{"id":510,"date":"2023-07-17T13:00:15","date_gmt":"2023-07-17T18:00:15","guid":{"rendered":"https:\/\/ceid1.wpenginepowered.com\/HYPAD\/?page_id=510"},"modified":"2024-07-08T11:32:37","modified_gmt":"2024-07-08T16:32:37","slug":"home","status":"publish","type":"page","link":"https:\/\/ceid.utsa.edu\/HYPAD\/","title":{"rendered":"Home"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"510\" class=\"elementor elementor-510\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-cfb4734 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"cfb4734\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-55263134\" data-id=\"55263134\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4d5a58fb elementor-widget elementor-widget-text-editor\" data-id=\"4d5a58fb\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"border-style: solid;border-color: #e3e3e3;--tw-border-spacing-x: 0;--tw-border-spacing-y: 0;--tw-translate-x: 0;--tw-translate-y: 0;--tw-rotate: 0;--tw-skew-x: 0;--tw-skew-y: 0;--tw-scale-x: 1;--tw-scale-y: 1;--tw-scroll-snap-strictness: proximity;--tw-ring-offset-width: 0px;--tw-ring-offset-color: #fff;--tw-ring-offset-shadow: 0 0 transparent;--tw-ring-shadow: 0 0 transparent;--tw-shadow: 0 0 transparent;--tw-shadow-colored: 0 0 transparent;margin-bottom: 1.25em\"><span style=\"color: #0d0d0d;font-family: S\u00f6hne, ui-sans-serif, system-ui, -apple-system, Segoe UI, Roboto, Ubuntu, Cantarell, Noto Sans, sans-serif, Helvetica Neue, Arial, Apple Color Emoji, Segoe UI Emoji, Segoe UI Symbol, Noto Color Emoji\">HYPercomplex Automatic Differentiation (HYPAD) is a methodology to infuse existing codes with automatic differentiation capabilities. The method consists of \u201caugmenting\u201d variables with one or more imaginary units to obtain partial derivatives that are step-size independent and machine precision accurate. It is an attractive method because the existing numerical method is enhanced in a straightforward manner. The purpose of this web site is to provide educational material (see Lecture Notes), example Python notebooks (see Software Downloads), and supporting libraries (see Software Downloads) to facilitate the implementation of HYPAD across scientific and engineering software.<\/span><\/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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5c23355 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5c23355\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-28ec1cf\" data-id=\"28ec1cf\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-555fe72 elementor-widget elementor-widget-image\" data-id=\"555fe72\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"300\" height=\"300\" src=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/05\/rowdy.png\" class=\"attachment-medium size-medium wp-image-1009\" alt=\"\" srcset=\"https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/05\/rowdy.png 300w, https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/05\/rowdy-150x150.png 150w, https:\/\/ceid.utsa.edu\/HYPAD\/wp-content\/uploads\/sites\/50\/2024\/05\/rowdy-160x160.png 160w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>\t\t\t\t\t\t\t\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":"<p>HYPercomplex Automatic Differentiation (HYPAD) is a methodology to infuse existing codes with automatic differentiation capabilities. The method consists of \u201caugmenting\u201d variables with one or more imaginary units to obtain partial derivatives that are step-size independent and machine precision accurate. It is an attractive method because the existing numerical method is enhanced in a straightforward manner. [&hellip;]<\/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-510","page","type-page","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.3 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Home - 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\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Home - HYPercomplex Automatic Differentiation\" \/>\n<meta property=\"og:description\" content=\"HYPercomplex Automatic Differentiation (HYPAD) is a methodology to infuse existing codes with automatic differentiation capabilities. 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