# Matrix v1.2-15

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## Sparse and Dense Matrix Classes and Methods

A rich hierarchy of matrix classes, including triangular, symmetric, and diagonal matrices, both dense and sparse and with pattern, logical and numeric entries. Numerous methods for and operations on these matrices, using 'LAPACK' and 'SuiteSparse' libraries.

## Functions in Matrix

 Name Description BunchKaufman-methods Bunch-Kaufman Decomposition Methods Cholesky-class Cholesky and Bunch-Kaufman Decompositions LU-class LU (dense) Matrix Decompositions Matrix-class Virtual Class "Matrix" Class of Matrices Matrix Construct a Classed Matrix MatrixClass The Matrix (Super-) Class of a Class Cholesky Cholesky Decomposition of a Sparse Matrix Diagonal Create Diagonal Matrix Object TsparseMatrix-class Class "TsparseMatrix" of Sparse Matrices in Triplet Form chol2inv-methods Inverse from Choleski or QR Decomposition -- Matrix Methods colSums Form Row and Column Sums and Means KNex Koenker-Ng Example Sparse Model Matrix and Response Vector CsparseMatrix-class Class "CsparseMatrix" of Sparse Matrices in Column-compressed Form USCounties USCounties Contiguity Matrix bdiag Construct a Block Diagonal Matrix KhatriRao Khatri-Rao Matrix Product MatrixFactorization-class Class "MatrixFactorization" of Matrix Factorizations all.equal-methods Matrix Package Methods for Function all.equal() Hilbert Generate a Hilbert matrix %&%-methods Boolean Arithmetic Matrix Products: %&% and Methods atomicVector-class Virtual Class "atomicVector" of Atomic Vectors RsparseMatrix-class Class "RsparseMatrix" of Sparse Matrices in Column-compressed Form diagU2N Transform Triangular Matrices from Unit Triangular to General Triangular and Back compMatrix-class Class "compMatrix" of Composite (Factorizable) Matrices condest Compute Approximate CONDition number and 1-Norm of (Large) Matrices diagonalMatrix-class Class "diagonalMatrix" of Diagonal Matrices dtCMatrix-class Triangular, (compressed) sparse column matrices dtRMatrix-class Triangular Sparse Compressed Row Matrices SparseM-conversions Sparse Matrix Coercion from and to those from package SparseM [-methods Methods for "[": Extraction or Subsetting in Package 'Matrix' abIndex-class Class "abIndex" of Abstract Index Vectors [<--methods Methods for "[<-" - Assigning to Subsets for 'Matrix' dpoMatrix-class Positive Semi-definite Dense (Packed | Non-packed) Numeric Matrices Schur-class Class "Schur" of Schur Matrix Factorizations dsparseMatrix-class Virtual Class "dsparseMatrix" of Numeric Sparse Matrices dsyMatrix-class Symmetric Dense (Packed | Non-packed) Numeric Matrices Schur Schur Decomposition of a Matrix dMatrix-class (Virtual) Class "dMatrix" of "double" Matrices ddenseMatrix-class Virtual Class "ddenseMatrix" of Numeric Dense Matrices band Extract bands of a matrix drop0 Drop "Explicit Zeroes" from a Sparse Matrix forceSymmetric Force a Matrix to 'symmetricMatrix' Without Symmetry Checks bandSparse Construct Sparse Banded Matrix from (Sup-/Super-) Diagonals formatSparseM Formatting Sparse Numeric Matrices Utilities abIseq Sequence Generation of "abIndex", Abstract Index Vectors all-methods "Matrix" Methods for Functions all() and any() image-methods Methods for image() in Package 'Matrix' indMatrix-class Index Matrices is.na-methods is.na(), is.infinite() Methods for 'Matrix' Objects is.null.DN Are the Dimnames dn NULL-like ? cBind Versions of 'cbind' and 'rbind' recursively built on cbind2/rbind2 chol Choleski Decomposition - 'Matrix' S4 Generic and Methods ddiMatrix-class Class "ddiMatrix" of Diagonal Numeric Matrices denseMatrix-class Virtual Class "denseMatrix" of All Dense Matrices dgTMatrix-class Sparse matrices in triplet form lsparseMatrix-classes Sparse logical matrices dgeMatrix-class Class "dgeMatrix" of Dense Numeric (S4 Class) Matrices dtpMatrix-class Packed Triangular Dense Matrices - "dtpMatrix" dtrMatrix-class Triangular, dense, numeric matrices lsyMatrix-class Symmetric Dense Logical Matrices dgCMatrix-class Compressed, sparse, column-oriented numeric matrices dgRMatrix-class Sparse Compressed, Row-oriented Numeric Matrices matrix-products Matrix (Cross) Products (of Transpose) nMatrix-class Class "nMatrix" of Non-zero Pattern Matrices generalMatrix-class Class "generalMatrix" of General Matrices sparseMatrix-class Virtual Class "sparseMatrix" --- Mother of Sparse Matrices sparseMatrix General Sparse Matrix Construction from Nonzero Entries graph-sparseMatrix Conversions "graph" <--> (sparse) Matrix symmpart Symmetric Part and Skew(symmetric) Part of a Matrix triangularMatrix-class Virtual Class of Triangular Matrices in Package Matrix ngeMatrix-class Class "ngeMatrix" of General Dense Nonzero-pattern Matrices dsCMatrix-class Numeric Symmetric Sparse (column compressed) Matrices dsRMatrix-class Symmetric Sparse Compressed Row Matrices nnzero The Number of Non-Zero Values of a Matrix expand Expand a Decomposition into Factors isSymmetric-methods Methods for Function isSymmetric in Package 'Matrix' isTriangular isTriangular() and isDiagonal() Methods number-class Class "number" of Possibly Complex Numbers rep2abI Replicate Vectors into 'abIndex' Result pMatrix-class Permutation matrices expm Matrix Exponential sparseQR-class Sparse QR decomposition of a sparse matrix replValue-class Virtual Class "replValue" - Simple Class for subassignment Values solve-methods Methods in Package Matrix for Function solve() uniqTsparse Unique (Sorted) TsparseMatrix Representations spMatrix Sparse Matrix Constructor From Triplet unpack Representation of Packed and Unpacked (Dense) Matrices sparseVector-class Sparse Vector Classes externalFormats Read and write external matrix formats norm Matrix Norms index-class Virtual Class "index" - Simple Class for Matrix Indices nsparseMatrix-classes Sparse "pattern" Matrices ldiMatrix-class Class "ldiMatrix" of Diagonal Logical Matrices invPerm Inverse Permutation Vector facmul Multiplication by Decomposition Factors rankMatrix Rank of a Matrix lgeMatrix-class Class "lgeMatrix" of General Dense Logical Matrices kronecker-methods Methods for Function 'kronecker()' in Package 'Matrix' rleDiff-class Class "rleDiff" of rle(diff(.)) Stored Vectors rcond Estimate the Reciprocal Condition Number ldenseMatrix-class Virtual Class "ldenseMatrix" of Dense Logical Matrices rsparsematrix Random Sparse Matrix ndenseMatrix-class Virtual Class "ndenseMatrix" of Dense Logical Matrices nearPD Nearest Positive Definite Matrix nsyMatrix-class Symmetric Dense Nonzero-Pattern Matrices ntrMatrix-class Triangular Dense Logical Matrices sparse.model.matrix Construct Sparse Design / Model Matrices sparseLU-class Sparse LU decomposition of a square sparse matrix ltrMatrix-class Triangular Dense Logical Matrices Unused-classes Virtual Classes Not Yet Really Implemented and Used lu (Generalized) Triangular Decomposition of a Matrix updown Up- and Down-Dating a Cholesky Decomposition printSpMatrix Format and Print Sparse Matrices Flexibly qr-methods QR Decomposition -- S4 Methods and Generic sparseVector Sparse Vector Construction from Nonzero Entries symmetricMatrix-class Virtual Class of Symmetric Matrices in Package Matrix CAex Albers' example Matrix with "Difficult" Eigen Factorization CHMfactor-class CHOLMOD-based Cholesky Factorizations No Results!