How to build AronModule.hs | ghc --make AronModule.hs

Strict ByteString Char8 Strict ByteString UTF8 Lazy ByteString Char8 <http://hackage.haskell.org/package/utf8-string-1.0.1.1/docs/Data-ByteString-Lazy-UTF8.html Lazy ByteString UTF8

• KEY: haskell ffi, c function SEE: UsersaaamyfilebitbuckethaskellffiAronCLibFFI.c

• KEY: haskell ffi, c function SEE: UsersaaamyfilebitbuckethaskellffiAronCLibFFI.c

Overloading the sin, cos to avoid Haskell crazy strict type | TODO: add test cases

No much to say

• Division is painful in Haskell
• Try to overload _div for many types
• TODO: add more combination?
• TODO: add test cases

define record for all the code blocks can not define [TS.Text] => sqlite3 does not support [TS.Text]

division is painful like hell in Haskell

Num => a ring

• Addition
• Addition inverse
• Multiplcation
• Multiplcation identity
• Associativity
• Distribution over multiplication

class Num a where (+):: a -> a -> a (-)::a -> a -> a (*)::a -> a -> a abs:: a -> a negate::a -> a signum::a -> a fromIntegral Integer -> a

• Fractional => field class Num a => Fractional a where (/)::a -> a -> a recip :: a -> a fromRational :: Rational -> a

KEY: real to Fractional

KEY: Integral to Num

simple matrix can be used in GHCi

Implement complex number operations

KEY: complex conjugate

KEY: complex magnitude

Convert Cartesian Coordinates to Polar Coordinates

Convert Polar Coordinates to Cartesian Coordinates

approximate nature log function with Integral function

\[ \log_e x = \int_{1}^{x} \frac{d t}{t} \]

• Partition the interval \( x \gt 1, [1, x] \text{ or } x \lt 1, [x, 1] \) to \( n = 100 \)
• Compute each step value on x-axis \( 1 + \frac{k - 1}{n}, k \gt 1 \) or \( \frac{1 - k}{n} - 1, k < 1\)
• Compute the average hight of \( \frac{1}{x} \) between \( x_{i}, x_{i+1} \), \( h_i = \frac{f (x_i) + f(x_{i+1})}{2} \)
• The width of each step is \( w = (k - 1) \times \frac{1}{n} \)
• Each \(i\) rectangle area is \( w \times h_i \)
• Total area of all rectanges are \( \sum_{i=1}^{n} w \times h_i \)
• NOTE: if \( k \) is close to \( n = 100 \), then \( \log_e \) is not longer accurate value.
• NOTE: There is no rational polynomial to approximate \( \log_e \) in large value in fast speed.
• approximate_log_e

square root for Complex number

  radianToDegree::Float->Float
  radianToDegree x = x*r where r = 180/pi
  

  degreeToRadian::Float->Float
  degreeToRadian x = x*d where d = pi/180
  

KEY: upper case string

Same as upperStr

KEY: lower case string

Same as toLower

KEY: upper case string

Same as toUpperStr

KEY: upper case

Lower string

https://hoogle.haskell.org/?hoogle=tolower tolower>

toLowerStr s = foldr(\x y -> (toLower x):y) [] s

KEY: concat string with delimter string s, concat str, join string

concatStr ["dog", "cat"] [] => "dogcat"
concatStr ["dog", "cat"] " " => "dog cat"
concatStr ["dog", "cat"] ":" => "dog:cat"

KEY: cat string, concat string

cat ["dog", "cat"] => "dogcat"

KEY: cat file, like command line cat

cat "/tmp/x.html"

KEY: read file, find pattern, read dir and find pattern, read all keys

 p <- getEnv "j"
readDirMatchKey p "\\.java$" "KEY:"

   [
   ,
       ( "        KEY: system.in, standard input"
       , "Userscatmyfilebitbucketjavatry_scanner.java"
       )
   ,
       ( "            // KEY: word boundary "
       , "Userscatmyfilebitbucketjavatry_word_boundary.java"
       )
   ]
   

Check whether a string p contains a string s pattern

• Use regex to check match

"^dog"
"dog$"
matchTest (mkRegex p) s

 containStr "^dog"  "dog cat" => True

str = "dog cat"
p = "dog"
containStr p str == return True
containStr p s   == matchTest (mkRegex p) s

• See containPrefix containSuffix

Check non-ascii char in a string

Check non-ascii char in a [String]

check file whether it contains non-ASCII char or line

[(Line #, Line)] = [(Integer, String)]

match once string and return Maybe (index, length)

matchAny (mkRegex "dog|cat") "mydog" => Just (2, 3)

See matchOnce or matchAll matchAll

match once string and return Maybe (index, length)

matchAnyRegex (mkRegex "dog|cat") "mydog" => Just (2, 3)

See matchOnce or matchAll matchAll

Match a string using index as score

• See matchAny matchAnyRegex

type SKey = String

Match a string using index as score

• See matchAny matchAnyRegex

type SKey = String

Check non-ascii char in a file

Jupyterlab

file has all the lines which contain a pattern

file has all the lines which contain a pattern

Same as fileContain

filter out a list of pattern from a list of string

[ mbox{De Morgan's laws: union and intersection} begin{aligned} A ∪ (B ∩ C) &= (A ∩ B) ∪ (A ∩ B) (A ∪ B)^¬ &= A^¬ ∩ B^¬ (A ∩ B)^¬ &= A^¬ ∪ B^¬

end{aligned} ]

• \( A ⊗ B \)
• containStr both "a" \( ⊗ \) "b"

filterList id ["a", "b"]  ["aa", "kk", "ab"] ⇒ ["ab"]

• containStr "a"

filterList id ["a"]      ["aa", "kk", "ab"] ⇒ ["aa", "ab"]

• \( (A ⊗ B)^¬ = A^¬ ⊕ B^¬ \)
• not containStr "a" \( ⊕ \) "b"

filterList not ["a", "b"] ["aa", "bb", "ab"] ⇒ ∅

KEY: intersection of two lists, intersection of two sets

• USE: interList

• Deprecated

KEY: Difference between two lists

   cx = ["a", "b"]
   cy = ["a", "c"]
   diffList cx cy => (["b"], ["c"])
   

KEY: Intersection between two lists

   cx = ["a", "b"]
   cy = ["a", "c"]
   diffList cx cy => (["b"], ["c"])
   

intersection of two files

KEY: filter non empty string, no empty line

Check whether str contains sub as prefix

containPrefix "dog" "dogcat"  => True
containPrefix "dog" " dogcat" => False

• See containStr containSuffix

KEY: Check whether str contains sub as suffix

containPrefix "cat" "dogcat"  => True
containPrefix "cat" "dogcat " => False

• See containStr containPrefix

KEY: Check whether str has sub as prefix

containPrefix "cat" "dogcat"  => True
containPrefix "cat" "dogcat " => False

• See containPrefix

check image, check png file

ls table

KEY: without any regex substitute,

ISSUE: See replaceFileLine ISSUE: See replaceList

   let sub = "\"  -- sub is one character => len sub == 1
   pp $ len sub
   ls <- replaceFileLineEscape "abc" sub  "tmp11.x"
   writeFileList "tmp22.x" ls
   

KEY: string with escape character

ISSUE: See replaceFileLine replaceList replaceFileLineEscape

   let s = ""
   let s1 = show "\"
   let s2 = dropEnd 1 $ drop 1 s1
   let s2 =      writeFileList "tmpx.x" [s2]  -- write s2 to file
   
   

KEY: without any regex substitute, remove string and append

ISSUE: See replaceFileLineEscape ISSUE: See replaceList

   let sub = "\"  -- sub is one character => len sub == 1
   let sub' = dropEnd 1 $ drop 1 $ show sub
   pp $ len sub
   ls <- replaceFileLine "abc" sub'  "tmp11.x"
   writeFileList "tmp22.x" ls
   

KEY: Generate [([String], Integer, [String])] from captureCppFun

   [(
       [ "AronLib.e"
       , "AronLib.ew"
       , "AronLib.ewl"
       , "AronLib.ewli"
       , "AronLib.ewlin"
       , "AronLib.ewline"
       , "AronLib.i"
       , "AronLib.in"
       , "AronLib.ine"
       , "AronLib.l"
       , "AronLib.li"
       , "AronLib.lin"            <-  [String]
       , "AronLib.line"
       , "AronLib.n"
       , "AronLib.ne"
       , "AronLib.new"
       , "AronLib.newl"
       , "AronLib.newli"
       , "AronLib.newlin"
       , "AronLib.newline"
       , "AronLib.w"
       , "AronLib.wl"
       , "AronLib.wli"
       , "AronLib.wlin"
       , "AronLib.wline"
       ]
   , 40007                        <- Integer
   , [ "void newline(){" ]        <- [String]
   )
   ]
   

   [([String], Integer, [String])]
   

       etags -e -f $PWDTAGS $cpplibAronLib.h $bclibAronCLibNew.h       
              ↑ 
              + -> has to be before '-f'
   

   [
       ( "string removeIndex(string s, int inx) {"
       , "removeIndex"
       ),
       ( "vectorT removeIndex(vectorT& vec, int inx){"
       , "removeIndex"
       ),
       ( "vectorT removeIndexRange(vectorT& vec, int fromInx, int toInx){"
       , "removeIndexRange"
       )
   ]
   

KEY: extra function from emacs TAGS file

       etags -e -f $PWDTAGS $cpplibAronLib.h $bclibAronCLibNew.h       
              ↑ 
              + -> has to be before '-f'
   

KEY: Replace a matching string with other string

replaceList [" pat ", "  pat"] "pat" "sub" ⟹   [" sub ", "  sub"]

ERROR: "\" and "\\" with same output

  let n = "\"
  let m = "\\"
  let n' = subRegex(mkRegex "abc") "abc" n
  let m' = subRegex(mkRegex "abc") "abc" m
  pp $ n' == m'
  

Search a pattern and partition it three parts: [(String, String, String)]

   searchSplitAny "my cat eats my 123 cat"  "[[:digit:]]+"
   [("my cat eats my ","123"," cat")]
   > searchSplitAny "my cat eats my 123 cat 44a"  "[[:digit:]]+"
   [("my cat eats my ","123"," cat 44a"),(" cat ","44","a")]
   

search and replace WORD only

   searchSplit "mydog dog-- dog pig cat" "dog"
   [("my","dog"," dog-- dog pig cat"),(" ","dog","-- dog pig cat"),("-- ","dog"," pig cat")]
   

KEY: search replace any char, substitude string

• The code is based on matchAllText in package: TDFA as TD

   searchReplaceAny "mydog dog-- dog pig cat" "dog" "[\0]" => "my[dog] [dog]-- [dog] pig cat"
   

• Regex is from TDFA, NOT Text.Regex

word => "[[:alpha:]]+"

• NOTE: support ONE String only, e.g. searchReplace s "dog" "[\0]"
• TODO: support multiple words, e.g. searchReplace s "dog|cat" "[\0]"

See searchReplace

TODO: add test

Search replace word, the code is based on matchAllText in package: Text.Regex.TDFA as TD

let s = "mydog dog-- dog pig cat dog fox"
searchReplace s "dog" "[\\0]"
"mydog [dog]-- [dog] pig cat [dog] fox"

• Text.Regex => subRegex does not support word boundary

r  = makeRegex ("\\<" ++ word ++ "\\>")::TD.Regex -- word boundary

• Regex is from TDFA, NOT Text.Regex >word => "[[:alpha:]]+"
• NOTE: support ONE word only, e.g. searchReplace s "dog" "[\0]"
• TODO: support multiple words, e.g. searchReplace s "dog|cat" "[\0]"

See searchReplaceAny

Sun 31 May 13:05:58 2020 1. Fixed bug: if no matches, then the origin string should be returned 2. Moved searchSplit outside so that searchReplaceAny can use it.

   searchSplit "mydog dog-- dog pig cat" "dog"
   [("my","dog"," dog-- dog pig cat"),(" ","dog","-- dog pig cat"),("-- ","dog"," pig cat")]
   

   > searchReplace "mydog dog-- dog pig cat" "dog" "[\0]"
   "mydog [dog]-- [dog] pig cat"
   > searchReplaceAny "mydog dog-- dog pig cat" "dog" "[\0]"
   "my[dog] [dog]-- [dog] pig cat"
   >
   

Same as searchReplace but it is better name

search and replace word

interleave two lists

interleave ["a", "b"] ["a1", "b1"]
["a", "a1", "b", "b1"]

Use two operation tran or transpose and concat

concat (tran [xs, ys])

SO Ref

intersperseInner a list

Same as intersperse from Data.List

intersperseInner "-", [] = []
intersperseInner "-", ["a"] = ["a"]
intersperseInner "-", ["a", "b"] = ["a", "-", "b"]

Add sth between list

listIn "-", [] = []
listIn "-", ["a"] = ["a"]
listIn "-", ["a", "b"] = ["a", "-", "b"]

concat $ listIn "-" ["a", "b"]  -- "a-b"

same as intersperseOuter but it is better name

Add sth OVER the list

listOut "-", [] = []
listOut "-", ["a"] = ["-", "a", "-"]
listOUt "-", ["a", "b"] = ["-", "a", "-", "b", "-"]

concat $ listOut "-" ["a", "b"]  -- "-a-b-"

Same as intersperseInner but it is better name

intersperseOuter a list

intersperseOuter "-", [] = []
intersperseOuter "-", ["a"] = ["-", "a", "-"]
intersperseOuter "-", ["a", "b"] = ["-", "a", "-", "b", "-"]

repeat a n times

repeat' 0 'a' => ""
repeat' 0 "a" => []
repeat' 3 'a' => aaa
repeat' 3 "a" => ["a", "a", "a"]

• Deprecated
• Use: repeatN

repeat n times

repeat's 0 'a' => "'
repeat's 0 "a" => []
repeat's 3 "pig" => ["pig", "pig", "pig"]

• Use repeatN instead of repeat`

repeat n times

repeat's 0 'a' => "'
repeat's 0 "a" => []
repeat's 3 "pig" => ["pig", "pig", "pig"]

• same as replicate but Integer type

replicate n times

replicate' 4 'a' => "aaaa"

fill a list with missing number

fillList 0 [1, 2, 4, 7]
[1, 2, 0, 4, 0, 0 7]

fillList 0 [-1, 2, 4, 6, 10]
[-1,0,0,2,0,4,0,6,0,0,0,10]

   pp $ fillList 0 [] == []
   pp $ fillList 0 [0] == [0]
   pp $ fillList 0 [1] == [1]
   pp $ fillList 0 [1, 2] == [1, 2]
   pp $ fillList 0 [1, 3] == [1, 0, 3]
   

KEY: read file strictly

See readFile SIO.run::NFData sa => SIO sa -> IO sa SIO.readFile::FilePath -> SIO String

KEY: read file strictly, return a list of string

See readFile

readfile to list of ByteString

read file and return strict ByteString

read file and return strict Text Text

IO Data.Text.IO

read file to list of Text

See linesSText readFileSText

Char to strict ByteString

KEY: break newlines

Like the lines function from Prelude, but treat the "\r\n" and "\r" sequences as newlines too, not just "\n".

See plines

KEY: replace pattern inside a file, replace string in a file

• NOTE: It only replace one string in a file, NOT all strings

See readFileRepPat, searchReplaceAny, searchReplace

KEY: replace pattern inside a file, new file is created. Old file is NOT modified

See readFileRepPat, searchReplaceAny, searchReplace, replaceByteStringFile

KEY: replace file with string, substitude string with a pattern

• replace all words in a file with pattern string

EXAMPLE: replaceDirWithStr pat sub dir

ISSUE: if sub contains \\ then, only one '\' is written to fname

NOTE: replace word only

    file.x
       replaceMe

     sub =
          begin{pmatrix}
          a & b             c & d
          
          end{pmatrix}

    replaceFileWithStr "replaceMe" sub "tmpf.x"

    cat tmpf.x
          begin{pmatrix}
          a & b             c & d
          
          end{pmatrix}
   

Search and replace word inside a file, the code is based on matchAllText in package: Text.Regex.TDFA as TD

See searchReplace replace word only

let s = "mydog dog-- dog pig cat dog fox"
searchReplace s "dog" "[\\0]"
"mydog [dog]-- [dog] pig cat [dog] fox"

Search replace words with a list of tuple in a file

See searchReplaceListWord and searchReplace

 > searchReplaceListWord [("dog", "cat")] "mydog dog"
 > "mydog cat"
 

Search replace String with a list of tuple in a file

See searchReplaceListStr and searchReplaceAny

 > searchReplaceListStr [("dog", "cat")] "mydog dog"
 > "mydog cat"
 

Search replace words with a list of tuple

See replaceFileListWord and searchReplace and searchReplaceAny

   > searchReplaceListWord [("dog", "cat")] "mydog dog"
   > "mydog cat"
   

Search replace words with a list of tuple

See replaceFileListWord and searchReplace and searchReplaceAny

   > searchReplaceListStr [("dog", "cat")] "mydog dog"
   > "mydog cat"
   

KEY: replace pattern with a string in all file in a dir

• See replaceFileWithStr

KEY: replace string, substitute string

Use subRegex

   -- Remove all punctuation
   replaceRegex (mkRegex "[[:punct:]]") "[mya,b,c]" ""  ⇒ myabc


   let r1 = mkRegex "google"
   let input = "http://google.com"
   let replacement = "[yahoo]"
   putStrLn $ subRegex r1 input replacement  -- http://[google].com
   

KEY: replace pattern inside a file, replace str in file, substitude str in a file

replaceByteStringFile

   bs <- readFileRepPat "src/searchForm.html" "replaceSearchForm" $ toSBS $ optionHtml autoList
   

KEY: replace pattern inside a file, replace str in file, substitude str in a file

replaceByteStringFile readFileRepPat

   bs <- replaceFileWithPat "src/searchForm.html" "replaceSearchForm" $ toSBS $ optionHtml autoList
   

Convert Lazy ByteString to Strict ByteString

Data.ByteString => Data.ByteString.Lazy

Convert Strict ByteString to String

strictBSToString = strictTextToStr . strictByteStringToStrictText

Empty Strict ByteString

Convert anything to Strict ByteString

Convert anything to Lazy ByteString

Convert String, ByteString, Text to Strict Text

   let st1 = let s = "a"::String in toSText s -- OK
   let st2 = toSText ("a"::String)            -- OK
   let st3 = toSText $ "a"::String            -- Error
   

Convert anything to Lazy Text

Convert anthing to String

• Lazy Text to String
• Strict Text to String
• Lazy ByteString to String
• Strict ByteString to String

can be replaced with following:

(++) <$> (Just [1]) <*> (Just [2])

remove white space from string

See trim trimEnd trimStart

removeSpace " a b c " => "abc"

Escape Html special characters, e.g. only [<, >] currently, remove angle bracket

Html special characters can be added ><, >, '\', %

escape amperspand & \( \Rightarrow \) '&#38'

• See escapePartial
• See escapeXML

escape <, >, '\'', '"'

• See escapeAmpersand
• See escapeXML

escape XML special characters <, >, '\'', '"', &

• See escapeAmpersand
• See escapePartial

Remove element from a list

removeRowCol

principleSubmatrix

insertIndexAt ⟹ insert to the next index

removeIndex 1 [1,2,3]
[1, 3]

removeIndex 3 []
[]


removeIndex 1 "abc"
"ac"

       removeIndex 100 [1, 2] => [1, 2]
       removeIndex -1  [1, 2] => [1, 2]
   

Remove specific row and column from a given matrix

removeRowCol 1 2  -- remove the first row and second column

removeIndex

principleSubmatrix

[ M =begin{bmatrix} 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9

end{bmatrix} rightarrow begin{bmatrix} 4 & 6 7 & 9

end{bmatrix} ]

Principle submatrix

Principle submatrix is a square matrix obtained by removing the same set of rows and columns.

removeIndex

removeRowCol

principleSubmatrix 1 mat

[ M = begin{bmatrix} a & b & c d & e & f g & h & i end{bmatrix}

rightarrow begin{bmatrix} a & c g & i end{bmatrix}

]

drop n elements from the end

pp $ dropEnd 3 "abcd" == "a"

take n elements from the end

pp $ takeEnd 3 "abcd" == "bcd"

take support negative number

     if n >= 0 then take n
     else           takeEnd (-n)
   

drop support negative number

     if n >= 0 then drop n
     else           dropEnd (-n)
   

same takeWhile

from GHC.List

take BS.ByteString

• strict ByteString Data.ByteString

drop BS.ByteString

• strict ByteString Data.ByteString

split BS.ByteString

BS.split (c2w_ 'a') "aXaXa" => ["", "X", "X", ""]

trim whitespace from the whole string, NOT just head and tail

see trim head and tail

trimWS s   = filter(not . isSpace) s

trimAll == trimWS, better name:)

Trim leading and tailing white space from Data.Text String, trim text, remove white space

trim String

trimT TS.Text

trimT = Data.Text.strip

Data.Text

trimBoth == trim, better name:)

trim lazy ByteString

• trim leading/trailing whitespace

Remove whitespace characters from the start of string.

" dog" => "dog"

Remove whitespace characters from the end of string.

" a b c " => " a b c"
"abc"     => "abc"

split list of string when string is empty/space

["dog", " ", "", "cat"] => [["dog"], [], ["cat"]]

split list into half

• split list into half, ["a", "b", "c"] => (["a", "b"], ["c"])

tuples to list

split list 2d with lambda function

Use splitWhen from Internals

   splitListWhen(x -> x == "b") ["a", "b"] => [["a"], []]
   splitListWhen(x -> x == "b") ["b", "c"] => [[], ["c"]]
   splitListWhen(x -> x == "b") ["b"] => [[], []]

   splitListWhen(x -> x == []) [["a"], ["b"], [], ["c"]]
   [[["a"], ["b"]], [["b"]]]
   

Calculate the length of a curve for *any* functions

\[ f(x) = x^2 \quad x \in [0, 1] \]

length_of_curve

f x = x*x
lengthcurve f (0, 1)
1.4689349039867374

[ begin{align*} & text{Divide the curve into } n text{ parts} &x_i in {x_0, x_1, x_2, cdots, x_{n-1}, x_n} &f(x_i) in {f(x_0), f(x_1), f(x_2), cdots, f(x_{n-1}), f(x_n) } &y_i in {x_0^{2}, x_1^{2}, x_2^{2}, cdots, x_{n-1}^{2}, x_n^{2} } s &= sum_{i=1}^{n} sqrt{(x_{i-1} - x_i)^2 + (y_{i-1} - y_i)^2} s_1 &= sqrt{(x_0 - x_1)^2 + (x_0^{2} - x_1^2)^2} s_2 &= sqrt{(x_1 - x_1)^2 + (x_1^{2} - x_2^2)^2} vdots s_{n-1} &= sqrt{(x_{n-2} - x_{n-1})^2 + (x_{n-2}^{2} - x_{n-1}^2)^2} s_n &= sqrt{(x_{n-1} - x_n)^2 + (x_{n-1}^{2} - x_n^2)^2} \ s &= sum_{i=1}^{n} sqrt{(x_{i-1} - x_i)^2 + (y_{i-1} - y_i)^2} s &= sum_{i=1}^{n} sqrt{ Delta x_{i}^2 + Delta y_{i}^2} qquad end{align*}

# 2356 "UsersaaamyfilebitbuckethaskelllibAronModule.hs" ]

• The code is based on length_of_curve

Calculate the length of a curve for *any* functions in a given interval

\[ f(x) = x^2 \quad x \in [0, 1] \]

lengthcurveInter f (0, 1) 200

KEY: balance bracket, check balanced bracket

    []   => True
    [{}] => True
    [}   => False
    [{]} => False
   

Find all bracket '{, }' until they are balanced

   "{{ {    <- 1
        }   <- 2
       }    <- 3
   }        <- 4
   }"       <- 5
   return  => ([(5,"}")],True)
   

balanceBracket

KEY: balance brackets

   pp $ isBalanced "" == True
   pp $ isBalanced "{" == False
   pp $ isBalanced "}" == False
   pp $ isBalanced "{}" == True
   pp $ isBalanced "}{" == False
   pp $ isBalanced "{}{" == False
   pp $ isBalanced "}{}" == False
   

balanceBracket

String to Lazy Text

KEYS: string to strict text, str to strict text, str to text

String to Text

Strict Text to String

KEY: strict text to str, text to string

lazy Text to lazy ByteString

KEY: lazy Text to lazy ByteString

strict Text to strict ByteString

Convert Strict ByteString to Strict Text

Convert lazy ByteString to strict ByteString

Lazy Text to Strict Text

String to Strict ByteString, String to ByteString, str to ByteString

strToStrictByteString = strictTextToStrictByteString . strToStrictText

String to lazy ByteString, only for ASCII, not for unicode

   str1 = "好"
   str2 = "good"

   main = do
           pp ((LC8.unpack $ LC8.pack str1) == str1) -- False
           pp ((LC8.unpack $ LC8.pack str2) == str2) -- True
   

padding whitespace to 2d list or matrix

KEY: String to Maybe DA.FromJSON

See toLBS

   toLBS::Typeable a => a -> BL.ByteString
   

KEY: JSON to record, JSON file to record

   SEE: UsersaaamyfilebitbucketstackprojectJsonAeson

   -- JSON file
   {"editorbeg":100,
    "editorend":200,
    "editorfile":"try919591",
    "editorcmd":"save",
    "editorcode":"Hello World",

    "mycat":{"name":"meowmers",
             "age":1,"list":["dog","cat"]
            }
   }
   --

   data EditorCode = EditorCode{
     editorbeg::Integer,
     editorend::Integer,
     editorfile::String,
     editorcmd::String,
     editorcode::String,
     mycat::Cat
     } deriving (Show, Generic)

   instance DA.ToJSON EditorCode where
     toEncoding = DA.genericToEncoding DA.defaultOptions

   instance DA.FromJSON EditorCode

   data Cat = Cat { name :: Text,
                    age :: Int,
                    list :: [String]
                  } deriving (Show, Generic)

   instance DA.ToJSON Cat where
     toEncoding = DA.genericToEncoding DA.defaultOptions

   instance DA.FromJSON Cat

   meowmers = Cat { name = "meowmers",
                    age = 1,
                    list = ["dog", "cat", "independency Injection"]
                  }

   editCode = EditorCode {
     editorbeg = 100,
     editorend = 200,
     editorfile = "try919591",
     editorcmd = "save",
     editorcode = "Hello World",
     mycat = meowmers
   }

   decodeStr <- jsonToRecord "/tmp/json.json" :: IO (Maybe EditorCode)
   case decodeStr of
     Nothing -> Prelude.putStrLn "Not a Valid JSON file"
     (Just x) -> Prelude.putStrLn $ show x
   

Compile java file

• Given an absoluate path
• return and ExitCode

• The function is used in filewatcher.

docExitCode <- compileJava "/Users/cat/myfile/bitbucket/testfile/compileJavaTest.java"
case docExitCode of
     ExitSuccess -> sys "notify.sh \"gene_javadoc.sh => ExitSuccess\""
     ExitFailure x -> sys "notify.sh \"gene_javadoc.sh => ExitFailure\""

Print matrix with label, print matrix with string,

pm "my matrix" mat
------------------------------------my matrix-----------------------------------
[1,2,3]
[4,5,6]
[7,8,10]

print list of string without double quotes

• rename: ps => pls (Wed Oct 16 22:18:00 2019)

KEY: print string without double quotes

KEY: print matrix, print 2d list

SEE pmat matrixToStr let ls = [[1..4] | _ <- [1..4]] printMat ls

KEY: print matrix, print 2d list

SEE printMat matrixToStr let ls = [[1..4] | _ <- [1..4]] pmat ls

KEY: matrix to string, 2d list to string, print matrix

SEE printMat

  > ls = [[1..4] | x <- [1..4]]
  > s = matrixToStr ls
  > mapM_ putStrLn s
    1 2 3 4
    1 2 3 4
    1 2 3 4
    1 2 3 4
  > wfl "tmpkk.x" s
  > :!cat tmpkk.x
    1 2 3 4
    1 2 3 4
    1 2 3 4
    1 2 3 4
  

prefix n tabs

psTab 3 "dog"

print matrix, show matrix

KEY: print matrix, print string without double quotes

• KEY: list slide, list sliding, window sliding, sliding window
• @ listSlide [a b c d] 2 > [[a, b], [b, c], [c, d]]

listSlide [a b c d] 5 > []

Partition list to n chunks

UPDATE: Thursday, 16 November 2023 14:42 PST FIXBUG: partList 0 [1, 2] => in infinite loop

Note: print partList n [] will cause error since print needs concrete type

split list to n blocks

   >partList 2 [1, 2, 3, 4, 5]
   >[[1,2], [3, 4],[5]]
   
   >partList 2 [1, 2, 3, 4, 5, 6]
   >[[1,2], [3, 4],[5, 6]]

   > partList 0 [1, 2]
   > [[1, 2]]

   > partList -1 [1, 2]
   > [[1, 2]]
   

Partition list to n chunks

Deprecated: Use: partListDiff

Partition list to n chunks

Note: print partList n [] will cause error since print needs concrete type

split list to n blocks @ partListDiff 1 2 [1, 2, 3, 4] ↑ ↑ | + -> block size | + -> distance 1

> [1, 2]

2, 3

3, 4

@

KEY: read line, read input, flush stdout

    hFlush stdout >> getLine
   

KEY: copy file, copyFile

copyFile from Directory

KEY: copy file, copyFile

copyFile from Directory copyFileX

See span

KEY: split string with "[ ]+"

KEY: split file with Regex e.g. empty line

NOTE: use better name, splitTable ? @ ls <- readFileToList "tmpx.x" let lss = splitBlock ls "^[[:space:]]*" => split file with whitespace pp lss

let lss = splitBlock ls "^[[:space:]]*(---){1,}[[:space:]]*" => split file "---" let lss = splitBlock ls "^[[:space:]]*(===){1,}[[:space:]]*" => split file "==="

let lss = splitBlock ["a", " ", "b"] "^[[:space:]]*" => [["a"], ["b"]] let lss = splitBlock ["a", "n", "b"] "^[[:space:]]*" => [["a"], ["b"]] let lss = splitBlock ["a", "t", "b"] "^[[:space:]]*" => [["a"], ["b"]]

• - It works in WhiteSpace

let lss = splitBlock ["a", " ", "b"] "^[[:space:]]*" => [["a"], ["b"]] let lss = splitBlock ["a", "n", "b"] "^[[:space:]]*" => [["a"], ["b"]] let lss = splitBlock ["a", "t", "b"] "^[[:space:]]*" => [["a"], ["b"]] @

NOTE: IT DOES NOT WORK if Empty string in the list. See following. let lss = splitBlock ["a", "", "b"] "^[[:space:]]*" => [["a", "", "b"]]

TestFile

KEY: parse file and partition it into blocks according to patterns: bs ws

bs = "^[[:space:]]*(---){1,}[[:space:]]*" -- split with delimiter "---"
ws = "[,. ]"                              -- split with [,. ]
parseFileBlock bs ws ["rat",
                      "-----",
                      "my dog eats my cat, my cat eats my dog."
                     ]
[(0, ["rat"]), (1, ["my", "dog", "eats", "my", "cat"])]

Test_File

KEY: all prefix strings from given string

substring length k

lengthK 2 ["abcd"]
["ab", "bc", "cd"]

substring length from 1 to len s

substr 1 "abc"
["a", "b", "c", "ab", "bc", "abc"]

all substrings length from 1 to len s

allSubstr "abcd"
[["a","b","c","d"],["ab","bc","cd"],["abc","bcd"],["abcd"]]

unique, remove duplicate elements from a list

Convert the list to Set and convert the Set back to List unique does not keep the order of elements

   2 3 4 4 5 3 5 => Remove from the right => 2 3 4 5 3
   2 3 4 4 5 3 5 => Remove from the left  => 2 3 4 3 5
   

uniqueOrder keeps the order of elements from left \( \Rightarrow \) right

remove duplicated elements and keep the order from left to right

   ["a", "b", "a", "b"] => ["a", "b"]
   s = ["a"]
   s = ["a", "b"]
   "a" elem s => ["a", "b"]
   "b" elem s => ["a", "b"]
   

Recur from the right => left instead of (x:cx)

The runtime will be \( \color{red}{\mathcal{O}(n^2)} \)

NOTE: can be better algorithm

merge two sorted lists | [1, 4] [3] => [1, 3, 4]

Binary Search

quick sort with lambda function

bad version

qqsort(\x y -> len x < len y) ["tiger", "dog"]  => ["dog", "tiger"]

Sort list in nature ordering, e.g. [2, 1] => [1, 2]

Quick Sort in Vector, Did not see any speed decreasing

quicksort better version

nice version

• TODO rename it

Use quickSortAny, Deprecated

• note: quickSort1 [] -- get error

print quickSort1 ([]::Int)  -- it works

Quick Sort for any type, same as quickSort1, just a better name

merge sorted list

rotate a list to the right

rotateRight 2 [1, 2, 3]
[2, 3, 1]

rotate a 2d matrix to the left

rotateLeft2 mat 

rotate a 2d matrix to the right

rotateRight2 mat 

rotate a list to the left

rotateLeft 2 [1, 2, 3]
[3, 1, 2]

Merge sort for any type

• TODO rename it

Merge sort for Int

Merge sort for matrix, special merge sort

   [0, 1]  [1]         => False
   [0, 1]  [1, 1]      => True
   [1, 1]  [0, 1]      => False
   [0, 1, 0] [1, 0, 0] => True
   

groupCount == groupBy . sort

groupCount ["a", "b", "a"] => [("b", 1), ("a", 2)]
groupCount == groupBy . sort

• See groupBy

Create Symbol link for vim under home

.vimrc -> $b/vim/vim.vimrc

• simplify link file in new system
• it might not be very useful

Watch directory

• If any file is modified, then return True
• If a file is added to directory, then return True

• The delay is one second

KEY: file modification time, timestamp, epoch time in second

EpochTime \( \Rightarrow \) Int64

KEY: file modification time, timestamp, epoch time in second

KEY: epochtime to int

EpochTime \( \Rightarrow \) Int

EpochTime \( \Rightarrow \) Int64

fromEnum Int64 \( \Rightarrow \) Int

KEY: file modification time, timestamp, epoch time in second

EpochTime \( \Rightarrow \) Int64 fromIntegral Int \( \Rightarrow \) Integer

KEY: convert int to CTime

Use toEnum

EpochTime \( \Rightarrow \) Int64

return a list of timestamps that any files is modified in a directory

EpochTime \( \Rightarrow \) Int64

KEY: Get file size in byte

See hFileSize openFile ReadMode Handle

Read Snippet file $bsnippetssnippet.hs

• See readSnippetStr
• snippet_test.hs
• Input file: $bsnippetssnippet.hs

   main:*.hs: my dog, my cat
   my fox eats my rat
   

output:
[([head1], [head1_content1]), ([head2], [head2_content2])]
[(["main", "*.hs", "my cat", "my dog"], ["main:*.hs: my dog, my cat","my fox eats my rat "])]

readFileLatin1ToList

 $b/snippet/snippet.hs
partition blocktexts into list

parse the header => latex_eqq:*.tex: latex equation
return [(["latex_eqq", "latex equation"]), ["latex_eqq:*.tex: latex equation", "code block"])]

TODO: write readSnippet for Data.ByteString ?

HELP: gx file://Userscatmyfilebitbucketstackprojectjupyterlab/jupyterlab.html

snippet_test.hs

readSnippetStr without any split

See readSnippet

[("key_name:*.tex: latex", "key_name:*.tex: latex\nline 1\n\line2"])]
readSnippetStr::FilePath->IO [(header, codeblock)]

KEY: Read snippet file, insert into database, snippet to database, snippet to db

• read snippet file, insert to database sqlite3

See CodeBlock data CodeBlock = CodeBlock { id :: Int64 , header :: TS.Text , codeblock :: TS.Text } deriving (Eq, Read, Show)

Query Table CodeBlock and write to a file

mapM_ :: Monad m => (a -> m b) -> [a] -> IO()

How To Use It

    import           Database.SQLite.Simple
    import           Database.SQLite.Simple.FromRow
    import           Database.SQLite.Simple.FromField
    import           Database.SQLite.Simple.ToField
    import           Database.SQLite.Simple.Internal
    import           Database.SQLite.Simple.Ok

    codeBlocks <- query_ conn "SELECT id, header, codeblock from CodeBlock" :: IO [CodeBlock]
    let codeList = map (x -> lines . toStr . codeblock $ x) codeBlocks
    mapM_ (b -> do
                 writeToFileAppend fp b
          ) codeList
    

KEY: Haskell connect to mysql

mysql-haskell

create user 'user1'@'localhost' identified by 'password';    # mysql => create new user
GRANT select, update, delete ON *.* TO 'user1'@'localhost';  # grand permission

GRANT ALL ON *.* to 'user1'@'localhost';                     # grand all permissions
ALTER USER 'user1'@'localhost' IDENTIFIED WITH mysql_native_password BY 'password'   # program can connect to
--------------------+
mysql> source /tmp/user.file
--------------------+

sudo mysql -u user1 -p   # password
---------------------
mysql> CREATE DATABASE testdb   # create database in mysql
mysql> USE testdb               # use testdb - database
mysql> source mytable.sql       # load table, source table, add table

   DROP TABLE mytable;
   CREATE TABLE mytable(
       id INTEGER NOT NULL AUTO_INCREMENT,
       name TEXT NOT NULL,
       email TEXT NOT NULL,
       PRIMARY KEY(id)
   );
   INSERT INTO mytable(name, email) VALUES("name1", "mailgmail.com");
   INSERT INTO mytable(name, email) VALUES("name2", "mailgmail.com");
   INSERT INTO mytable(name, email) VALUES("name3", "mail@gmail.com");
   

strToStrictByteString

Create a config map for different OS

Use it to replace readConfig

   config =[
            [("os", "darwin")],
             [
               ("testdb",          "myfilebitbuckettestfile/test.db"),
               ("webappdb",        "myfilebitbuckettestfile/haskellwebapp2.db"),
               ("host",            "http://localhost"),
               ("snippetpath",     "myfilebitbucketsnippets/snippet.hs"),
               ("port",            "8000"),
               ("readSnippetFile", False)
             ]
           ]
   

read file remotely and write to local file

readFileRemote "https://some.com/file.txt"  "/tmp/file.xt"

read file remotely and return IO BL.ByteString

bs <- readFileRemoteToList "https://some.com/file.txt"

Read generic type from a file and conver to two dim list, read table

• Seperator is Space
• See splitSPC

   fn = "tmpf.x"
   
   tmpf.x
   1 2 3
   3 4 5

   ls <- readFile2d fn :: IO[[Integer]]
   pre ls

   fn = "tmpf.x"
   
   tmpf.x
   0.2 0.3
   0.1 0.5

   ls <- readFile2d fn :: IO[[Float]]
   ls ls
   

FIX: trim string before read it

read two dim matrix from a file, read a list of list Integer from a file

readFile2d for different type

p1 = "/Users/cat/myfile/bitbucket/testfile/matrix.txt"
lss <- readFileToInteger2d p1
pa lss

Read dir, all dir or files in [String]

There is error when reading some non utf8 or weird char.

Deprecated, use readFileLatin1ToList

 hGetContents: invalid argument (invalid byte sequence)

["f1", "f2"]

Emacs Org mod forms a list

["dog", "cat"] => ["|", "dog", "|", "cat", "|"]

Emacs Org mode forms a table

• | cat | dog |
• | cow | pig |

Write [String] to file

• write string to file writeFile

• Append string to file appendFile

Write BS.ByteString to file

• writeFileBS used BS.writeFile, nothing else

writeFileBS "file.x" (strToStrictByteString "data")

writeFile

Write [BS.ByteString] to file

• writeFileListBS uses BS.writeFile and BS.concat, nothing else

writeFile

append list to file

TODO: rename it

Same as writeFileListAppend

append list to file

TODO: rename it

Same as writeToFileAppend

Matrix: Integer to Fractional, convert integer matrix to Fractional matrix

see nToNumMat

class (Num a)=>Fractional a where
class (Num a, Ord a)=> Real where
class (Real a, Enum a)=> Integral where

Conver Integer to Num

Convert an Integer matrix to an Num Matrix

see nToFractMat

Matrix: Real to Rational

see nToFractMat, nToNumMat

data Rational = Ratio Integer

Write an 2d Matrix to file, write an 2d list to file, write matrix to file

see writeToFileMat

[ begin{bmatrix} 1 & 2 3 & 4 end{bmatrix} Rightarrow

begin{matrix} 1 & 2 3 & 4 end{matrix}

]

m = [[1, 2], [3, 4]]
writeToFile2dMat "/tmp/m.x" m
:!cat /tmp/m.x

write String matrix to file

see writeToFile2dMat

KEY: filter and map simultaneous

filtermap(\x -> elem x ['a', 'e', 'i', 'o', 'u', 'y'] then Nothing else Just (toUpper x)) "abc"
remove all the vowels and toUpper => "BC"

Prepend an element to a list if available. Leave the list as it is if the first argument is Nothing. Variant of map which deletes elements if the map function returns Nothing.

https://snipplr.com/view/59474/simultaneous-filter-and--map/

Backward substitute

Given an upper triangle matrix \(A\) and a vector \(\vec{b}\), solve for \(x\)

backward_substitute

\[ Ax = b \] [ A = begin{bmatrix} 1 & 2 0 & 4 end{bmatrix}

begin{bmatrix} x_1 x_2

end{bmatrix} = begin{bmatrix} b_1 b_2

end{bmatrix} ]

forward substitute

Given a lower triangle matrix \(A\) and a vector \(\vec{b}\), solve for \(x\)

backward_substitute

\[ Ax = b \] [ A = begin{bmatrix} 1 & 0 2 & 4 end{bmatrix}

begin{bmatrix} x_1 x_2

end{bmatrix} = begin{bmatrix} b_1 b_2

end{bmatrix} ]

Find the dimension of a matrix -> (nrow, ncol)

dim [] => (0, 0)

NOTE: there is bug >dim [1]

zipWith two mutable array

TODO: change Int to generic type with forall a. ? Problem: when you initialize the array, you need a concrete type such as Int, Float Solution: constrain to (Num a) type

zipWith two mutable array, and convert to list

TODO: change Int to generic type with forall a. ? Problem: when you initialize the array, you need a concrete type such as Int, Float Solution: constrain to (Num a) type

Use co-factor expantion to find a determinant of n by n matrix.

• co-factor expantion
• It is very slow.
• Note: \( \det M = \det M^{T} \)
• NOTE: the function should not been used for Floating type

Proof

matrix multiplicaiton in Int

KEY: matrix multiply a column vector

NOTE: return a column-matrix, the vector is in the first column

INPUT: column-matrix RETURN: column-matix

   -- treat v as column vector
   fw "mat"
   printMat mat
   v = [1, 2, 3]
   fw "v"
   v
   m1 = mat multiVec v
   fw "m1"
   printMat m1
 

Matrix multiplication in String

   m1 =
   ["a","b"]
   ["c","d"]
   m2 =
   ["x","y"]
   ["z","w"]

   > mapM_ print $ multiMatStr m1 m2
   ["axbz","aybw"]
   ["cxdz","cydw"]

   > mapM_ print m1
   ["a","b"]
   ["c","d"]

   > mapM_ print m2
   ["x","y"]
   ["z","w"]

   > pmat mat
   1 2 3
   4 5 6
   7 8 10
   > pmat $ tran mat
   1 4 7
   2 5 8
   3 6 10
   > pmat $ (map . map) (r -> concatStr r "+") $ (out . zipWith) (a b -> show a ++ "x" ++ show b) mat $ tran mat
   "1x1+2x4+3x7"  "1x2+2x5+3x8"  "1x3+2x6+3x10"
   "4x1+5x4+6x7"  "4x2+5x5+6x8"  "4x3+5x6+6x10"
   "7x1+8x4+10x7" "7x2+8x5+10x8" "7x3+8x6+10x10"
   >
   

 cart::[[a]] ->[[a]] -> [[([a], [a])]]
 cart cx cy = tran $ [[(x, y) | x <- cx] | y <- tran cy]
 

matrix multiplication in Double multiMatDouble::[[Double]]->[[Double]]->[[Double]] multiMatDouble a b = [ [sum $ zipWith (*) ar bc | bc <- (L.transpose b)] | ar <- a]

matrix multiplication in Rational Number

 > pmat matr
 1 % 1 2 % 1 3 % 1
 4 % 1 5 % 1 6 % 1
 7 % 1 8 % 1 10 % 1

 > pmat $ multiMatR matr matr
 30 % 1  36 % 1  45 % 1
 66 % 1  81 % 1  102 % 1
 109 % 1 134 % 1 169 % 1
 

KEY: Use outer product to compute matrix multiplication.

[ begin{bmatrix} 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9

end{bmatrix} ]

• use outer product to compute matrix mulitplication
• outer(col_1 row_1) + outer(col_2 row_2) + outer(col_3 row_3)
• matrix multiply vector

  -- column vector
  [[1],
   [2],
   [3]]
  -- row vector
   [[1, 2, 3]]

  -- matrix * vector

  -- matrix m
  m = [
       [1, 2, 3],
       [4, 5, 6],
       [7, 8, 9]
      ]
  -- vector V
    [a,
     b, 
     c]
   to matrix form
   v = [
        [a, 0, 0],
        [b, 0, 0],
        [c, 0, 0]
       ]
   matrix multiply vector
   m * v
  

[ begin{bmatrix} 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 end{bmatrix}

times begin{bmatrix} 1 2 3 end{bmatrix} Can be written as following

begin{bmatrix} 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 end{bmatrix}

times begin{bmatrix} 1 & 0 & 0 2 & 0 & 0 3 & 0 & 0 end{bmatrix}

]

matrix multiplication in String/Rational

KEY: identity matrix

  matId 3
  out (a b -> a == b ? 1 $ 0) [1..3] [1..3]
  

KEY: zero matrix

  matId 3
  out (_ _ -> 0) [1..3] [1..3]
  

Convert Rational to Integer:

>>> ratToInt "3/1"
3

normalR -3-1 = 31, 3-2 => -32

reduceForm list of rational

reduce numerator and denominator:

>>> reduce 6/2
3/1

Convert string to Float, string to Double

• strToF

stringToFloat "123"
123

stringToFloat "123.3"
123.3

stringToFloat "a"
error

• The Read class Text.Read

Convert string to a list of Int

stringToListInt "[1, 2]"
[1, 2]

stringToListInt "[1..3]"
error

Text.Read

split first word by delimiter: isSpace

split "my dog eats my cat"
("my", "dog eats my cat")

parser

split all words with delimiter: isSpace

parser

print $ sentence "dog cat 133"
["dog", "cat", "133"]

Check a string whether it is a word or not

 Word is defined as  "^[[:alpha:]]+$"
isWord "dog"
True

isWord "dog1"
False

isWord::String -> Bool
isWord s = matchTest (mkRegex "^[[:alpha:]]+$") s

Check a string whether it is a word or not

Word should be defined as [a-zA-Z0-9_] according to vim doc :h pattern

Check whether String contain Word char

     Word = [a-zA-Z0-9_]
     hasWordChar "abc_efg"  -- True
     hasWordChar "abc-"     -- False
   

Non negative integer

• \( 0, 1, 2, \cdot \)

Permutation of any type, the algo is based on prefix string

permutation_tree

   fun (prefix, int index, removeIndex(index str))
   

 perm "12"
[["12", "21"]]

TODO: fix, the code has error.

Permutation of any type

The code is based on prefix string algorithm

 perm "12"
[["12", "21"]]

       abc
       a p(bc)
          b p(c)
            c p()
          c p(b)
            b p()
       b p(ac)
         a p(c)
           c p()
         c p(a)
           a p()
       c p(ab)
         a p(b)
           b p()
         b p(a)
           a p()
   

       abc
           a   bc
               b c
                   [[]]
               c b
                   [[]]

           b   ac
               a c
                   [[]]
               c a
                   [[]]

           c   ab
               a b
                   [[]]
               b a
                   [[]]
   

KEY: facebook interview question

• find all the list that in increasing order, and the length is n

rangeNum 3 [1, 2, 3, 4]
[1, 2, 3], [2, 3, 4], [1, 2, 4]

And other Permutation

SO

1, 2, 3

x : xs 1 [2,3] x : xs 2 [3] x : xs 3 []

perm([1, 2, 3]) 1 : perm([2, 3]) 2 : perm([3]) 3: perm([])

1 2 3

[2 3 1] [3 1 2] x : cx x:cx x : cx 1:[2,3] 2:[3,1] 3:[1,2] 1:[3,2] 2:[1,3] 3:[2,1]

Normalize a list as vector

 [[1, 2, 3]]     is row vector
 [[1], [2], [3]] is column vector
 

\[ \| \vec{v} \| = \sqrt{x^2 + y^2 + z^2} \quad \text{ where } \vec{v} = \begin{bmatrix} x & y & z \end{bmatrix} \]

projection from u onto v in n dimensional list | | puv = (u v /v) v | |

Form a almost R matrix: almost an upper triangle matrix

QR_Decomposition [ R' = begin{bmatrix} leftv_1 right & leftv_2 right & leftv_3 right emptyset & leftv_2 right & leftv_3 right emptyset & emptyset & leftv_3 right

end{bmatrix} quad R = begin{bmatrix} leftv_1 right & leftv_2 right & leftv_3 right 0 & leftv_2 right & leftv_3 right 0 & 0 & leftv_3 right

end{bmatrix} R' neq R

]

rejection \(v_k\) onto span of \( \{ a_1 \dots a_{k-1} \} \)

QR_Decomposition \[ a_k = v_k - \sum_{i=1}^{k-1} \frac{\left<v_k, a_i \right>}{\left<a_i, a_i \right> } a_i \]

• v3 projects onto \( \{a_1, a_2 \} \)

a3 = v3 - ((projn v3 a1) + (projn v3 a2))

• if the matrix is singular then one of \( \left\| a_k \right\| = 0 \)
• that can be used to determinate the determinant of a matrix, but not the sign of a determinant
• compute the determiant is hard problem: \( \mathcal{O}(n^3) \), there is better algo.

QR decomposition or QR factorization

QR_Decomposition

• Given \(M\) is square matrix, there exists a pair of matrices \( Q \) is unitary matrix and \( R \) is upper triangle matrix such that: \[ M = QR \]

Addition for two list of Rational strings

addRL ["1/2", "1/2"] ["1/2", "1/2"]
["1/1", "1/1"]

Division for Rational string

divR "1/2" "3/4"
"2/3"

The algorithm uses backtrack.

• Move top left corner to right and down
• IF the move is valid THEN set (c, r) = 1, AND move one level down to (c+1, 0)
• IF the move is not valid THEN move to (c, r+1)
• Move (c,r) from left to right
• IF (c,r) is valid move
• THEN go down one level deep, => (c+1,0)
• ELSE goto (c, r+1)
• IF (c, r) is the right most position, AND IF (c,r) is valid move
• THEN go down to (c+1, 0)
• ELSE backtrack => take the previous valid move and reset (c,r)=0 AND check whether (c, r+1) is valid move.
• IF (c, 0) is the bottom level,
• THEN we are done!

let m1 = geneMat 10 Zero
pa $ eightQueen m1 [] 0 0

Replace element in position (c, r) with element n in 2d matrix. replace element, replace matrix, replace 2d array

Replace index p element with a function f

  replace1d 1 (const 2) [0, 0, 0] -- [0, 2, 0]
  

Replace index (c, r) element with a value v

   replace2d 1 (const 2) [0, 0, 0] -- [0, 2, 0]
   replace2d 5 (2, 1) [[1, 1, 1], [1, 1, 1], [1, 1, 1]]
   [[1,1,1],[1,1,1],[1,5,1]]

  

get the diagonal of the matrix

get upper triangle of matrix

Collect all the elements from left diagonal of a matrix.

   mat = [
         [1, 2, 3],
         [4, 5, 6],
         [7, 8, 10]
         ]
   leftDiagonal mat 0 0
   [7, 5, 3]
   

Collect all the elements from right diagonal of a matrix.

   mat = [
         [1, 2, 3],
         [4, 5, 6],
         [7, 8, 10]
         ]
   rightDiagonal mat 0 0
   [10, 5, 1]
   

reverse words in string

Transpose matrix

[ begin{bmatrix} a & b c & d end{bmatrix} Rightarrow

begin{bmatrix} a & c b & d end{bmatrix}

]

• NOTE: > map tail [[1], [2]] => [[], []]

   -- Fri 14 Oct 23:32:14 2022 
   -- The code DOES NOT work if the matrix:
   m = [[1, 2], [3]]
   
   tran::[[a]]->[[a]]
   tran [] = []
   tran ([]:_) = []
   tran x = (map head x):tran(map tail x)

    [1, 2, 3] : 
   x0 = [1, 2, 3] => [2, 3] => [3] => [] => []
   x1 = [4, 5, 6] => [5, 6] => [6] => [] => []
   x2 = [7, 8, 9] => [8, 9] => [9] => [] => []
                
                       1 :  <-  4 :    <-   7 : []

                       2 :  <-  5 :    <-   8 : [] 

                       3 :  <-  6 :    <-   9 : []


                       (9 ) <-  (8)  <-  (7)
                       (6)  <-  (5)  <-  (4)
                       (3)  <-  (2)  <-  (1) 

   

concat operator | pp $ "n=" +: fun x | (+:)::(Show a)=> String-> a -> String | (+:) s a = s ++ (show a)

sort row for list of list

Tranform the matrix to echolon/upper triangle form

KEY: upper triangle, matrix to upper triangle

• Thu Jan 10 23:29:20 2019
• gx Matrix to Upper Triangle
• gf Userscatmyfilebitbucketmathupper_triangle.tex
• Note: the determinant is different than the original matrix
• Thu Jan 10 23:29:27 2019
• Add lcm to the multiplier, make matrix dim from 6 to 13
• TODO: fix the num overflow issue
• Wednesday, 15 May 2024 11:45 PDT
• Update: Use mergeSortC with compare function

Division is painful

   class (Num a)=> Fractional  a where
       (/):: a -> a -> a

   divI::(Fractional a)=>Integer -> Integer -> a

   class Num a where
       fromInteger::Integer -> a

   class (Num a, Ord a)=> Real a where


   fromIntegral::(Integral a, Num b) => a -> b
   fromIntegral = fromInteger . toInteger

   class (Real a, Enum)=> Integral a where   [1]
   toInteger(Real a, Enum a)=> a -> Integer  [2]
   fromInteger::(Num a)=>Integer -> a        [3]

   proof:
   [1] [2] [3] =>
   fromIntegral(Num a) => Integral -> a

   

Find the invertible matrix, return ([[]], [[]]) if the matrix is singular

• The code does not check whether the matrix is singular or not

m <- randomMatrix 7 7  -- Int matrix
m' = (map . map) rf m  -- Double matrix
inverse m'

inverse::(Integral a, Fractional a, Real a, Show a, Eq a)=>[[a]]->([[a]], [[String]])
inverse::(Fractional a, Show a, Eq a)=>[[a]]->([[a]], [[String]])

• TODO: Remove division

check whether a matrix is singular using QR_Decompoisition

Multiply all the diagonal elements and check whether the product is zero or not

Algorithm:

1. Find the upper triangle of m
2. Multiply all the diagonal entries
3. If their product is NOT zero then it is invertible, otherwise singular

   -- Test case:
   rm <- randomMatrix 100 100
   pp $ isInvertible rm
   

Generate n dimentional identity matrix

Integer multiply integer list

reverse $ 9 x [9, 8] = [8, 8, 2]

KEY: random temp file name, random tmp file

   randomTemp::IO String  -- randomTemp  =>  tmp223423423.txt
   

KEY: random Integer

• generate Integer from x to y random number

KEY: random Integer

• alias of drawInteger

Generate list of Double in \( x \in [0 \dots n], n = 100 \)

[0.3, 0.4, 0]

Use randomFrac

Generate list of Double in \( x \in [0 \dots n], n = 100 \)

[0.3, 0.4, 0]

Use randomFrac

Generate list of Fractional in \( x \in [0 \dots n], n = 100 \)

[0.3, 0.4, 0]

Num and Fractional are type class so you can NOT do [Num] or [Fractional]

Type class in Haskell is similar like interface in Java, but there are many differences

e.g. Integer implement Num => Integer is a concrete class e.g. Fractional inherits from Num => Fractional type class e.g. Float implement Fractional => Float is concrete class

generate random of list Integer

List of random Int

NOTE: Use randomIntegerList

   randomIntList::Integer ->(Integer, Integer) -> IO [Integer]
   randomIntList 0 _ = return []
   randomIntList n (s, e)= do
     r <- randomRIO (s, e)
     rs <- randomIntList (n - 1) (s, e)
     return (r:rs)
   

list of random Int

Same as randIntList SEE: randomIntegerList

Generate \( m \times n \) random matrix.

Generate \( m \times n \) random matrix.

Same as randomMatrix

generate zero matrix

Generate a matrix from 1 to \( n \times n \) with dimention n

geneMat1ToN 2
[[1, 2],
 [3, 4]]

Generate a matrix from 1 to \( m \times n \)

geneMat1ToN 2 3
[[1, 2, 3],
 [4, 5, 6]]

generate zero or identity matrix |

Add more doc here

Compile haskell code to $ffmybinmyHaskell => create symbol link $sym/sym | [file:myHaskell.hs] [sym:symbol] link name in $sym

compare two string ignore cases

file base name

KEY: file extension, extension, basename, base name, file ext

baseName "/dog/file.txt" => "file"
takeFileName gives "file.ext"
takeDirectory gives "/directory"
takeExtension gives ".ext"
dropExtension gives "/directory/file"
takeBaseName gives "file"
"/directory" </> "file.ext".
"/directory/file" <.> "ext".
"/directory/file.txt" -<.> "ext".

take file name

See takeFileName

drop file name from a path

See dropFileName

KEY: take directory only, same as dropName

See dropFileName dropName

• It is the same name as in Python AronLib.py

KEY: dropName TS.Text

KEY: dropExt TS.Text

Take the base name from dir in Text

Goto current directory, use in script

KEY: Walking directory with filter or lambda function: upper case file extension

• if there is file, then append it to list

• otherwise, walking inside the dir
• Pass lambda func: (FilePath -> IO [String]) as argument

   -- ls all files recursively
   let f fn = return [fn] in dirWalk f "/tmp"

   let f fname = takeExtension fname == ".png" then return [fname] else return []
   ls <- dirWalk f "/tmp"

   ls dirWalk (x - x == ".png") "/tmp"
   

KEY: walk through a list of dir

   p1 <- getEnv "m"
   p2 getEnv "www">= x -> return $ x / "pdf"
   dirWalkPathList (p -> let ex = takeExt p in ex == ".tex" ? return [x] $ return []) [p1, p2]
   

KEY: list all files in dir, not recursive

get directory contents

KEY: list file with regex match, see lsRegexFull, list file with filter, file filter

ff <- lsRegex (getEnv j) "\\.java$" -- list all java file
ff <- lsRegex (getEnv j) "^try"     -- list all file names starts with "try"

KEY: touch a file

remove file only, delete file

check whether a given file is a directory or symbol link to a directory

isDir p = doesDirectoryExist p

doesDirectoryExist

Also see isFile

Check if file exist

NOTE: ONLY for file

Same as fExist

remove directory recursive

rm "dir"

Show current directory

change dir

set current directory

KEY: get environment variable, getEnv

SEE: getEnv

Sleep n seconds

sleepSec 2

sleep 1 sec = 100000

split path

asplitPath "/dot/cat/"
["dog", "cat"]

asplitPath "dot/cat/"
["dog", "cat"]

asplitPath "/dot/cat"
["dog", "cat"]

asplitPath "dot/cat"
["dog", "cat"]

splitPathA from System.FilePath.Posix.splitPath

splitPathA "/dog/cat/"
["/", "dog/", "cat/"]

splitPathA "/dog/cat"
["/", "dog/", "cat"]

splitPathA "dog/cat"
["dog/", "cat"]

splitPathA "/"
["/"]

splitPathA "./"
["./"]

take all the elements if \( f(x) \) condition is true

• It is same as takeWhile

takeIf (\x -> head x == '-') ["-a", "-b", "cc"]
["cc"]

drop all the elements if \( f(x) \) condition is true

• It is same as dropWhile

dropIf (\x -> head x == '-') ["-a", "-b", "cc"]
["-a", "-b"]

dropIf (\x -> x == ' ') "   abc"
"abc"

Integer type

1. copy FilePath to "/tmp" | 2. move the file back to dir with newName | copy file and rename it in the same dir

If source is valid file and dest is valid dir, otherwise error

create empty file

List file with a Regex filter

SEE: Same as lsFileFilter

e.g. all html files >ls <- listDirFilter pa "\.html$"

List file with a Regex filter

SEE: Same as listDirFilter

e.g. all html files >ls <- lsFileFilter pa "\.html$"

copy dir to other dir

rename dir or file => dir or file

mv file, rename file

rename all files in path, e.g. s=XXX img.JPG => img_XXX.JPG

Create directory, make directory

KEY: set cursor position, move cursor

+ - - - - - > | | | - - + (nrow, ncol) | | V

       ESC[{line};{col}H
       ESC[{line};{col}f
             ↑ 
             + -> move cursor to line 
   

Escape code

KEY: get terminal size, get screen size, get console size

• See getScreenSize
• See ANSI

KEY: get screen size, get console size

• See getTerminalSize
• See ANSI

Do not need to return IO [String] like run

If command error, process will not be terminated unless following error:

• PermissionDenied
• ResourceExhausted
• UnsupportedOperation

More detail system

• following will not work if use run

mapM (\x -> run "git lone " ++ x) listdir

• change to

mapM (\x -> system "git clone " ++ x) listdir

system::String -> IO ExitCode
sys s = system s

Use inside GHCi or use :! cmd in GHCi

ExitCode See ExitCode document

• Defines the exit codes that a program can return.

      data ExitCode
           = ExitSuccess -- ^ indicates successful termination;
           | ExitFailure Int
               -- ^ indicates program failure with an exit code.
               -- The exact interpretation of the code is
               -- operating-system dependent.  In particular, some values
               -- may be prohibited (e.g. 0 on a POSIX-compliant system).
           deriving (Eq, Ord, Read, Show, Generic)
   

The power of typeable

Data.Typeable

Check type of list of String

Data.Typeable

Check type of list of ByteString

Data.Typeable

Check type of String

Data.Typeable

KEY: lines for strict Text

Deprecated USE: linesST

KEY: lines for strict Text

Check if char is hex.

• Same as isHexDigit

Does string contain hex only.

• See isHexDigit

Does string contain digit only.

• See isDigit

Does string contain letter only.

• See isLetter isLetterChar

Check letter

• It is same as isLetter

• See isLetterChar isDigitStr

Check digit

• It is same as isDigit

• See isDigitStr isLetterStr

run shell cmd, send output to std_out

• run' does not wait for the process to finish

Run shell cmd, capture std_out

• some issue with waitForProcess
• it might be deadlock, e.g. run "ps aux"
• man ps -x => still d't underand why the process is not terminated
• top command issue => process is not terminated
• 1. Change it to System, there is issue with the function
• TODO: fix it:o
• There is still some issues, use system instead, Tue Jan 28 11:46:22 2020

Run shell command with Turtle lib, shell command (ExitCode, stdoutx, stderr)

   (e2, so, si2) <- runShellcmd
   if e2 /= ExitSuccess then let rcode = ReplyCode{rcmd="", rerror = si2, stdoutx=si2}
                                 replyJson = toSBS $ DA.encode $ rcode
                             in response $ responseNothingBS replyJson
   else do
       pp so
       let replyCode = ReplyCode{rcmd="", rerror="", stdoutx= so}
       let replyJson = toSBS $ DA.encode $ replyCode
       response $ responseNothingBS replyJson
   

See runSh, runRawCmd, run

runShell is same as runSh, cmd is String

Turtle shellStrictWithErr

   shellStrictWithErr
       :: MonadIO io
       => Text
       -- ^ Command line
       -> Shell ByteString
       -- ^ Chunks of bytes written to process input
       -> io (ExitCode, ByteString, ByteString)
       -- ^ (Exit code, stdoutx, stderr)
   shellStrictWithErr cmdline =
       systemStrictWithErr (Process.shell (Data.Text.unpack cmdline))
   

Differentiate on \(f(x)\)

Find the first derivative at \( x \) on function \( (a \rightarrow a)) \)

x = 1.0
df (\x ->x^2) x
2.0

\( f(x) = x^2 \Rightarrow f'(x) = 2x \Rightarrow f'(1.0) = 2.0 \)

First derivative on f or slop of f at point x

\( f'(x) = \lim_{h \rightarrow 0} \frac{f(x + h) - f(x)}{h} \)

Compute the tangent equation at point \((x_0, f(x_0))\) for function \( f \)

Find a tangent equation at \( x_0 = 1.0 \) in \( f(x) = x^2 \)

tanglent (\x -> x^2) 0 1

Tangent equation:

\( f'(x) = \frac{y - y_0}{x - x_0} \)

\( y = f'(x_0)(x - x_0) + y_0 \)

e.g.

\( f(x) = x^2 \)

\( \Rightarrow f'(x_0) = 2x_0 \)

\( f (x) = x^2 \) where \( x = x_0 \)

\( y = 2x_0(x - x_0) + y_0 \) where \( y_0 = f (x_0) \)

\( f' (x_0) = \frac{y - y_0}{x - x0} \)

\( y = f'(x_0)(x - x_0) + y_0 \)

Compute the tangent vector at point (x0, f x0)

Generate prime number with Sieve Algorithm

Find root for any polynomial function

• Example: FindRoot

• Partition the interval [x0, xn] into list = [x0, x1) [x1, x2) [x2, x3) ..[x(n-1), xn)
• Concat [xn, xn] with the list since the left boundary is checked only
• Note: f(xn) might be zero, we need to check the xn boundary
• TODO: need to check f(xn), DONE, concat [xn, xn] to the list

Good test cases:

\( f(x) = x^2 - 4 \quad x \in [-2, 2] \)

\( f(x) = x^5 -4x^4 + 0.1x^3 + 4x^2 - 0.5 \quad x \in [-4, 4] \Rightarrow \) 5 solutions

• limitation:
• if each subinterval contains two or more values, then ONLY one value can be found
• subinterval can be adjusted in arbitrary small

[0, 2] (2-0)/2 = [0, 1, 2] = [0, 1) ∪ [1, 2) ∪ [2, 2]

Find all the roots for a given close interval: [1, 2], 1 or 2 might be the root |

outer product = col ⊗ row

• Sun O21 00:00:05 2018

generic outer product or sth, inspired by APL

Update: Switch row and column to similar to 2d array or APL outer product

   out (x y -> x == y ? 1 $ 0) [1, 2, 3] [1 2]

      | 1 | 2 |
   -----------+
   1  | x | 0 |
   -----------+
   2  | 0 | x |
   -----------+
   3  | 0 | 0 |
   -----------+

   -- identity matrix
   > m = out (a b -> a == b ? 1 $ 0) [1..4] [1..4]
   > pmat m
   1 0 0 0
   0 1 0 0
   0 0 1 0
   0 0 0 1
   

outer sum

outer modulus = col

KEY: outer product for string

DATE: Wednesday, 28 February 2024 12:10 PST

 > v0 = [
         ["x"],
         ["y"]
        ]
 > h0 = [["x", "y"]]
 > 
 > printMat $ outerStr (a b -> a ++ b) v0 h0
 > "xx" "xy"
 > "yx" "yy"
 

KEY: symbol operator, unicode operator