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 |

`upper.tri` |
logical; if |

`transpose` |
logical; if |

### 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.

### See Also

### 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
```

*base*version 4.4.0 Index]