Третье задание

task3/01lu/.gitignore

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+.stack-work/
+*~

task3/01lu/01lu.cabal

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+cabal-version: 1.12
+
+-- This file has been generated from package.yaml by hpack version 0.35.2.
+--
+-- see: https://github.com/sol/hpack
+
+name:           01lu
+version:        0.0.0
+build-type:     Simple
+
+executable 01lu-exe
+  main-is: Main.hs
+  other-modules:
+      Paths_01lu
+  hs-source-dirs:
+      app
+  ghc-options: -Wall -Wcompat -Widentities -Wincomplete-record-updates -Wincomplete-uni-patterns -Wmissing-export-lists -Wmissing-home-modules -Wpartial-fields -Wredundant-constraints -threaded -rtsopts -with-rtsopts=-N
+  build-depends:
+      base >=4.7 && <5
+    , easyplot
+    , hmatrix
+  default-language: Haskell2010

task3/01lu/app/Main.hs

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+module Main where
+
+import Numeric.LinearAlgebra as LA
+import Graphics.EasyPlot
+
+data TriangType = Up | Low | None deriving Show
+
+a n = build (n, n) $ gen n :: Matrix Double
+
+gen n x y | x == (fromIntegral $ n - 1) = 1
+          | x == y = 1
+          | x < y = -1
+          | x > y = 0
+
+luGet a = case lu a of
+    (l, u , p, s) -> (p, ((l, Low), (u, Up)))
+
+solveTriang (a, t) f = case t of
+    Up -> let rs = toRows a in
+        calcu (cols a) (reverse rs) f 
+    Low -> let rs = toRows a in
+        calcl (cols a) rs f 
+    None -> error "Not triang"
+
+calcu nrs rs f = calc' rs 0 [] where 
+    calc' [] n us = us
+    calc' (r:rs) n us = calc' rs (n + 1) (ui : us) where
+        ui = (fi - (subVector 0 n $ vector us) <.> (subVector (nrs - n) n r)) / ri where 
+                  fi = f `atIndex` (nrs - n - 1)
+                  ri = (r `atIndex` (nrs - n - 1))
+
+calcl nrs rs f = calc' rs 0 [] where 
+    calc' [] n us = reverse us
+    calc' (r:rs) n us = calc' rs (n + 1) (ui : us) where
+        ui = (fi - ((subVector 0 n $ vector $ reverse us) <.> (subVector 0 n r))) / ri where
+                  fi = f `atIndex` n
+                  ri =  r `atIndex` n
+
+-- Для вычисления числа обусловенности
+norm1 = maximum . map (sum . map abs) . toLists
+norm2 = norm1 . tr
+norm3 m =  sqrt $ maximum $  map magnitude $ toList $ eigenvalues $ m LA.<> (tr m)
+
+mu norm m = norm m * (norm $ inv m)
+
+collectDots norm 1 = [(0, mu norm (a 1))]
+collectDots norm n = (fromIntegral n, mu norm (a n)) : collectDots norm (n - 1)
+
+main :: IO ()
+main = do
+    -- Пример решения системы n = 5
+    let m = a 5
+    let f = vector $ take 5 $ repeat 1
+    let v = vector $ solveTriang (fst $ snd $ luGet m) f
+    let u = solveTriang (snd $ snd $ luGet m) v
+    --print u :: Vector R
+
+    let dots = collectDots norm1 100
+    plot X11 $ Data2D [Title "norm1", Style Lines] [] dots
+    print dots

task3/01lu/package.yaml

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+name:                01lu
+
+dependencies:
+- base >= 4.7 && < 5
+- hmatrix
+- easyplot
+
+ghc-options:
+- -Wall
+- -Wcompat
+- -Widentities
+- -Wincomplete-record-updates
+- -Wincomplete-uni-patterns
+- -Wmissing-export-lists
+- -Wmissing-home-modules
+- -Wpartial-fields
+- -Wredundant-constraints
+
+executables:
+  01lu-exe:
+    main:                Main.hs
+    source-dirs:         app
+    ghc-options:
+    - -threaded
+    - -rtsopts
+    - -with-rtsopts=-N

task3/01lu/stack.yaml

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+# This file was automatically generated by 'stack init'
+#
+# Some commonly used options have been documented as comments in this file.
+# For advanced use and comprehensive documentation of the format, please see:
+# https://docs.haskellstack.org/en/stable/yaml_configuration/
+
+# Resolver to choose a 'specific' stackage snapshot or a compiler version.
+# A snapshot resolver dictates the compiler version and the set of packages
+# to be used for project dependencies. For example:
+#
+# resolver: lts-3.5
+# resolver: nightly-2015-09-21
+# resolver: ghc-7.10.2
+#
+# The location of a snapshot can be provided as a file or url. Stack assumes
+# a snapshot provided as a file might change, whereas a url resource does not.
+#
+# resolver: ./custom-snapshot.yaml
+# resolver: https://example.com/snapshots/2018-01-01.yaml
+resolver:
+  url: https://raw.githubusercontent.com/commercialhaskell/stackage-snapshots/master/lts/21/14.yaml
+
+# User packages to be built.
+# Various formats can be used as shown in the example below.
+#
+# packages:
+# - some-directory
+# - https://example.com/foo/bar/baz-0.0.2.tar.gz
+#   subdirs:
+#   - auto-update
+#   - wai
+packages:
+- .
+# Dependency packages to be pulled from upstream that are not in the resolver.
+# These entries can reference officially published versions as well as
+# forks / in-progress versions pinned to a git hash. For example:
+#
+extra-deps:
+  - easyplot-1.0@sha256:3fec6ccf425b370ab668eb342bc4cd92777880653e27a982db7b225fd007cb2b,1936
+# - acme-missiles-0.3
+# - git: https://github.com/commercialhaskell/stack.git
+#   commit: e7b331f14bcffb8367cd58fbfc8b40ec7642100a
+#
+# extra-deps: []
+
+# Override default flag values for local packages and extra-deps
+# flags: {}
+
+# Extra package databases containing global packages
+# extra-package-dbs: []
+
+# Control whether we use the GHC we find on the path
+# system-ghc: true
+#
+# Require a specific version of stack, using version ranges
+# require-stack-version: -any # Default
+# require-stack-version: ">=2.7"
+#
+# Override the architecture used by stack, especially useful on Windows
+# arch: i386
+# arch: x86_64
+#
+# Extra directories used by stack for building
+# extra-include-dirs: [/path/to/dir]
+# extra-lib-dirs: [/path/to/dir]
+#
+# Allow a newer minor version of GHC than the snapshot specifies
+# compiler-check: newer-minor

task3/01lu/stack.yaml.lock

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+# This file was autogenerated by Stack.
+# You should not edit this file by hand.
+# For more information, please see the documentation at:
+#   https://docs.haskellstack.org/en/stable/lock_files
+
+packages:
+- completed:
+    hackage: easyplot-1.0@sha256:3fec6ccf425b370ab668eb342bc4cd92777880653e27a982db7b225fd007cb2b,1936
+    pantry-tree:
+      sha256: a5de94b54a51732bf70a601fca8c905fe074ecf870ea573db36d53a3bbb282f4
+      size: 219
+  original:
+    hackage: easyplot-1.0@sha256:3fec6ccf425b370ab668eb342bc4cd92777880653e27a982db7b225fd007cb2b,1936
+snapshots:
+- completed:
+    sha256: 60e54c1ba3c1e7163acf6dafa9d56b2d3b23f88a31ad53a1c9d888f32561f8da
+    size: 639819
+    url: https://raw.githubusercontent.com/commercialhaskell/stackage-snapshots/master/lts/21/14.yaml
+  original:
+    url: https://raw.githubusercontent.com/commercialhaskell/stackage-snapshots/master/lts/21/14.yaml