backsolve {base} | R Documentation |
Solves a system of linear equations where the coefficient matrix is upper or lower triangular.
backsolve(r, x, k= ncol(r), upper.tri = TRUE, transpose = FALSE) forwardsolve(l, x, k= ncol(l), upper.tri = FALSE, transpose = FALSE)
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.
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) ( y2 <- backsolve(r, x, transpose = TRUE)) # 8 -12 -5 all(t(r) %*% y2 == x)# exactly on Linux (Pentium) all(y == backsolve(t(r), x, upper = FALSE, transpose = TRUE)) all(y2 == backsolve(t(r), x, upper = FALSE, transpose = FALSE))