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graphblas-commands.tex
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graphblas-commands.tex
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\hyphenation{Suite-Sparse}
\hyphenation{Graph-BLAS}
\hyphenation{Suite-Sparse-Graph-BLAS}
\newcommand{\suitesparse}{SuiteSparse\xspace}
\newcommand{\grb}{GraphBLAS\xspace}
\newcommand{\ssgrb}{SuiteSparse:GraphBLAS\xspace}
\newcommand{\gxb}{\ssgrb}
\newcommand{\lagraph}{LAGraph\xspace}
\newcommand{\pygrb}{pygraphblas\xspace}
\newcommand{\grblas}{grblas\xspace}
% Define new boolean flags using etoolbox ('\newbool' is similar to '\newtoggle').
% This workaround is needed as simply putting the newcommands inside 'IfFileExists' did not do the job
% as it broke with 'Illegal parameter number in definition of \reserved@a', a symptom probably caused
% by the lack of protection (\protect). Anyways, the workaround is actually cleaner.
%\newcommand{\grbreduce}[2]{\left[{#1}_j \, {#2}(:, j) \right]}
% \ifbool{ascii}{ % ASCII mode ======================================================================
% \newcommand{\grbm}[1]{{\ifbool{colored}{\color{brown}}{}{\mathtt{#1}}}}% matrix
% \newcommand{\grbv}[1]{{\ifbool{colored}{\color{lilac}}{}{\mathtt{#1}}}}% vector
% \newcommand{\grba}[1]{{\ifbool{colored}{\color{gray}}{}{\mathtt{#1}}}}% array
% \newcommand{\grbs}[1]{{\ifbool{colored}{\color{blue}}{}{\mathtt{#1}}}}% scalar
% \newcommand{\grbstr}[1]{{\{#1\}}}
% \newcommand{\grbmask}[1]{<\! #1 \!>}
% \newcommand{\grbmaskreplace}[1]{<\!<\! #1 \!>\!>}
% \newcommand{\grbneg}{\texttt{!}}
% \newcommand{\grbassign}{\mathrel{\texttt{<-}}}
% \newcommand{\grbf}[2]{\grboperation{#1}(#2)}
% \newcommand{\grbreduce}[4]{[ {#1 #3} ]} % omit the indices
% \newcommand{\grbt}{\texttt{'}} % transpose
% \newcommand{\grbdiv}{\grbbinaryop{DIV}}
% \newcommand{\grbminus}{\grbbinaryop{MINUS}}
% \newcommand{\grbaccum}{\texttt{\ensuremath{+}}}
% \newcommand{\grbaccumeq}[1]{\mathbin{\texttt{\ensuremath{\ifstrempty{#1}{\grbaccum}{#1}=}}}}
% \newcommand{\grbplus}{\grbbinaryop{+}}
% \newcommand{\grbtimes}{\grbbinaryop{\times}}
% \newcommand{\grbapply}{\grbbinaryop{\odot}}
% \newcommand{\grbfrac}[2]{(#1)/(#2)}
% \newcommand{\grbbool}{\mathtt{bool}} % booleans
% \newcommand{\grbuint}{\mathtt{uint}} % unsigned integers
% \newcommand{\grbint}{\mathtt{int}} % integers
% \newcommand{\grbfloat}{\mathtt{fp}} % floats (?)
% \newcommand{\grbplaceholder}[1]{\mathsf{#1}}
% \newcommand{\grbscalartype}[2]{\mathtt{#1#2()}}
% \newcommand{\grbvectortype}[3]{\mathtt{#1#2(#3)}}
% \newcommand{\grbmatrixtype}[4]{\mathtt{#1#2(#3, #4)}}
% \newcommand{\grbnewscalar}[3]{\mathtt{#1 = \grbscalartype{#2}{#3}}}
% \newcommand{\grbnewvector}[4]{\mathtt{#1 = \grbvectortype{#2}{#3}{#4}}}
% \newcommand{\grbnewmatrix}[5]{\mathtt{#1 = \grbmatrixtype{#2}{#3}{#4}{#5}}}
% \newcommand{\grbalpha}{\mathtt{alpha}}
% \newcommand{\grboperator}[1]{\mathtt{#1}}
% \newcommand{\grbrange}[2]{#1:#2}
% \newcommand{\grbdontcare}{\_}
% \newcommand{\grboperationnoarg}[1]{\mathtt{#1}}
% \newcommand{\grbewiseadd}[1]{\grbbinaryop{#1[intersection]}}
% \newcommand{\grbewisemult}[1]{\grbbinaryop{#1[union]}}
% }{ % LaTeX mode ===================================================================================
\newcommand{\grbm}[1]{{\ifbool{colored}{\color{brown}}{}{\mathbf{#1}}}}% matrix
\newcommand{\grbv}[1]{{\ifbool{colored}{\color{lilac}}{}{\mathbf{#1}}}}% vector
\newcommand{\grba}[1]{{\ifbool{colored}{\color{gray}}{}{\textbf{\textit{#1}}}}}% array
\newcommand{\grbs}[1]{{\ifbool{colored}{\color{blue}}{}{\mathit{#1}}}}% scalar
\newcommand{\grbmask}[1]{\langle #1 \rangle}
%\newcommand{\grbstr}[1]{{\{#1\}}}
\newcommand{\grbstr}[1]{s(#1)}
\newcommand{\grbval}[1]{\mathit{val}(#1)}
%\newcommand{\grbmaskreplace}[1]{\langle\!\langle #1 \rangle\!\rangle}
\newcommand{\grbmaskreplace}[1]{\langle #1, \mathrm{r} \rangle}
\newcommand{\grbneg}{\neg}
% use the \mapsfrom symbol extracted from the stix package as suggested in https://tex.stackexchange.com/a/331899/71109
\DeclareFontEncoding{LS1}{}{}
\DeclareFontSubstitution{LS1}{stix}{m}{n}
\DeclareSymbolFont{arrows1}{LS1}{stixsf}{m}{n}
\global\let\mapsfrom\undefined % undefine \mapsfrom because some templates such as acmart already have it
\DeclareMathSymbol{\mapsfrom}{\mathrel}{arrows1}{"AB}
\newcommand{\grbassign}{\mapsfrom}
\newcommand{\grbf}[2]{\mathit{#1}(#2)}
\newcommand{\grbreduce}[4]{[ {#1}_{#2}\, #3(#4) ]}
\newcommand{\grbtransposesymbol}{\mathsf{T}}
\newcommand{\grbt}{^\grbtransposesymbol} %^{\top}} % transpose
%\newcommand{\grbdiv}{\grbbinaryop{\oslash}}
%\newcommand{\grbminus}{\grbbinaryop{\ominus}}
\newcommand{\grbdiv}{\grbbinaryop{div}}
\newcommand{\grbminus}{\grbbinaryop{minus}}
\newcommand{\grbaccum}{\ensuremath{\odot}}
\newcommand{\grbaccumeq}[1]{\mathbin{\ensuremath{\ifstrempty{#1}{\grbaccum}{#1}\!\!=}}}
%\newcommand{\grbaccumeq}[1]{\mathbin{\ensuremath{\ifstrempty{#1}{\grbaccum}{#1}_\cup\!\!=}}}
\newcommand{\grbplus}{\oplus}
\newcommand{\grbtimes}{\otimes}
\newcommand{\grbapply}{\odot}
\newcommand{\grbfrac}[2]{\frac{#1}{#2}}
\newcommand{\grbbool}{\mathbb{B}} % booleans
%\newcommand{\grbuint}{\mathbb{N}} % unsigned integers
\newcommand{\grbuint}{\mathtt{UINT64}} % doubles
\newcommand{\grbint}{\mathbb{Z}} % integers
\newcommand{\grbfloat}{\mathbb{Q}} % floats (?)
\newcommand{\grbdouble}{\mathtt{FP64}} % doubles
\newcommand{\grbplaceholder}[1]{\mathsf{#1}}
\newcommand{\grbscalartype}[2]{#1_{#2}}
\newcommand{\grbvectortype}[3]{#1_{#2}^{#3}}
\newcommand{\grbmatrixtype}[4]{#1_{#2}^{#3 \times #4}}
\newcommand{\grbnewscalar}[3]{\text{let: } #1 \in \grbscalartype{#2}{#3}}
\newcommand{\grbnewvector}[4]{\text{let: } #1 \in \grbvectortype{#2}{#3}{#4}}
\newcommand{\grbnewmatrix}[5]{\text{let: } #1 \in \grbmatrixtype{#2}{#3}{#4}{#5}}
%\newcommand{\grbalpha}{\alpha}
\newcommand{\grboperator}[1]{\mathsf{#1}}
\newcommand{\grbrange}[2]{#1 \! : \! #2}
\newcommand{\grbdontcare}{\textvisiblespace}
\newcommand{\grboperationnoarg}[1]{\mathrm{#1}}
\newcommand{\grbewiseadd}[1]{\grbbinaryop{#1_\cup}}
\newcommand{\grbewisemult}[1]{\grbbinaryop{#1_\cap}}
\newcommand{\grbdim}[1]{\mathrm{dim}(#1)}
% }
% do not lange/rangle for tuples as it is already used for masks
% do not use grbtuple for the time being
%\newcommand{\grbtuple}[1]{( #1 )}
\newcommand{\tuple}[1]{(#1)}
% trying to avoid too much syntax (e.g. using wedge/vee symbols for LAND/LOR)
%\newcommand{\grblorland}{\lor\!.\!\land}
\newcommand{\grbsemiringops}[2]{\mathbin{\grboperator{#1.#2}}}
\newcommand{\grbplustimes}{\grbsemiringops{\grbplus}{\grbtimes}}
%\newcommand{\grbplustimes}{\grbsemiringops{\grbplus_\cup}{\grbtimes_\cap}}
\newcommand{\grbpluspair}{\grbsemiringops{plus}{pair}}
\newcommand{\grbplussecond}{\grbsemiringops{plus}{second}}
\newcommand{\grbplusfirst}{\grbsemiringops{plus}{first}}
\newcommand{\grbanypair}{\grbsemiringops{any}{pair}}
\newcommand{\grbanyfirst}{\grbsemiringops{any}{first}}
\newcommand{\grbanysecond}{\grbsemiringops{any}{second}}
\newcommand{\grbanyfirstj}{\grbsemiringops{any}{firstj}}
\newcommand{\grbanyfirstjone}{\grbsemiringops{any}{firstj1}}
\newcommand{\grbminfirstj}{\grbsemiringops{min}{firstj}}
\newcommand{\grbminfirstjone}{\grbsemiringops{min}{firstj1}}
\newcommand{\grbanysecondi}{\grbsemiringops{any}{secondi}}
\newcommand{\grbanysecondione}{\grbsemiringops{any}{secondi1}}
\newcommand{\grbminsecondi}{\grbsemiringops{min}{secondi}}
\newcommand{\grbminsecondione}{\grbsemiringops{min}{secondi1}}
\newcommand{\grblorland}{\grbsemiringops{lor}{land}}
\newcommand{\grbminplus}{\grbsemiringops{min}{plus}}
\newcommand{\grbmaxplus}{\grbsemiringops{max}{plus}}
\newcommand{\grbmaxfirst}{\grbsemiringops{max}{first}}
\newcommand{\grbminfirst}{\grbsemiringops{min}{first}}
\newcommand{\grbminsecond}{\grbsemiringops{min}{second}}
\newcommand{\grbmaxsecond}{\grbsemiringops{max}{second}}
\newcommand{\grbsecondmin}{\grbsemiringops{second}{min}}
\newcommand{\grbsecondmax}{\grbsemiringops{second}{max}}
\newcommand{\grbarithmeticplustimes}{\grbsemiringops{+}{\times}}
\newcommand{\grbarithmeticplustimestext}{\grbsemiringops{plus}{times}}
\newcommand{\grbbinaryop}[1]{\mathbin{\grboperator{#1}}}
\newcommand{\grbany}{\grbbinaryop{any}}
\newcommand{\grbpair}{\grbbinaryop{pair}}
\newcommand{\grbland}{\grbbinaryop{land}}
\newcommand{\grblor}{\grbbinaryop{lor}}
\newcommand{\grbband}{\grbbinaryop{band}}
\newcommand{\grbbor}{\grbbinaryop{bor}}
\newcommand{\grbmin}{\grbbinaryop{min}}
\newcommand{\grbmax}{\grbbinaryop{max}}
\newcommand{\grbfirst}{\grbbinaryop{first}}
\newcommand{\grbsecond}{\grbbinaryop{second}}
\newcommand{\grbfirsti}{\grbbinaryop{firsti}}
\newcommand{\grbsecondi}{\grbbinaryop{secondi}}
\newcommand{\grbfirstione}{\grbbinaryop{firsti1}}
\newcommand{\grbsecondione}{\grbbinaryop{secondi1}}
\newcommand{\grbfirstj}{\grbbinaryop{firstj}}
\newcommand{\grbsecondj}{\grbbinaryop{secondj}}
\newcommand{\grbfirstjone}{\grbbinaryop{firstj1}}
\newcommand{\grbsecondjone}{\grbbinaryop{secondj1}}
\newcommand{\grbarithmeticplus}{\grbbinaryop{+}}
\newcommand{\grbarithmetictimes}{\grbbinaryop{\times}}
\newcommand{\grbarithmeticplustext}{\grbbinaryop{plus}}
\newcommand{\grbarithmetictimestext}{\grbbinaryop{times}}
\newcommand{\grbisne}{\grbbinaryop{isne}}
\newcommand{\grbplustext}{\grbbinaryop{plus}}
\newcommand{\grbtimestext}{\grbbinaryop{times}}
\newcommand{\grbgenericop}{\grboperator{op}}
% boolean values
\newcommand{\grbbooleanvalue}[1]{\mathtt{#1}}
\newcommand{\grbtrue}{\grbbooleanvalue{TRUE}}
\newcommand{\grbfalse}{\grbbooleanvalue{FALSE}}
\newcommand{\grbT}{\grbbooleanvalue{T}}
\newcommand{\grbF}{\grbbooleanvalue{F}}
\newcommand{\grbstring}{\textrm{String}}
\newcommand{\grbdate}{\textrm{Date}}
% cardinality / count
\newcommand{\grbcnt}[1]{| #1 |}
% operations
\newcommand{\grboperation}[2]{\grboperationnoarg{#1}(#2)}
\newcommand{\grbnrows}[1]{\grboperation{nrows}{#1}}
\newcommand{\grbncols}[1]{\grboperation{ncols}{#1}}
\newcommand{\grbnvals}[1]{\grboperation{nvals}{#1}}
\newcommand{\grbclear}[1]{\grboperation{clear}{#1}}
\newcommand{\grbdiag}[1]{\grboperation{diag}{#1}}
\newcommand{\grbselect}[1]{\grbmask{#1}}
\newcommand{\grbkron}[1]{\grboperation{kron}{#1}}
\newcommand{\grbtril}[1]{\grboperation{tril}{#1}}
\newcommand{\grbtriu}[1]{\grboperation{triu}{#1}}
\newcommand{\grbondiag}[1]{\grboperation{ondiag}{#1}}
\newcommand{\grboffdiag}[1]{\grboperation{offdiag}{#1}}
\newcommand{\grbind}[1]{\mathrm{ind}(#1)}