{"id":7449,"date":"2022-10-19T06:00:54","date_gmt":"2022-10-19T04:00:54","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7449"},"modified":"2022-12-14T12:29:42","modified_gmt":"2022-12-14T10:29:42","slug":"producto-escalar","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/producto-escalar\/","title":{"rendered":"Producto escalar"},"content":{"rendered":"

El producto escalar de dos listas de enteros xs y ys de longitud n viene dado por la suma de los productos de los elementos correspondientes.<\/p>\n

Definir la funci\u00f3n<\/p>\n

\n   productoEscalar :: [Integer] -> [Integer] -> Integer\n<\/pre>\n
tal que productoEscalar xs ys<\/code> es el producto escalar de las listas xs<\/code> e ys<\/code>. Por ejemplo,<\/p>\n
\n   productoEscalar [1,2,3] [4,5,6]  ==  32\n<\/pre>\n
Soluciones<\/b><\/p>\n
A continuaci\u00f3n se muestran las soluciones en Haskell<\/a> y las soluciones en Python<\/a>.<\/p>\n
<\/a>
\nSoluciones en Haskell<\/b><\/p>\n
\nimport Numeric.LinearAlgebra ((<.>), vector)\nimport Test.QuickCheck (quickCheck)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nproductoEscalar1 :: [Integer] -> [Integer] -> Integer\nproductoEscalar1 xs ys = sum [x*y | (x,y) <- zip xs ys]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nproductoEscalar2 :: [Integer] -> [Integer] -> Integer\nproductoEscalar2 xs ys = sum (zipWith (*) xs ys)\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nproductoEscalar3 :: [Integer] -> [Integer] -> Integer\nproductoEscalar3 = (sum .) . zipWith (*)\n\n-- 4\u00aa soluci\u00f3n\n-- ===========\n\nproductoEscalar4 :: [Integer] -> [Integer] -> Integer\nproductoEscalar4 [] _          = 0\nproductoEscalar4 _ []          = 0\nproductoEscalar4 (x:xs) (y:ys) = x*y + productoEscalar4 xs ys\n\n-- 5\u00aa soluci\u00f3n\n-- ===========\n\nproductoEscalar5 :: [Integer] -> [Integer] -> Integer\nproductoEscalar5 (x:xs) (y:ys) = x*y + productoEscalar5 xs ys\nproductoEscalar5 _ _           = 0\n\n-- 6\u00aa soluci\u00f3n\n-- ===========\n\nproductoEscalar6 :: [Integer] -> [Integer] -> Integer\nproductoEscalar6 xs ys =\n  round (vector xs' <.> vector ys')\n  where xs' = map fromIntegral xs\n        ys' = map fromIntegral ys\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_productoEscalar :: [Integer] -> [Integer] -> Bool\nprop_productoEscalar xs ys =\n  all (== productoEscalar1 xs ys)\n      [productoEscalar2 xs ys,\n       productoEscalar3 xs ys,\n       productoEscalar4 xs ys,\n       productoEscalar5 xs ys,\n       productoEscalar6 xs' ys']\n  where n = min (length xs) (length ys)\n        xs' = take n xs\n        ys' = take n ys\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_productoEscalar\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> productoEscalar1 (replicate (2*10^6) 1) (replicate (2*10^6) 1)\n--    2000000\n--    (1.37 secs, 803,827,520 bytes)\n--    \u03bb> productoEscalar2 (replicate (2*10^6) 1) (replicate (2*10^6) 1)\n--    2000000\n--    (0.69 secs, 611,008,272 bytes)\n--    \u03bb> productoEscalar3 (replicate (2*10^6) 1) (replicate (2*10^6) 1)\n--    2000000\n--    (0.69 secs, 611,008,536 bytes)\n--    \u03bb> productoEscalar4 (replicate (2*10^6) 1) (replicate (2*10^6) 1)\n--    2000000\n--    (1.64 secs, 742,290,272 bytes)\n--    \u03bb> productoEscalar5 (replicate (2*10^6) 1) (replicate (2*10^6) 1)\n--    2000000\n--    (1.63 secs, 742,290,064 bytes)\n--    \u03bb> productoEscalar6 (replicate (2*10^6) 1) (replicate (2*10^6) 1)\n--    2000000\n--    (0.32 secs, 835,679,200 bytes)\n--\n--    \u03bb> productoEscalar2 (replicate (6*10^6) 1) (replicate (6*10^6) 1)\n--    6000000\n--    (1.90 secs, 1,831,960,336 bytes)\n--    \u03bb> productoEscalar3 (replicate (6*10^6) 1) (replicate (6*10^6) 1)\n--    6000000\n--    (1.87 secs, 1,831,960,600 bytes)\n--    \u03bb> productoEscalar6 (replicate (6*10^6) 1) (replicate (6*10^6) 1)\n--    6000000\n--    (0.78 secs, 2,573,005,952 bytes)\n<\/pre>\n
El c\u00f3digo se encuentra en GitHub<\/a>.<\/p>\n
<\/a>
\nSoluciones en Python<\/b><\/p>\n
\nfrom operator import mul\nfrom sys import setrecursionlimit\nfrom timeit import Timer, default_timer\n\nfrom hypothesis import given\nfrom hypothesis import strategies as st\nfrom numpy import dot\n\nsetrecursionlimit(10**6)\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef productoEscalar1(xs: list[int], ys: list[int]) -> int:\n    return sum(x * y for (x, y) in zip(xs, ys))\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef productoEscalar2(xs: list[int], ys: list[int]) -> int:\n    return sum(map(mul, xs, ys))\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef productoEscalar3(xs: list[int], ys: list[int]) -> int:\n    if xs and ys:\n        return xs[0] * ys[0] + productoEscalar3(xs[1:], ys[1:])\n    return 0\n\n# 4\u00aa soluci\u00f3n\n# ===========\n\ndef productoEscalar4(xs: list[int], ys: list[int]) -> int:\n    return dot(xs, ys)\n\n# Comprobaci\u00f3n de equivalencia\n# ============================\n\n# La propiedad es\n@given(st.lists(st.integers(min_value=1, max_value=100)),\n       st.lists(st.integers(min_value=1, max_value=100)))\ndef test_productoEscalar(xs: list[int], ys: list[int]) -> None:\n    r = productoEscalar1(xs, ys)\n    assert productoEscalar2(xs, ys) == r\n    assert productoEscalar3(xs, ys) == r\n    n = min(len(xs), len(ys))\n    xs1 = xs[:n]\n    ys1 = ys[:n]\n    assert productoEscalar4(xs1, ys1) == r\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q producto_escalar.py\n#    1 passed in 0.37s\n\n# Comparaci\u00f3n de eficiencia\n# =========================\n\ndef tiempo(e: str) -> None:\n    \"\"\"Tiempo (en segundos) de evaluar la expresi\u00f3n e.\"\"\"\n    t = Timer(e, \"\", default_timer, globals()).timeit(1)\n    print(f\"{t:0.2f} segundos\")\n\n# La comparaci\u00f3n es\n#    >>> tiempo('productoEscalar1([1]*(10**4), [1]*(10**4))')\n#    0.00 segundos\n#    >>> tiempo('productoEscalar3([1]*(10**4), [1]*(10**4))')\n#    0.55 segundos\n#\n#    >>> tiempo('productoEscalar1([1]*(10**7), [1]*(10**7))')\n#    0.60 segundos\n#    >>> tiempo('productoEscalar2([1]*(10**7), [1]*(10**7))')\n#    0.26 segundos\n#    >>> tiempo('productoEscalar4([1]*(10**7), [1]*(10**7))')\n#    1.73 segundos\n<\/pre>\n
El c\u00f3digo se encuentra en GitHub<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"
El producto escalar de dos listas de enteros xs y ys de longitud n viene dado por la suma de los productos de los elementos correspondientes. Definir la funci\u00f3n productoEscalar :: [Integer] -> [Integer] -> Integer tal que productoEscalar xs ys es el producto escalar de las listas xs e ys. Por ejemplo, productoEscalar [1,2,3]…<\/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":[581],"tags":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7449"}],"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=7449"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7449\/revisions"}],"predecessor-version":[{"id":7667,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7449\/revisions\/7667"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7449"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7449"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7449"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}