norm
Compute the Norm of a Matrix
Description
Displays the norm of a matrix according to the norm type.
Usage
norm(x, type, ...)
Arguments
| x |
a numeric or a complex matrix.
|
| type |
a character string specified as the norm type.
The norm type can be one of "O", "I", "1", "2", "F", or "M".
See the Details section for their descriptions.
|
Details
norm() uses the LAPACK routine
"DLANGE" (numeric) or
"ZLANGE" (complex) to calculate the norm
of a matrix, except for
type="2", which uses the
svd function.
The
type argument defines the norm types:
- "O" or "1": The one norm of x (maximum column sum of abs(x)).
- "I": The infinity norm of x (maximum row sum abs(x)).
- "F": The Frobenius norm of x (square root of sum of squares of abs(x)).
- "M": The largest value in abs(x).
- "2": The largest singular value of x.
Note that a matrix norm is not the same as a vector norm.
Value
returns a numeric value representing the norm of a matrix.
Differences between Spotfire Enterprise Runtime for R and Open-source R
Open-source R does not handle complex matrices.
References
Examples
x <- cbind( -(1:4), (0:3), c(-3.5,-3.5,3.5,3.5))
norm(x)
norm(x, "M")
norm(x, "O")
norm(x, "I")
norm(x, "F")
norm(x, "2")