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)
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 “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
triangular 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.
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