Solve an Upper or Lower Triangular System
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.
- a matrix whose columns give the right-hand sides for the equations.
- The number of columns of
rand rows of
- logical; if
TRUE(default), the upper triangular part of
ris used. Otherwise, the lower one.
- logical; if
TRUE, solve $r' * y = x$ for $y$, i.e.,
t(r) %*% y == x.
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.
l must have at least
k rows and columns,
x must have at least
This is a wrapper for the level-3 BLAS routine
The solution of the triangular system. The result will be a vector if
xis a vector and a matrix if
xis a matrix.
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.
## 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