Matrix Norm for Triangular Matrices.
DESCRIPTION:
Computes either the one or infinity norm, the Frobenius norm, or the maximum modulus among elements of a triangular matrix.
USAGE: 
norm.LowerTriangular(x, type = "M")
norm.UpperTriangular(x, type = "M")
norm.UnitLowerTriangular(x, type = "M")
norm.UnitUpperTriangular(x, type = "M")
REQUIRED ARGUMENTS:
x:
A triangular Matrix, that is, a Matrix inheriting from class "Matrix" and one of "LowerTriangular", "UpperTriangular", "UnitLowerTriangular", or "UnitUpperTriangular".
OPTIONAL ARGUMENTS:
type:
A character indication the type of norm desired. "1" indicates the one norm, (maximum absolute column sum), "I" indicates the infinity norm (maximum absolute row sum), "F" indicates the Frobenius norm (the Euclidean norm of x treated as if it were a vector), and "M" indicates the maximum modulus of all the elements in x. The default is "M".
VALUE:
A numeric value of class "norm", representing the quantity chosen according to type. A copy of the call to "norm" is returned as an attribute.
DETAILS:
Based on the functions dlantr and zlantr from Lapack (Anderson et al. (1994)).
REFERENCES:
Anderson, E., et al. (1994). LAPACK User's Guide, 2nd edition, SIAM, Philadelphia. Golub, G., and Van Loan, C. F. (1989). Matrix Computations, 2nd edition, Johns Hopkins, Baltimore.
SEE ALSO:
norm.Matrix , vecnorm .
EXAMPLES: 
x <- Matrix( sample(-3:3, size = 9, replace = T), nrow = 3, ncol = 3)
x[row(x) > col(x)] <- 0        # construct triangular matrix
class(x) <- Matrix.class(x)
norm(x, "1")
norm(x, "I")
norm(x, "F")
norm(x, "M")