| backsolve | R Documentation |
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)
r, l | an upper (or lower) triangular matrix giving thecoefficients for the system to be solved. Values below (above)the diagonal are ignored. |
x | a matrix whose columns give the right-hand sides forthe equations. |
k | The number of columns of |
upper.tri | logical; if |
transpose | logical; if |
Solves a system of linear equations where the coefficient matrix isupper (or ‘right’, ‘R’) or lower (‘left’,‘L’) triangular.
x <- backsolve (R, b) solvesR x = b, andx <- forwardsolve(L, b) solvesL x = b, respectively.
Ther/l must have at leastk rows and columns,andx must have at leastk rows.
This is a wrapper for the level-3 BLAS routinedtrsm.
The solution of the triangular system. The result will be a vector ifx is a vector and a matrix ifx is a matrix.
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.
chol,qr,solve.
## 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 1r %*% y # == x = (8,4,2)backsolve(r, x, transpose = TRUE) # 8 -12 -5
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