2] }
}
).ToArray()
).ToArray();
FWriter.WriteLine(transNodesByElms, nameof(transNodesByElms));
var transNodes = Enumerable.Range(0, 10).Select(row => // Create an empty 10 by 10 array.
Enumerable.Range(0, 10).Select(col =>
new double[2] {
0.0, 0.0
}
).ToArray()
).ToArray();
Enumerable.Range(0, 3).Select(i => // This will fill the lower left part of the new array.
Enumerable.Range(0, 3).Select(j =>
Enumerable.Range(0, 3).Select(k =>
Enumerable.Range(0, 3).Select(m =>
transNodes[3 * i + k][3 * j + m] = (double[])transNodesByElms[i][j][k][m].Clone()
).ToArray()
).ToArray()
).ToArray()
).ToArray();
Enumerable.Range(0, 3).Select(i => // Over 3 elements in last row.
Enumerable.Range(0, 3).Select(j => { // Over 3 nodes in last row of each element.
transNodes[9][3 * i + j] = transNodesByElms[2][i][3][j]; // Add the upper most row.
transNodes[3 * i + j][9] = transNodesByElms[i][2][j][3]; // Add the right most col.
return(j);
}).ToArray()
).ToArray();
transNodes[9][9] = transNodesByElms[2][2][3][3]; // Assign the last corner element.
FWriter.WriteLine(transNodes, nameof(transNodes));
var transNodesM =
transNodes.Where((row, i) => i > 2 && i < 7) // Take only middle nodes.
.Select(row =>
row.Where((col, j) => j > 2 && j < 7)
.ToArray()
).ToArray();
FWriter.WriteLine(transNodesM, nameof(transNodesM));
FReader.SetFile("nodes", ".txt");
var nodes = (double[][][])FReader.ReadArray <double>();
var nodes3dF =
nodes.Select(row =>
row.Select(col =>
col.Append(0.0).ToArray()
).ToArray()
).ToArray();
FWriter.WriteLine(nodes3dF, nameof(nodes3dF));
var transNodes3dF =
transNodes.Select(row =>
row.Select(col =>
col.Append(0.0).ToArray()
).ToArray()
).ToArray();
FWriter.WriteLine(transNodes3dF, nameof(transNodes3dF));
var nodes3dMF =
nodes.Take(7).Skip(3).Select(row =>
row.Take(7).Skip(3).Select(col =>
col.Append(0.0).ToArray()
).ToArray()
).ToArray();
FWriter.WriteLine(nodes3dMF, nameof(nodes3dMF));
var nodes3dMT =
nodes.Take(7).Skip(3).Select(row =>
row.Take(7).Skip(3).Select(col =>
col.Append(1.0).ToArray()
).ToArray()
).ToArray();
FWriter.WriteLine(nodes3dMT, nameof(nodes3dMT));
var transNodes3dMF =
transNodesM.Select(row =>
row.Select(col =>
col.Append(0.0).ToArray()
).ToArray()
).ToArray();
FWriter.WriteLine(transNodes3dMF, nameof(transNodes3dMF));
var transNodes3dMT =
transNodesM.Select(row =>
row.Select(col =>
col.Append(1.0).ToArray()
).ToArray()
).ToArray();
FWriter.WriteLine(transNodes3dMT, nameof(transNodes3dMT));
}
static int Point()
{
R("Writing solution to file.");
FWriter.SetDirAndFile("ChannelFlow/Results", "solution", ".txt");
return(0);
}