I$\heartsuit$LA: Compilable Markdown for Linear Algebra

\begin{align*} A_{i, j} & = \begin{cases} 1 & \text{if} \left( i, j \right) \in E \\ 0 & \text{otherwise} \end{cases} \\ D_{i,i} & = \sum_j A_{i, j} \\ L & = D^{-1}\left( D A \right) \\ \intertext{where} E & \in \{\mathbb{Z} \times \mathbb{Z}\} \\ A & \in \mathbb{R}^{ n \times n } \\ n & \in \mathbb{Z} \end{align*} A = sparse(E(:,1),E(:,2),1,n,n); D = diag(sum(A,2)); L = D\(D-A); \centering \resizebox{\textwidth}{!} { \begin{minipage}[c]{\textwidth} \begin{align*} \textit{A}_{\textit{i}, \textit{j}} & = \begin{cases} 1 & \text{if} \left( \textit{i}, \textit{j} \right) \in \textit{E} \\ 0 & \text{otherwise} \end{cases} \\ \textit{D}_{\textit{i},\textit{i}} & = \sum_\textit{j} \textit{A}_{\textit{i}, \textit{j}} \\ \textit{L} & = \textit{D}^{-1}\left( \textit{D} \textit{A} \right) \\ \intertext{where} \textit{E} & \in \{\mathbb{Z} \times \mathbb{Z}\} \\ \textit{A} & \in \mathbb{R}^{ \textit{n} \times \textit{n} } \\ \textit{n} & \in \mathbb{Z} \end{align*} \end{minipage} } LaTeX output

[1]  Wojciech Matusik,et al.  Simit , 2016, ACM Trans. Graph..

[2]  Theodore Kim,et al.  Anisotropic elasticity for inversion-safety and element rehabilitation , 2019, ACM Trans. Graph..

[3]  Jonas Unger,et al.  A Unified Framework for Compression and Compressed Sensing of Light Fields and Light Field Videos , 2019, ACM Trans. Graph..

[4]  Leonard McMillan,et al.  Plenoptic Modeling: An Image-Based Rendering System , 2023 .

[5]  Vikram S. Adve,et al.  LLVM: a compilation framework for lifelong program analysis & transformation , 2004, International Symposium on Code Generation and Optimization, 2004. CGO 2004..

[6]  Shoaib Kamil,et al.  The tensor algebra compiler , 2017, Proc. ACM Program. Lang..

[7]  Olga Sorkine-Hornung,et al.  Properties of Laplace Operators for Tetrahedral Meshes , 2020, Comput. Graph. Forum.

[8]  Szymon Rusinkiewicz,et al.  A symmetric objective function for ICP , 2019, ACM Trans. Graph..

[9]  Yong He,et al.  Slang: language mechanisms for extensible real-time shading systems , 2018, ACM Trans. Graph..

[10]  Mikhail Bessmeltsev,et al.  Vectorization of Line Drawings via Polyvector Fields , 2018, ACM Trans. Graph..

[11]  Olga Sorkine-Hornung,et al.  Deformation Capture via Soft and Stretchable Sensor Arrays , 2018, ACM Trans. Graph..

[12]  C. H. Flood,et al.  The Fortress Language Specification , 2007 .

[13]  Soren Laue,et al.  GENO - GENeric Optimization for Classical Machine Learning , 2019, NeurIPS.

[14]  Andrei Jalba,et al.  Efficient and Accurate Collision Response for Elastically Deformable Models , 2019, ACM Trans. Graph..

[15]  U. Norell,et al.  Towards a practical programming language based on dependent type theory , 2007 .

[16]  Alan Edelman,et al.  Julia: A Fresh Approach to Numerical Computing , 2014, SIAM Rev..

[17]  Theodore Kim,et al.  Analytic Eigensystems for Isotropic Distortion Energies , 2019, ACM Trans. Graph..

[18]  David Coeurjolly,et al.  SPOT , 2019, ACM Trans. Graph..

[19]  Iain Dunning,et al.  JuMP: A Modeling Language for Mathematical Optimization , 2015, SIAM Rev..

[20]  Michel Goossens,et al.  The LaTeX companion , 1993 .

[21]  Olga Sorkine-Hornung,et al.  Robust inside-outside segmentation using generalized winding numbers , 2013, ACM Trans. Graph..

[22]  Emily Whiting,et al.  Computational design of fabric formwork , 2019, ACM Trans. Graph..

[23]  Maaz Bin Safeer Ahmad,et al.  Automatically translating image processing libraries to halide , 2019, ACM Trans. Graph..

[24]  Ken Perlin,et al.  An image synthesizer , 1988 .

[25]  Marc Levoy,et al.  Handheld multi-frame super-resolution , 2019, ACM Trans. Graph..

[26]  Adrian Sampson,et al.  Geometry types for graphics programming , 2020, Proc. ACM Program. Lang..

[27]  Matthew Turk,et al.  A Morphable Model For The Synthesis Of 3D Faces , 1999, SIGGRAPH.

[28]  Kenneth E. Iverson,et al.  Notation as a tool of thought , 1980, APLQ.

[29]  David Coeurjolly,et al.  Code replicability in computer graphics , 2020, ACM Trans. Graph..

[30]  Keenan Crane,et al.  Penrose: from mathematical notation to beautiful diagrams , 2020, ACM Trans. Graph..

[31]  Skipper Seabold,et al.  Statsmodels: Econometric and Statistical Modeling with Python , 2010, SciPy.

[32]  Markus Püschel,et al.  A Basic Linear Algebra Compiler , 2014, CGO '14.

[33]  Jernej Barbic,et al.  Hand modeling and simulation using stabilized magnetic resonance imaging , 2019, ACM Trans. Graph..

[34]  Xiao-Ming Fu,et al.  Atlas refinement with bounded packing efficiency , 2019, ACM Trans. Graph..

[35]  Michael Wimmer,et al.  Gaussian-product subdivision surfaces , 2019, ACM Trans. Graph..

[36]  Margaret M. Burnett,et al.  A practical guide to controlled experiments of software engineering tools with human participants , 2013, Empirical Software Engineering.

[37]  Yuting Yang,et al.  VizGen: accelerating visual computing prototypes in dynamic languages , 2016, ACM Trans. Graph..

[38]  Marc Alexa,et al.  Conforming weighted delaunay triangulations , 2020, ACM Trans. Graph..

[39]  J. P. Lewis,et al.  Direct delta mush skinning and variants , 2019, ACM Trans. Graph..

[40]  Fabio Pellacini,et al.  Eurographics Symposium on Rendering 2010 Safegi: Type Checking to Improve Correctness in Rendering System Implementation , 2022 .

[41]  Keenan Crane,et al.  The Vector Heat Method , 2018, ACM Trans. Graph..

[42]  L. Lamport How to write a 21st century proof , 2012 .

[43]  J. Lofberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).

[44]  Pat Hanrahan,et al.  A language for shading and lighting calculations , 1990, SIGGRAPH.

[45]  Frédo Durand,et al.  Decoupling algorithms from schedules for easy optimization of image processing pipelines , 2012, ACM Trans. Graph..

[46]  Philip Levis,et al.  Ebb: A DSL for Physical Simluation on CPUs and GPUs , 2015, ACM Trans. Graph..

[47]  Frédo Durand,et al.  Taichi , 2019, ACM Trans. Graph..

[48]  Mohan Ganesalingam,et al.  The Language of Mathematics , 2013, Lecture Notes in Computer Science.

[49]  Gordon Wetzstein,et al.  Wave-based non-line-of-sight imaging using fast f-k migration , 2019, ACM Trans. Graph..

[50]  Sebastian Raschka,et al.  MLxtend: Providing machine learning and data science utilities and extensions to Python's scientific computing stack , 2018, J. Open Source Softw..

[51]  Pierre Alliez,et al.  Polygon Mesh Processing , 2010 .

[52]  Philipp Slusallek,et al.  Optimal multiple importance sampling , 2019, ACM Trans. Graph..

[53]  Alec Jacobson,et al.  Collision‐Aware and Online Compression of Rigid Body Simulations via Integrated Error Minimization , 2018, Comput. Graph. Forum.

[54]  Jeremy Avigad,et al.  The Lean Theorem Prover (System Description) , 2015, CADE.