{"id":3759,"date":"2018-02-21T06:00:23","date_gmt":"2018-02-21T04:00:23","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=3759"},"modified":"2018-02-28T08:23:50","modified_gmt":"2018-02-28T06:23:50","slug":"representacion-ampliada-de-matrices-dispersas","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/representacion-ampliada-de-matrices-dispersas\/","title":{"rendered":"Representaci\u00f3n ampliada de matrices dispersas"},"content":{"rendered":"<p>En el ejercicio anterior se explic\u00f3 una representaci\u00f3n reducida de las matrices dispersas. A partir del n\u00famero de columnas y la representaci\u00f3n reducida se puede construir la matriz.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   ampliada :: Num a => Int -> [[(Int,a)]] -> Matrix a\n<\/pre>\n<p>tal que (ampliada n xss) es la matriz con n columnas cuya representaci\u00f3n reducida es xss. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> ampliada 3 [[(3,4)],[(2,5)],[]]\n   ( 0 0 4 )\n   ( 0 5 0 )\n   ( 0 0 0 )\n   \n   \u03bb> ampliada 3 [[],[]]\n   ( 0 0 0 )\n   ( 0 0 0 )\n   \n   \u03bb> ampliada 2 [[],[],[]]\n   ( 0 0 )\n   ( 0 0 )\n   ( 0 0 )\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Matrix (Matrix, fromLists)\nimport Data.List   (lookup)\n\nampliada :: Num a => Int -> [[(Int,a)]] -> Matrix a\nampliada n xss =\n  fromLists [filaAmpliada n xs | xs <- xss]\n\n-- Se puede redefinir con un argumento\nampliada2 :: Num a => Int -> [[(Int,a)]] -> Matrix a\nampliada2 n = fromLists . map (filaAmpliada n)\n\n-- Se puede redefinir sin argumentos usando las siguientes reducciones\n--      fromLists . map (filaAmpliada n)\n--    = fromLists . ((map . filaAmpliada) n)\n--    = ((fromLists .) . (map . filaAmpliada)) n\n--    = ((fromLists .) . map . filaAmpliada) n\nampliada3 :: Num a => Int -> [[(Int,a)]] -> Matrix a\nampliada3 = (fromLists .) . map . filaAmpliada\n\n-- (filaAmpliada n xs) es la fila ampliada de la representaci\u00f3n reducida\n-- xs de una matriz con n columnas. Por ejemplo, \n--    filaAmpliada 3 [(2,5)]        ==  [0,5,0]\n--    filaAmpliada 7 [(2,5),(1,3)]  ==  [3,5,0,0,0,0,0]\nfilaAmpliada :: Num a => Int -> [(Int,a)] -> [a]\nfilaAmpliada n xs =\n  [f (lookup i xs) | i <- [1..n]]\n  where f Nothing  = 0\n        f (Just x) = x\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>En el ejercicio anterior se explic\u00f3 una representaci\u00f3n reducida de las matrices dispersas. A partir del n\u00famero de columnas y la representaci\u00f3n reducida se puede construir la matriz. Definir la funci\u00f3n ampliada :: Num a => Int -> [[(Int,a)]] -> Matrix a tal que (ampliada n xss) es la matriz con n columnas cuya representaci\u00f3n&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[5],"tags":[8,96,414,10,42,11],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3759"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/comments?post=3759"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3759\/revisions"}],"predecessor-version":[{"id":3826,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3759\/revisions\/3826"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=3759"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=3759"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=3759"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}