EigenCore

C# wrapper for the Eigen library.

Dense

Vector Constructors

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 6

Basic Vectors

VectorXD 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);

Matrix Constructors

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

Basic Matrices

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 });

Matrix Operations

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 3

MatrixXD 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 2

MatrixXD 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

Matrix-Vector Operations

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 26

EigenSolvers

Computes 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

SVD

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

Least Squares

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 0.0421

Basic linear solving

MatrixXD 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 0.448

QR decomposition

MatrixXD 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 0.816

MatrixXD 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

LU Decomposition

// 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

Concatenate and Slice Matrices

// 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

Norms

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();

Reductions

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 rows

Count and Replace

A.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.

Sparse

Matrix Constructors

(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

Direct Solvers

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

Iterative Solvers

 (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

References

https://eigen.tuxfamily.org/dox/group__QuickRefPage.html
https://github.com/hughperkins/jeigen
https://github.com/dotnet/machinelearning

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README.md

README.md

EigenCore

Dense

Vector Constructors

Basic Vectors

Matrix Constructors

Basic Matrices

Matrix Operations

Matrix-Vector Operations

EigenSolvers

SVD

Least Squares

Basic linear solving

QR decomposition

LU Decomposition

Concatenate and Slice Matrices

Norms

Reductions

Count and Replace

Sparse

Matrix Constructors

Direct Solvers

Iterative Solvers

References

Files

README.md

Latest commit

History

README.md

File metadata and controls

EigenCore

Dense

Vector Constructors

Basic Vectors

Matrix Constructors

Basic Matrices

Matrix Operations

Matrix-Vector Operations

EigenSolvers

SVD

Least Squares

Basic linear solving

QR decomposition

LU Decomposition

Concatenate and Slice Matrices

Norms

Reductions

Count and Replace

Sparse

Matrix Constructors

Direct Solvers

Iterative Solvers

References