norm: Matrix Norms

In bedatadriven/renjin-matrix: Sparse and Dense Matrix Classes and Methods

Description

Computes a matrix norm of x, using Lapack for dense matrices. The norm can be the one norm, the infinity norm, the Frobenius norm, or the maximum modulus among elements of a matrix, as determined by the value of type.

Usage

norm(x, type, ...)

Arguments

x	a real or complex matrix.
type	A character indicating the type of norm desired. "O", "o" or "1" specifies the one norm, (maximum absolute column sum); "I" or "i" specifies the infinity norm (maximum absolute row sum); "F" or "f" specifies the Frobenius norm (the Euclidean norm of x treated as if it were a vector); and "M" or "m" specifies the maximum modulus of all the elements in x. The default is "O". Only the first character of type[1] is used.
...	further arguments passed to or from other methods.

Details

For dense matrices, the methods eventually call the Lapack functions dlange, dlansy, dlantr, zlange, zlansy, and zlantr.

Value

A numeric value of class "norm", representing the quantity chosen according to type.

References

Anderson, E., et al. (1994). LAPACK User's Guide, 2nd edition, SIAM, Philadelphia.

See Also

onenormest(), an approximate randomized estimate of the 1-norm condition number, efficient for large sparse matrices.

Examples

x <- Hilbert(9)
norm(x, "1")
norm(x, "I")
norm(x, "F")
norm(x, "M")

bedatadriven/renjin-matrix documentation built on May 12, 2019, 10:05 a.m.