#lapack

[thesafewaystobereckless]

Oldschool determinants & floating points

Forget those easypeasy 2x2, 3x3, and 4x4 (if you're feeling spicy) formulas for matrix determinants that you forced yourself to memorize in linear algebra. Real ones know that you can get the determinant of any matrix through LU decomposition.

Fun fact though, because Python floating point numbers aren't really the same as floating point numbers in C (python does everything with infinite precision), I was getting different answers for determinants I computed with my LU algorithm versus what NumPy was getting with the algorithm it uses from LAPACK.

For instant with a 99x99 random matrix, the absolute difference in our determinants was over 1 trillion.

BUT

Each determinant was on the order of 10^25 (because the matrices were filled with values from a uniform random distribution and to oversimplify these don't really play nice with det algorithms).

This was my value: -1.3562741025533489e+25

This was NumPy's value: -1.3562741025534902e+25

I bolded the digits where they differed in value. The actual percentage difference between them is basically 0, ~10^-10

I'm sure in some applications this would matter, but for me it doesn't really.

[codezup]

C++ and Scientific Computing: Using OpenBLAS and LAPACK

Introduction C++ and Scientific Computing: Using OpenBLAS and LAPACK is a powerful combination for high-performance numerical computations. In this tutorial, we will explore the basics of C++ and its application in scientific computing, focusing on the use of OpenBLAS and LAPACK libraries. By the end of this tutorial, you will have a solid understanding of how to use these libraries to perform…

[alanshemper]

Open-source linear algebra software FTW!

This shit really was a game changer. Before LINPACK/LAPACK, you had to license commercial software like MA27 from the Harwell Subroutine Library (now, of course, superseded by MA57).

Now you can just

pip install numpy

[soleddotme]

#nike #vandal #lapack #clicklinkinbio #nikes #vandals

[stevenfusco]

Armadillo is a high quality linear algebra library (matrix maths) for the C++ language, aiming towards a good balance between speed and ease of use

[hersonls]

Apple M1 para desenvolvedores do zero - Part 1

Eae, essa vai ser uma série ( espero ) de artigos de tudo que fiz assim que recebi o meu Macbook Air com processador M1. Espero que te ajude migrar todo seu ambiente Intel para M1 ( arm64 ).

Infelizmente ainda temos um caminho longo pela frente, boa parte dos softwares já conseguem ser compilados nativamente, porem, outros ainda precisam ser emulados atrav'ées do Rosetta por conta de bibliotecas de sistema com "ffi" que ainda não estao 100% compativels.

Separei em topicos de passos que segui exatamente na ordem que estão, espero que ajude.

Xcode + Rosetta

A instalação é feita através da App Store. Antes de começar toda a configuração da maquina instale a versão mais recente.

Em seguida instalar componentes de desenvolvimento: xcode-select --install

Brew no M1 ( Gerenciador de Pacotes )

As instalação do brew eu segui as instruções dadas a partir do artigo:

https://gist.github.com/nrubin29/bea5aa83e8dfa91370fe83b62dad6dfa

Instalando dependências de sistema

Essas bibliotecas servirão para diversos softwares como Python, Pillow, Node e etc. Elas são necessárias para a compilação e uso dos mesmos.

brew install libtiff libjpeg webp little-cms2 freetype harfbuzz fribidi brew install openblas brew install blis brew install zlib brew install gdal brew install pyenv brew install geoip brew install libgeoip brew install libffi brew install xz

Opcionais:

brew install postgres

Instalando Pyenv no M1

Instalando pyenv para facilitar o isolavento e definição de versões do python no sistema.

Eu tive problemas instalando diretamente no sistema, utilizando o brew. Algumas bibliotecas não eram encontradas e o trabalho para configuração de PATHs me fez migrar para pyenv.

brew install pyenv

Variaveis de ambiente

Para que as futuras compilações e instalações consigam encontrar todas as bibliotecas instaladas através do brew, é necessário configurar variáveis de ambiente para isso.

Adicione as linhas abaixo em seu arquivo de configuração do shell.

Se for bash: .bashrc Se for zsh: .zshrc

Eu fiz um script onde faz cache das chamadas do homebrew. Fique atento as versões das bibliotecas, se por ventura algumas delas não forem encontradas, confira o path das variaveis de ambiente.

Obs.: A melhor forma para obter o path das bibliotecas seria através do comando brew --prefix mas fazer inumeras chamadas pode deixar a inicialização do shell lenta.

Segue o que deve ser inserido em um dos arquivos acima:

if [ -z "$HOMEBREW_PREFIX" ]; then export PATH="/opt/homebrew/bin:$PATH" if command -v brew 1>/dev/null 2>&1; then SHELL_ENV="$(brew shellenv)" echo -n "$SHELL_ENV $(cat ~/.zshrc)" > .zshrc eval $SHELL_ENV fi fi export PATH="$HOMEBREW_PREFIX/opt/openssl@1.1/bin:$PATH" export LDFLAGS="-L/opt/homebrew/lib -L/opt/homebrew/opt/openssl@1.1/lib -L/opt/homebrew/opt/sqlite/lib -L/opt/homebrew/opt/python@3.8/lib -L/opt/homebrew/opt/libffi/lib -L/opt/homebrew/opt/openblas/lib -L/opt/homebrew/opt/lapack/lib -L/opt/homebrew/opt/zlib/lib -L/opt/homebrew/Cellar/bzip2/1.0.8/lib -L/opt/homebrew/opt/readline/lib" export CPPFLAGS="-I/opt/homebrew/include -I/opt/homebrew/opt/openssl@1.1/include -I/opt/homebrew/opt/sqlite/include -I/opt/homebrew/opt/libffi/include -I/opt/homebrew/opt/openblas/include -I/opt/homebrew/opt/lapack/include -I/opt/homebrew/opt/zlib/include -I/opt/homebrew/Cellar/bzip2/1.0.8/include -I/opt/homebrew/opt/readline/include" export PKG_CONFIG_PATH="$HOMEBREW_PREFIX/opt/openssl@1.1/lib/pkgconfig" export PKG_CONFIG_PATH="$PKG_CONFIG_PATH:$HOMEBREW_PREFIX/opt/python@3.8/lib/pkgconfig:$HOMEBREW_PREFIX/opt/libffi/lib/pkgconfig:$HOMEBREW_PREFIX/opt/openblas/lib/pkgconfig:$HOMEBREW_PREFIX/opt/lapack/lib/pkgconfig:$HOMEBREW_PREFIX/opt/zlib/lib/pkgconfig" export GDAL_LIBRARY_PATH="/opt/homebrew/opt/gdal/lib/libgdal.dylib" export GEOS_LIBRARY_PATH=$GDAL_LIBRARY_PATH export LD_LIBRARY_PATH=$HOMEBREW_PREFIX/lib:$LD_LIBRARY_PATH export DYLD_LIBRARY_PATH=$HOMEBREW_PREFIX/lib:$DYLD_LIBRARY_PATH export OPENBLAS="$(brew --prefix openblas)" if command -v pyenv 1>/dev/null 2>&1; then eval "$(pyenv init -)" fi

Instalando Python 3 no M1

Para instalar o Python através do pipenv no m1 é necessário aplicar um patch para corrigir algumas informações da arquitetura.

O time do Homebrew disponibilizou esses patchs e pode ser localizado em: https://github.com/Homebrew/formula-patches/tree/master/python

Como estou instalando a versão 3.8, segue o comando:

PYTHON_CONFIGURE_OPTS="--with-openssl=$(brew --prefix openssl)" \ pyenv install --patch 3.8.7 <<(curl -sSL "https://raw.githubusercontent.com/Homebrew/formula-patches/master/python/3.8.7.patch")

NVM e Node no M1

mkdir ~/.nvm

Colocar no .zshrc ou .bashrc

export NVM_DIR="$HOME/.nvm" [ -s "/opt/homebrew/opt/nvm/nvm.sh" ] && . "/opt/homebrew/opt/nvm/nvm.sh" # This loads nvm [ -s "/opt/homebrew/opt/nvm/etc/bash_completion.d/nvm" ] && . "/opt/homebrew/opt/nvm/etc/bash_completion.d/nvm" # This loads nvm bash_completion

Fim da primeira parte:

Essa primeira parte mostrei como instalar o gerenciador de pacores, Python e Node. Irei fazer Posts sobre partes especificas como Android Studio, Xcode, Docker e etc.

Espero que me acompanhem e qualquer dúvida pode deixar o comentário.

Até mais

[oomorigohan]

Lapack release 1

[parentingroundabout]

Roundabout Roundup: Dance & Co., Lapacker Laptop Backpack, and Hugimals

[tonkitk]

Numpy random permute

#Numpy random permute full

Returns outndarray Permuted sequence or array range. axisint, optional The axis which x is shuffled along. If x is an array, make a copy and shuffle the elements randomly. Parameters xint or arraylike If x is an integer, randomly permute np.arange (x). To permute both rows and columns I think you either have to run it twice, or pull some ugly shenanigans with numpy.unravel_index that hurts my head to think about. Randomly permute a sequence, or return a permuted range. PVec0, pVec1 = calcMyPermutationVectors()Īrr.take(pVec0, axis=0, out=arr, mode="clip")Īrr.take(pVec1, axis=1, out=arr, mode="clip") Numba supports top-level functions from the numpy.random module. So in total you call should look something like the following: #Inplace Rearrange On a final note, take seems to be a array method, so instead of np.take(i, rr, axis=0) If x is an integer, randomly permute np.arange (x). If x is a multi-dimensional array, it is only shuffled along its first index. If you don't set the mode it will make a copy to restore the array state on a Python exception (see here). Randomly permute a sequence, or return a permuted range. To do it in-place, all you need to do is specify the "out" parameter to be the same as the input array AND you have to set the mode="clip" or mode="wrap". Here is an example of doing a random permutation of an identity matrix's rows: import numpy as npĪrray(, We are using Excel’s RANDBETWEEN functions for Column B here. axisint, optional Slices of x in this axis are shuffled. Parameters xarraylike, at least one-dimensional Array to be shuffled. Unlike shuffle, each slice along the given axis is shuffled independently of the others. The trick here is we pre- generate the random m’s. method (x, axisNone, outNone) Randomly permute x along axis axis. You can do this in-place with numpy's take() function, but it requires a bit of hoop jumping. For simplicity, we assume N 5, but this methodology works with any N (as long as Excel can hold it) First, you need to set up k’s and m’s.

#Numpy random permute full

Warning: The below example works properly, but using the full set of parameters suggested at the post end exposes a bug, or at least an "undocumented feature" in the numpy.take() function. I currently copy matrices this large unnecessarily, but I would hope this could be easily avoided for permutation. Actually I would like to use matrices as large as possible, but I don't want to deal with the inconvenience of not being able to hold them in RAM, and I do O(N^3) LAPACK operations on the matrix which would also limit the practical matrix size. The matrix is small enough to fit into desktop RAM but big enough that I do not want to copy it thoughtlessly. shuffle: the order of the sub-arrays along the first axis, but the content remains the same, which is equivalent to. Or they mean counting or enumerating all possible permutations. Sometimes when people talk about permutations, they only mean the sampling of random permutations, for example as part of a procedure to obtain p-values in statistics. Also for some simple situations it may be sufficient to just separately track an index permutation, but this is not convenient in my case. Something like this might be possible with numpy's "advanced indexing" but my understanding is that such a solution would not be in-place. Maybe I am just failing at searching the internet. Now, let x be a permutation of the elements of x. Right now I am manually swapping rows and columns, but I would have expected numpy to have a nice function f(M, v) where M has n rows and columns, and v has n entries, so that f(M, v) updates M according to the index permutation v. Write a Python program to print all permutations of a given string (including. Given a 2D array, I would like to permute this array row-wise. Mathematically this corresponds to pre-multiplying the matrix by the permutation matrix P and post-multiplying it by P^-1 = P^T, but this is not a computationally reasonable solution. Efficiently permute array in row wise using Numpy. np.ed is a function, which you need to call, not assign to it. Julia sample without replacement.I want to modify a dense square transition matrix in-place by changing the order of several of its rows and columns, using python's numpy library.

[assettrust]

Beat saber mod manager 2.2.

#Beat saber mod manager 2.2. install

#Beat saber mod manager 2.2. pro

#Beat saber mod manager 2.2. mods

#Beat saber mod manager 2.2. software

#Beat saber mod manager 2.2. simulator

Follow mappers you enjoy and automatically have it download new maps of theirs when they release them.

Magically send any song from to your game with a single click of a button (and from any device, whether that’s from your phone, your work computer, the library, etc.).

#Beat saber mod manager 2.2. install

To install mods, either download it on your PC and drag it into BMBF (See “Managing BMBF On Your PC” above) or click on the mod download links on QuestBoard from within BMBF, then toggle it on in the BMBF mod section.Įasily Download Songs From Bsaber using SyncSaber / BeatSyncīeatSyncis the ultimate plugin for getting amazing new Beat Saber songs to play.

#Beat saber mod manager 2.2. mods

There’s a lot of mods to do really fantastic things that you can find in the #quest-mods section of the BSMG Discord or in the Released mods tab of QuestBoard.

#Beat saber mod manager 2.2. pro

If you want to manage playlists easier on your PC, want to automated backing up your save data, switch versions easily between the modded version and a version you can play official multiplayer and more, download the PC app Playlist Editor Pro here To find your Quest’s IP, you can look at the top of Sidequest. To view BMBF on your PC or Mac and manage your songs and mods there, type in your Quest’s IP address along with :50000 at the end. Note: Scoresaber has NOT yet been updated for Beat saber 1.13.2.įor a fantastic written guide, visit our BSMG Wiki Here! Managing BMBF on your PC (optional) Scoresaber does not replace the base game leaderboards, it only adds leaderboards for custom songs. This link takes you to the ScoreSaber page to set it up. To get leaderboards on custom songs and to be able to get Performance Points (PP) from ranked songs you need the ScoreSaber mod. The mod can be found in the Beat Saber Modding Group in #quest-mods or on the Questboard (opens new window)site. If you would like to play modded multiplayer, you need the mod, Beat Together, which allows for cross-play between pc and quest and allows for custom songs to be used if both parties own said song. If placed in the proper directory, this script greets the user and offers some potentially interesting information about the system's current resources.Also, installing BMBF and modding your game, Official Multiplayer as well as viewing and uploading scores on the base game leaderboards will no longer work. High-performance object-based library for DLA computationsĪ lightweight session manager written in bash. Program to help executing outside programs in proton Rosie Pattern Language (RPL) and the Rosie Pattern Engine. Windows VST2 wrapper that allows them to be used as Linux VST2s in compatible DAWs using Wine.Ī command-line cheatsheet for the command-line High quality music player w/ gapless support Systemd service to download packages updatesĬommand-line client, protocol and server for Java programsĬompile semicolon seperated assembly instructions and hexdumpįrench program to create mathematical exercises and models, cli versionĬryFS encrypts your files, so you can safely store them anywhere Systemd-service-pacman-download-updates-git Systemd timer to download packages updates Systemd-timer-pacman-download-updates-git

#Beat saber mod manager 2.2. simulator

RISC-V CPU simulator for education purposes Move workspaces up or down in the GNOME overviewĪ simple terminal emulator using Vte and Gtk+ writting using the Zig programming languageĪn optimized BLAS library based on GotoBLAS2 1.13 BSD (providing blas, lapack and cblas)Īn optimized BLAS library based on GotoBLAS2 1.13 BSDĪ feature-rich, hardware-independent MIDI toolkit for PythonĪ loudness normalizer that scans music files and calculates loudness-normalized gain and loudness peak values according to the EBU R128 standard, and can optionally write ReplayGain-compatible metadata. Gnome-shell-extension-reorder-workspaces-git Sewing pattern drafting tool aiming to remake the garment industry Michael Park's C++ pattern matching library Handy scripts for i3 window manager: smart resize/open new workspace.

#Beat saber mod manager 2.2. software

Keyboard remapping tool that emulates keyplus firmwareĪ free software library that implements the rsync remote-delta algorithm (rdiff) - development versionĪn object oriented C++ wrapper for cURL tool. Ported to LibreWolf.Ī template-driven engine to generate documentation, API clients and server stubs Native Messaging Host for ff2mpv firefox addon. Ported to LibreWolf.įf2mpv-native-messaging-host-librewolf-git It relies on FFmpeg to read medias and remains consistent with SFML's naming conventions. SfeMovie is a simple C++ library that lets you play movies in SFML based applications.

[codezup]

C++ for Scientific Computing: Using Libraries like OpenBLAS and LAPACK

Introduction C++ for Scientific Computing: Using Libraries like OpenBLAS and LAPACK is a powerful tool for solving complex mathematical problems. This tutorial will guide you through the process of using C++ to perform scientific computing tasks, leveraging the capabilities of popular libraries like OpenBLAS and LAPACK. What Readers Will Learn and Prerequisites In this tutorial, you will learn…

[dltonki]

Magic matrix in freemat

MAGIC MATRIX IN FREEMAT CODE

It is a weakly typed language because types are implicitly converted. MATLAB is a weakly typed programming language. Variables are defined using the assignment operator, =.

MAGIC MATRIX IN FREEMAT CODE

The MATLAB application is built around the MATLAB language, and most use of MATLAB involves typing MATLAB code into the Command Window (as an interactive mathematical shell), or executing text files containing MATLAB code and functions. It is now also used in education, in particular the teaching of linear algebra and numerical analysis, and is popular amongst scientists involved in image processing. MATLAB was first adopted by researchers and practitioners in control engineering, Little's specialty, but quickly spread to many other domains. In 2000, MATLAB was rewritten to use a newer set of libraries for matrix manipulation, LAPACK. These rewritten libraries were known as JACKPAC. They rewrote MATLAB in C and founded MathWorks in 1984 to continue its development. Recognizing its commercial potential, he joined with Moler and Steve Bangert. Jack Little, an engineer, was exposed to it during a visit Moler made to Stanford University in 1983. It soon spread to other universities and found a strong audience within the applied mathematics community. He designed it to give his students access to LINPACK and EISPACK without them having to learn Fortran.

3 Graphics and graphical user interface programmingĬleve Moler, the chairman of the computer-science department at the University of New Mexico, started developing MATLAB in the late 1970s.

MATLAB is widely used in academic and research institutions as well as industrial enterprises. MATLAB users come from various backgrounds of engineering, science, and economics. In 2004, MATLAB had around one million users across industry and academia. An additional package, Simulink, adds graphical multi-domain simulation and Model-Based Design for dynamic and embedded systems. Developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages, including C, C++, Java, and Fortran.Īlthough MATLAB is intended primarily for numerical computing, an optional toolbox uses the MuPAD symbolic engine, allowing access to symbolic computing capabilities. MATLAB ( matrix laboratory) is a numerical computing environment and fourth-generation programming language. Multi-paradigm: imperative, procedural, object-oriented, array For the region in Bangladesh, see Matlab Upazila.

[akshitimr]

Numerical analysis: the hands-on mathematical method

According to this latest study, the growth in the Numerical Analysis Software market will change significantly from the previous year. Over the next five years, Numerical Analysis Software will register a CAGR in terms of revenue, and the global market size will reach USD in millions by 2028.

Analytica is a popular proprietary software programme for creating and evaluating numerical models. It is an impact diagram-based declarative and visual programming language. Numerical analysis is used to create and examine numerical methods for addressing problems in other fields of mathematics such as calculus, linear algebra, and differential equations. Of course, methods for handling such problems already exist in these domains, but they are analytical in nature.

The study addresses the elements driving the worldwide Numerical Analysis Software. Traders and investors can use this data to strategize to increase market share, and newcomers can use it to locate opportunities and grow in the business. There are also some restrictions on the expansion of this market. The Numerical Analysis Software Market study also provides company biographies, SWOT analysis, and business strategies for major industry players. In addition, the research focuses on key industry players, providing details such as business descriptions, skills, current financials, and company advancements.

Read More: https://introspectivemarketresearch.com/reports/numerical-analysis-software-market/

Key Players Mentioned in the Market Numerical Analysis Software Research Report:

Analytica

Matlab

GNU     Octave

Plotly

FlexPro

Julia

Scilab

LAPACK

ScaLAPACK

NAG     Library

FreeMat

Calerga

LabVIEW

This Numerical Analysis Software Market report covers important market segments on the basis of type, application, and region. The regional analysis segment includes key regions such as Europe, North America, the Middle East, Africa, and the Asia Pacific. It shows important business metrics including population density, quality, development, and overall market scenarios. It also discusses important data covering key industry topics such as market expansion and market situation developments. This in-depth Numerical Analysis Software market report also sheds light on important technologies and helps organizations better understand their customers’ buying habits. It shows the global market scenario for the forecast period 2022-2028

Numerical Analysis Software Market Segmentation

The report surveys the presence of the distinctive market segment a global as well as the regional scale that defines the Numerical Analysis Software market size, demands and growth opportunities, and market areas that need to work on.

Numerical Analysis Software Market Segment by Types, Estimates, and Forecast by 2028

Cloud, On Premise

Numerical Analysis Software Market Segment by Applications, Estimates, and Forecast by 2028

Scientific Research, Financial 

The base on geography, the world market of Numerical Analysis Software has been segmented as follows:

North  America includes the United States, Canada, and Mexico

Europe includes     Germany, France, UK, Italy, Spain, Russia, and the Rest of Europe

South America includes Brazil, Argentina, Nigeria, Chile, and South America

The  Asia Pacific includes Japan, China, South Korea, Australia, India, Rest of     Europe

The scope of the Report:

The report segments the global Numerical Analysis Software market based on application, type, service, technology, and region. Each chapter under Numerical Analysis Software segmentation allows readers to grasp the nitty-gritty of the market. A magnified look at the segment-based analysis is aimed at giving the readers a closer look at the opportunities and threats in the Numerical Analysis Software market. It also addresses political scenarios that are expected to impact the Numerical Analysis Software market in both small and big ways. The report on the global Numerical Analysis Software Market examines changing regulatory scenarios to make accurate projections about potential investments. It also evaluates the risk for new entrants and the intensity of the competitive rivalry

Feel free to ask your queries at

https://www.introspectivemarketresearch.com/inquiry/15189

Note – The Covid-19 (coronavirus) pandemic is impacting society and the overall economy across the world. The impact of this pandemic is growing day by day as well as affecting the supply chain including Numerical Analysis Software industry. The COVID-19 crisis is creating uncertainty in the stock market, massive slowing of supply chain, falling business confidence, and increasing panic among the customer segments. The overall effect of the pandemic is impacting the production process of several industries including Numerical Analysis Software

[imrmarket]

Numerical Analysis Software Market Analysis, Growth, Shares, Size, Trends, Challenges with Forecast to 2028

The Final Report will cover the analysis of the Impact of Covid-19 on this industry.

The global Numerical Analysis Software Market provides qualitative and quantitative information on growth rate, market segmentation, market size, future trends and regional prospects. The research study represents a modern perspective aimed at securing the future potential of the Numerical Analysis Software market. This report analyzes and evaluates the latest prospects for the new retail space, as well as the general and future market performance of Covid-19. In addition, this report provides a detailed overview of competition between some industries and others.

According to this latest study, the growth in the Numerical Analysis Software market will change significantly from the previous year. Over the next five years, the Numerical Analysis Software market will register a CAGR in terms of revenue, and the global market size will reach USD in millions by 2027.

Numerical Analysis Software Market - Size, Competitive Landscape and Segmentation Analysis:

Numerical Analysis Software Market Reports provide a high-level overview of market segments by product type, applications, leading key players, and regions, as well as market statistics. The research insights focuses on the impact of the Covid-19 epidemic on performance and offers a thorough examination of the current market and market dynamics. This crucial understanding of the report's objective can help you make better strategic decisions about investment markets by assessing elements that may affect current and future market circumstances. The leading key players in the Global and Regional market are summarized in a research to understand their future strategies for growth in the market.

The key players covered in the Numerical Analysis Software market report are:

·         Analytica

·         Matlab

·         GNU Octave

·         Plotly

·         FlexPro

·         Julia

·         Scilab

·         LAPACK

·         ScaLAPACK

·         NAG Library

·         FreeMat

·         Calerga

·         LabVIEW

By Type, Numerical Analysis Software has been segmented into:

·         Cloud,

·         On Premise

By Application, Numerical Analysis Software has been segmented into:

·         Scientific Research,

·         Financial,

·         Other

Market Segment by Regions and Countries Level Analysis:

·         North America (U.S., Canada, Mexico)

·         Europe (Germany, U.K., France, Italy, Russia, Spain, Rest of Europe)

·         Asia-Pacific (China, India, Japan, Southeast Asia, Rest of APAC)

·         Middle East & Africa (GCC Countries, South Africa, Rest of MEA)

·         South America (Brazil, Argentina, Rest of South America)

Covid-19 Impact and Recovery Analysis on Industry:

We've kept track of Covid-19's direct impact on this market as well as its indirect impact on other industries. During the analysis period, the impact of the Covid-19 pandemic on the market is predicted to be significant. From a worldwide and regional viewpoint, this report examines the influence of the pandemic on the Numerical Analysis Software industry. The study categorises the Cluster Numerical Analysis Software industry by type, application, and consumer sector to determine market size, market features, and market growth. It also includes a thorough examination of the factors that influenced market development before and after the Covid-19 pandemic. In addition, the research did a pest analysis in the sector to investigate major influencers and entrance obstacles.

[wozziebear]

Dongarra has led the world of high-performance computing through his contributions to efficient numerical algorithms for linear algebra operations, parallel computing programming mechanisms, and performance evaluation tools. For nearly forty years, Moore’s Law produced exponential growth in hardware performance. During that same time, while most software failed to keep pace with these hardware advances, high performance numerical software did—in large part due to Dongarra’s algorithms, optimization techniques, and production-quality software implementations.

These contributions laid a framework from which scientists and engineers made important discoveries and game-changing innovations in areas including big data analytics, healthcare, renewable energy, weather prediction, genomics, and economics, to name a few. Dongarra’s work also helped facilitate leapfrog advances in computer architecture and supported revolutions in computer graphics and deep learning.

Dongarra’s major contribution was in creating open-source software libraries and standards which employ linear algebra as an intermediate language that can be used by a wide variety of applications. These libraries have been written for single processors, parallel computers, multicore nodes, and multiple GPUs per node. Dongarra’s libraries also introduced many important innovations including autotuning, mixed precision arithmetic, and batch computations.

As a leading ambassador of high-performance computing, Dongarra led the field in persuading hardware vendors to optimize these methods, and software developers to target his open-source libraries in their work. Ultimately, these efforts resulted in linear algebra-based software libraries achieving nearly universal adoption for high performance scientific and engineering computation on machines ranging from laptops to the world’s fastest supercomputers. These libraries were essential in the growth of the field—allowing progressively more powerful computers to solve computationally challenging problems.

“Today’s fastest supercomputers draw headlines in the media and excite public interest by performing mind-boggling feats of a quadrillion calculations in a second,” explains ACM President Gabriele Kotsis. “But beyond the understandable interest in new records being broken, high performance computing has been a major instrument of scientific discovery. HPC innovations have also spilled over into many different areas of computing and moved our entire field forward. Jack Dongarra played a central part in directing the successful trajectory of this field. His trailblazing work stretches back to 1979, and he remains one of the foremost and actively engaged leaders in the HPC community. His career certainly exemplifies the Turing Award’s recognition of ‘major contributions of lasting importance.’”

[...]

For over four decades, Dongarra has been the primary implementor or principal investigator for many libraries such as LINPACK, BLAS, LAPACK, ScaLAPACK, PLASMA, MAGMA, and SLATE. These libraries have been written for single processors, parallel computers, multicore nodes, and multiple GPUs per node. His software libraries are used, practically universally, for high performance scientific and engineering computation on machines ranging from laptops to the world’s fastest supercomputers.

These libraries embody many deep technical innovations such as:

Autotuning: through his 2016 Supercomputing Conference Test of Time award-winning ATLAS project, Dongarra pioneered methods for automatically finding algorithmic parameters that produce linear algebra kernels of near-optimal efficiency, often outperforming vendor-supplied codes.

Mixed precision arithmetic: In his 2006 Supercomputing Conference paper, “Exploiting the Performance of 32 bit Floating Point Arithmetic in Obtaining 64 bit Accuracy,” Dongarra pioneered harnessing multiple precisions of floating-point arithmetic to deliver accurate solutions more quickly. This work has become instrumental in machine learning applications, as showcased recently in the HPL-AI benchmark, which achieved unprecedented levels of performance on the world’s top supercomputers.

Batch computations: Dongarra pioneered the paradigm of dividing computations of large dense matrices, which are commonly used in simulations, modeling, and data analysis, into many computations of smaller tasks over blocks that can be calculated independently and concurrently. Based on his 2016 paper, “Performance, design, and autotuning of batched GEMM for GPUs,” Dongarra led the development of the Batched BLAS Standard for such computations, and they also appear in the software libraries MAGMA and SLATE.

Dongarra has collaborated internationally with many people on the efforts above, always in the role of the driving force for innovation by continually developing new techniques to maximize performance and portability while maintaining numerically reliable results using state of the art techniques.  Other examples of his leadership include the Message Passing Interface (MPI) the de-facto standard for portable message-passing on parallel computing architectures, and the Performance API (PAPI), which provides an interface that allows collection and synthesis of performance from components of a heterogeneous system. The standards he helped create, such as MPI, the LINPACK Benchmark, and the Top500 list of supercomputers, underpin computational tasks ranging from weather prediction to climate change to analyzing data from large scale physics experiments.