table.md

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Table

operation/method	description	notation
mxm	matrix-matrix multiplication	$\grbm{C} \grbmask{\grbm{M}} \grbaccumeq{} \grbm{A} \grbplustimes \grbm{B}$
vxm	vector-matrix multiplication	$\grbv{w}\grbt \grbmask{\grbv{m}\grbt} \grbaccumeq{} \grbv{u}\grbt \grbplustimes \grbm{A}$
mxv	matrix-vector multiplication	$\grbv{w} \grbmask{\grbv{m}} \grbaccumeq{} \grbm{A} \grbplustimes \grbv{u}$
eWiseAdd	element-wise addition using operator $\grbgenericop$	$\grbm{C} \grbmask{\grbm{M}} \grbaccumeq{} \grbm{A} \grbewiseadd{\grbgenericop} \grbm{B}$
	on elements in the set union of structures of $\grbm{A}/\grbm{B}$ and $\grbv{u}$/$\grbv{v}$	$\grbv{w} \grbmask{\grbv{m}} \grbaccumeq{} \grbv{u} \grbewiseadd{\grbgenericop} \grbv{v}$
eWiseMult	element-wise multiplication using operator $\grbgenericop$	$\grbm{C} \grbmask{\grbm{M}} \grbaccumeq{} \grbm{A} \grbewisemult{\grbgenericop} \grbm{B}$
	on elements in the set intersection of structures of $\grbm{A}/\grbm{B}$ and $\grbv{u}$/$\grbv{v}$	$\grbv{w} \grbmask{\grbv{m}} \grbaccumeq{} \grbv{u} \grbewisemult{\grbgenericop} \grbv{v}$
extract	extract submatrix from matrix $\grbm{A}$ using indices $\grba{i}$ and indices $\grba{j}$	$\grbm{C} \grbmask{\grbm{M}} \grbaccumeq{} \grbm{A}(\grba{i}, \grba{j})$
	extract the $\grbs{i}$th row vector from matrix $\grbm{A}$	$\grbv{w} \grbmask{\grbv{m}} \grbaccumeq{} \grbv{A}(\grbs{i}, :)$
	extract the $\grbs{j}$th column vector from matrix $\grbm{A}$	$\grbv{w} \grbmask{\grbv{m}} \grbaccumeq{} \grbv{A}(:, \grbs{j})$
	extract subvector from $\grbv{u}$ using indices $\grba{i}$	$\grbv{w} \grbmask{\grbv{m}} \grbaccumeq{} \grbv{u}(\grba{i})$
assign	assign matrix to submatrix with mask for $\grbm{C}$	$\grbm{C} \grbmask{\grbm{M}} (\grba{i},\grba{j}) \grbaccumeq{} \grbm{A}$
	assign scalar to submatrix with mask for $\grbm{C}$	$\grbm{C} \grbmask{\grbm{M}} (\grba{i},\grba{j}) \grbaccumeq{} \grbs{s}$
	assign vector to subvector with mask for $\grbv{w}$	$\grbv{w} \grbmask{\grbv{m}} (\grba{i}) \grbaccumeq{} \grbv{u}$
	assign scalar to subvector with mask for $\grbv{w}$	$\grbv{w} \grbmask{\grbv{m}} (\grba{i}) \grbaccumeq{} \grbs{s}$
apply	apply unary operator $\mathit{f}$ with optional thunk $k$	$\grbm{C} \grbmask{\grbm{M}} \grbaccumeq{} \grbf{f}{\grbm{A}, \grbs{k}}$
		$\grbv{w} \grbmask{\grbv{m}} \grbaccumeq{} \grbf{f}{\grbv{u}, \grbs{k}}$
select	apply select operator $\mathit{f}$ with optional thunk $k$	$\grbm{C} \grbmask{\grbm{M}} \grbaccumeq{} \grbm{A}\grbselect{\grbf{f}{\grbm{A}, \grbs{k}}}$
		$\grbv{w} \grbmask{\grbv{m}} \grbaccumeq{} \grbv{u}\grbselect{\grbf{f}{\grbv{u}, \grbs{k}}}$
reduce	row-wise reduce matrix to column vector	$\grbv{w} \grbmask{\grbv{m}} \grbaccumeq{} \grbreduce{\grbplus}{\grbs{j}}{\grbm{A}}{:,\grbs{j}}$
	reduce matrix to scalar	$\grbs{s} \grbaccumeq{} \grbreduce{\grbplus}{\grbs{i}, \grbs{j}}{\grbm{A}}{\grbs{i},\grbs{j}}$
	reduce vector to scalar	$\grbs{s} \grbaccumeq{} \grbreduce{\grbplus}{\grbs{i}}{\grbm{u}}{\grbs{i}}$
transpose	transpose	$\grbm{C} \grbmask{\grbm{M}} \grbaccumeq{} \grbm{A}\grbt$
kronecker	Kronecker multiplication using operator $\grbgenericop$	$\grbm{C} \grbmask{\grbm{M}} \grbaccumeq{} \grbkron{\grbm{A}, \grbgenericop, \grbm{B}}$

GraphBLAS operations and methods. Notation: Matrices and vectors are typeset in bold, starting with uppercase ($\grbm{A}$) and lowercase ($\grbv{u}$) letters, respectively. Scalars including indices are lowercase italic ($\grbs{k}$, $\grbs{i}$, $\grbs{j}$) while arrays are lowercase bold italic ($\grba{x}$, $\grba{i}$, $\grba{j}$). $\grbplus$ and $\grbtimes$ are the addition and multiplication operators forming a semiring and default to conventional arithmetic $+$ and $\times$ operators. $\grbaccum$ is the accumulator operator. Operations can be modified via a descriptor; matrices can be transposed ($\grbm{B}\grbt$), the mask can be complemented ($\grbm{C}\grbmask{\neg \grbm{M}}$), and the mask can be valued (shown above) or structural ($\grbm{C}\grbmask{\grbstr{\grbm{M}}}$). A structural mask can also be complemented ($\grbm{C}\grbmask{\grbneg\grbstr{\grbm{M}}}$). The result can be cleared (replaced) after using it as input to the mask/accumulator step ($\grbm{C}\grbmaskreplace{\grbm{M}}$). Not all methods are listed (creating new operators, monoids, and semirings, clearing a matrix/vector, etc.).