/// <summary> /// Run example /// </summary> /// <seealso cref="http://en.wikipedia.org/wiki/Triangular_matrix">Triangular matrix</seealso> public void Run() { // Format matrix output to console var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); formatProvider.TextInfo.ListSeparator = " "; // Create square matrix var matrix = new DenseMatrix(10); 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 square matrix"); Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 1. Retrieve a new matrix containing the lower triangle of the matrix var lower = matrix.LowerTriangle(); // Puts the lower triangle of the matrix into the result matrix. matrix.LowerTriangle(lower); Console.WriteLine(@"1. Lower triangle of the matrix"); Console.WriteLine(lower.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Retrieve a new matrix containing the upper triangle of the matrix var upper = matrix.UpperTriangle(); // Puts the upper triangle of the matrix into the result matrix. matrix.UpperTriangle(lower); Console.WriteLine(@"2. Upper triangle of the matrix"); Console.WriteLine(upper.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 3. Retrieve a new matrix containing the strictly lower triangle of the matrix var strictlylower = matrix.StrictlyLowerTriangle(); // Puts the strictly lower triangle of the matrix into the result matrix. matrix.StrictlyLowerTriangle(strictlylower); Console.WriteLine(@"3. Strictly lower triangle of the matrix"); Console.WriteLine(strictlylower.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 4. Retrieve a new matrix containing the strictly upper triangle of the matrix var strictlyupper = matrix.StrictlyUpperTriangle(); // Puts the strictly upper triangle of the matrix into the result matrix. matrix.StrictlyUpperTriangle(strictlyupper); Console.WriteLine(@"4. Strictly upper triangle of the matrix"); Console.WriteLine(strictlyupper.ToString("#0.00\t", formatProvider)); Console.WriteLine(); }
/// <summary> /// Run example /// </summary> /// <seealso cref="http://en.wikipedia.org/wiki/Transpose">Transpose</seealso> /// <seealso cref="http://en.wikipedia.org/wiki/Invertible_matrix">Invertible matrix</seealso> public void Run() { // Format matrix output to console var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); formatProvider.TextInfo.ListSeparator = " "; // Create random square matrix var matrix = new DenseMatrix(5); var rnd = new Random(1); for (var i = 0; i < matrix.RowCount; i++) { for (var j = 0; j < matrix.ColumnCount; j++) { matrix[i, j] = rnd.NextDouble(); } } Console.WriteLine(@"Initial matrix"); Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 1. Get matrix inverse var inverse = matrix.Inverse(); Console.WriteLine(@"1. Matrix inverse"); Console.WriteLine(inverse.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Matrix multiplied by its inverse gives identity matrix var identity = matrix * inverse; Console.WriteLine(@"2. Matrix multiplied by its inverse"); Console.WriteLine(identity.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 3. Get matrix transpose var transpose = matrix.Transpose(); Console.WriteLine(@"3. Matrix transpose"); Console.WriteLine(transpose.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 4. Get orthogonal matrix, i.e. do QR decomposition and get matrix Q var orthogonal = matrix.QR().Q; Console.WriteLine(@"4. Orthogonal matrix"); Console.WriteLine(orthogonal.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 5. Transpose and multiply orthogonal matrix by iteslf gives identity matrix identity = orthogonal.TransposeAndMultiply(orthogonal); Console.WriteLine(@"Transpose and multiply orthogonal matrix by iteslf"); Console.WriteLine(identity.ToString("#0.00\t", formatProvider)); Console.WriteLine(); }
/// <summary> /// Run example /// </summary> /// <seealso cref="http://en.wikipedia.org/wiki/Cholesky_decomposition">Cholesky decomposition</seealso> public void Run() { // Format matrix output to console var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); formatProvider.TextInfo.ListSeparator = " "; // Create square, symmetric, positive definite matrix var matrix = new DenseMatrix(new[,] { { 2.0, 1.0 }, { 1.0, 2.0 } }); Console.WriteLine(@"Initial square, symmetric, positive definite matrix"); Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Perform Cholesky decomposition var cholesky = matrix.Cholesky(); Console.WriteLine(@"Perform Cholesky decomposition"); // 1. Lower triangular form of the Cholesky matrix Console.WriteLine(@"1. Lower triangular form of the Cholesky matrix"); Console.WriteLine(cholesky.Factor.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Reconstruct initial matrix: A = L * LT var reconstruct = cholesky.Factor * cholesky.Factor.Transpose(); Console.WriteLine(@"2. Reconstruct initial matrix: A = L*LT"); Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 3. Get determinant of the matrix Console.WriteLine(@"3. Determinant of the matrix"); Console.WriteLine(cholesky.Determinant); Console.WriteLine(); // 4. Get log determinant of the matrix Console.WriteLine(@"4. Log determinant of the matrix"); Console.WriteLine(cholesky.DeterminantLn); Console.WriteLine(); }
/// <summary> /// Run example /// </summary> public void Run() { // 1. Initialize a new instance of the matrix from a 2D array. This constructor will allocate a completely new memory block for storing the dense matrix. var matrix1 = new DenseMatrix(new[,] { { 1.0, 2.0, 3.0 }, { 4.0, 5.0, 6.0 } }); // 2. Initialize a new instance of the empty square matrix with a given order. var matrix2 = new DenseMatrix(3); // 3. Initialize a new instance of the empty matrix with a given size. var matrix3 = new DenseMatrix(2, 3); // 4. Initialize a new instance of the matrix with all entries set to a particular value. var matrix4 = new DenseMatrix(2, 3, 3.0); // 4. Initialize a new instance of the matrix from a one dimensional array. This array should store the matrix in column-major order. var matrix5 = new DenseMatrix(2, 3, new[] { 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 }); // 5. Initialize a square matrix with all zero's except for ones on the diagonal. Identity matrix (http://en.wikipedia.org/wiki/Identity_matrix). var matrixI = DenseMatrix.Identity(5); // Format matrix output to console var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); formatProvider.TextInfo.ListSeparator = " "; Console.WriteLine(@"Matrix 1"); Console.WriteLine(matrix1.ToString("#0.00\t", formatProvider)); Console.WriteLine(); Console.WriteLine(@"Matrix 2"); Console.WriteLine(matrix2.ToString("#0.00\t", formatProvider)); Console.WriteLine(); Console.WriteLine(@"Matrix 3"); Console.WriteLine(matrix3.ToString("#0.00\t", formatProvider)); Console.WriteLine(); Console.WriteLine(@"Matrix 4"); Console.WriteLine(matrix4.ToString("#0.00\t", formatProvider)); Console.WriteLine(); Console.WriteLine(@"Matrix 5"); Console.WriteLine(matrix5.ToString("#0.00\t", formatProvider)); Console.WriteLine(); Console.WriteLine(@"Identity matrix"); Console.WriteLine(matrixI.ToString("#0.00\t", formatProvider)); Console.WriteLine(); }
/// <summary> /// Run example /// </summary> public void Run() { // Format vector output to console var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); formatProvider.TextInfo.ListSeparator = " "; // Create new empty square matrix var matrix = new DenseMatrix(10); Console.WriteLine(@"Empty matrix"); Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 1. Fill matrix by data using indexer [] 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(@"1. Fill matrix by data using indexer []"); Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Fill matrix by data using At. The element is set without range checking. for (var i = 0; i < matrix.RowCount; i++) { for (var j = 0; j < matrix.ColumnCount; j++) { matrix.At(i, j, k--); } } Console.WriteLine(@"2. Fill matrix by data using At"); Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 3. Clone matrix var clone = matrix.Clone(); Console.WriteLine(@"3. Clone matrix"); Console.WriteLine(clone.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 4. Clear matrix clone.Clear(); Console.WriteLine(@"4. Clear matrix"); Console.WriteLine(clone.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 5. Copy matrix into another matrix matrix.CopyTo(clone); Console.WriteLine(@"5. Copy matrix into another matrix"); Console.WriteLine(clone.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 6. Get submatrix into another matrix var submatrix = matrix.SubMatrix(2, 2, 3, 3); Console.WriteLine(@"6. Copy submatrix into another matrix"); Console.WriteLine(submatrix.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 7. Get part of the row as vector. In this example: get 4 elements from row 5 starting from column 3 var row = matrix.Row(5, 3, 4); Console.WriteLine(@"7. Get part of the row as vector"); Console.WriteLine(row.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 8. Get part of the column as vector. In this example: get 3 elements from column 2 starting from row 6 var column = matrix.Column(2, 6, 3); Console.WriteLine(@"8. Get part of the column as vector"); Console.WriteLine(column.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 9. Get columns using column enumerator. If you need all columns you may use ColumnEnumerator without parameters Console.WriteLine(@"9. Get columns using column enumerator"); foreach (var keyValuePair in matrix.ColumnEnumerator(2, 4)) { Console.WriteLine(@"Column {0}: {1}", keyValuePair.Item1, keyValuePair.Item2.ToString("#0.00\t", formatProvider)); } Console.WriteLine(); // 10. Get rows using row enumerator. If you need all rows you may use RowEnumerator without parameters Console.WriteLine(@"10. Get rows using row enumerator"); foreach (var keyValuePair in matrix.RowEnumerator(4, 3)) { Console.WriteLine(@"Row {0}: {1}", keyValuePair.Item1, keyValuePair.Item2.ToString("#0.00\t", formatProvider)); } Console.WriteLine(); // 11. Convert matrix into multidimensional array var data = matrix.ToArray(); Console.WriteLine(@"11. Convert matrix into multidimensional array"); for (var i = 0; i < data.GetLongLength(0); i++) { for (var j = 0; j < data.GetLongLength(1); j++) { Console.Write(data[i, j].ToString("#0.00\t")); } Console.WriteLine(); } Console.WriteLine(); // 12. Convert matrix into row-wise array var rowwise = matrix.ToRowWiseArray(); Console.WriteLine(@"12. Convert matrix into row-wise array"); for (var i = 0; i < matrix.RowCount; i++) { for (var j = 0; j < matrix.ColumnCount; j++) { Console.Write(rowwise[(i * matrix.ColumnCount) + j].ToString("#0.00\t")); } Console.WriteLine(); } Console.WriteLine(); // 13. Convert matrix into column-wise array var columnise = matrix.ToColumnWiseArray(); Console.WriteLine(@"13. Convert matrix into column-wise array"); for (var i = 0; i < matrix.RowCount; i++) { for (var j = 0; j < matrix.ColumnCount; j++) { Console.Write(columnise[(j * matrix.RowCount) + i].ToString("#0.00\t")); } Console.WriteLine(); } Console.WriteLine(); // 14. Get matrix diagonal as vector var diagonal = matrix.Diagonal(); Console.WriteLine(@"14. Get matrix diagonal as vector"); Console.WriteLine(diagonal.ToString("#0.00\t", formatProvider)); Console.WriteLine(); }
/// <summary> /// Run example /// </summary> /// <seealso cref="http://en.wikipedia.org/wiki/Determinant">Determinant</seealso> /// <seealso cref="http://en.wikipedia.org/wiki/Rank_%28linear_algebra%29">Rank (linear algebra)</seealso> /// <seealso cref="http://en.wikipedia.org/wiki/Trace_%28linear_algebra%29">Trace (linear algebra)</seealso> /// <seealso cref="http://en.wikipedia.org/wiki/Condition_number">Condition number</seealso> public void Run() { // Format matrix output to console var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); formatProvider.TextInfo.ListSeparator = " "; // Create random square matrix var matrix = new DenseMatrix(5); var rnd = new Random(1); for (var i = 0; i < matrix.RowCount; i++) { for (var j = 0; j < matrix.ColumnCount; j++) { matrix[i, j] = rnd.NextDouble(); } } Console.WriteLine(@"Initial matrix"); Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 1. Determinant Console.WriteLine(@"1. Determinant"); Console.WriteLine(matrix.Determinant()); Console.WriteLine(); // 2. Rank Console.WriteLine(@"2. Rank"); Console.WriteLine(matrix.Rank()); Console.WriteLine(); // 3. Condition number Console.WriteLine(@"2. Condition number"); Console.WriteLine(matrix.ConditionNumber()); Console.WriteLine(); // 4. Trace Console.WriteLine(@"4. Trace"); Console.WriteLine(matrix.Trace()); Console.WriteLine(); }
/// <summary> /// Run example /// </summary> /// <seealso cref="http://en.wikipedia.org/wiki/Singular_value_decomposition">SVD decomposition</seealso> public void Run() { // Format matrix output to console var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); formatProvider.TextInfo.ListSeparator = " "; // Create square matrix var matrix = new DenseMatrix(new[,] { { 4.0, 1.0 }, { 3.0, 2.0 } }); Console.WriteLine(@"Initial square matrix"); Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Perform full SVD decomposition var svd = matrix.Svd(true); Console.WriteLine(@"Perform full SVD decomposition"); // 1. Left singular vectors Console.WriteLine(@"1. Left singular vectors"); Console.WriteLine(svd.U().ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Singular values as vector Console.WriteLine(@"2. Singular values as vector"); Console.WriteLine(svd.S().ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 3. Singular values as diagonal matrix Console.WriteLine(@"3. Singular values as diagonal matrix"); Console.WriteLine(svd.W().ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 4. Right singular vectors Console.WriteLine(@"4. Right singular vectors"); Console.WriteLine(svd.VT().ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 5. Multiply U matrix by its transpose var identinty = svd.U() * svd.U().Transpose(); Console.WriteLine(@"5. Multiply U matrix by its transpose"); Console.WriteLine(identinty.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 6. Multiply V matrix by its transpose identinty = svd.VT().TransposeAndMultiply(svd.VT()); Console.WriteLine(@"6. Multiply V matrix by its transpose"); Console.WriteLine(identinty.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 7. Reconstruct initial matrix: A = U*Σ*VT var reconstruct = svd.U() * svd.W() * svd.VT(); Console.WriteLine(@"7. Reconstruct initial matrix: A = U*S*VT"); Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 8. Condition Number of the matrix Console.WriteLine(@"8. Condition Number of the matrix"); Console.WriteLine(svd.ConditionNumber); Console.WriteLine(); // 9. Determinant of the matrix Console.WriteLine(@"9. Determinant of the matrix"); Console.WriteLine(svd.Determinant); Console.WriteLine(); // 10. 2-norm of the matrix Console.WriteLine(@"10. 2-norm of the matrix"); Console.WriteLine(svd.Norm2); Console.WriteLine(); // 11. Rank of the matrix Console.WriteLine(@"11. Rank of the matrix"); Console.WriteLine(svd.Rank); Console.WriteLine(); // Perform partial SVD decomposition, without computing the singular U and VT vectors svd = matrix.Svd(false); Console.WriteLine(@"Perform partial SVD decomposition, without computing the singular U and VT vectors"); // 12. Singular values as vector Console.WriteLine(@"12. Singular values as vector"); Console.WriteLine(svd.S().ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 13. Singular values as diagonal matrix Console.WriteLine(@"13. Singular values as diagonal matrix"); Console.WriteLine(svd.W().ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 14. Access to left singular vectors when partial SVD decomposition was performed try { Console.WriteLine(@"14. Access to left singular vectors when partial SVD decomposition was performed"); Console.WriteLine(svd.U().ToString("#0.00\t", formatProvider)); } catch (Exception ex) { Console.WriteLine(ex.Message); Console.WriteLine(); } // 15. Access to right singular vectors when partial SVD decomposition was performed try { Console.WriteLine(@"15. Access to right singular vectors when partial SVD decomposition was performed"); Console.WriteLine(svd.VT().ToString("#0.00\t", formatProvider)); } catch (Exception ex) { Console.WriteLine(ex.Message); Console.WriteLine(); } }
/// <summary> /// Run example /// </summary> public void Run() { // Format matrix output to console var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); formatProvider.TextInfo.ListSeparator = " "; // Solve next system of linear equations (Ax=b): // 5*x + 2*y - 4*z = -7 // 3*x - 7*y + 6*z = 38 // 4*x + 1*y + 5*z = 43 // Create matrix "A" with coefficients var matrixA = new DenseMatrix(new[,] { { 5.00, 2.00, -4.00 }, { 3.00, -7.00, 6.00 }, { 4.00, 1.00, 5.00 } }); Console.WriteLine(@"Matrix 'A' with coefficients"); Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Create vector "b" with the constant terms. var vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 }); Console.WriteLine(@"Vector 'b' with the constant terms"); Console.WriteLine(vectorB.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 1. Solve linear equations using LU decomposition var resultX = matrixA.LU().Solve(vectorB); Console.WriteLine(@"1. Solution using LU decomposition"); Console.WriteLine(resultX.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Solve linear equations using QR decomposition resultX = matrixA.QR().Solve(vectorB); Console.WriteLine(@"2. Solution using QR decomposition"); Console.WriteLine(resultX.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 3. Solve linear equations using SVD decomposition matrixA.Svd(true).Solve(vectorB, resultX); Console.WriteLine(@"3. Solution using SVD decomposition"); Console.WriteLine(resultX.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 4. Solve linear equations using Gram-Shmidt decomposition matrixA.GramSchmidt().Solve(vectorB, resultX); Console.WriteLine(@"4. Solution using Gram-Shmidt decomposition"); Console.WriteLine(resultX.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 5. Verify result. Multiply coefficient matrix "A" by result vector "x" var reconstructVecorB = matrixA * resultX; Console.WriteLine(@"5. Multiply coefficient matrix 'A' by result vector 'x'"); Console.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // To use Cholesky or Eigenvalue decomposition coefficient matrix must be // symmetric (for Evd and Cholesky) and positive definite (for Cholesky) // Multipy matrix "A" by its transpose - the result will be symmetric and positive definite matrix var newMatrixA = matrixA.TransposeAndMultiply(matrixA); Console.WriteLine(@"Symmetric positive definite matrix"); Console.WriteLine(newMatrixA.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 6. Solve linear equations using Cholesky decomposition newMatrixA.Cholesky().Solve(vectorB, resultX); Console.WriteLine(@"6. Solution using Cholesky decomposition"); Console.WriteLine(resultX.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 7. Solve linear equations using eigen value decomposition newMatrixA.Evd().Solve(vectorB, resultX); Console.WriteLine(@"7. Solution using eigen value decomposition"); Console.WriteLine(resultX.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 8. Verify result. Multiply new coefficient matrix "A" by result vector "x" reconstructVecorB = newMatrixA * resultX; Console.WriteLine(@"8. Multiply new coefficient matrix 'A' by result vector 'x'"); Console.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider)); Console.WriteLine(); }
/// <summary> /// Run example /// </summary> public void Run() { // Format matrix output to console var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); formatProvider.TextInfo.ListSeparator = " "; // Solve next system of linear equations (Ax=b): // 5*x + 2*y - 4*z = -7 // 3*x - 7*y + 6*z = 38 // 4*x + 1*y + 5*z = 43 // Create matrix "A" with coefficients var matrixA = new DenseMatrix(new[,] { { 5.00, 2.00, -4.00 }, { 3.00, -7.00, 6.00 }, { 4.00, 1.00, 5.00 } }); Console.WriteLine(@"Matrix 'A' with coefficients"); Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Create vector "b" with the constant terms. var vectorB = new DenseVector(new[] { -7.0, 38.0, 43.0 }); Console.WriteLine(@"Vector 'b' with the constant terms"); Console.WriteLine(vectorB.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Create stop criteriums to monitor an iterative calculation. There are next available stop criteriums: // - DivergenceStopCriterium: monitors an iterative calculation for signs of divergence; // - FailureStopCriterium: monitors residuals for NaN's; // - IterationCountStopCriterium: monitors the numbers of iteration steps; // - ResidualStopCriterium: monitors residuals if calculation is considered converged; // Stop calculation if 1000 iterations reached during calculation var iterationCountStopCriterium = new IterationCountStopCriterium(1000); // Stop calculation if residuals are below 1E-10 --> the calculation is considered converged var residualStopCriterium = new ResidualStopCriterium(1e-10); // Create monitor with defined stop criteriums var monitor = new Iterator(new IIterationStopCriterium[] { iterationCountStopCriterium, residualStopCriterium }); // Create Multiple-Lanczos Bi-Conjugate Gradient Stabilized solver var solver = new MlkBiCgStab(monitor); // 1. Solve the matrix equation var resultX = solver.Solve(matrixA, vectorB); Console.WriteLine(@"1. Solve the matrix equation"); Console.WriteLine(); // 2. Check solver status of the iterations. // Solver has property IterationResult which contains the status of the iteration once the calculation is finished. // Possible values are: // - CalculationCancelled: calculation was cancelled by the user; // - CalculationConverged: calculation has converged to the desired convergence levels; // - CalculationDiverged: calculation diverged; // - CalculationFailure: calculation has failed for some reason; // - CalculationIndetermined: calculation is indetermined, not started or stopped; // - CalculationRunning: calculation is running and no results are yet known; // - CalculationStoppedWithoutConvergence: calculation has been stopped due to reaching the stopping limits, but that convergence was not achieved; Console.WriteLine(@"2. Solver status of the iterations"); Console.WriteLine(solver.IterationResult); Console.WriteLine(); // 3. Solution result vector of the matrix equation Console.WriteLine(@"3. Solution result vector of the matrix equation"); Console.WriteLine(resultX.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 4. Verify result. Multiply coefficient matrix "A" by result vector "x" var reconstructVecorB = matrixA * resultX; Console.WriteLine(@"4. Multiply coefficient matrix 'A' by result vector 'x'"); Console.WriteLine(reconstructVecorB.ToString("#0.00\t", formatProvider)); Console.WriteLine(); }
public string ToString(DenseMatrix m) { return m.ToString("",formatProvider); }
/// <summary> /// Run example /// </summary> /// <seealso cref="http://en.wikipedia.org/wiki/QR_decomposition">QR decomposition</seealso> public void Run() { // Format matrix output to console var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); formatProvider.TextInfo.ListSeparator = " "; // Create 3 x 2 matrix var matrix = new DenseMatrix(new[,] { { 1.0, 2.0 }, { 3.0, 4.0 }, { 5.0, 6.0 } }); Console.WriteLine(@"Initial 3x2 matrix"); Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Perform QR decomposition (Householder transformations) var qr = matrix.QR(); Console.WriteLine(@"QR decomposition (Householder transformations)"); // 1. Orthogonal Q matrix Console.WriteLine(@"1. Orthogonal Q matrix"); Console.WriteLine(qr.Q.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Multiply Q matrix by its transpose gives identity matrix Console.WriteLine(@"2. Multiply Q matrix by its transpose gives identity matrix"); Console.WriteLine(qr.Q.TransposeAndMultiply(qr.Q).ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 3. Upper triangular factor R Console.WriteLine(@"3. Upper triangular factor R"); Console.WriteLine(qr.R.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 4. Reconstruct initial matrix: A = Q * R var reconstruct = qr.Q * qr.R; Console.WriteLine(@"4. Reconstruct initial matrix: A = Q*R"); Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Perform QR decomposition (Gram–Schmidt process) var gramSchmidt = matrix.GramSchmidt(); Console.WriteLine(@"QR decomposition (Gram–Schmidt process)"); // 5. Orthogonal Q matrix Console.WriteLine(@"5. Orthogonal Q matrix"); Console.WriteLine(gramSchmidt.Q.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 6. Multiply Q matrix by its transpose gives identity matrix Console.WriteLine(@"6. Multiply Q matrix by its transpose gives identity matrix"); Console.WriteLine((gramSchmidt.Q.Transpose() * gramSchmidt.Q).ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 7. Upper triangular factor R Console.WriteLine(@"7. Upper triangular factor R"); Console.WriteLine(gramSchmidt.R.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 8. Reconstruct initial matrix: A = Q * R reconstruct = gramSchmidt.Q * gramSchmidt.R; Console.WriteLine(@"8. Reconstruct initial matrix: A = Q*R"); Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider)); Console.WriteLine(); }
/// <summary> /// Run example /// </summary> /// <seealso cref="http://en.wikipedia.org/wiki/Matrix_norm">Matrix norm</seealso> public void Run() { // Format matrix output to console var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); formatProvider.TextInfo.ListSeparator = " "; // Create square matrix var matrix = new DenseMatrix(new[,] { { 1.0, 2.0, 3.0 }, { 6.0, 5.0, 4.0 }, { 8.0, 9.0, 7.0 } }); Console.WriteLine(@"Initial square matrix"); Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 1. 1-norm of the matrix Console.WriteLine(@"1. 1-norm of the matrix"); Console.WriteLine(matrix.L1Norm()); Console.WriteLine(); // 2. 2-norm of the matrix Console.WriteLine(@"2. 2-norm of the matrix"); Console.WriteLine(matrix.L2Norm()); Console.WriteLine(); // 3. Frobenius norm of the matrix Console.WriteLine(@"3. Frobenius norm of the matrix"); Console.WriteLine(matrix.FrobeniusNorm()); Console.WriteLine(); // 4. Infinity norm of the matrix Console.WriteLine(@"4. Infinity norm of the matrix"); Console.WriteLine(matrix.InfinityNorm()); Console.WriteLine(); // 5. Normalize matrix columns Console.WriteLine(@"5. Normalize matrix columns: before normalize"); foreach (var keyValuePair in matrix.ColumnEnumerator()) { Console.WriteLine(@"Column {0} 2-nd norm is: {1}", keyValuePair.Item1, keyValuePair.Item2.Norm(2)); } Console.WriteLine(); var normalized = matrix.NormalizeColumns(2); Console.WriteLine(@"5. Normalize matrix columns: after normalize"); foreach (var keyValuePair in normalized.ColumnEnumerator()) { Console.WriteLine(@"Column {0} 2-nd norm is: {1}", keyValuePair.Item1, keyValuePair.Item2.Norm(2)); } Console.WriteLine(); // 6. Normalize matrix columns Console.WriteLine(@"6. Normalize matrix rows: before normalize"); foreach (var keyValuePair in matrix.RowEnumerator()) { Console.WriteLine(@"Row {0} 2-nd norm is: {1}", keyValuePair.Item1, keyValuePair.Item2.Norm(2)); } Console.WriteLine(); normalized = matrix.NormalizeRows(2); Console.WriteLine(@"6. Normalize matrix rows: after normalize"); foreach (var keyValuePair in normalized.RowEnumerator()) { Console.WriteLine(@"Row {0} 2-nd norm is: {1}", keyValuePair.Item1, keyValuePair.Item2.Norm(2)); } }
/// <summary> /// Run example /// </summary> /// <seealso cref="http://en.wikipedia.org/wiki/LU_decomposition">LU decomposition</seealso> /// <seealso cref="http://en.wikipedia.org/wiki/Invertible_matrix">Invertible matrix</seealso> public void Run() { // Format matrix output to console var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); formatProvider.TextInfo.ListSeparator = " "; // Create square matrix var matrix = new DenseMatrix(new[,] { { 1.0, 2.0 }, { 3.0, 4.0 } }); Console.WriteLine(@"Initial square matrix"); Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Perform LU decomposition var lu = matrix.LU(); Console.WriteLine(@"Perform LU decomposition"); // 1. Lower triangular factor Console.WriteLine(@"1. Lower triangular factor"); Console.WriteLine(lu.L.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Upper triangular factor Console.WriteLine(@"2. Upper triangular factor"); Console.WriteLine(lu.U.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 3. Permutations applied to LU factorization Console.WriteLine(@"3. Permutations applied to LU factorization"); for (var i = 0; i < lu.P.Dimension; i++) { if (lu.P[i] > i) { Console.WriteLine(@"Row {0} permuted with row {1}", lu.P[i], i); } } Console.WriteLine(); // 4. Reconstruct initial matrix: PA = L * U var reconstruct = lu.L * lu.U; // The rows of the reconstructed matrix should be permuted to get the initial matrix reconstruct.PermuteRows(lu.P.Inverse()); Console.WriteLine(@"4. Reconstruct initial matrix: PA = L*U"); Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 5. Get the determinant of the matrix Console.WriteLine(@"5. Determinant of the matrix"); Console.WriteLine(lu.Determinant); Console.WriteLine(); // 6. Get the inverse of the matrix var matrixInverse = lu.Inverse(); Console.WriteLine(@"6. Inverse of the matrix"); Console.WriteLine(matrixInverse.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 7. Matrix multiplied by its inverse var identity = matrix * matrixInverse; Console.WriteLine(@"7. Matrix multiplied by its inverse "); Console.WriteLine(identity.ToString("#0.00\t", formatProvider)); Console.WriteLine(); }
/// <summary> /// Run example /// </summary> /// <seealso cref="http://en.wikipedia.org/wiki/Eigenvalue,_eigenvector_and_eigenspace">EVD decomposition</seealso> public void Run() { // Format matrix output to console var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); formatProvider.TextInfo.ListSeparator = " "; // Create square symmetric matrix var matrix = new DenseMatrix(new[,] { { 1.0, 2.0, 3.0 }, { 2.0, 1.0, 4.0 }, { 3.0, 4.0, 1.0 } }); Console.WriteLine(@"Initial square symmetric matrix"); Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Perform eigenvalue decomposition of symmetric matrix var evd = matrix.Evd(); Console.WriteLine(@"Perform eigenvalue decomposition of symmetric matrix"); // 1. Eigen vectors Console.WriteLine(@"1. Eigen vectors"); Console.WriteLine(evd.EigenVectors().ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Eigen values as a complex vector Console.WriteLine(@"2. Eigen values as a complex vector"); Console.WriteLine(evd.EigenValues().ToString("N", formatProvider)); Console.WriteLine(); // 3. Eigen values as the block diagonal matrix Console.WriteLine(@"3. Eigen values as the block diagonal matrix"); Console.WriteLine(evd.D().ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 4. Multiply V by its transpose VT var identity = evd.EigenVectors().TransposeAndMultiply(evd.EigenVectors()); Console.WriteLine(@"4. Multiply V by its transpose VT: V*VT = I"); Console.WriteLine(identity.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 5. Reconstruct initial matrix: A = V*D*V' var reconstruct = evd.EigenVectors() * evd.D() * evd.EigenVectors().Transpose(); Console.WriteLine(@"5. Reconstruct initial matrix: A = V*D*V'"); Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 6. Determinant of the matrix Console.WriteLine(@"6. Determinant of the matrix"); Console.WriteLine(evd.Determinant); Console.WriteLine(); // 7. Rank of the matrix Console.WriteLine(@"7. Rank of the matrix"); Console.WriteLine(evd.Rank); Console.WriteLine(); // Fill matrix by random values var rnd = new Random(1); for (var i = 0; i < matrix.RowCount; i++) { for (var j = 0; j < matrix.ColumnCount; j++) { matrix[i, j] = rnd.NextDouble(); } } Console.WriteLine(@"Fill matrix by random values"); Console.WriteLine(matrix.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Perform eigenvalue decomposition of non-symmetric matrix evd = matrix.Evd(); Console.WriteLine(@"Perform eigenvalue decomposition of non-symmetric matrix"); // 8. Eigen vectors Console.WriteLine(@"8. Eigen vectors"); Console.WriteLine(evd.EigenVectors().ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 9. Eigen values as a complex vector Console.WriteLine(@"9. Eigen values as a complex vector"); Console.WriteLine(evd.EigenValues().ToString("N", formatProvider)); Console.WriteLine(); // 10. Eigen values as the block diagonal matrix Console.WriteLine(@"10. Eigen values as the block diagonal matrix"); Console.WriteLine(evd.D().ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 11. Multiply A * V var av = matrix * evd.EigenVectors(); Console.WriteLine(@"11. Multiply A * V"); Console.WriteLine(av.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 12. Multiply V * D var vd = evd.EigenVectors() * evd.D(); Console.WriteLine(@"12. Multiply V * D"); Console.WriteLine(vd.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 13. Reconstruct non-symmetriv matrix A = V * D * Vinverse reconstruct = evd.EigenVectors() * evd.D() * evd.EigenVectors().Inverse(); Console.WriteLine(@"13. Reconstruct non-symmetriv matrix A = V * D * Vinverse"); Console.WriteLine(reconstruct.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 14. Determinant of the matrix Console.WriteLine(@"14. Determinant of the matrix"); Console.WriteLine(evd.Determinant); Console.WriteLine(); // 15. Rank of the matrix Console.WriteLine(@"15. Rank of the matrix"); Console.WriteLine(evd.Rank); Console.WriteLine(); }
/// <summary> /// Run example /// </summary> /// <seealso cref="http://en.wikipedia.org/wiki/Matrix_multiplication#Scalar_multiplication">Multiply matrix by scalar</seealso> /// <seealso cref="http://reference.wolfram.com/mathematica/tutorial/MultiplyingVectorsAndMatrices.html">Multiply matrix by vector</seealso> /// <seealso cref="http://en.wikipedia.org/wiki/Matrix_multiplication#Matrix_product">Multiply matrix by matrix</seealso> /// <seealso cref="http://en.wikipedia.org/wiki/Matrix_multiplication#Hadamard_product">Pointwise multiplies matrix with another matrix</seealso> /// <seealso cref="http://en.wikipedia.org/wiki/Matrix_%28mathematics%29#Basic_operations">Addition and subtraction</seealso> public void Run() { // Initialize IFormatProvider to print matrix/vector data var formatProvider = (CultureInfo)CultureInfo.InvariantCulture.Clone(); formatProvider.TextInfo.ListSeparator = " "; // Create matrix "A" var matrixA = new DenseMatrix(new[,] { { 1.0, 2.0, 3.0 }, { 4.0, 5.0, 6.0 }, { 7.0, 8.0, 9.0 } }); Console.WriteLine(@"Matrix A"); Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Create matrix "B" var matrixB = new DenseMatrix(new[,] { { 1.0, 3.0, 5.0 }, { 2.0, 4.0, 6.0 }, { 3.0, 5.0, 7.0 } }); Console.WriteLine(@"Matrix B"); Console.WriteLine(matrixB.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Multiply matrix by scalar // 1. Using operator "*" var resultM = 3.0 * matrixA; Console.WriteLine(@"Multiply matrix by scalar using operator *. (result = 3.0 * A)"); Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Using Multiply method and getting result into different matrix instance resultM = (DenseMatrix)matrixA.Multiply(3.0); Console.WriteLine(@"Multiply matrix by scalar using method Multiply. (result = A.Multiply(3.0))"); Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 3. Using Multiply method and updating matrix itself matrixA.Multiply(3.0, matrixA); Console.WriteLine(@"Multiply matrix by scalar using method Multiply. (A.Multiply(3.0, A))"); Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Multiply matrix by vector (right-multiply) var vector = new DenseVector(new[] { 1.0, 2.0, 3.0 }); Console.WriteLine(@"Vector"); Console.WriteLine(vector.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 1. Using operator "*" var resultV = matrixA * vector; Console.WriteLine(@"Multiply matrix by vector using operator *. (result = A * vec)"); Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Using Multiply method and getting result into different vector instance resultV = (DenseVector)matrixA.Multiply(vector); Console.WriteLine(@"Multiply matrix by vector using method Multiply. (result = A.Multiply(vec))"); Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 3. Using Multiply method and updating vector itself matrixA.Multiply(vector, vector); Console.WriteLine(@"Multiply matrix by vector using method Multiply. (A.Multiply(vec, vec))"); Console.WriteLine(vector.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Multiply vector by matrix (left-multiply) // 1. Using operator "*" resultV = vector * matrixA; Console.WriteLine(@"Multiply vector by matrix using operator *. (result = vec * A)"); Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Using LeftMultiply method and getting result into different vector instance resultV = (DenseVector)matrixA.LeftMultiply(vector); Console.WriteLine(@"Multiply vector by matrix using method LeftMultiply. (result = A.LeftMultiply(vec))"); Console.WriteLine(resultV.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 3. Using LeftMultiply method and updating vector itself matrixA.LeftMultiply(vector, vector); Console.WriteLine(@"Multiply vector by matrix using method LeftMultiply. (A.LeftMultiply(vec, vec))"); Console.WriteLine(vector.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Multiply matrix by matrix // 1. Using operator "*" resultM = matrixA * matrixB; Console.WriteLine(@"Multiply matrix by matrix using operator *. (result = A * B)"); Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Using Multiply method and getting result into different matrix instance resultM = (DenseMatrix)matrixA.Multiply(matrixB); Console.WriteLine(@"Multiply matrix by matrix using method Multiply. (result = A.Multiply(B))"); Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 3. Using Multiply method and updating matrix itself matrixA.Multiply(matrixB, matrixA); Console.WriteLine(@"Multiply matrix by matrix using method Multiply. (A.Multiply(B, A))"); Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Pointwise multiplies matrix with another matrix // 1. Using PointwiseMultiply method and getting result into different matrix instance resultM = (DenseMatrix)matrixA.PointwiseMultiply(matrixB); Console.WriteLine(@"Pointwise multiplies matrix with another matrix using method PointwiseMultiply. (result = A.PointwiseMultiply(B))"); Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Using PointwiseMultiply method and updating matrix itself matrixA.PointwiseMultiply(matrixB, matrixA); Console.WriteLine(@"Pointwise multiplies matrix with another matrix using method PointwiseMultiply. (A.PointwiseMultiply(B, A))"); Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Pointwise divide matrix with another matrix // 1. Using PointwiseDivide method and getting result into different matrix instance resultM = (DenseMatrix)matrixA.PointwiseDivide(matrixB); Console.WriteLine(@"Pointwise divide matrix with another matrix using method PointwiseDivide. (result = A.PointwiseDivide(B))"); Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Using PointwiseDivide method and updating matrix itself matrixA.PointwiseDivide(matrixB, matrixA); Console.WriteLine(@"Pointwise divide matrix with another matrix using method PointwiseDivide. (A.PointwiseDivide(B, A))"); Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Addition // 1. Using operator "+" resultM = matrixA + matrixB; Console.WriteLine(@"Add matrices using operator +. (result = A + B)"); Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Using Add method and getting result into different matrix instance resultM = (DenseMatrix)matrixA.Add(matrixB); Console.WriteLine(@"Add matrices using method Add. (result = A.Add(B))"); Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 3. Using Add method and updating matrix itself matrixA.Add(matrixB, matrixA); Console.WriteLine(@"Add matrices using method Add. (A.Add(B, A))"); Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Subtraction // 1. Using operator "-" resultM = matrixA - matrixB; Console.WriteLine(@"Subtract matrices using operator -. (result = A - B)"); Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Using Subtract method and getting result into different matrix instance resultM = (DenseMatrix)matrixA.Subtract(matrixB); Console.WriteLine(@"Subtract matrices using method Subtract. (result = A.Subtract(B))"); Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 3. Using Subtract method and updating matrix itself matrixA.Subtract(matrixB, matrixA); Console.WriteLine(@"Subtract matrices using method Subtract. (A.Subtract(B, A))"); Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // Divide by scalar // 1. Using Divide method and getting result into different matrix instance resultM = (DenseMatrix)matrixA.Divide(3.0); Console.WriteLine(@"Divide matrix by scalar using method Divide. (result = A.Divide(3.0))"); Console.WriteLine(resultM.ToString("#0.00\t", formatProvider)); Console.WriteLine(); // 2. Using Divide method and updating matrix itself matrixA.Divide(3.0, matrixA); Console.WriteLine(@"Divide matrix by scalar using method Divide. (A.Divide(3.0, A))"); Console.WriteLine(matrixA.ToString("#0.00\t", formatProvider)); Console.WriteLine(); }
/// <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(); }