Test for Triangularity in a Matrix
DESCRIPTION:
Either tests whether or not a Matrix is lower or upper triangular, or
else gives a metric by which such a test can be made.
.LB Matrix
USAGE:
is.LowerTriangular(x, tol)
is.UpperTriangular(x, tol)
LowerTriangular.test(x)
UpperTriangular.test(x)
REQUIRED ARGUMENTS:
- x
-
an numeric or complex matrix.
OPTIONAL ARGUMENTS:
- tol
-
tolerance for the maximum modulus of the elements in the upper or lower
triangle of the matrix.
VALUE:
For
is.LowerTriangular
and
is.UpperTriangular
, a logical value is returned.
If
tol
is missing, this value is equivalent to
inherits(x, "LowerTriangular")
or
inherits(x, "UpperTriangular")
.
Otherwise the result is
TRUE
if the maximum modulus for the elements in the
upper (repectively, lower) triangle is less than or equal to
tol
and
FALSE
otherwise.
For
LowerTriangular.test
and
UpperTriangular.test
, the maximum modulus for
the in the upper (respectively, lower) triangle is returned.
EXAMPLES:
x <- Matrix(1:9,3,3)
x[row(x) > col(x)] <- 0
is.UpperTriangular(x)
# [1] F
is.UpperTriangular(x, tol = 0)
# [1] T
UpperTriangular.test(x)
# [1] 0