Solve an Upper Triangular System
Usage
backsolve(r, x, k=ncol(r))
Arguments
r
|
an upper triangular matrix giving the coefficients for
the system to be solved. Values below the diagonal are ignored.
|
x
|
a matrix whose columns give ``right-hand sides'' for the equations.
|
k
|
The number or columns of r and rows of x to use.
|
Value
The solution of the triangular system. The result will be a
a vector if x
is a vector and a matrix if x
is a matrix.References
Dongarra, J. J., J. R. Bunch, C. B. Moler and G. W. Stewart (1978).
LINPACK Users Guide. Philadelphia: SIAM Publications.See Also
chol
,
qr
,
solve
.Examples
## 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)