C# wrapper for the Eigen library.
VectorXD v = new VectorXD("1 2 5 6");
VectorXD v = new VectorXD( new double[] { 1, 2, 5, 6 });
Console.WriteLine(v.ToString());
VectorXD, 4:
1 2 5 6VectorXD zeros = VectorXD.Zeros(10);
VectorXD ones = VectorXD.Ones(10);
VectorXD ident = VectorXD.Identity(10);
VectorXD random = VectorXD.Random(10);
VectorXD linspace = VectorXD.Linespace(1, 10, 10);MatrixXD A = new MatrixXD("1 3 2; 0 2 1");
MatrixXD B = new MatrixXD(new double[][] { new double[] { 1, 3, 2 } , new double[] { 0, 2, 1 } });
MatrixXD C = new MatrixXD(new double[,] { { 1, 3, 2 }, { 0, 2, 1 } });
Console.WriteLine(A.ToString());
MatrixXD, 2 * 3:
1 3 2
0 2 1 MatrixXD zeros = MatrixXD.Zeros(2, 3);
MatrixXD ones = MatrixXD.Ones(2, 2);
MatrixXD ident = MatrixXD.Identity(3);
MatrixXD random = MatrixXD.Random(3,3);
MatrixXD diag = MatrixXD.Diag(new[] { 3.5, 2, 4.5 });MatrixXD A = new MatrixXD("4 3; 3 2");
MatrixXD B = new MatrixXD("2 2; 1 1");
var result = A.Plus(B);
Console.WriteLine(result.ToString());
MatrixXD, 2 * 2:
6 5
4 3MatrixXD A = new MatrixXD("1 2; 3 5");
MatrixXD B = new MatrixXD("1 2; 3 2");
MatrixXD result = A.Mult(B);
Console.WriteLine(result.ToString());
MatrixXD, 2 * 2:
7 18
6 16 MatrixXD A = new MatrixXD("1 2 4; 3 5 7");
MatrixXD B = A.Transpose();
Console.WriteLine(A.ToString());
MatrixXD, 2 * 3:
1 2 4
3 5 7
Console.WriteLine(B.ToString());
MatrixXD, 3 * 2:
1 3
2 5
4 7 // X = A * B^T
MatrixXD A = new MatrixXD("1 2 1; 2 5 2");
MatrixXD B = new MatrixXD("1 0 1; 1 1 0");
MatrixXD result = A.MultT(B);
Console.WriteLine(result.ToString());
MatrixXD, 2 * 2:
2 3
4 7 // X = A + A^T
MatrixXD A = new MatrixXD("2 2; 1 1");
MatrixXD result = A.PlusT();
Console.WriteLine(result.ToString());
MatrixXD, 2 * 2:
4 3
3 2MatrixXD A = new MatrixXD("1 2 1; 2 1 0 ; -1 1 2");
double result = A.Determinant();MatrixXD A = new MatrixXD("1 2 1; 2 1 0 ; -1 1 2");
MatrixXD result = A.Inverse();
Console.WriteLine(result.ToString());
MatrixXD, 3 * 3:
-0.667 1 0.333
1.33 -1 -0.667
-1 1 1 MatrixXD A = new MatrixXD("1 -2 ; 2 5 ; 4 -2");
VectorXD v = new VectorXD(new[] { 3.0, -7.0 });
VectorXD result = A.Mult(v);
Console.WriteLine(result.ToString());
VectorXD, 3:
17 -29 26Computes eigenvalues and eigenvectors of general matrices. EigenSolver
MatrixXD A = new MatrixXD("0 1; -2 -3");
EigenSolverResult result = A.Eigen();
VectorXD eigenvalues = result.Eigenvalues.Real();
MatrixXD eigenvectors = result.Eigenvectors.Real();
Console.WriteLine(eigenvalues.ToString());
VectorXD, 2:
-1 -2
Console.WriteLine(eigenvectors.ToString());
MatrixXD, 2 * 2:
0.707 -0.447
-0.707 0.894
Computes eigenvalues and eigenvectors of selfadjoint matrices. SelfAdjointEigenSolver
MatrixXD A = new MatrixXD("2 1; 1 2");
SAEigenSolverResult result = A.SymmetricEigen();
VectorXD eigenvalues = result.Eigenvalues;
MatrixXD eigenvectors = result.Eigenvectors;
Console.WriteLine(eigenvalues.ToString());
VectorXD, 2:
1 3
Console.WriteLine(eigenvectors.ToString());
MatrixXD, 2 * 2:
-0.707 0.707
0.707 0.707
MatrixXD A = new MatrixXD("3 2 2 ; 2 3 -2");
SVDResult result = A.SVD(); // default Jacobi.
SVDResult result = A.SVD(SVDType.BdcSvd);
Console.WriteLine(result.U.ToString());
MatrixXD, 2 * 2:
-0.707 0.707
-0.707 -0.707
Console.WriteLine(result.S.ToString());
VectorXD, 2:
5 3
Console.WriteLine(result.V.ToString());
MatrixXD, 3 * 2:
-0.707 0.236
-0.707 -0.236
-2.22E-16 0.943 MatrixXD A = new MatrixXD("-1 -0.0827; -0.737 0.0655; 0.511 -0.562 ");
VectorXD rhs = new VectorXD("-0.906 0.358 0.359");
// A^TAx = A^b
VectorXD result = A.LeastSquaresNE(rhs);
VectorXD result = A.LeastSquaresSVD(rhs); // default Jacobi.
VectorXD result = A.LeastSquaresSVD(rhs, SVDType.BdcSvd);
Console.WriteLine(result.ToString());
VectorXD, 2:
0.463 0.0421MatrixXD A = new MatrixXD("1 2 3; 4 5 6; 7 8 10");
VectorXD rhs = new VectorXD("3 3 4");
VectorXD result = A.Solve(rhs) // default DenseSolverType.ColPivHouseholderQR;
Console.WriteLine(result.ToString());
VectorXD, 3:
-2 1 1
MatrixXD A = new MatrixXD("6 4 0;4 4 1;0 1 8");
VectorXD rhs = new VectorXD("3 3 4");
VectorXD result = A.Solve(rhs, DenseSolverType.LLT);
Console.WriteLine(result.ToString());
VectorXD, 3:
0.224 0.414 0.448MatrixXD A = new MatrixXD("1 -2 4; 1 -1 1;1 0 0");
QRResult result = A.QR(); // default QRType.HouseholderQR
Console.WriteLine(result.Q.ToString());
MatrixXD, 3 * 3:
-0.577 0.707 0.408
-0.577 0 -0.816
-0.577 -0.707 0.408
Console.WriteLine(result.R.ToString());
MatrixXD, 3 * 3:
-1.73 1.73 -2.89
0 -1.41 2.83
0 0 0.816MatrixXD A = new MatrixXD("1 -2 4; 1 -1 1;1 0 0");
QRResult result = A.QR(QRType.ColPivHouseholderQR);
//Note: AP = QR
Console.WriteLine(result.Q.ToString());
MatrixXD, 3 * 3:
-0.97 0.143 0.196
-0.243 -0.571 -0.784
0 -0.809 0.588
Console.WriteLine(result.R.ToString());
MatrixXD, 3 * 3:
-4.12 -1.21 2.18
0 -1.24 0.285
0 0 0.392
Console.WriteLine(result.P.ToString());
MatrixXD, 3 * 3:
0 1 0
0 0 1
1 0 0 // FullPivLU
MatrixXD A = new MatrixXD("-1 -0.562 -0.233;-0.737 -0.906 0.0388; 0.511 0.358 0.662; -0.0827 0.359 -0.931; 0.0655 0.869 -0.893");
FullPivLUResult result = A.FullPivLU();
Console.WriteLine(result.L.ToString());
MatrixXD, 5 * 5:
1 0 0 0 0
0.0827 1 0 0 0
-0.0655 0.996 1 0 0
0.737 -0.231 -0.93 1 0
-0.511 -0.596 0.729 0 1
Console.WriteLine(result.U.ToString());
MatrixXD, 5 * 3:
-1 -0.233 -0.562
0 -0.912 0.405
0 0 0.428
0 0 0
0 0 0
Console.WriteLine(result.P.ToString());
MatrixXD, 5 * 5:
1 0 0 0 0
0 0 0 1 0
0 0 0 0 1
0 1 0 0 0
0 0 1 0 0
Console.WriteLine(result.Q.ToString());
MatrixXD, 3 * 3:
1 0 0
0 0 1
0 1 0 // Provide indices to extract.
MatrixXD A = new MatrixXD("1 2 3; 4 5 5; 7 8 2");
MatrixXD result = A.Slice(new[] { 1, 2 }, new[] { 0, 1 });
Console.WriteLine(result.ToString());
MatrixXD, 2 * 2:
4 5
7 8
// Provide start and end indices.
MatrixXD A = new MatrixXD("1 2 3; 4 5 6; 7 8 2");
MatrixXD result = A.Slice(0, 1, 1, 2);
MatrixXD, 2 * 2:
2 3
5 6
// Concatenate Horizontal.
MatrixXD A = new MatrixXD("1 2; 4 5");
MatrixXD B = MatrixXD.Diag("1 0; 0 2");
MatrixXD result = A.Concat(B, ConcatType.Horizontal);
Console.WriteLine(result.ToString());
MatrixXD, 2 * 4:
1 2 1 0
4 5 0 2
// Concatenate vertical.
MatrixXD A = new MatrixXD("1 2; 4 5");
MatrixXD B = MatrixXD.Diag("1 0; 0 2");
MatrixXD result = A.Concat(B, ConcatType.Vertical);
Console.WriteLine(result.ToString());
MatrixXD, 4 * 2:
1 2
4 5
1 0
0 2 VectorXD v = new VectorXD("2 2 1");
v.Norm();
v.SquaredNorm();
v.Lp1Norm();
v.LpInfoNorm();
MatrixXD A = new MatrixXD("2 2 1; 1 2 -3; 1 0 1");
A.Norm();
A.SquaredNorm();
A.Lp1Norm();
A.LpInfNorm();A.Min() // Min of all elements
A.Max() // Max of all elements
A.Sum()) // Sum of all elements
A.Prod() // Product of all elements
A.Mean() // Mean of all elements.
A.Trace(); // Trace of the matrix.
VectorXD result = A.ColwiseMin(); // Min over columns
VectorXD result = A.RowwiseMin(); // Min over rows
VectorXD result = A.ColwiseMax(); // Max over columns
VectorXD result = A.RowwiseMax(); // Max over rows
VectorXD result = A.ColwiseSum(); // Sum over columns
VectorXD result = A.RowwiseSum(); // Sum over rows
VectorXD result = A.ColwiseProd(); // Product over columns
VectorXD result = A.RowwiseProd(); // Product over rows
VectorXD result = A.ColwiseMean(); // Mean over columns
VectorXD result = A.RowwiseMean(); // Mean over rowsA.Count(x => double.IsNaN(x))); // count NaN values.
A.Count(x => double.IsInfinity(x))); // count infinity values.
A.Replace(x => double.IsNaN(x) ? 0.0 : x); // replace NaN values with 0.0.
A.Replace(x => double.IsInfinity(x) ? 0.0 : x); // replace infinity values with 0.0. (int, int, double)[] elements = {
(0, 1, 3.0),
(1, 0, 22),
(2, 0, 7),
(2, 1, 5),
(4, 2, 14),
(2, 3, 1),
(1, 4, 17),
(4, 4, 8)
};
// Compressed sparse column (CSC) format.
SparseMatrixD A = new SparseMatrixD(elements, 5, 5);
Console.WriteLine(A.ToString());
SparseMatrixD, 5 * 5:
0 3 0 0 0
22 0 0 0 17
7 5 0 1 0
0 0 0 0 0
0 0 14 0 8
SparseMatrixD A = new MatrixXD("6 4 0;4 4 1;0 1 8").ToSparse();
VectorXD rhs = new VectorXD("3 3 4");
VectorXD result = A.DirectSolve(rhs, DirectSolverType.SimplicialLLT);
VectorXD result = A.DirectSolve(rhs, DirectSolverType.SimplicialLDLT);
VectorXD result = A.DirectSolve(rhs, DirectSolverType.SparseLU);
VectorXD result = A.DirectSolve(rhs, DirectSolverType.SparseQR);
Console.WriteLine(result.ToString());
VectorXD, 3:
0.224 0.414 0.448 (int, int, double)[] elements = {
(0, 0, 6),
(0, 1, 4),
(0, 2, 0),
(1, 0, 4),
(1 ,1, 4),
(1, 2, 1),
(2, 0, 0),
(2, 1, 1),
(2, 2, 8)
};
SparseMatrixD A = new SparseMatrixD(elements, 3, 3);
VectorXD rhs = new VectorXD("3 3 4");
VectorXD result = A.IterativeSolve(rhs); // Default IterativeSolverType.ConjugateGradient
VectorXD result = A.IterativeSolve(rhs, new IterativeSolverInfo(IterativeSolverType.BiCGSTAB));
VectorXD result = A.IterativeSolve(rhs, new IterativeSolverInfo(IterativeSolverType.GMRES));
VectorXD result = A.IterativeSolve(rhs, new IterativeSolverInfo(IterativeSolverType.MINRES));
VectorXD result = A.IterativeSolve(rhs, new IterativeSolverInfo(IterativeSolverType.DGMRES))
VectorXD result = A.IterativeSolve(rhs, new IterativeSolverInfo(IterativeSolverType.LeastSquaresConjugateGradient));
i.e:
{EigenCore.Core.Sparse.LinearAlgebra.IterativeSolverResult}
Error: 2.1912858061200212E-16
Interations: 2
Result: {VectorXD, 3: 0.224 0.414 0.448}
Solver: ConjugateGradient
Success: true