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 righthand sides for the equations.
 k
 The number of columns of
r
and rows ofx
to use.  upper.tri
 logical; if
TRUE
(default), the upper triangular part ofr
is 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 level3 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)
## 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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