Solves a system of linear equations when the matrix representing the
system is upper triangular.
USAGE:
backsolve(r, x, k = ncol(r))
REQUIRED ARGUMENTS:
r:
square, upper triangular matrix. Missing values are not accepted.
x:
vector or matrix containing the right-hand sides to equations.
The length (or number of rows if a matrix) must be the same as the number of
rows of r (even if k is smaller than ncol(*)). Missing values are not accepted.
OPTIONAL ARGUMENTS:
k:
number of columns of r to use in solving the system.
The first k columns are used.
VALUE:
vector or matrix like x of the solutions y to the equations r %*% y == x.
If k is smaller than the number of rows in r, then only the first k
values are meaningful (the first k values in each column if x is a matrix).
DETAILS:
The lower triangle of r is not looked at (in particular, it
does not need to be zero, but missing values are not allowed there).
NOTE:
Suitable r matrices can be obtained from chol and qr.