Compiler optimizations | Distributed computing problems
Automatic vectorization, in parallel computing, is a special case of automatic parallelization, where a computer program is converted from a scalar implementation, which processes a single pair of operands at a time, to a vector implementation, which processes one operation on multiple pairs of operands at once. For example, modern conventional computers, including specialized supercomputers, typically have vector operations that simultaneously perform operations such as the following four additions (via SIMD or SPMD hardware): However, in most programming languages one typically writes loops that sequentially perform additions of many numbers. Here is an example of such a loop, written in C: for (i = 0; i < n; i++) c[i] = a[i] + b[i]; A vectorizing compiler transforms such loops into sequences of vector operations. These vector operations perform additions on blocks of elements from the arrays a, b and c. Automatic vectorization is a major research topic in computer science. (Wikipedia).
Linear Algebra for Computer Scientists. 1. Introducing Vectors
This computer science video is one of a series on linear algebra for computer scientists. This video introduces the concept of a vector. A vector is essentially a list of numbers that can be represented with an array or a function. Vectors are used for data analysis in a wide range of f
From playlist Linear Algebra for Computer Scientists
Gilles Pagès: Optimal vector Quantization: from signal processing to clustering and ...
Abstract: Optimal vector quantization has been originally introduced in Signal processing as a discretization method of random signals, leading to an optimal trade-off between the speed of transmission and the quality of the transmitted signal. In machine learning, similar methods applied
From playlist Probability and Statistics
In this second part on Motion, we take a look at calculating the velocity and position vectors when given the acceleration vector and initial values for velocity and position. It involves as you might imagine some integration. Just remember that when calculating the indefinite integral o
From playlist Life Science Math: Vectors
Introducing vectors. Vectors are powerful representations of the real world. In this video I introduce you to the concept of a vector in linear algebra, both as an abstract concept and also as an object in a coordinate system. You can learn more about Mathematica on my Udemy course at h
From playlist Introducing linear algebra
What is a Vector Space? (Abstract Algebra)
Vector spaces are one of the fundamental objects you study in abstract algebra. They are a significant generalization of the 2- and 3-dimensional vectors you study in science. In this lesson we talk about the definition of a vector space and give a few surprising examples. Be sure to su
From playlist Abstract Algebra
In this section I introduce plane autonomous systems, which form beautiful and useful vector fields.
From playlist A Second Course in Differential Equations
11H Orthogonal Projection of a Vector
The orthogonal projection of one vector along another.
From playlist Linear Algebra
This shows an small game that illustrates the concept of a vector. The clip is from the book "Immersive Linear Algebra" at http://www.immersivemath.com
From playlist Chapter 2 - Vectors
Matthijs Vákár: Mathematical foundations of automatic differentiation
HYBRID EVENT Recorded during the meeting "Logic of Probabilistic Programming" the January 31, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Aud
From playlist Virtual Conference
Live CEOing Ep 172: Visualization in Wolfram Language
Watch Stephen Wolfram and teams of developers in a live, working, language design meeting. This episode is about Visualization in the Wolfram Language.
From playlist Behind the Scenes in Real-Life Software Design
Adjoint Equation of a Linear System of Equations - by implicit derivative
Automatic Differentiation allows for easily propagating derivatives through explicit relations. The adjoint method also enables efficient derivatives over implicit relations like linear systems, which enables the computation of sensitivities. Here are the notes: https://raw.githubuserconte
From playlist Summer of Math Exposition Youtube Videos
This is the first video of a linear algebra-series on orthogonality. In this video, I define the notion of orthogonal sets, then show that an orthogonal set without the 0 vector is linearly independent, and finally I show that it's easy to calculate the coordinates of a vector in terms of
From playlist Orthogonality
Dive Into Deep Learning, Lecture 2: PyTorch Automatic Differentiation (torch.autograd and backward)
In this video, we discuss PyTorch’s automatic differentiation engine that powers neural networks and deep learning training (for stochastic gradient descent). In this section, you will get a conceptual understanding of how autograd works to find the gradient of multivariable functions. We
From playlist Dive into Deep Learning - Dr. Data Science Series
Affinity Designer - Control the pressure of the Pencil Tool
:: Support Me :: http://www.alecaddd.com/support-me/ :: Tutorial Series :: WordPress 101 - Create a theme from scratch: http://bit.ly/1RVHRLj WordPress Premium Theme Development: http://bit.ly/1UM80mR Learn SASS from Scratch: http://bit.ly/220yzmZ Design Factory: http://bit.ly/1X7Csaz Aff
From playlist Affinity Designer
How well do you know Conservation Laws
Going through a series of questions, test your understanding of the Law of Conservation of momentum and energy Check out www.physicshigh.com and follow me on facebook and twitter @physicshigh Support me on www.patreon.com/highschoolphysicsexplained
From playlist Dynamics
Eigenvectors and linear independence
Eigenvectors corresponding to different eigenvalues are linearly independent In this video, I prove one of my favorite linear algebra facts: Nonzero eigenvectors of a matrix corresponding to different eigenvalues are automatically linearly independent. This fact is crucial for diagonaliza
From playlist Diagonalization
Lec 11 | MIT Finite Element Procedures for Solids and Structures, Nonlinear Analysis
Lecture 11: Solution of Nonlinear Static FE Equations II Instructor: Klaus-Jürgen Bathe View the complete course: http://ocw.mit.edu/RES2-002S10 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT Nonlinear Finite Element Analysis
After our introduction to matrices and vectors and our first deeper dive into matrices, it is time for us to start the deeper dive into vectors. Vector spaces can be vectors, matrices, and even function. In this video I talk about vector spaces, subspaces, and the porperties of vector sp
From playlist Introducing linear algebra
07 Backpropagation and Automatic Differentiation
Introduction to chain rule of differentiation and automatic differentiation
From playlist There and Back Again: A Tale of Slopes and Expectations (NeurIPS-2020 Tutorial)