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 lower triangular.

### 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 “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.

### 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 2.1.0 Index]