backsolve: Solve an Upper or Lower Triangular System
In bdsmatrix: Routines for Block Diagonal Symmetric matrices

Description Usage Arguments Details Value Methods Note See Also

Solves a system of linear equations where the coefficient matrix is upper (or ‘right’, ‘R’) or lower (‘left’, ‘L’) triangular.

x <- backsolve(R, b) solves R x = b.

  backsolve(r, ...)
  ## S4 method for signature 'gchol'
backsolve(r, x, k=ncol(r), upper.tri=TRUE, ...)
  ## S4 method for signature 'gchol.bdsmatrix'
backsolve(r, x, k=ncol(r), upper.tri=TRUE, ...)

`r`	a matrix or matrix-like object
`x`	a vector or a matrix whose columns give the right-hand sides for the equations.
`k`	The number of columns of `r` and rows of `x` to use.
`upper.tri`	logical; if `TRUE` (default), the upper triangular part of `r` is used. Otherwise, the lower one.
`...`	further arguments passed to other methods

The generalized Cholesky decompostion of a symmetric matrix A is A= LD t(L) where D is diagonal, L is lower triangular, and t(L) is the transpose of L. These functions solve either L sqrt(D) x=b (when upper.tri=FALSE) or sqrt(D) t(L) x=b.

The solution of the triangular system. The result will be a vector if x is a vector and a matrix if x is a matrix.

Note that forwardsolve(L, b) is just a wrapper for backsolve(L, b, upper.tri=FALSE).

Use showMethods(backsolve) to see all the defined methods; the two created by the bdsmatrix library are described here:

bdsmatrix: signature=(r= "gchol") for a generalized cholesky decomposition
bdsmatrix: signature=(r= "gchol.bdsmatrix") for the generalize cholesky decomposition of a bdsmatrix object

The bdsmatrix package promotes the base R backsolve function to a generic. To see the full documentation for the default method, view backsolve from the base package.

forwardsolve, gchol

bdsmatrix documentation built on May 2, 2019, 4:45 p.m.