R: Solve an Upper or Lower Triangular System

backsolve {base}

R Documentation

Solve an Upper or Lower Triangular System

Description

Solves a triangular system of linear equations.

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.

Details

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.

The r/l must have at least k rows and columns, and x must have at least k rows.

This is a wrapper for the level-3 BLAS routine dtrsm.

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.

References

⁠Becker RA, Chambers JM, Wilks AR (1988). The New S Language. Chapman and Hall/CRC, London.

⁠Dongarra J, Bunch J, Moler C, Stewart G (1979). LINPACK Users' Guide, series Other Titles in Applied Mathematics. Society for Industrial and Applied Mathematics. ISBN 9780898711721. doi:10.1137/1.9780898719604.

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 4.6.0 Index]