{"id":3755,"date":"2018-02-19T06:00:20","date_gmt":"2018-02-19T04:00:20","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=3755"},"modified":"2018-02-26T08:47:57","modified_gmt":"2018-02-26T06:47:57","slug":"matrices-dispersas","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/matrices-dispersas\/","title":{"rendered":"Matrices dispersas"},"content":{"rendered":"<p>Una matriz es <a href=\"http:\/\/bit.ly\/2HpHxI2\">dispersa<\/a> si la mayori\u00e1 de sus elementos son ceros. Por ejemplo, la primera de las siguientes matrices es dispersa y la segunda no lo es<\/p>\n<pre lang=\"text\">\n   ( 0 0 4 )   ( 0 1 4 )\n   ( 0 5 0 )   ( 0 5 1 )\n   ( 0 0 0 )\n<\/pre>\n<p>Usando la librer\u00eda Data.Matrix, las anteriores matrices se pueden definir por<\/p>\n<pre lang=\"text\">\n   ej1, ej2 :: Matrix Int\n   ej1 = fromList 3 3 [0,0,4,0,5,0,0,0,0]\n   ej2 = fromList 2 3 [0,1,4,0,5,1]\n<\/pre>\n<p>La dispersi\u00f3n de una matriz es el cociente entre el n\u00famero de ceros de la matriz y el producto de sus n\u00fameros de filas y de columnas.<\/p>\n<p>Definir las siguientes funciones<\/p>\n<pre lang=\"text\">\n   dispersion :: (Num a, Eq a) => Matrix a -> Double\n   esDispersa :: (Num a, Eq a) => Matrix a -> Bool\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li>(dispersion p) es la dispersi\u00f3n de la matriz p. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     dispersion ej1              ==  0.7777777777777778\n     dispersion ej2              ==  0.3333333333333333\n     dispersion (fmap (+1) ej1)  ==  0.0\n     dispersion (identity 3)     ==  0.6666666666666666\n     dispersion (zero 9 9)       ==  1.0\n<\/pre>\n<ul>\n<li>(esDispersa p) se verifica si la matriz p es dispersa. Por ejemplo, <\/li>\n<\/ul>\n<pre lang=\"text\">\n     esDispersa ej1              ==  True\n     esDispersa ej2              ==  False\n     esDispersa (fmap (+1) ej1)  ==  False\n     esDispersa (identity 3)     ==  True\n     esDispersa (zero 9 9)       ==  True\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Matrix (Matrix, fromList, nrows, ncols, toList)\n\nej1, ej2 :: Matrix Int\nej1 = fromList 3 3 [0,0,4,0,5,0,0,0,0]\nej2 = fromList 2 3 [0,1,4,0,5,1]\n\ndispersion :: (Num a, Eq a) => Matrix a -> Double\ndispersion p =\n  fi nCeros \/ (fi nrows * fi ncols)\n  where fi f = (fromIntegral . f) p\n\n-- (nCeros p) es el n\u00famero de ceros de la matriz p. Por ejemplo,\n--    nCeros ej1  ==  7\n--    nCeros ej2  ==  2\nnCeros :: (Num a, Eq a) => Matrix a -> Int\nnCeros p = length (filter (== 0) (toList p))\n\n-- La funci\u00f3n anterior se puede definir sin argumentos:\nnCeros2 :: (Num a, Eq a) => Matrix a -> Int\nnCeros2 = length . filter (== 0) . toList\n\nesDispersa :: (Num a, Eq a) => Matrix a -> Bool\nesDispersa p = dispersion p > 0.5\n\n-- La funci\u00f3n anterior se puede definir sin argumentos:\nesDispersa2 :: (Num a, Eq a) => Matrix a -> Bool\nesDispersa2 = (> 0.5) . dispersion \n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Una matriz es dispersa si la mayori\u00e1 de sus elementos son ceros. Por ejemplo, la primera de las siguientes matrices es dispersa y la segunda no lo es ( 0 0 4 ) ( 0 1 4 ) ( 0 5 0 ) ( 0 5 1 ) ( 0 0 0 ) Usando la&#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":[38,183,28,42,99,98,11,260],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3755"}],"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=3755"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3755\/revisions"}],"predecessor-version":[{"id":3823,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3755\/revisions\/3823"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=3755"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=3755"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=3755"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}