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.
TRUE (default), the upper
triangular part of
r is used. Otherwise, the lower one.
TRUE, solve \(r' * y = x\) for
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.
l must have at least
k rows and columns,
x must have at least
This is a wrapper for the level-3 BLAS routine
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.