dsCMatrix-class function

Numeric Symmetric Sparse (column compressed) Matrices

The dsCMatrix class is a class of symmetric, sparse numeric matrices in the compressed, c olumn-oriented format. In this implementation the non-zero elements in the columns are sorted into increasing row order.

The dsTMatrix class is the class of symmetric, sparse numeric matrices in t riplet format.

class

Objects from the Class

Objects can be created by calls of the form new("dsCMatrix", ...) or new("dsTMatrix", ...), or automatically via e.g., as(*, "symmetricMatrix"), or (for dsCMatrix) also from Matrix(.).

Creation from scratch most efficiently happens via sparseMatrix(*, symmetric=TRUE).

Slots

• uplo:: A character object indicating if the upper triangle ("U") or the lower triangle ("L") is stored.
• i:: Object of class "integer" of length nnZ (half number of non-zero elements). These are the row numbers for each non-zero element in the lower triangle of the matrix.
• p:: (only in class "dsCMatrix":) an integer vector for providing pointers, one for each column, see the detailed description in CsparseMatrix.
• j:: (only in class "dsTMatrix":) Object of class "integer" of length nnZ (as i). These are the column numbers for each non-zero element in the lower triangle of the matrix.
• x:: Object of class "numeric" of length nnZ -- the non-zero elements of the matrix (to be duplicated for full matrix).
• factors:: Object of class "list" - a list of factorizations of the matrix.
• Dim:: Object of class "integer" - the dimensions of the matrix - must be an integer vector with exactly two non-negative values.

Extends

Both classes extend classes and symmetricMatrix

dsparseMatrix directly; dsCMatrix further directly extends CsparseMatrix, where dsTMatrix does TsparseMatrix.

Methods

• solve: signature(a = "dsCMatrix", b = "...."): x <- solve(a,b) solves $A x = b$ for $x$; see solve-methods.

• chol: signature(x = "dsCMatrix", pivot = "logical"): Returns (and stores) the Cholesky decomposition of x, see chol.

• Cholesky: signature(A = "dsCMatrix",...): Computes more flexibly Cholesky decompositions, see Cholesky.

• determinant: signature(x = "dsCMatrix", logarithm = "missing"): Evaluate the determinant of x on the logarithm scale. This creates and stores the Cholesky factorization.

• determinant: signature(x = "dsCMatrix", logarithm = "logical"): Evaluate the determinant of x on the logarithm scale or not, according to the logarithm

   argument. This creates and stores the Cholesky factorization.
  

• t: signature(x = "dsCMatrix"): Transpose. As for all symmetric matrices, a matrix for which the upper triangle is stored produces a matrix for which the lower triangle is stored and vice versa, i.e., the uplo slot is swapped, and the row and column indices are interchanged.

• t: signature(x = "dsTMatrix"): Transpose. The uplo slot is swapped from "U" to "L" or vice versa, as for a "dsCMatrix", see above.

See Also

Classes dgCMatrix, dgTMatrix, dgeMatrix and those mentioned above.

Examples

mm <- Matrix(toeplitz(c(10, 0, 1, 0, 3)), sparse = TRUE)
mm # automatically dsCMatrix
str(mm)
mT <- as(as(mm, "generalMatrix"), "TsparseMatrix")

## Either
(symM <- as(mT, "symmetricMatrix")) # dsT
(symC <- as(symM, "CsparseMatrix")) # dsC
## or
sT <- Matrix(mT, sparse=TRUE, forceCheck=TRUE) # dsT

sym2 <- as(symC, "TsparseMatrix")
## --> the same as 'symM', a "dsTMatrix"