A Dimension Abstraction Approach to Vectorization in Matlab
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The document presents an approach to vectorizing Matlab source code while preserving correctness and improving efficiency. It describes representing variable dimensionalities, rules for determining when vectorization is valid, and techniques like transpose transformations and additive reduction to enable more vectorizations. Evaluation on image processing and linear algebra examples showed speedups of 1.56x to 4.6x from vectorizing loop-based code.
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4. It introduces algorithms to find shortest paths between all pairs of vertices in a weighted graph using Floyd's and Warshall's algorithms. It includes algorithms to output a shortest path between two vertices.
Chap08alg
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Lect5 v2
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R Language Introduction
The document outlines various statistical and data analysis techniques that can be performed in R including importing data, data visualization, correlation and regression, and provides code examples for functions to conduct t-tests, ANOVA, PCA, clustering, time series analysis, and producing publication-quality output. It also reviews basic R syntax and functions for computing summary statistics, transforming data, and performing vector and matrix operations.
Introduction to MATLAB
MatLab is a matrix-based program used for numeric computation and visualization. It contains functions for creating matrices and performing operations on them like addition, subtraction, multiplication, etc. It also allows plotting of functions and special matrices like magic squares, identity matrices, and Toeplitz matrices. Polynomial operations can also be performed such as addition, multiplication, differentiation and evaluation.
Computer graphics
The document discusses 2D and 3D transformations used in computer graphics. It covers topics like scaling, rotation, translation and how they can be represented using matrices. Matrix representations allow multiple transformations to be combined through matrix multiplication. Both linear transformations like scaling and rotation, as well as affine transformations like translation, can be captured with matrices. The order of matrix multiplications is important, as transformations are not commutative. These concepts extend from 2D to 3D graphics using homogeneous coordinates.
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Robotic Manipulator with Revolute and Prismatic Joints
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