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Raku convergence methods to solve lineal and non lineal equations


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Math::ConvergenceMethods


Raku package of fast Damerau-Levenshtein distance functions based on C code via NativeCall.


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package\n",{"meta":"https://github.com/antononcube/Raku-DSL-Translators","type":"fcode","name":"L","content":["\"DSL::Translators\""]},", [AAp1].\nAfter profiling, it turned out about 50% of the time is spent in the function ",{"type":"fcode","name":"C","content":["dld"]}," by \"Text::Levenshtein::Demerau\"."]},{"type":"para","id":"ZpPZlCtr_rHgv3LXBxJWX","margin":"","location":{"start":{"line":67,"column":1,"offset":2327},"end":{"line":67,"column":78,"offset":2404}},"text":"text","content":["That is the case because of the fuzzy marching which \"DSL::Translators\" does:"]},{"type":"block","id":"v1mFtCZ4feaJajY41sx7R","margin":"","name":"code","config":[{"name":"lang","value":"perl6","type":"string"}],"location":{"start":{"line":69,"column":1,"offset":2406},"end":{"line":73,"column":4,"offset":2522}},"content":[{"type":"verbatim","value":"use DSL::Translators;\n\ndsl-translation('use @dfTitanic; group by sex; show couns;', to => 'Raku')<CODE>"}]},{"type":"block","id":"m-Us7DXrozYH5AYIXo30B","margin":"","name":"code","config":[],"location":{"start":{"line":75,"column":1,"offset":2524},"end":{"line":80,"column":4,"offset":2669}},"content":[{"type":"verbatim","value":"#ERROR: Possible misspelling of 'count' as 'couns'.\n# $obj = @dfTitanic ;\n# $obj = group-by($obj, \"sex\") ;\n# say \"counts: \", $obj>>.elems"}]},{"type":"para","id":"11P027o_tNt2qQUpG91vG","margin":"","location":{"start":{"line":82,"column":1,"offset":2671},"end":{"line":82,"column":88,"offset":2758}},"text":"text","content":["The slowdown effect of the \"expensive\" to compute results by ",{"type":"fcode","name":"C","content":["dld"]}," can be addressed by:"]},{"type":"list","id":"PGHBQZ6MM4D4ama1n2BFB","margin":"","level":1,"list":"itemized","content":[{"type":"block","id":"UYGMpJenQvshPz4JHx2hw","margin":"","name":"item","level":1,"location":{"start":{"line":84,"column":1,"offset":2760},"end":{"line":84,"column":59,"offset":2818}},"content":[{"type":"para","id":"W0VgTyvYHcRotFGPswNwF","margin":"","location":{"start":{"line":84,"column":3,"offset":2762},"end":{"line":84,"column":59,"offset":2818}},"text":"text","content":["Certain clever checks can be made before invoking ",{"type":"fcode","name":"C","content":["dld"]},"."]}]},{"type":"block","id":"3MfDS6eqaxnYpOfAWpsZg","margin":"","name":"item","level":1,"location":{"start":{"line":85,"column":1,"offset":2819},"end":{"line":85,"column":96,"offset":2914}},"content":[{"type":"para","id":"ZhWHnLaJ-N_X4Cx4RqSOu","margin":"","location":{"start":{"line":85,"column":3,"offset":2821},"end":{"line":85,"column":96,"offset":2914}},"text":"text","content":["Create a new function called ",{"type":"fcode","name":"C","content":["edit-distance"]}," in C and set up a \"NativeCall\" connection to it."]}]}]},{"type":"para","id":"jzF7uS4REC2VKPMfnu3cI","margin":"","location":{"start":{"line":87,"column":1,"offset":2916},"end":{"line":87,"column":130,"offset":3045}},"text":"text","content":["So, at this point, both approaches were taken: the first in \"DSL::Shared\", [AAp2], the second by \"Math::DistanceFunctions::Edit\"."]},{"type":"block","id":"vgvKu4uKFPqiOS08aBUYj","margin":"","level":2,"name":"head","location":{"start":{"line":91,"column":1,"offset":3052},"end":{"line":91,"column":18,"offset":3069}},"content":["Implementation"]},{"type":"para","id":"otdU-KNd9TlkVIGjClDp2","margin":"","location":{"start":{"line":93,"column":1,"offset":3071},"end":{"line":93,"column":132,"offset":3202}},"text":"text","content":["The design of \"NativeCall\" hook-up is taken from ",{"meta":"https://raku.land/github:titsuki/Algorithm::KdTree","type":"fcode","name":"L","content":["\"Algorithm::KdTree\""]},", [ITp1]."]},{"type":"para","id":"fO7KejGlIUNM1ZaBfCamA","margin":"","location":{"start":{"line":95,"column":1,"offset":3204},"end":{"line":95,"column":83,"offset":3286}},"text":"text","content":["The actual C-implementation was made by several iterations of LLM code generation."]},{"type":"para","id":"AeqPFmFk_H72a0rP1TLeR","margin":"","location":{"start":{"line":97,"column":1,"offset":3288},"end":{"line":100,"column":47,"offset":3591}},"text":"text","content":["I considered re-programming to C the Raku code of ",{"type":"fcode","name":"C","content":["dld"]}," in [NLp1], but since\n",{"meta":"https://en.wikipedia.org/wiki/Damerau–Levenshtein_distance","type":"fcode","name":"L","content":["Damerau-Levenshtein distance"]}," is a\n",{"meta":"https://rosettacode.org/wiki/Levenshtein_distance","type":"fcode","name":"L","content":["very well known, popular topic"]},"\nLLM generations with simple prompts were used."]},{"type":"para","id":"j2BeNNI_fqP7v-01NeCoj","margin":"","location":{"start":{"line":102,"column":1,"offset":3593},"end":{"line":102,"column":43,"offset":3635}},"text":"text","content":["(And, yes, I read the code and tested it.)"]},{"type":"block","id":"KSs-A3gLF-UuExMrk80zl","margin":"","level":2,"name":"head","location":{"start":{"line":106,"column":1,"offset":3642},"end":{"line":106,"column":29,"offset":3670}},"content":["Profiling and performance"]},{"type":"para","id":"3PP7Uq9K6saNMjYB_XfKF","margin":"","location":{"start":{"line":108,"column":1,"offset":3672},"end":{"line":109,"column":126,"offset":3896}},"text":"text","content":["Since the speed is the most important reason for this package, after its complete initial version,\nprofiling was done each refactoring step. See the file ",{"meta":"./examples/faster-word-distances.raku","type":"fcode","name":"L","content":["\"faster-word-distances.raku\""]},"."]},{"type":"list","id":"VKBPTw7FAlWvk5whKUsuA","margin":"","level":1,"list":"itemized","content":[{"type":"block","id":"qbw5NJuCSpQHEGSA0xWo_","margin":"","name":"item","level":1,"location":{"start":{"line":111,"column":1,"offset":3898},"end":{"line":111,"column":80,"offset":3977}},"content":[{"type":"para","id":"bkwbxeXwPNJB0XR8KwJLB","margin":"","location":{"start":{"line":111,"column":3,"offset":3900},"end":{"line":111,"column":80,"offset":3977}},"text":"text","content":["For ASCII (non-UTF-8) strings ",{"type":"fcode","name":"C","content":["edit-distance"]}," is ≈70 times faster than ",{"type":"fcode","name":"C","content":["dld"]},"."]}]},{"type":"block","id":"-OQn9K7lwJVLqvydzbFgq","margin":"","name":"item","level":1,"location":{"start":{"line":112,"column":1,"offset":3978},"end":{"line":112,"column":37,"offset":4014}},"content":[{"type":"para","id":"tDsZYCwZfbHGj0WdlxUx_","margin":"","location":{"start":{"line":112,"column":3,"offset":3980},"end":{"line":112,"column":37,"offset":4014}},"text":"text","content":["For UTF-8 strings ≈5 times faster."]}]}]},{"type":"para","id":"EfJsMDl1iZUIdIM-Z8R8S","margin":"","location":{"start":{"line":114,"column":1,"offset":4016},"end":{"line":114,"column":111,"offset":4126}},"text":"text","content":["Here is en example output of the normalized profiling times done with the script \"faster-word-distances.raku\":"]},{"type":"block","id":"p5a-S7NzcZDm2gLeCC5QH","margin":"","name":"code","config":[],"location":{"start":{"line":116,"column":1,"offset":4128},"end":{"line":122,"column":4,"offset":4274}},"content":[{"type":"verbatim","value":"StrDistance => 1\ndld => 0.847204294559419\nedit-distance => 0.011560672845434399\nrosetta => 2.5342606961356466\nsift => 0.021171925438510746"}]},{"type":"para","id":"pNWDhjgQX5vjSxNjbhc9l","margin":"","location":{"start":{"line":124,"column":1,"offset":4276},"end":{"line":124,"column":144,"offset":4419}},"text":"text","content":[{"type":"fcode","name":"B","content":["Remark:"]}," The timing of Raku's built-in ",{"meta":"https://docs.raku.org/type/StrDistance","type":"fcode","name":"L","content":[{"type":"fcode","name":"C","content":["StrDistance"]}]}," is used to normalize the rest of the timings."]},{"type":"para","id":"Ms3iubNDWsjdDySu4IpjY","margin":"","location":{"start":{"line":126,"column":1,"offset":4421},"end":{"line":127,"column":28,"offset":4593}},"text":"text","content":[{"type":"fcode","name":"B","content":["Remark:"]}," In the profiling also ",{"type":"fcode","name":"C","content":["sift4"]}," from ",{"meta":"https://raku.land/github:MasterDuke17/Text::Diff::Sift4","type":"fcode","name":"L","content":["\"Text::Diff::Sift4\""]},", [MDp1], was used.\n(NQP-based implementation.)"]},{"type":"block","id":"n2N60i4So42j6vHO_6Gxa","margin":"","level":2,"name":"head","location":{"start":{"line":131,"column":1,"offset":4600},"end":{"line":131,"column":14,"offset":4613}},"content":["References"]},{"type":"para","id":"DedVda9ADaNrr1vk2ihd_","margin":"","location":{"start":{"line":133,"column":1,"offset":4615},"end":{"line":136,"column":55,"offset":4790}},"text":"text","content":["[AAp1] Anton Antonov,\n",{"meta":"https://github.com/antononcube/Raku-DSL-Translators","type":"fcode","name":"L","content":["DSL::Translators Raku package"]},",\n(2020-2024),\n",{"meta":"https://github.com/antononcube/","type":"fcode","name":"L","content":["GitHub/antononcube"]},"."]},{"type":"para","id":"-MKY3AqhbSQeCMPRhiS-r","margin":"","location":{"start":{"line":138,"column":1,"offset":4792},"end":{"line":141,"column":55,"offset":4953}},"text":"text","content":["[AAp2] Anton Antonov,\n",{"meta":"https://github.com/antononcube/Raku-Shared","type":"fcode","name":"L","content":["DSL::Shared Raku package"]},",\n(2020-2024),\n",{"meta":"https://github.com/antononcube/","type":"fcode","name":"L","content":["GitHub/antononcube"]},"."]},{"type":"para","id":"hRG2x1snSsQddUjyYtJY-","margin":"","location":{"start":{"line":143,"column":1,"offset":4955},"end":{"line":146,"column":46,"offset":5117}},"text":"text","content":["[ITp1] Itsuki Toyota,\n",{"meta":"https://github.com/titsuki/p6-Algorithm-KdTree","type":"fcode","name":"L","content":["Algorithm::KdTree Raku package"]},",\n(2016-2024),\n",{"meta":"https://github.com/titsuki","type":"fcode","name":"L","content":["GitHub/titsuki"]},"."]},{"type":"para","id":"BEwRXsFaMD80KgeC1y7sJ","margin":"","location":{"start":{"line":148,"column":1,"offset":5119},"end":{"line":151,"column":55,"offset":5289}},"text":"text","content":["[MDp1] MaterDuke17,\n",{"meta":"https://github.com/MasterDuke17/Text-Diff-Sift4","type":"fcode","name":"L","content":["Text::Diff::Sift4 Raku package"]},",\n(2016-2021),\n",{"meta":"https://github.com/MasterDuke17","type":"fcode","name":"L","content":["GitHub/MaterDuke17"]},"."]},{"type":"para","id":"_hBPhZMfGtBoNZn5Vxu5s","margin":"","location":{"start":{"line":153,"column":1,"offset":5291},"end":{"line":156,"column":43,"offset":5466}},"text":"text","content":["[NLp1] Nick Logan,\n",{"meta":"https://github.com/ugexe/Raku-Text--Levenshtein--Damerau","type":"fcode","name":"L","content":["Text::Levenshtein::Damerau Raku package"]},",\n(2016-2022),\n",{"meta":"https://github.com/ugexe/","type":"fcode","name":"L","content":["GitHub/ugexe"]},"."]}]},"publishUrl":"/mods/zef/Math::DistanceFunctions::Edit/dist/README.md","pluginsData":{"moduleInfo":{"meta":{"api":"1","auth":"zef:antononcube","authors":["Anton Antonov"],"build-depends":["LibraryMake","Distribution::Builder::MakeFromJSON","Math::DistanceFunctions::Edit::CustomBuilder"],"builder":"Math::DistanceFunctions::Edit::CustomBuilder","depends":["NativeHelpers::Array"],"description":"Raku package of fast Damerau-Levenshtein distance functions based on C code via NativeCall.","dist":"Math::DistanceFunctions::Edit:ver<0.1.0>:auth<zef:antononcube>","license":"Artistic-2.0","name":"Math::DistanceFunctions::Edit","path":"M/AT/MATH_DISTANCEFUNCTIONS_EDIT/9c5ca481792af202c0f48ad1958c182a7fbe409b.tar.gz","perl":"6.d","provides":{"Math::DistanceFunctions::Edit":"lib/Math/DistanceFunctions/Edit.rakumod","Math::DistanceFunctions::Edit::CustomBuilder":"lib/Math/DistanceFunctions/Edit/CustomBuilder.rakumod"},"resources":["libraries/EditDistance"],"source-url":"https://github.com/antononcube/Raku-Math-DistanceFunctions-Edit.git","test-depends":[],"version":"0.1.0"},"files":[{"file":"work_mods/zef/Math::DistanceFunctions::Edit/dist/README.md","publishUrl":"/mods/zef/Math::DistanceFunctions::Edit/dist/README.md"},{"file":"work_mods/zef/Math::DistanceFunctions::Edit/dist/README-work.md","publishUrl":"/mods/zef/Math::DistanceFunctions::Edit/dist/README-work.md"}],"src":"zef","url":"/mods/zef/Math::DistanceFunctions::Edit"}}}
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    =end React

Math::DistanceFunctions::Edit


A few Math and Physics constants


Math::Constants


The Raku Knowledge Base


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Math::ConvergenceMethods

Math-ConvergenceMethods

Methods

Stop conditions

LICENSE

Math::ConvergenceMethods v0.6.0

Authors

License

Dependencies

Test Dependencies

Provides

Documentation