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.TH norm 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
norm - matrix norms
.SH CALLING SEQUENCE
.nf
[y]=norm(x [,flag])
.fi
.SH PARAMETERS
.TP 10
x
: real or complex vector or matrix (full or sparse storage)
.TP 10
flag
: string (type of norm) (default value =2)
.SH DESCRIPTION
For matrices
.RS
.TP 15
norm(x)
: or \fVnorm(x,2)\fR is the largest singular value of \fVx\fR
(\fVmax(svd(x))\fR).
.TP
norm(x,1)
: The l_1 norm \fVx\fR (the largest column sum :
\fVmaxi(sum(abs(x),'r'))\fR ).
.TP
norm(x,'inf'),norm(x,%inf)
: The infinity norm of \fVx\fR (the largest row sum :
\fVmaxi(sum(abs(x),'c'))\fR ).
.TP
norm(x,'fro')
: Frobenius norm i.e. \fVsqrt(sum(diag(x'*x)))\fR
.RE
For vectors
.RS
.TP 15
norm(v,p)
: l_p norm (\fVsum(v(i)^p))^(1/p)\fR .
.TP
norm(v)
: \fV=norm(v,2)\fR : l_2 norm
.TP
norm(v,'inf')
: \fVmax(abs(v(i)))\fR.
.RE
.SH EXAMPLE
.nf
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)
.fi
.SH SEE ALSO
h_norm, dhnorm, h2norm, abs
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