| backsolve {base} | R Documentation |
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.
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 |
upper.tri |
logical; if |
transpose |
logical; if |
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.
Note that forwardsolve(L, b) is just a wrapper for
backsolve(L, b, upper.tri=FALSE).
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