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.TH diag 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
diag - diagonal including or extracting
.SH CALLING SEQUENCE
.nf
[y]=diag(vm, [k])
.fi
.SH PARAMETERS
.TP 10
vm
: vector or matrix (full or sparse storage)
.TP 10
k
: integer (default value 0)
.TP 10
y
: vector or matrix
.SH DESCRIPTION
for \fVvm\fR a (row or column) n-vector \fVdiag(vm)\fR returns a diagonal
matrix with entries of \fVvm\fR along the main diagonal.
.LP
\fVdiag(vm,k)\fR is a \fV(n+abs(k))x(n+abs(k))\fR matrix with the entries
of \fVvm\fR along the kth diagonal. \fVk=0\fR is the main diagonal
\fVk>0\fR is for upper diagonals and \fVk<0\fR for lower
diagonals.
.LP
For a matrix \fVvm\fR, \fVdiag(vm,k)\fR is the column vector made of entries
of the kth diagonal of \fVvm\fR. \fVdiag(vm)\fR is the main diagonal of \fVvm\fR.
\fVdiag(diag(x))\fR is a diagonal matrix.
.LP
If \fVvm\fR is a sparse matrix \fVdiag(vm,k)\fR returns a
sparse matrix.
.LP
To construct a diagonal linear system, use \fVsysdiag\fR.
.LP
Note that \fVeye(A).*A\fR returns a diagonal matrix made with the
diagonal entries of \fVA\fR. This is valid for any matrix (constant,
polynomial, rational, state-space linear system,...).
.SH EXAMPLE
.nf
diag([1,2])
A=[1,2;3,4];
diag(A) // main diagonal
diag(A,1)
diag(sparse(1:10)) // sparse diagonal matrix
// form a tridiagonal matrix of size 2*m+1
m=5;diag(-m:m) + diag(ones(2*m,1),1) +diag(ones(2*m,1),-1)
.fi
.SH SEE ALSO
sysdiag, sparse
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