backsolve {bdsmatrix} | R Documentation |
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
.
backsolve(r, ...)
## S4 method for signature 'gchol'
backsolve(r, x, k=ncol(r), upper.tri=TRUE, ...)
## S4 method for signature 'gchol.bdsmatrix'
backsolve(r, x, k=ncol(r), upper.tri=TRUE, ...)
r |
a matrix or matrix-like object |
x |
a vector or a matrix whose columns give the right-hand sides for the equations. |
k |
The number of columns of |
upper.tri |
logical; if |
... |
further arguments passed to other methods |
The generalized Cholesky decompostion of a symmetric matrix A is
A = LDL'
where D is diagonal, L is lower triangular,
and L'
is the transpose of L.
These functions solve either L\sqrt{D} x =b
(when upper.tri=FALSE
) or \sqrt{D}L' x=b
.
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.
Note that forwardsolve(L, b)
is just a wrapper for
backsolve(L, b, upper.tri=FALSE)
.
Use showMethods(backsolve)
to see all the defined methods;
the two created by the bdsmatrix library are described here:
signature=(r= "gchol")
for a generalized
cholesky decomposition
signature=(r= "gchol.bdsmatrix")
for the
generalize cholesky decomposition of a bdsmatrix object
The bdsmatrix
package promotes the base R backsolve
function to a
generic.
To see the full documentation for the default method, view backsolve
from the base
package.