R: Basic Linear Algebra for Sparse Matrices

SparseM.ops {SparseM} | R Documentation

## Basic Linear Algebra for Sparse Matrices

### Description

Basic linear algebra operations for sparse matrices of class `matrix.csr`.

### Arguments

`x` | matrix of class `matrix.csr`.
`y` | matrix of class `matrix.csr` or a dense matrix or vector.
`value` | replacement values.
`i,j` | vectors of elements to extract or replace.
`nrow` | optional number of rows for the result.
`lag` | an integer indicating which lag to use.
`differences` | an integer indicating the order of the difference.

### Details

Linear algebra operations for matrices of class `matrix.csr` are designed to behave exactly as for regular matrices. In particular, matrix multiplication, kronecker product, addition, subtraction and various logical operations should work as with the conventional dense form of matrix storage, as does indexing, rbind, cbind, and diagonal assignment and extraction. The method diag may be used to extract the diagonal of a `matrix.csr` object, to create a sparse diagonal see `SparseM.ontology`.

The function `determinant` computes the (log) determinant, of the argument, returning a `"det"` object as the base function. This is preferred over using the function `det()` which is a simple wrapper for `determinant()`. Using `det()` in the following way is somewhat deprecated:
`det()` computes the determinant of the argument matrix. If the matrix is of class `matrix.csr` then it must be symmetric, or an error will be returned. If the matrix is of class `matrix.csr.chol` then the determinant of the Cholesky factor is returned, ie the product of the diagonal elements.

The function `norm` is used to check for symmetry by computing the maximum of the elements of the difference between the matrix and its transpose. Optionally, this sup norm can be replaced by the Hilbert-Schmidt norm, or the l1 norm.

### References

Koenker, R and Ng, P. (2002). SparseM: A Sparse Matrix Package for R,
http://www.econ.uiuc.edu/~roger/research

### See Also

`slm` for sparse linear model fitting. `SparseM.ontology` for coercion and other class relations involving the sparse matrix classes.

### Examples

    n1 <- 10
    n2 <- 10
    p <- 6
    y <- rnorm(n1)
    a <- rnorm(n1*p)
    a[abs(a) < 0.5] <- 0
    A <- matrix(a,n1,p)
    A.csr <- as.matrix.csr(A)
    b <- rnorm(n2*p)
    b[abs(b)<1.0] <- 0
    B <- matrix(b,n2,p)
    B.csr <- as.matrix.csr(B)

    # matrix transposition and multiplication
    A.csr%*%t(B.csr)

    # kronecker product - via kronecker() methods:
    A.csr %x% matrix(1:4,2,2)

[Package SparseM version 1.77 Index]