Solves a triangular system of linear equations.

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

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*
*tri*angular 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`

.

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.

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`

.

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.

# NOT RUN { ## 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 # }

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