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, 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.

chol, qr, solve.

### 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 4.3.0 Index]