/// <summary>
/// Run example
/// </summary>
public void Run()
{
// Format matrix output to console
var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone();
formatProvider.TextInfo.ListSeparator = " ";
// Create square matrix
var matrix = new DenseMatrix(5);
var k = 0;
for (var i = 0; i < matrix.RowCount; i++)
{
for (var j = 0; j < matrix.ColumnCount; j++)
{
matrix[i, j] = k++;
}
}
Console.WriteLine(@"Initial matrix");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Create vector
var vector = new DenseVector(new[] { 50.0, 51.0, 52.0, 53.0, 54.0 });
Console.WriteLine(@"Sample vector");
Console.WriteLine(vector.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 1. Insert new column
var result = matrix.InsertColumn(3, vector);
Console.WriteLine(@"1. Insert new column");
Console.WriteLine(result.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 2. Insert new row
result = matrix.InsertRow(3, vector);
Console.WriteLine(@"2. Insert new row");
Console.WriteLine(result.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 3. Set column values
matrix.SetColumn(2, (Vector)vector);
Console.WriteLine(@"3. Set column values");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 4. Set row values.
matrix.SetRow(3, (double[])vector);
Console.WriteLine(@"4. Set row values");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 5. Set diagonal values. SetRow/SetColumn/SetDiagonal accepts Vector and double[] as input parameter
matrix.SetDiagonal(new[] { 5.0, 4.0, 3.0, 2.0, 1.0 });
Console.WriteLine(@"5. Set diagonal values");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 6. Set submatrix values
matrix.SetSubMatrix(1, 3, 1, 3, DenseMatrix.Identity(3));
Console.WriteLine(@"6. Set submatrix values");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// Permutations.
// Initialize a new instance of the Permutation class. An array represents where each integer is permuted too:
// indices[i] represents that integer "i" is permuted to location indices[i]
var permutations = new Permutation(new[] { 0, 1, 3, 2, 4 });
// 7. Permute rows 3 and 4
matrix.PermuteRows(permutations);
Console.WriteLine(@"7. Permute rows 3 and 4");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 8. Permute columns 1 and 2, 3 and 5
permutations = new Permutation(new[] { 1, 0, 4, 3, 2 });
matrix.PermuteColumns(permutations);
Console.WriteLine(@"8. Permute columns 1 and 2, 3 and 5");
Console.WriteLine(matrix.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 9. Concatenate the matrix with the given matrix
var append = matrix.Append(matrix);
// Concatenate into result matrix
matrix.Append(matrix, append);
Console.WriteLine(@"9. Append matrix to matrix");
Console.WriteLine(append.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 10. Stack the matrix on top of the given matrix matrix
var stack = matrix.Stack(matrix);
// Stack into result matrix
matrix.Stack(matrix, stack);
Console.WriteLine(@"10. Stack the matrix on top of the given matrix matrix");
Console.WriteLine(stack.ToString("#0.00\t", formatProvider));
Console.WriteLine();
// 11. Diagonally stack the matrix on top of the given matrix matrix
var diagoinalStack = matrix.DiagonalStack(matrix);
// Diagonally stack into result matrix
matrix.DiagonalStack(matrix, diagoinalStack);
Console.WriteLine(@"11. Diagonally stack the matrix on top of the given matrix matrix");
Console.WriteLine(diagoinalStack.ToString("#0.00\t", formatProvider));
Console.WriteLine();
}
public static ResultFEM Solve(Matrix<double> K, Matrix<double> f, int[] bc)
{
// Create dof array:
int ndof = f.RowCount;
// Initialize displacement vector
Matrix u = new DenseMatrix(ndof, 1);
int[] dof = new int[ndof];
for (int i = 0; i < ndof; i++)
{
dof[i] = i;
}
// Create the free dofs:
int[] fdof = dof.Except(bc).ToArray();
int nfdof = fdof.Length; // Number of free dofs.
int nbdof = ndof - nfdof; //Constrained dofs
// Create the permutation array which puts the constrained dofs last:
int[] permute = bc.Union(fdof).ToArray();
Permutation perm = new Permutation(permute);
Permutation invPerm = perm.Inverse();
Matrix<double> KPermuted = DenseMatrix.OfMatrix(K);
KPermuted.PermuteRows(invPerm);
KPermuted.PermuteColumns(invPerm);
// Split K:::
Matrix<double> Kff = KPermuted.SubMatrix(nbdof, nfdof, nbdof, nfdof);
System.Console.WriteLine(Kff); //Down right corner of matrix
Matrix<double> Kfp = KPermuted.SubMatrix(nbdof, nfdof, 0, nbdof); //Down left corner of matrix
// Split F:::
Matrix<double> fPermuted = DenseMatrix.OfMatrix(f);
fPermuted.PermuteRows(invPerm);
Matrix<double> ff = fPermuted.SubMatrix(nbdof, nfdof, 0, 1);
Matrix<double> up = u.SubMatrix(0, nbdof, 0, 1); // Must set up to constrained values in bc.
// Solve for the unknown displacements:::
Matrix<double> s = Kff.Solve(ff.Subtract(Kfp.Multiply(up)));
u.SetSubMatrix(nbdof, 0, s); // Set displacements back.
System.Console.WriteLine(u);
// Permute back u
u.PermuteRows(perm);
System.Console.WriteLine("U after permut");
System.Console.WriteLine(K);
System.Console.WriteLine(u);
System.Console.WriteLine(f);
// Get reaction forces:
Matrix<double> Q = K.Multiply(u).Subtract(f);
ResultFEM result = new ResultFEM(u, Q);
return result;
}
