backsolve
Solve an Upper or Lower Triangular System
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
rand rows ofxto use.- upper.tri
logical; if
TRUE(default), the upper triangular part ofris used. Otherwise, the lower one.- transpose
logical; if
TRUE, solve \(r' * y = x\) for \(y\), i.e.,t(r) %*% y == x.
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
library(base)
# 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
# }