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\newpage
%===============================================================================
\subsection{{\sf GrB\_kronecker:} Kronecker product} %==========================
%===============================================================================
\label{kron}
\begin{mdframed}[userdefinedwidth=6in]
{\footnotesize
\begin{verbatim}
GrB_Info GrB_kronecker // C<Mask> = accum (C, kron(A,B))
(
GrB_Matrix C, // input/output matrix for results
const GrB_Matrix Mask, // optional mask for C, unused if NULL
const GrB_BinaryOp accum, // optional accum for Z=accum(C,T)
const <operator> op, // defines '*' for T=kron(A,B)
const GrB_Matrix A, // first input: matrix A
const GrB_Matrix B, // second input: matrix B
const GrB_Descriptor desc // descriptor for C, Mask, A, and B
) ;
\end{verbatim} } \end{mdframed}
\verb'GrB_kronecker' computes the Kronecker product,
${\bf C \langle M \rangle = C \odot \mbox{kron}(A,B)}$ where
\[
\mbox{kron}{\bf (A,B)} =
\left[
\begin{array}{ccc}
a_{00} \otimes {\bf B} & \ldots & a_{0,n-1} \otimes {\bf B} \\
\vdots & \ddots & \vdots \\
a_{m-1,0} \otimes {\bf B} & \ldots & a_{m-1,n-1} \otimes {\bf B} \\
\end{array}
\right]
\]
The $\otimes$ operator is defined by the \verb'op' parameter. It is applied in
an element-wise fashion (like \verb'GrB_eWiseMult'), where the pattern of the
submatrix $a_{ij} \otimes {\bf B}$ is the same as the pattern of ${\bf B}$ if
$a_{ij}$ is an entry in the matrix ${\bf A}$, or empty otherwise. The input
matrices \verb'A' and \verb'B' can be of any dimension, and both matrices may
be transposed first via the descriptor, \verb'desc'. Entries in \verb'A' and
\verb'B' are typecast into the input types of the \verb'op'. The matrix
\verb'T=kron(A,B)' has the same type as the \verb'ztype' of the binary
operator, \verb'op'. The final step is ${\bf C \langle M \rangle = C \odot
T}$, as described in Section~\ref{accummask}.
The operator \verb'op' may be a \verb'GrB_BinaryOp', a \verb'GrB_Monoid', or a
\verb'GrB_Semiring'. In the latter case, the multiplicative operator of
the semiring is used.
%
The \verb'op' may be a binary operator
created by \verb'GxB_BinaryOp_new_IndexOp'.
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