backsolve {base}

R Documentation

Solve an Upper or Lower Triangular System

Description

Solves a system of linear equations where the coefficient matrix is upper or lower triangular.

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 “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 triangular part of r is used. Otherwise, the lower one.
transpose	logical; if TRUE, solve r' * y = x for y, i.e., t(r) %*% y == x.

Value

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.

References

Dongarra, J. J., Bunch,J. R., Moler, C. B. and Stewart, G. W. (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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