backsolve {base} | R Documentation |
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. |
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 |
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
.
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