Eigen: Dense and Sparse Matrices

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Eigen: Dense and Sparse Matrices

• Creating scalars and matrices
  • Creating a matrix, and converting from compatible data types
    • CtxEigen.MatT()
  • Creating a matrix of zeros
    • CtxEigen.MatZeros()
  • Creating a matrix of ones
    • CtxEigen.MatOnes()
  • Creating an identity matrix
    • CtxEigen.MatIdentity()
  • Creating a matrix with linearly increasing values
    • CtxEigen.MatLinspace()
  • Creating a general random matrix
    • CtxEigen.MatRandom()
  • Creating a symmetric random matrix
    • CtxEigen.MatRandomSymmetric()
  • Creating a self-adjoint random matrix
    • CtxEigen.MatRandomHermitian()
  • Creating a positive definite self-adjoint matrix
    • CtxEigen.MatRandomPosDefinite()
• Read-only properties: information about a matrix
  • Rows of a matrix
    • mat.Rows()
  • Columns of a matrix
    • mat.Cols()
  • Size of a matrix
    • mat.Size()
• Accessing and setting parts of a matrix
  • Getting and setting a matrix coefficient
  • Getting and setting a matrix row
    • mat.GetRow()
    • mat.SetRow()
  • Getting and setting a matrix column
    • mat.GetCol()
    • mat.SetCol()
  • Getting and setting a block
    • mat.GetBlock()
    • mat.SetBlock()
  • Getting and setting a block in the top left corner
    • mat.GetTopLeftCorner()
    • mat.SetTopLeftCorner()
  • Getting and setting a block in the bottom left corner
    • mat.GetBottomLeftCorner()
    • mat.SetBottomLeftCorner()
  • Getting and setting a block in the top right corner
    • mat.GetTopRightCorner()
    • mat.SetTopRightCorner()
  • Getting and setting a block in the bottom right corner
    • mat.GetBottomRightCorner()
    • mat.SetBottomRightCorner()
  • Getting and setting a block containing the first q rows
    • mat.GetTopRows()
    • mat.SetTopRows()
  • Getting and setting a block containing the last q rows
    • mat.GetBottomRows()
    • mat.SetBottomRows()
  • Getting and setting a block containing the first p columns
    • mat.GetLeftCols()
    • mat.SetLeftCols()
  • Getting and setting a block containing the last q columns
    • mat.GetRightCols()
    • mat.SetRightCols()
  • Getting and setting a diagonal
    • mat.GetDiagonal()
    • mat.SetDiagonal()
  • Getting and setting middle rows
    • mat.GetMiddleRows()
    • mat.SetMiddleRows()
  • Getting and setting middle columns
    • mat.GetMiddleCols()
    • mat.SetMiddleCols()
  • Getting and setting the lower triangle
    • mat.GetLowerTriangle()
    • mat.SetLowerTriangle()
  • Getting and setting the upper triangle
    • mat.GetUpperTriangle()
    • mat.SetUpperTriangle()
  • Getting and setting the strictly lower triangle
    • mat.GetStrictlyLowerTriangle()
    • mat.SetStrictlyLowerTriangle()
  • Getting and setting the strictly upper triangle
    • mat.GetStrictlyUpperTriangle()
    • mat.SetStrictlyUpperTriangle()
  • Getting and setting the unit lower triangle
    • mat.GetUnitLowerTriangle()
    • mat.SetUnitLowerTriangle()
  • Getting and setting the unit upper triangle
    • mat.GetUnitUpperTriangle()
    • mat.SetUnitUpperTriangle()
• Changing the shape of a matrix and/or the order of coefficients
  • Sorting a whole matrix
    • mat.Sorted()
  • Sorting the rows of a matrix by a given column
    • mat.SortedRowsByCol()
  • Sorting a whole matrix in place
    • mat.SortInplace()
  • Sorting the rows of a matrix by a given column, in place
    • mat.SortRowsByCol()
  • Resize a matrix
    • mat.Resize()
  • Conservatively resize a matrix
    • mat.ConservativeResize()
  • Convert vector to diagonal matrix
    • mat.AsDiagonal()
  • Adjoint of a matrix
    • mat.Adjoint()
  • Conjugate of a matrix
    • mat.Conjugate()
  • Transpose of a matrix
    • mat.Transpose()
  • Full Reverse of a matrix
    • mat.ReverseFull()
  • Row-wise Reverse of a matrix
    • mat.ReverseRowwise()
  • Column-wise Reverse of a matrix
    • mat.ReverseColwise()
  • Full Replication of a matrix
    • mat.ReplicateFull()
  • Row-wise Replication of a matrix
    • mat.ReplicateRowwise()
  • Column-wise Replication of a matrix
    • mat.ReplicateColwise()
  • Horizontal concatenation of two matrices
    • mat.ConcatHorizontal()
  • Vertical concatenation of two matrices
    • mat.ConcatVertical()
• Basic arithmetic operations
  • Matrix deep copy (unary plus)
  • Matrix negation (unary minus)
  • General matrix addition
  • Matrix addition of a vector as diagonal matrix
  • Matrix: addition of a scalar
  • General matrix subtraction
  • Matrix: subtraction of a scalar
  • General matrix multiplication (“gemm”)
  • Rank-k update (“syrk”, “herk”)
    • mat.RankKUpdate()
  • Rank-2k update (“syr2k”, “her2k”)
    • mat.Rank2KUpdate()
  • Quadratic forms (statistics), and related expressions
    • mat.QuadraticForm()
  • Matrix Multiplication with a selfadjoint matrix (“symm”, “hemm”)
  • Matrix Multiplication with a triangular matrix (“trmm”)
  • Matrix multiplication with a vector as diagonal matrix
  • Matrix coefficient-wise multiplication (array multiplication)
  • Matrix Multiplication with scalar
  • Matrix multiplication with the inverse of a general invertible matrix (“matrix division”)
  • Matrix multiplication with the inverse of a self-adjoint matrix (“ldlt solve”)
  • Matrix multiplication with the inverse of a triangular matrix (“trsm”)
  • Matrix coefficient-wise division (array division)
  • Matrix division by scalar
  • Arithmetic comparisons with a scalar or a matrix
    • mat.count()
• Descriptive Statistics
  • Partial Sum
    • mat.PartialSum()
  • Partial Product
    • mat.PartialProd()
  • Partial Arithmetic Mean
    • mat.PartialMean()
  • Partial Minimal Coefficient
    • mat.PartialMinCoeff()
  • Partial Maximal Coefficient
    • mat.PartialMaxCoeff()
  • Trace
    • mat.Trace()
  • Partial Squared Norm
    • mat.PartialSquaredNorm()
  • Partial Norm
    • mat.PartialNorm()
  • Partial Stable Norm
    • mat.PartialStableNorm()
  • Covariance matrix
    • mat.Covariance()
  • Correlation matrix
    • mat.Correlation_mat()
• Standard decompositions and linear solving
  • Cholesky Decomposition with Pivoting
    • mat.CholeskyLDLT()
    • Example for a real symmetric matrix
    • Example for a hermitian matrix
  • LU Decomposition with partial Pivoting
    • mat.PartialPivLU()
    • Example for a real general square matrix (Python)
    • Example for a complex matrix
  • LU Decomposition with full Pivoting
    • mat.FullPivLU()
    • Example for a real matrix
    • Example for a complex matrix
  • Cholesky Decomposition without Pivoting
    • mat.CholeskyLLT()
    • Example for a real symmetric matrix
    • Example for a hermitian matrix
  • QR Decomposition without Pivoting
    • mat.HouseholderQR()
    • Example for a real general square matrix (Python)
    • Example for a complex matrix
  • QR Decomposition with column Pivoting
    • mat.ColPivHouseholderQR()
    • Example for a real matrix
    • Example for a complex matrix
  • QR Decomposition with full Pivoting
    • mat.FullPivHouseholderQR()
    • Example for a real matrix
    • Example for a complex matrix
  • Complete orthogonal decomposition (COD)
    • mat.CODHouseholderQR()
    • Example for a real matrix
    • Example for a complex matrix
• Singular Value and Eigen (selfadjoint) decompositions
  • Singular Value Decomposition, only singular values
    • mat.JacobiSVD()
    • Example for a real matrix: only singular values
    • Example for a complex matrix: only singular values
  • Singular Value Decomposition, singular values and thin singular vectors
    • mat.JacobiThinSVD()
    • Example for a real matrix: the singular values, pseudoinverse and thin singular vectors
    • Example for a complex matrix: the singular values, pseudoinverse and thin singular vectors
  • Singular Value Decomposition, singular values and full singular vectors
    • mat.JacobiFullSVD()
    • Example for a complex matrix: the singular values, pseudoinverse and full singular vectors
  • Symmetric/Hermitian Eigensystem, only eigen values
    • mat.SelfAdjointEigenValues()
    • Example for a real symmetric matrix: only eigenvalues
    • Example for a hermitian matrix: only eigenvalues
  • Symmetric/Hermitian Eigensystem, eigenvalues and eigenvectors
    • mat.SelfAdjointEigenSystem()
    • Example for a real symmetric matrix: eigenvalues and eigenvectors
    • Example for a hermitian matrix: eigenvalues and eigenvectors
  • Generalized Selfadjoint Eigensystem, only eigenvalues
    • mat.GeneralizedSelfAdjointEigenValues()
    • Example for a real symmetric matrix: eigenvalues only
    • Example for a hermitian matrix: eigenvalues only
  • Generalized Selfadjoint Eigensystem: eigenvalues and eigenvectors
    • mat.GeneralizedSelfAdjointEigenSystem()
    • Example for a real symmetric matrix: eigenvalues and eigenvectors
    • Example for a hermitian matrix: eigenvalues and eigenvectors
  • Tridiagonalization
    • mat.Tridiagonalization()
    • Example for a real matrix
    • Example for a complex matrix
  • Square root of a selfadjoint matrix
    • mat.MatrixSquareRootSA()
    • Example for a real matrix
    • Example for a complex matrix
• Eigen decompositions of general square matrices
  • Matrix balancing and eigenvalue/eigenvector computation
  • Hessenberg Decomposition
    • mat.Hessenberg()
    • Example for a real matrix
    • Example for a complex matrix
  • Schur Decomposition
    • mat.Schur()
    • Example for a real matrix
    • Example for a complex matrix
  • Eigensystem of a general square matrix: only eigenvalues
    • mat.Eigenvalues()
    • Example for a real matrix: only eigenvalues
    • Example for a complex matrix: only eigenvalues
  • Eigensystem of a general square matrix: eigenvalues and eigenvectors
    • mat.Eigensystem()
    • Example for a real matrix: eigenvalues and eigenvectors
    • Example for a complex matrix: eigenvalues and eigenvectors
  • Real QZ Decomposition
    • mat.RealQZ()
  • PseudoEigenSystem
    • mat.PseudoEigenValues()
  • Real Generalized Nonsymmetric Eigenvalues
    • mat.GenEigenValues()
  • Real Generalized Nonsymmetric Eigensystem
    • mat.GenEigenSystem()
• Eigen: Functions of matrix argument
  • Matrix Exponential
    • matA.Expm()
  • Matrix Sine
    • matA.Sinm()
  • Matrix Cosine
    • matA.Cosm()
  • Matrix Hyperbolic Sine
    • matA.Sinhm()
  • Matrix Hyperbolic Cosine
    • matA.Coshm()
  • Matrix Square Root
    • matA.Sqrtm()
  • Matrix Logarithm
    • matA.Logm()
  • Matrix power
    • mat.Powm()
• Eigen: Fast Fourier Transform
  • FFT FORWARD(X)
    • matA.FFTFwd()
  • FFT BACKWARD(X)
    • matA.FFTInv()