Solve an Upper or Lower Triangular System (original) (raw)
backsolve {base} | R Documentation |
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Description
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 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 _tri_angular part of r is used. Otherwise, the lower one. |
transpose | logical; if TRUE, solve r' * y = x fory, 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
, andx <- 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
.
Value
The solution of the triangular system. The result will be a vector ifx
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
[chol](../../base/help/chol.html)
,[qr](../../base/help/qr.html)
,[solve](../../base/help/solve.html)
.
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)
backsolve(r, x, transpose = TRUE) # 8 -12 -5
[Package _base_ version 4.6.0 Index]