Calculates the norm of a series or array.
NORM(a, mode)
a |
- |
Optional. An input series or array. Defaults to the current Window. |
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mode |
- |
Optional. Type of norm calculation. Defaults to 2, the largest singular value. Valid inputs can be any positive integer or:
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A real representing the norm value.
a = {{1, 2, 3},
{4, 5, 6},
{7, 8, 9}}
norm(a) returns: 16.848103
norm(a, 1) returns: 18
norm(a, 2) returns: 16.848103
norm(a, inf) returns: 24
norm(a, -inf) returns: 6
norm(a, "fro") returns: 16.881943
The mode parameter specifies the following norm calculations:
Mode Series Input ArrayInput
_____________________________________________________
1 sum(mag(m)) max(colsum(mag(m)))
2 max(svd(m)) max(svd(m))
N sum(mag(m)^N)/(1/N) undefined
inf max(mag(m)) max(colsum(mag(m)')')
-inf min(mag(m)) min(colsum(mag(m)')')
"fro" undefined sqrt(sum(diag(m' *^ m)))