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\newpage
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{GraphBLAS Operations} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\label{operations}
The next sections define each of the GraphBLAS operations, also listed in the
table below.
\vspace{0.2in}
{\small
\begin{tabular}{lll}
\hline
\verb'GrB_mxm' & matrix-matrix multiply & ${\bf C \langle M \rangle = C \odot AB}$ \\
\verb'GrB_vxm' & vector-matrix multiply & ${\bf w^{\sf T}\langle m^{\sf T}\rangle = w^{\sf T}\odot u^{\sf T}A}$ \\
\verb'GrB_mxv' & matrix-vector multiply & ${\bf w \langle m \rangle = w \odot Au}$ \\
\hline
\verb'GrB_eWiseMult' & element-wise, & ${\bf C \langle M \rangle = C \odot (A \otimes B)}$ \\
& set intersection & ${\bf w \langle m \rangle = w \odot (u \otimes v)}$ \\
\hline
\verb'GrB_eWiseAdd' & element-wise, & ${\bf C \langle M \rangle = C \odot (A \oplus B)}$ \\
& set union & ${\bf w \langle m \rangle = w \odot (u \oplus v)}$ \\
\hline
\verb'GxB_eWiseUnion'& element-wise, & ${\bf C \langle M \rangle = C \odot (A \oplus B)}$ \\
& set union & ${\bf w \langle m \rangle = w \odot (u \oplus v)}$ \\
\hline
\verb'GrB_extract' & extract submatrix & ${\bf C \langle M \rangle = C \odot A(I,J)}$ \\
& & ${\bf w \langle m \rangle = w \odot u(i)}$ \\
\hline
\verb'GrB_assign' & assign submatrix & ${\bf C \langle M \rangle (I,J) = C(I,J) \odot A}$ \\
& with submask for ${\bf C}$
& ${\bf w \langle m \rangle (i) = w(i) \odot u}$ \\
\hline
\verb'GxB_subassign' & assign submatrix, & ${\bf C (I,J) \langle M \rangle = C(I,J) \odot A}$ \\
& with submask for ${\bf C(I,J)}$
& ${\bf w (i) \langle m \rangle = w(i) \odot u}$ \\
\hline
\verb'GrB_apply' & apply unary operator & ${\bf C \langle M \rangle = C \odot} f{\bf (A)}$ \\
& & ${\bf w \langle m \rangle = w \odot} f{\bf (u)}$ \\
& apply binary operator & ${\bf C \langle M \rangle = C \odot} f(x,{\bf A})$ \\
& & ${\bf C \langle M \rangle = C \odot} f({\bf A},y)$ \\
& & ${\bf w \langle m \rangle = w \odot} f(x,{\bf x})$ \\
& & ${\bf w \langle m \rangle = w \odot} f({\bf u},y)$ \\
& apply index-unary op & ${\bf C \langle M \rangle = C \odot} f({\bf A},i,j,k)$ \\
& & ${\bf w \langle m \rangle = w \odot} f({\bf u},i,0,k)$ \\
\hline
\verb'GrB_select' & select entries & ${\bf C \langle M \rangle = C \odot} \mbox{select}({\bf A},i,j,k)$ \\
& & ${\bf w \langle m \rangle = w \odot} \mbox{select}({\bf u},i,0,k)$ \\
\hline
\verb'GrB_reduce' & reduce to vector & ${\bf w \langle m \rangle = w \odot} [{\oplus}_j {\bf A}(:,j)]$ \\
& reduce to scalar & $s = s \odot [{\oplus}_{ij} {\bf A}(I,J)]$ \\
\hline
\verb'GrB_transpose' & transpose & ${\bf C \langle M \rangle = C \odot A^{\sf T}}$ \\
\hline
\verb'GrB_kronecker' & Kronecker product & ${\bf C \langle M \rangle = C \odot \mbox{kron}(A, B)}$ \\
\hline
\end{tabular}
}
\vspace{0.2in}
If an error occurs, \verb'GrB_error(&err,C)' or \verb'GrB_error(&err,w)'
returns details about the error, for operations that return a modified matrix
\verb'C' or vector \verb'w'. The only operation that cannot return an error
string is reduction to a C scalar with \verb'GrB_reduce'.
\input{UserGuide/GrB_operations_mxm.tex}
\input{UserGuide/GrB_operations_vxm.tex}
\input{UserGuide/GrB_operations_mxv.tex}
\input{UserGuide/GrB_operations_eWiseMult.tex}
\input{UserGuide/GrB_operations_eWiseAdd.tex}
\input{UserGuide/GrB_operations_eWiseUnion.tex}
\input{UserGuide/GrB_operations_extract.tex}
\input{UserGuide/GrB_operations_assign.tex}
\input{UserGuide/GrB_operations_subassign.tex}
\input{UserGuide/GrB_operations_assign_duplicates.tex}
\input{UserGuide/GrB_operations_assign_vs_subassign.tex}
\input{UserGuide/GrB_operations_apply.tex}
\input{UserGuide/GrB_operations_select.tex}
\input{UserGuide/GrB_operations_reduce.tex}
\input{UserGuide/GrB_operations_transpose.tex}
\input{UserGuide/GrB_operations_kronecker.tex}
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