{"id":"https://openalex.org/W2588061952","doi":"https://doi.org/10.1137/16m108968x","title":"High-Performance Tensor Contraction without Transposition","display_name":"High-Performance Tensor Contraction without Transposition","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2588061952","doi":"https://doi.org/10.1137/16m108968x","mag":"2588061952"},"language":"en","primary_location":{"id":"doi:10.1137/16m108968x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m108968x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1607.00291","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019062687","display_name":"Devin A. Matthews","orcid":"https://orcid.org/0000-0003-2795-5483"},"institutions":[{"id":"https://openalex.org/I86519309","display_name":"The University of Texas at Austin","ror":"https://ror.org/00hj54h04","country_code":"US","type":"education","lineage":["https://openalex.org/I86519309"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Devin A. Matthews","raw_affiliation_strings":["Institute for Computational Engineering and Sciences, the University of Texas at Austin, Austin, TX 78712, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Computational Engineering and Sciences, the University of Texas at Austin, Austin, TX 78712, USA","institution_ids":["https://openalex.org/I86519309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5019062687"],"corresponding_institution_ids":["https://openalex.org/I86519309"],"apc_list":null,"apc_paid":null,"fwci":8.301,"has_fulltext":false,"cited_by_count":78,"citation_normalized_percentile":{"value":0.98377528,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"40","issue":"1","first_page":"C1","last_page":"C24"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12303","display_name":"Tensor decomposition and applications","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11181","display_name":"Advanced Data Storage Technologies","score":0.9922000169754028,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/matrix-multiplication","display_name":"Matrix multiplication","score":0.6793985366821289},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5356903076171875},{"id":"https://openalex.org/keywords/multithreading","display_name":"Multithreading","score":0.5315523147583008},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5212672352790833},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.5184371471405029},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.467346727848053},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.43057122826576233},{"id":"https://openalex.org/keywords/supercomputer","display_name":"Supercomputer","score":0.4292471408843994},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.4284685552120209},{"id":"https://openalex.org/keywords/multiplication","display_name":"Multiplication (music)","score":0.42075973749160767},{"id":"https://openalex.org/keywords/tensor-contraction","display_name":"Tensor contraction","score":0.41584789752960205},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.41417717933654785},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4014877378940582},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3226844072341919},{"id":"https://openalex.org/keywords/tensor-product","display_name":"Tensor product","score":0.17657145857810974},{"id":"https://openalex.org/keywords/thread","display_name":"Thread (computing)","score":0.13136011362075806},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.09879550337791443},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.08259782195091248}],"concepts":[{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.6793985366821289},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5356903076171875},{"id":"https://openalex.org/C201410400","wikidata":"https://www.wikidata.org/wiki/Q1064412","display_name":"Multithreading","level":3,"score":0.5315523147583008},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5212672352790833},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5184371471405029},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.467346727848053},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.43057122826576233},{"id":"https://openalex.org/C83283714","wikidata":"https://www.wikidata.org/wiki/Q121117","display_name":"Supercomputer","level":2,"score":0.4292471408843994},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.4284685552120209},{"id":"https://openalex.org/C2780595030","wikidata":"https://www.wikidata.org/wiki/Q3860309","display_name":"Multiplication (music)","level":2,"score":0.42075973749160767},{"id":"https://openalex.org/C124007464","wikidata":"https://www.wikidata.org/wiki/Q428091","display_name":"Tensor contraction","level":3,"score":0.41584789752960205},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.41417717933654785},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4014877378940582},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3226844072341919},{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.17657145857810974},{"id":"https://openalex.org/C138101251","wikidata":"https://www.wikidata.org/wiki/Q213092","display_name":"Thread (computing)","level":2,"score":0.13136011362075806},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.09879550337791443},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.08259782195091248},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","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/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m108968x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m108968x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1607.00291","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.00291","pdf_url":"https://arxiv.org/pdf/1607.00291","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1607.00291","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.00291","pdf_url":"https://arxiv.org/pdf/1607.00291","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1828173312","display_name":null,"funder_award_id":"ACI-1148125/1340293","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2343997261","display_name":null,"funder_award_id":"ACI-1148125","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7583143427","display_name":"Collaborative Research: SI2-SSI: A Linear Algebra Software Infrastructure for Sustained Innovation in Computational Chemistry and other Sciences","funder_award_id":"1148125","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320307102","display_name":"Intel Corporation","ror":"https://ror.org/01ek73717"},{"id":"https://openalex.org/F4320310620","display_name":"University of Texas at Austin","ror":"https://ror.org/00hj54h04"},{"id":"https://openalex.org/F4320332414","display_name":"Department of Mechanical Engineering, University of Texas at Austin","ror":"https://ror.org/00hj54h04"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1967329527","https://openalex.org/W1988425770","https://openalex.org/W1993079359","https://openalex.org/W2002257715","https://openalex.org/W2004182761","https://openalex.org/W2004642969","https://openalex.org/W2006973305","https://openalex.org/W2024165284","https://openalex.org/W2026858719","https://openalex.org/W2037271374","https://openalex.org/W2038469228","https://openalex.org/W2051325990","https://openalex.org/W2071465375","https://openalex.org/W2072800519","https://openalex.org/W2073061372","https://openalex.org/W2084379367","https://openalex.org/W2087158689","https://openalex.org/W2092930273","https://openalex.org/W2093135480","https://openalex.org/W2098614082","https://openalex.org/W2113055885","https://openalex.org/W2143119605","https://openalex.org/W2146292423","https://openalex.org/W2164864640","https://openalex.org/W2252007067","https://openalex.org/W2412152731","https://openalex.org/W2963964033","https://openalex.org/W3099935781"],"related_works":["https://openalex.org/W3099313426","https://openalex.org/W4287593139","https://openalex.org/W752783541","https://openalex.org/W1506547947","https://openalex.org/W4206811032","https://openalex.org/W2995605830","https://openalex.org/W4239424132","https://openalex.org/W2596457687","https://openalex.org/W3212757063","https://openalex.org/W2086123442"],"abstract_inverted_index":{"Tensor":[0],"computations---in":[1],"particular":[2],"tensor":[3,34,72],"contraction":[4],"(TC)---are":[5],"important":[6],"kernels":[7],"in":[8,40,101,125,141,148],"many":[9],"scientific":[10,149],"computing":[11],"applications.":[12,150],"Due":[13],"to":[14,20,24,73,119],"the":[15,25,32,58,71],"fundamental":[16],"similarity":[17],"of":[18,27,42,70,97,108,133],"TC":[19,56],"matrix":[21,98,123],"multiplication":[22,124],"and":[23,49,79,100],"availability":[26],"optimized":[28],"implementations":[29],"such":[30],"as":[31],"BLAS,":[33],"operations":[35,86],"have":[36],"traditionally":[37],"been":[38],"implemented":[39],"terms":[41],"BLAS":[43],"operations,":[44,81],"incurring":[45],"both":[46],"a":[47,50],"performance":[48,94,129],"storage":[51],"overhead.":[52],"Instead,":[53],"we":[54],"implement":[55],"using":[57,115],"flexible":[59],"BLAS-like":[60],"Instantiation":[61],"Software":[62],"(BLIS)":[63],"framework,":[64],"which":[65],"allows":[66],"for":[67,122],"transposition":[68,85],"(reshaping)":[69],"be":[74],"fused":[75],"with":[76,127],"internal":[77],"partitioning":[78],"packing":[80],"requiring":[82],"no":[83],"explicit":[84],"or":[87],"additional":[88],"workspace.":[89],"This":[90],"implementation,":[91],"TBLIS,":[92],"achieves":[93],"approaching":[95],"that":[96,107,120],"multiplication,":[99],"some":[102],"cases":[103],"considerably":[104],"higher":[105],"than":[106],"traditional":[109],"TC.":[110],"Our":[111],"implementation":[112],"supports":[113],"multithreading":[114],"an":[116],"approach":[117],"identical":[118],"used":[121],"BLIS,":[126],"similar":[128],"characteristics.":[130],"The":[131],"complexity":[132],"managing":[134],"tensor-to-matrix":[135],"transformations":[136],"is":[137],"also":[138],"handled":[139],"automatically":[140],"our":[142],"approach,":[143],"greatly":[144],"simplifying":[145],"its":[146],"use":[147]},"counts_by_year":[{"year":2026,"cited_by_count":6},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":15},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":13},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}