{"id":"https://openalex.org/W2001861853","doi":"https://doi.org/10.1080/10556780802413769","title":"Fast higher-order derivative tensors with Rapsodia","display_name":"Fast higher-order derivative tensors with Rapsodia","publication_year":2008,"publication_date":"2008-12-12","ids":{"openalex":"https://openalex.org/W2001861853","doi":"https://doi.org/10.1080/10556780802413769","mag":"2001861853"},"language":"en","primary_location":{"id":"doi:10.1080/10556780802413769","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780802413769","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080904380","display_name":"Isabelle Charpentier","orcid":"https://orcid.org/0000-0001-9079-8236"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210100753","display_name":"Laboratoire de M\u00e9canique des Sols, Structures et Mat\u00e9riaux","ror":"https://ror.org/0156gk772","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I4210095849","https://openalex.org/I4210100753"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"I. Charpentier","raw_affiliation_strings":["Laboratoire de Physique et M\u00e9canique des Mat\u00e9riaux, UMR CNRS 7554, Ile du Saulcy, Metz Cedex 1, France","Laboratoire de Physique et Mecanique des Materiaux, Metz Cedex 1, France#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Physique et M\u00e9canique des Mat\u00e9riaux, UMR CNRS 7554, Ile du Saulcy, Metz Cedex 1, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210100753"]},{"raw_affiliation_string":"Laboratoire de Physique et Mecanique des Materiaux, Metz Cedex 1, France#TAB#","institution_ids":["https://openalex.org/I4210100753"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060826513","display_name":"Jean Utke","orcid":"https://orcid.org/0000-0002-3377-1990"},"institutions":[{"id":"https://openalex.org/I1282105669","display_name":"Argonne National Laboratory","ror":"https://ror.org/05gvnxz63","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282105669","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"J. Utke","raw_affiliation_strings":["Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, USA","Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, USA","institution_ids":["https://openalex.org/I1282105669"]},{"raw_affiliation_string":"Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL USA","institution_ids":["https://openalex.org/I1282105669"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060826513"],"corresponding_institution_ids":["https://openalex.org/I1282105669"],"apc_list":null,"apc_paid":null,"fwci":3.2237,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.92372549,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"24","issue":"1","first_page":"1","last_page":"14"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10818","display_name":"Astrophysics and Cosmic Phenomena","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10818","display_name":"Astrophysics and Cosmic Phenomena","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/3106","display_name":"Nuclear and High Energy Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13126","display_name":"Scientific Research and Discoveries","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13650","display_name":"Computational Physics and Python Applications","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/automatic-differentiation","display_name":"Automatic differentiation","score":0.8605735301971436},{"id":"https://openalex.org/keywords/intrinsics","display_name":"Intrinsics","score":0.8337125182151794},{"id":"https://openalex.org/keywords/fortran","display_name":"Fortran","score":0.7705831527709961},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.635809600353241},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.629718542098999},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.61421799659729},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.6119190454483032},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5936587452888489},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5545324087142944},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.5398638844490051},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5360470414161682},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.4930696189403534},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.4895506799221039},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.474517285823822},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.41911476850509644},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3692684769630432},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32860368490219116},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2776397466659546},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.2664245367050171},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.1959308385848999},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1535523533821106},{"id":"https://openalex.org/keywords/multivariate-statistics","display_name":"Multivariate statistics","score":0.1284657120704651}],"concepts":[{"id":"https://openalex.org/C133512626","wikidata":"https://www.wikidata.org/wiki/Q787371","display_name":"Automatic differentiation","level":3,"score":0.8605735301971436},{"id":"https://openalex.org/C2908650547","wikidata":"https://www.wikidata.org/wiki/Q20999234","display_name":"Intrinsics","level":2,"score":0.8337125182151794},{"id":"https://openalex.org/C2778241615","wikidata":"https://www.wikidata.org/wiki/Q83303","display_name":"Fortran","level":2,"score":0.7705831527709961},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.635809600353241},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.629718542098999},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.61421799659729},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.6119190454483032},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5936587452888489},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5545324087142944},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.5398638844490051},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5360470414161682},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.4930696189403534},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.4895506799221039},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.474517285823822},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41911476850509644},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3692684769630432},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32860368490219116},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2776397466659546},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.2664245367050171},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.1959308385848999},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1535523533821106},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.1284657120704651},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556780802413769","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780802413769","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W196269863","https://openalex.org/W1585773866","https://openalex.org/W1602512706","https://openalex.org/W1984308883","https://openalex.org/W1988699107","https://openalex.org/W1992493944","https://openalex.org/W1994309501","https://openalex.org/W2003305312","https://openalex.org/W2052104590","https://openalex.org/W2052926756","https://openalex.org/W2058760524","https://openalex.org/W2078272972","https://openalex.org/W2085269425","https://openalex.org/W2096180633","https://openalex.org/W2109100930","https://openalex.org/W2155212612"],"related_works":["https://openalex.org/W2544447312","https://openalex.org/W1588787849","https://openalex.org/W2005242289","https://openalex.org/W1966377066","https://openalex.org/W2146534684","https://openalex.org/W2097111574","https://openalex.org/W2088317231","https://openalex.org/W2952748252","https://openalex.org/W1537531080","https://openalex.org/W1572832656"],"abstract_inverted_index":{"A":[0],"number":[1,43],"of":[2,32,44,104],"practical":[3],"problems":[4],"in":[5,120],"physics":[6],"can":[7,17],"be":[8,18,27],"solved":[9],"by":[10,70],"using":[11,48,64],"accurate":[12],"higher-order":[13,34],"derivatives.":[14],"Such":[15],"derivatives":[16],"obtained":[19],"with":[20,29,52,57],"automatic":[21,66],"differentiation.":[22],"However,":[23],"one":[24],"has":[25],"to":[26],"concerned":[28],"the":[30,75,85,92,109,121],"complexity":[31],"computing":[33],"derivative":[35],"tensors":[36],"even":[37],"for":[38,84,115],"a":[39,101],"modest":[40],"order":[41],"and":[42,54,82,96,112],"independents.":[45],"Initial":[46],"experiments":[47],"univariate":[49],"Taylor":[50],"polynomials":[51],"interpolation":[53],"operator":[55],"overloading":[56],"unrolled":[58],"loops":[59],"showed":[60],"better":[61],"runtimes":[62],"than":[63],"other":[65],"differentiation":[67],"tools.":[68],"Motivated":[69],"these":[71],"results,":[72],"we":[73,90],"developed":[74],"Rapsodia":[76,110],"code":[77],"generator":[78],"that":[79],"produces":[80],"Fortran":[81],"C++libraries":[83],"most":[86],"common":[87],"intrinsics.":[88],"Here":[89],"explain":[91],"algorithmic":[93],"approach,":[94],"implementation,":[95],"present":[97],"test":[98],"results":[99],"on":[100,108],"select":[102],"set":[103],"applications.":[105],"Further":[106],"details":[107],"tool,":[111],"an":[113],"example":[114],"user":[116],"extensions":[117],"are":[118],"given":[119],"Appendix.":[122]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
