fixed minor typos, mostly in section headings

GraphBLAS · Nov 13, 2021 · 9964941 · 9964941
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diff --git a/graph-api-c/GraphBLAS_API_C.tex b/graph-api-c/GraphBLAS_API_C.tex
@@ -308,9 +308,9 @@ \chapter{Introduction}
 \item Chapter~\ref{Chp:Concepts}: Basic Concepts
 \item Chapter~\ref{Chp:Objects}: Objects
 \item Chapter~\ref{Chp:Methods}: Methods
-\item Chapter~\ref{Chp:Nonpolymorphic}: Nonpolymorphic Interface
-\item Appendix~\ref{Chp:RevHistory}: Revision History
-\item Appendix~\ref{App:Matrix_format_details}: Non-Opaque Data Format Definitions
+\item Chapter~\ref{Chp:Nonpolymorphic}: Nonpolymorphic interface
+\item Appendix~\ref{Chp:RevHistory}: Revision history
+\item Appendix~\ref{App:Matrix_format_details}: Non-opaque data format definitions
 \item Appendix~\ref{Chp:Examples}: Examples
 \end{itemize}
 
@@ -332,7 +332,7 @@ \chapter{Methods}
 
 \input{context_methods}
 
-\section{Object Methods}
+\section{Object methods}
 
 This section describes methods that setup and operate on GraphBLAS opaque objects
 but are not part of the the GraphBLAS math specification.

diff --git a/graph-api-c/algebra_methods.tex b/graph-api-c/algebra_methods.tex
@@ -1,4 +1,4 @@
-\subsection{Algebra Methods}
+\subsection{Algebra methods}
 \label{Sec:AlgebraMethods}
 
 %-----------------------------------------------------------------------------

diff --git a/graph-api-c/appendices.tex b/graph-api-c/appendices.tex
@@ -1,4 +1,4 @@
-\chapter{Revision History}
+\chapter{Revision history}
 \label{Chp:RevHistory}
 %--------------------------------------------------------------
 
@@ -105,7 +105,7 @@ \chapter{Revision History}
 %--------------------------------------------------------------
 %--------------------------------------------------------------
 
-\chapter{Non-Opaque Data Format Definitions}
+\chapter{Non-opaque data format definitions}
 \label{App:Matrix_format_details}
 
 \section{{\sf GrB\_Format}: Specify the format for input/output of a GraphBLAS matrix.}
@@ -242,31 +242,31 @@ \chapter{Examples}
 
 \pagebreak
 \nolinenumbers
-\section{Example: level breadth-first search (BFS) in GraphBLAS}
+\section{Example: Level breadth-first search (BFS) in GraphBLAS}
 {\scriptsize
 \lstinputlisting[language=C,numbers=left]{BFS5M.c}
 }
 \vfill
 
 \pagebreak
 \nolinenumbers
-\section{Example: level BFS in GraphBLAS using apply}
+\section{Example: Level BFS in GraphBLAS using apply}
 {\scriptsize
 \lstinputlisting[language=C,numbers=left]{BFS6_apply.c}
 }
 \vfill
 
 \pagebreak
 \nolinenumbers
-\section{Example: parent BFS in GraphBLAS}
+\section{Example: Parent BFS in GraphBLAS}
 {\scriptsize
 \lstinputlisting[language=C,numbers=left]{BFS7_parents.c}
 }
 \vfill
 
 \pagebreak
 \nolinenumbers
-\section{Example: betweenness centrality (BC) in GraphBLAS}
+\section{Example: Betweenness centrality (BC) in GraphBLAS}
 \label{App:BCnobatch}
 {\scriptsize
 \lstinputlisting[language=C,numbers=left]{BC1M_update.c}
@@ -275,23 +275,23 @@ \section{Example: betweenness centrality (BC) in GraphBLAS}
 
 \pagebreak
 \nolinenumbers
-\section{Example: batched BC in GraphBLAS}
+\section{Example: Batched BC in GraphBLAS}
 {\scriptsize
 \lstinputlisting[language=C,escapechar=|,numbers=left]{BC1_batch.c}
 }
 \vfill
 
 \pagebreak
 \nolinenumbers
-\section{Example: maximal independent set (MIS) in GraphBLAS}
+\section{Example: Maximal independent set (MIS) in GraphBLAS}
 {\scriptsize
 \lstinputlisting[language=C,numbers=left]{MIS1.c}
 }
 \vfill
 
 \pagebreak
 \nolinenumbers
-\section{Example: counting triangles in GraphBLAS}
+\section{Example: Counting triangles in GraphBLAS}
 {\scriptsize
 \lstinputlisting[language=C,numbers=left]{TC1.c}
 }

diff --git a/graph-api-c/basic_concepts.tex b/graph-api-c/basic_concepts.tex
@@ -1,4 +1,4 @@
-\chapter{Basic Concepts}
+\chapter{Basic concepts}
 \label{Chp:Concepts}
 
 The GraphBLAS C API is used to construct  
@@ -339,7 +339,7 @@ \section{Notation}
 \restoregeometry
 
 
-\section{Mathematical Foundations}
+\section{Mathematical foundations}
 
 Graphs can be represented in terms of matrices. The values stored in these 
 matrices correspond to attributes (often weights) of edges in the graph.\footnote{More information on the mathematical foundations can be found in the following paper: J. Kepner, P. Aaltonen, D. Bader,  A. Buluç, F. Franchetti, J. Gilbert, D. Hutchison, M. Kumar, A. Lumsdaine, H. Meyerhenke, S. McMillan, J. Moreira, J. Owens, C. Yang, M. Zalewski, and T. Mattson. 2016, September. Mathematical foundations of the GraphBLAS. In \emph{2016 IEEE High Performance Extreme Computing Conference (HPEC)} (pp. 1-9). IEEE.} 
@@ -402,7 +402,7 @@ \section{Mathematical Foundations}
 the problem itself is ill-conditioned and needs to be reformulated.
 
 
-\section{GraphBLAS Opaque Objects}
+\section{GraphBLAS opaque objects}
 
 Objects defined in the GraphBLAS standard include types (the domains of 
 elements), collections of elements (matrices, vectors, and scalars), operators 
@@ -526,7 +526,7 @@ \section{GraphBLAS Opaque Objects}
 
 % ========================================================================
 
-\section{Execution Model}
+\section{Execution model}
 \label{Sec:ExecutionModel}
 
 A program using the GraphBLAS C API is called
@@ -738,7 +738,7 @@ \subsection{Multi-threaded execution}
 
 
 %============================================================================
-\section{Error Model}
+\section{Error model}
 \label{Sec:ErrorModel}
 
 All GraphBLAS methods return a value of type {\sf GrB\_Info} (an enum) to 

diff --git a/graph-api-c/context_methods.tex b/graph-api-c/context_methods.tex
@@ -1,4 +1,4 @@
-\section{Context Methods}
+\section{Context methods}
 
 The methods in this section set up and tear down the GraphBLAS
 context within which all GraphBLAS methods must be executed.  The initialization

diff --git a/graph-api-c/descriptor_methods.tex b/graph-api-c/descriptor_methods.tex
@@ -1,4 +1,4 @@
-\subsection{Descriptor Methods}
+\subsection{Descriptor methods}
 
 The methods in this section create and set values in descriptors. 
 A descriptor is an opaque GraphBLAS object the values of which are used to

diff --git a/graph-api-c/graphblas_operations.tex b/graph-api-c/graphblas_operations.tex
@@ -1,4 +1,4 @@
-\section{GraphBLAS Operations}
+\section{GraphBLAS operations}
 \label{Sec:Operations}
 
 The GraphBLAS operations are defined in the GraphBLAS math specification and summarized in 

diff --git a/graph-api-c/nonpolymorphic.tex b/graph-api-c/nonpolymorphic.tex
@@ -1,4 +1,4 @@
-\chapter{Nonpolymorphic Interface\scott{NEW CONTENT}}
+\chapter{Nonpolymorphic interface\scott{NEW CONTENT}}
 \label{Chp:Nonpolymorphic}
 
 Each polymorphic GraphBLAS method (those with multiple parameter

diff --git a/graph-api-c/objects.tex b/graph-api-c/objects.tex
@@ -22,7 +22,7 @@ \section{Enumerations for {\sf init()} and {\sf wait()}}
 the {\sf GrB\_wait()} method for completing or materializing opaque objects.
 
 %============================================================================
-\section{Indices, Index Arrays, and Scalar Arrays}
+\section{Indices, index arrays, and scalar arrays}
 
 In order to interface with third-party software (\ie, software other than
 an implementation of the GraphBLAS), operations 
@@ -89,7 +89,7 @@ \section{Indices, Index Arrays, and Scalar Arrays}
 \end{table}
 
 %============================================================================
-\section{Types (Domains)}
+\section{Types (domains)}
 \label{Sec:Domains}
 
 In GraphBLAS, domains correspond to the valid values for types from the
@@ -145,7 +145,7 @@ \section{Types (Domains)}
 \end{table}
 
 %============================================================================
-\section{Algebraic Objects, Operators and Associated Functions}
+\section{Algebraic objects, operators and associated functions}
 
 GraphBLAS operators operate on elements stored in GraphBLAS collections. A 
 \emph{binary operator} is a function that maps two input values to one 
@@ -727,7 +727,7 @@ \subsection{Matrices}
 (j,i,A_{ij}) : (i,j,A_{ij}) \in \mathbf{L}(\matrix{A}) \} \rangle$.
 
 %----------------------------------------------------------------------------
-\subsubsection{External Matrix Formats}\label{Sec:GrB_Format}
+\subsubsection{External matrix formats}\label{Sec:GrB_Format}
 
 The specification also supports the export and import of matrices to/from a 
 number of commonly used formats, such as COO, CSR, and CSC formats.  When
@@ -994,7 +994,7 @@ \section{Descriptors}
 \end{table}
 
 %============================================================================
-\section{{GrB\_Info} Return Values}
+\section{{GrB\_Info} return values}
 
 All GraphBLAS methods return a {\sf GrB\_Info} enumeration value. The three
 types of return codes (informational, API error, and execution error) and their

diff --git a/graph-api-c/ops_assign.tex b/graph-api-c/ops_assign.tex
@@ -1,4 +1,4 @@
-\subsection{{\sf assign}: Modifying Sub-Graphs}
+\subsection{{\sf assign}: Modifying sub-graphs}
 \label{Sec:assign}
 
 Assign the contents of a subset of a matrix or vector.

diff --git a/graph-api-c/ops_extract.tex b/graph-api-c/ops_extract.tex
@@ -1,4 +1,4 @@
-\subsection{{\sf extract}: Selecting Sub-Graphs}
+\subsection{{\sf extract}: Selecting sub-graphs}
 \label{Sec:extract}
 
 Extract a subset of a matrix or vector.