Eigen: Dense and Sparse Matrices

The source code for the C# tests in Visual Studio is divided in 4 parts:

Part 1 contains the source code for test procedures which work for real and complex dense matrices, and which work for floating point and ball arithmetic. It can be found online in the XlCalcNet repository or in the corresponding local XlCalcNet folder in the file B06a_MatAll.cs.

Part 2 contains the source code for test procedures which work for real and complex dense matrices, but which work only for floating point arithmetic. It can be found online in the XlCalcNet repository or in the corresponding local XlCalcNet folder in the file B06b_MatFp.cs.

Part 3 contains the source code for test procedures which work only for real dense matrices, and only for floating point arithmetic. It can be found online in the XlCalcNet repository or in the corresponding local XlCalcNet folder in the file B06c_MatFpReal.cs.

Part 4 contains the source code for test procedures which work only for real and complex sparse matrices, and only for floating point arithmetic. It can be found online in the XlCalcNet repository or in the corresponding local XlCalcNet folder in the file B06d_SpMat.cs.

Eigen: Dense and Sparse Matrices

• Creating scalars and matrices
  • Creating a matrix, and converting from compatible data types
    • ctx.mat_t()
  • Creating a matrix of zeros
    • ctx.mat_zeros()
  • Creating a matrix of ones
    • ctx.mat_ones()
  • Creating an identity matrix
    • ctx.mat_identity()
  • Creating a general random matrix
    • ctx.mat_random()
  • Creating a symmetric random matrix
    • ctx.mat_random_symmetric()
  • Creating a self-adjoint random matrix
    • ctx.mat_random_selfadjoint()
  • Creating a positive definite self-adjoint matrix
    • ctx.mat_random_selfadjoint_posdef()
  • Creating a matrix with linearly increasing values
    • ctx.mat_fill_linear()
• Read-only properties: information about a matrix
  • Rows of a matrix
    • ctx.mat_rows()
  • Columns of a matrix
    • ctx.mat_cols()
  • Size of a matrix
    • ctx.mat_size()
• Accessing and setting parts of a matrix
  • Getting and setting a matrix coefficient
  • Getting and setting a block
    • ctx.mat_get_block()
    • ctx.mat_set_block()
  • Getting and setting a matrix row
    • ctx.mat_get_row()
    • ctx.mat_set_row()
  • Getting and setting a matrix column
    • ctx.mat_get_col()
    • ctx.mat_set_col()
  • Getting and setting a diagonal
    • ctx.mat_get_diagonal()
    • ctx.mat_set_diagonal()
  • Getting and setting a triangular view
    • ctx.mat_get_triangular_view()
    • ctx.mat_set_triangular_view()
• Changing the shape of a matrix and/or the order of coefficients
  • Sorting a whole matrix
    • ctx.mat_sort()
  • Sorting the rows of a matrix by a given column
    • ctx.mat_sort_rows_by_col()
  • Resize a matrix
    • ctx.mat_resize()
  • Resize a matrix like another matrix
    • ctx.mat_resize_like()
  • Conservatively resize a matrix
    • ctx.mat_conservative_resize()
  • Convert vector to diagonal matrix
    • ctx.mat_as_diagonal()
  • Adjoint of a matrix
    • ctx.mat_adjoint()
  • Conjugate of a matrix
    • ctx.mat_conjugate()
  • Transpose of a matrix
    • ctx.mat_transpose()
  • Full Reverse of a matrix
    • ctx.mat_reverse_full()
  • Row-wise Reverse of a matrix
    • ctx.mat_reverse_row_wise()
  • Column-wise Reverse of a matrix
    • ctx.mat_reverse_col_wise()
  • Full Replication of a matrix
    • ctx.mat_replicate_full()
  • Row-wise Replication of a matrix
    • ctx.mat_replicate_row_wise()
  • Column-wise Replication of a matrix
    • ctx.mat_replicate_col_wise()
  • Horizontal concatenation of two matrices
    • ctx.mat_concat_horizontal()
  • Vertical concatenation of two matrices
    • ctx.mat_concat_vertical()
• 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”)
  • Arithmetic comparisons with a scalar or a matrix
    • ctx.mat_count()
• Descriptive Statistics
  • Partial Sum
    • ctx.mat_sum()
  • Partial Product
    • ctx.mat_prod()
  • Partial Arithmetic Mean
    • ctx.mat_mean()
  • Partial Minimal Coefficient
    • ctx.mat_min_coeff()
  • Partial Maximal Coefficient
    • ctx.mat_max_coeff()
  • Trace
    • ctx.mat_trace()
  • Partial Squared Norm
    • ctx.mat_squared_norm()
  • Partial Norm
    • ctx.mat_norm()
  • Partial Stable Norm
    • ctx.mat_stable_norm()
  • Covariance matrix
    • ctx.mat_covariance()
  • Correlation matrix
    • ctx.mat_correlation()
• Standard decompositions and linear solving
  • Cholesky Decomposition with Pivoting
    • ctx.mat_ldlt()
    • Example for a real symmetric matrix
    • Example for a hermitian matrix
  • LU Decomposition with partial Pivoting
    • ctx.mat_partial_piv_lu()
    • Example for a real general square matrix (Python)
    • Example for a complex matrix
  • LU Decomposition with full Pivoting
    • ctx.mat_full_piv_lu()
    • Example for a real matrix
    • Example for a complex matrix
  • Cholesky Decomposition without Pivoting
    • ctx.mat_llt()
    • Example for a real symmetric matrix
    • Example for a hermitian matrix
  • QR Decomposition without Pivoting
    • ctx.mat_householder_qr()
    • Example for a real general square matrix (Python)
    • Example for a complex matrix
  • QR Decomposition with column Pivoting
    • ctx.mat_col_piv_householder_qr()
    • Example for a real matrix
    • Example for a complex matrix
  • QR Decomposition with full Pivoting
    • ctx.mat_full_piv_householder_qr()
    • Example for a real matrix
    • Example for a complex matrix
  • Complete orthogonal decomposition (COD)
    • ctx.mat_cod_householder_qr()
    • Example for a real matrix
    • Example for a complex matrix
• Singular Value and Eigen (selfadjoint) decompositions
  • Singular Value Decomposition, only singular values
    • ctx.mat_jacobi_svd()
    • 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
    • ctx.mat_jacobi_svd_thin()
    • 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
    • ctx.mat_jacobi_svd_full()
    • Example for a complex matrix: the singular values, pseudoinverse and full singular vectors
  • Symmetric/Hermitian Eigensystem, only eigen values
    • ctx.mat_self_adjoint_eigen_values()
    • Example for a real symmetric matrix: only eigenvalues
    • Example for a hermitian matrix: only eigenvalues
  • Symmetric/Hermitian Eigensystem, eigenvalues and eigenvectors
    • ctx.mat_self_adjoint_eigen_system()
    • Example for a real symmetric matrix: eigenvalues and eigenvectors
    • Example for a hermitian matrix: eigenvalues and eigenvectors
  • Generalized Selfadjoint Eigensystem, only eigenvalues
    • ctx.mat_generalized_self_adjoint_eigen_values()
    • Example for a real symmetric matrix: eigenvalues only
    • Example for a hermitian matrix: eigenvalues only
  • Generalized Selfadjoint Eigensystem: eigenvalues and eigenvectors
    • ctx.mat_generalized_self_adjoint_eigen_system()
    • Example for a real symmetric matrix: eigenvalues and eigenvectors
    • Example for a hermitian matrix: eigenvalues and eigenvectors
  • Tridiagonalization
    • ctx.mat_tridiagonalization()
    • Example for a real matrix
    • Example for a complex matrix
• Eigen decompositions of general square matrices
  • Matrix balancing and eigenvalue/eigenvector computation
  • Hessenberg Decomposition
    • ctx.mat_hessenberg()
    • Example for a real matrix
    • Example for a complex matrix
  • Schur Decomposition
    • ctx.mat_schur()
    • Example for a real matrix
    • Example for a complex matrix
  • Eigensystem of a general square matrix: only eigenvalues
    • ctx.mat_eigen_values()
    • Example for a real matrix: only eigenvalues
    • Example for a complex matrix: only eigenvalues
  • Eigensystem of a general square matrix: eigenvalues and eigenvectors
    • ctx.mat_eigen_system()
    • Example for a real matrix: eigenvalues and eigenvectors
    • Example for a complex matrix: eigenvalues and eigenvectors
  • Real QZ Decomposition
    • ctx.mat_real_qz()
  • PseudoEigenSystem
    • ctx.mat_pseudo_eigen_system()
  • Real Generalized Nonsymmetric Eigenvalues
    • ctx.mat_gen_eigen_values()
  • Real Generalized Nonsymmetric Eigensystem
    • ctx.mat_gen_eigen_system()
• Eigen: Polynomials
  • Building a polynomial from its roots
    • ctx.roots_to_monic_poly()
  • Polynomial evaluation
    • ctx.poly_eval()
  • Polynomial roots
    • ctx.poly_roots()
• Eigen: Fast Fourier Transform
  • Forward transform
    • ctx.mat_fft_fwd()
  • Inverse transform
    • ctx.mat_fft_inv()
• Eigen and Numpy (Multiprecision): Functions of matrix argument
  • Matrix Exponential
    • ctx.mat_expm()
  • Matrix Sine
    • ctx.mat_sinm()
  • Matrix Cosine
    • ctx.mat_cosm()
  • Matrix Hyperbolic Sine
    • ctx.mat_sinhm()
  • Matrix Hyperbolic Cosine
    • ctx.mat_coshm()
  • Matrix Square Root
    • ctx.mat_sqrtm()
  • Matrix Logarithm
    • ctx.mat_logm()
  • Matrix power
    • ctx.mat_powm()