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)
an upper (or lower) triangular matrix giving the coefficients for the system to be solved. Values below (above) the diagonal are ignored.
a matrix whose columns give the right-hand sides for the equations.
The number of columns of r
and rows of x
to use.
logical; if TRUE
(default), the upper
triangular part of r
is used. Otherwise, the lower one.
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.
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
.
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.
# 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 # }
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