{"id":633,"date":"2023-07-19T13:17:44","date_gmt":"2023-07-19T18:17:44","guid":{"rendered":"https:\/\/ceid1.wpenginepowered.com\/HYPAD\/?page_id=633"},"modified":"2024-05-10T11:38:49","modified_gmt":"2024-05-10T16:38:49","slug":"background","status":"publish","type":"page","link":"https:\/\/ceid.utsa.edu\/HYPAD\/background\/","title":{"rendered":"Background"},"content":{"rendered":"\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t

What is HYPAD?<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t\t
\n\t\t\t
\n\t\t\t\t\t\t
\n\t\t\t\t
\n\t\t\t\t\t\t\t\t\t

HYPAD stands as a beacon of innovation in the realm of automatic differentiation, offering a seamless method for extending numerical codes to automatically provide derivatives. As a form of Automatic Differentiation, its brilliance lies in its ability to effortlessly integrate with existing algorithms, enhancing them with one or more imaginary axes, thereby enabling hypercomplex algebra to automatically compute the derivative(s) during execution.<\/p>\n

What sets HYPAD apart is its remarkable precision. The derivatives computed through HYPAD maintain machine precision, ensuring that they do not introduce any additional errors beyond what the original algorithm already possesses. This precision is paramount, especially in fields where accuracy is non-negotiable, such as scientific computing, engineering, and machine learning.<\/p>\n

This website serves as a gateway to demystify and democratize HYPAD, making it accessible and implementable to a wide audience, regardless of their familiarity with hypercomplex algebras. Whether you’re a seasoned researcher or a curious enthusiast, you’ll find resources tailored to your needs. From comprehensive lecture notes elucidating the underlying principles to a specialized numerical library for handling hypercomplex operations (MultiZ), and an array of source code examples in Python, Mathematica, and Matlab, this website provides everything you need to embark on your journey with HYPAD.<\/p>\n

Notably, the Python examples featured on this platform can be seamlessly executed directly within your browser, further lowering the barrier to entry and facilitating rapid experimentation and learning.<\/p>\n

Join us as we unravel the mysteries of automatic differentiation and embrace the transformative power of HYPAD. Together, let’s embark on a journey of exploration and discovery, where the boundaries of computation are continually pushed, and innovation knows no bounds. Welcome to the world of HYPAD.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"

What is HYPAD? HYPAD stands as a beacon of innovation in the realm of automatic differentiation, offering a seamless method for extending numerical codes to automatically provide derivatives. As a form of Automatic Differentiation, its brilliance lies in its ability to effortlessly integrate with existing algorithms, enhancing them with one or more imaginary axes, thereby […]<\/p>\n","protected":false},"author":248,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-633","page","type-page","status-publish","hentry"],"yoast_head":"\nBackground - HYPercomplex Automatic Differentiation<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ceid.utsa.edu\/HYPAD\/background\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Background - HYPercomplex Automatic Differentiation\" \/>\n<meta property=\"og:description\" content=\"What is HYPAD? HYPAD stands as a beacon of innovation in the realm of automatic differentiation, offering a seamless method for extending numerical codes to automatically provide derivatives. As a form of Automatic Differentiation, its brilliance lies in its ability to effortlessly integrate with existing algorithms, enhancing them with one or more imaginary axes, thereby […]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/ceid.utsa.edu\/HYPAD\/background\/\" \/>\n<meta property=\"og:site_name\" content=\"HYPercomplex Automatic Differentiation\" \/>\n<meta property=\"article:modified_time\" content=\"2024-05-10T16:38:49+00:00\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/background\\\/\",\"url\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/background\\\/\",\"name\":\"Background - HYPercomplex Automatic Differentiation\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/#website\"},\"datePublished\":\"2023-07-19T18:17:44+00:00\",\"dateModified\":\"2024-05-10T16:38:49+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/background\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/background\\\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/background\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Background\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/#website\",\"url\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/\",\"name\":\"HYPercomplex Automatic Differentiation\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/#organization\",\"name\":\"UTSA College of Engineering\",\"url\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/wp-content\\\/uploads\\\/sites\\\/50\\\/2020\\\/12\\\/cropped-cropped-HYPAD-Logo-e1716582453721.png\",\"contentUrl\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/wp-content\\\/uploads\\\/sites\\\/50\\\/2020\\\/12\\\/cropped-cropped-HYPAD-Logo-e1716582453721.png\",\"width\":511,\"height\":511,\"caption\":\"UTSA College of Engineering\"},\"image\":{\"@id\":\"https:\\\/\\\/ceid.utsa.edu\\\/HYPAD\\\/#\\\/schema\\\/logo\\\/image\\\/\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Background - HYPercomplex Automatic Differentiation","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/ceid.utsa.edu\/HYPAD\/background\/","og_locale":"en_US","og_type":"article","og_title":"Background - HYPercomplex Automatic Differentiation","og_description":"What is HYPAD? HYPAD stands as a beacon of innovation in the realm of automatic differentiation, offering a seamless method for extending numerical codes to automatically provide derivatives. As a form of Automatic Differentiation, its brilliance lies in its ability to effortlessly integrate with existing algorithms, enhancing them with one or more imaginary axes, thereby […]","og_url":"https:\/\/ceid.utsa.edu\/HYPAD\/background\/","og_site_name":"HYPercomplex Automatic Differentiation","article_modified_time":"2024-05-10T16:38:49+00:00","twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/ceid.utsa.edu\/HYPAD\/background\/","url":"https:\/\/ceid.utsa.edu\/HYPAD\/background\/","name":"Background - HYPercomplex Automatic Differentiation","isPartOf":{"@id":"https:\/\/ceid.utsa.edu\/HYPAD\/#website"},"datePublished":"2023-07-19T18:17:44+00:00","dateModified":"2024-05-10T16:38:49+00:00","breadcrumb":{"@id":"https:\/\/ceid.utsa.edu\/HYPAD\/background\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/ceid.utsa.edu\/HYPAD\/background\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/ceid.utsa.edu\/HYPAD\/background\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/ceid.utsa.edu\/HYPAD\/"},{"@type":"ListItem","position":2,"name":"Background"}]},{"@type":"WebSite","@id":"https:\/\/ceid.utsa.edu\/HYPAD\/#website","url":"https:\/\/ceid.utsa.edu\/HYPAD\/","name":"HYPercomplex Automatic Differentiation","description":"","publisher":{"@id":"https:\/\/ceid.utsa.edu\/HYPAD\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/ceid.utsa.edu\/HYPAD\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/ceid.utsa.edu\/HYPAD\/#organization","name":"UTSA College of Engineering","url":"https:\/\/ceid.utsa.edu\/HYPAD\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/ceid.utsa.edu\/HYPAD\/#\/schema\/logo\/image\/","url":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2020\/12\/cropped-cropped-HYPAD-Logo-e1716582453721.png","contentUrl":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2020\/12\/cropped-cropped-HYPAD-Logo-e1716582453721.png","width":511,"height":511,"caption":"UTSA College of Engineering"},"image":{"@id":"https:\/\/ceid.utsa.edu\/HYPAD\/#\/schema\/logo\/image\/"}}]}},"_links":{"self":[{"href":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-json\/wp\/v2\/pages\/633","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-json\/wp\/v2\/users\/248"}],"replies":[{"embeddable":true,"href":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-json\/wp\/v2\/comments?post=633"}],"version-history":[{"count":0,"href":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-json\/wp\/v2\/pages\/633\/revisions"}],"wp:attachment":[{"href":"https:\/\/ceid.utsa.edu\/HYPAD\/wp-json\/wp\/v2\/media?parent=633"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}