Man Scilab
norm
Scilab Function
norm - matrix norms
Calling Sequence
-
[y]=norm(x [,flag])
Parameters
-
x
: real or complex vector or matrix (full or sparse storage)
-
flag
: string (type of norm) (default value =2)
Description
For matrices
-
norm(x)
: or
norm(x,2)
is the largest singular value of
x
(
max(svd(x))
).
-
norm(x,1)
: The l_1 norm
x
(the largest column sum :
maxi(sum(abs(x),'r'))
).
-
norm(x,'inf'),norm(x,%inf)
: The infinity norm of
x
(the largest row sum :
maxi(sum(abs(x),'c'))
).
-
norm(x,'fro')
: Frobenius norm i.e.
sqrt(sum(diag(x'*x)))
For vectors
-
norm(v,p)
: l_p norm (
sum(v(i)^p))^(1/p)
.
-
norm(v)
:
=norm(v,2)
: l_2 norm
-
norm(v,'inf')
:
max(abs(v(i)))
.
Examples
A=[1,2,3];
norm(A,1)
norm(A,'inf')
A=[1,2;3,4]
max(svd(A))-norm(A)
A=sparse([1 0 0 33 -1])
norm(A)
See Also
h_norm
,
dhnorm
,
h2norm
,
abs
,
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