backsolve {bdsmatrix} R Documentation

## Solve an Upper or Lower Triangular System

### Description

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.

### Usage

  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, ...)


### Arguments

 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

### Details

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

### Value

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).

### Methods

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

### Note

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