Solve an Upper or Lower Triangular System

Usage

   backsolve(r, x, k= ncol(r), upper.tri = TRUE, transpose = FALSE)
forwardsolve(l, x, k= ncol(l), upper.tri = FALSE, transpose = FALSE)

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)
( y2 <- backsolve(r, x, transpose = TRUE)) # 8 -12 -5
all(t(r) %*% y2 == x)# exactly on Linux (Pentium)
all(y  == backsolve(t(r), x, upper = FALSE, transpose = TRUE))
all(y2 == backsolve(t(r), x, upper = FALSE,  transpose = FALSE))

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