/// <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();
        }
示例#2
0
        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;
        }