R: Solve an Upper or Lower Triangular System

backsolve {base}

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, and
x <- forwardsolve(L, b) solves L x = b, respectively.

Usage

   backsolve(r, x, k=ncol(r), upper.tri=TRUE, transpose=FALSE)
forwardsolve(l, x, k=ncol(l), upper.tri=FALSE, transpose=FALSE)

Arguments

`r,l`	an upper (or lower) triangular matrix giving the coefficients for the system to be solved. Values below (above) the diagonal are ignored.
`x`	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.
`transpose`	logical; if `TRUE`, solve r' y = x* for y, i.e., `t(r) %*% y == x`.

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).

References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

Dongarra, J. J., Bunch,J. R., Moler, C. B. and Stewart, G. W. (1978) LINPACK Users Guide. Philadelphia: SIAM Publications.

Examples

## upper triangular matrix 'r':
r <- rbind(c(1,2,3),
           c(0,1,1),
           c(0,0,2))
( y <- backsolve(r, x <- c(8,4,2)) ) # -1 3 1
r %*% y # == x = (8,4,2)
backsolve(r, x, transpose = TRUE) # 8 -12 -5

[Package base version 2.15.1 Index]