/3¤      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~ portable experimental#Reiner Pope <reiner.pope@gmail.com>A matrix with m rows, n columns.  portable experimental#Reiner Pope <reiner.pope@gmail.com>A vector with elements of type t and length n.  The type n encodes the vector's length, and will  usually either be Unknown or will satisfy  PositiveT. *Operations which return vectors of length Unknown 2 will return vectors whose lengths are determined * at runtime. All operations which mention Unknown 3 lengths will have names ending in an uppercase U,  for example  fromListU,  subVectorU.  The use of Unknown facilitates manipulation ) of dynamically-lengthed vectors without / using continuations for each operation, since 0 most operations work equally well for lengthed - as well as unlengthed vectors. When vectors  of Unknown! length are used, runtime length 1 mismatches may arise, and the system is as safe  as hmatrix. -When the length of every vector is known, if ) the code typechecks, then there will be 4 no runtime vector length mismatches. Equivalently, 3 there will be no runtime vector length mismatches  if: $ no unsafe functions are used; and  no functions mentioning Unknown5 are used, i.e. no functions with suffix U are used.  portable experimental#Reiner Pope <reiner.pope@gmail.com>portable experimental#Reiner Pope <reiner.pope@gmail.com> #Less-typed, hmatrix representation  standard 'unknown' shape. For vectors, Unknown; for matrices, (Unknown,Unknown). "Convert to hmatrix representation $Convert from hmatrix representation *Coerce the static shape. Unsafe; the user 2 of this function has an obligation to prove that  the object'$s dynamic shape is the same as that  represented by s'. .Uninhabited type. Represents unknown lengths.  Instances of  use   for the  type. For type hints.  > constant (5::Double)   d4  [$vec| 5.0, 5.0, 5.0, 5.0 |] :: Vector D4 DoubleImplementation: atShape = const. For type hints.  > constant (5::Double)   shapeOf [$vec|1|]  [$vec| 5.0 |]Implementation: shapeOf _ = undefined "unsafeWrap = unsafeReshape . wrapU. .Changes the static shape to the UnknownShape. & Dynamic representation is unchanged.    portable experimental#Reiner Pope <reiner.pope@gmail.com>      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                           ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                            ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                            ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                            ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                            ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~        !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                           ! 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~!~"~#~$~%~&~'~(~)~*~+~,~-~.~/~0~1~2~3~4~5~6~7~8~9~:~;~<~=~>~?~@~A~B~C~D~E~F~G~H~I~J~K~L~M~N~O~P~Q~R~S~T~U~V~W~X~Y~Z~[~\~]~^~_~`~a~b~c~d~e~f~g~h~i~j~k~l~m~n~o~p~q~r~s~t~u~v~w~x~y~z~{~|~}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~  !"#$%&'()*+,-./01portable experimental#Reiner Pope <reiner.pope@gmail.com> A matrix with m rows, n columns.   !"#$%&'()*  !"#$%&'()*  !"#$%&'()*portable experimental#Reiner Pope <reiner.pope@gmail.com>%.Fixes a matrix's static row length. 5Essentially a mechanism for partial type signatures: 7you can specify the row length without specifying the rest of matrix's type. >ident `atRows` d5  [$mat| 1.0, 0.0, 0.0, 0.0, 0.0;  0.0, 1.0, 0.0, 0.0, 0.0;  0.0, 0.0, 1.0, 0.0, 0.0;  0.0, 0.0, 0.0, 1.0, 0.0;  0.0, 0.0, 0.0, 0.0, 1.0 |]/Fixes a matrix's static column length. > ident `atCols` d4 [$mat| 1.0, 0.0, 0.0, 0.0;  0.0, 1.0, 0.0, 0.0;  0.0, 0.0, 1.0, 0.0;  0.0, 0.0, 0.0, 1.0 |]4*Constructs a matrix from a list. The size  in the matrix's type and the list's length must agree or %else a runtime error will be raised. > matFromList [1,2,3,4,5,6] `atShape` (d2,d3) [$mat| 1.0, 2.0, 3.0;  4.0, 5.0, 6.0 |]5*Constructs a matrix from a list. The size  in the matrix's type and the list's length must agree or %else a runtime error will be raised. > (d2 >< d3)[1,2,3,4,5,6] [$mat| 1.0, 2.0, 3.0;  4.0, 5.0, 6.0 |]66Constructs a matrix from a list of lists of elements. 6Each sublist must be of equal size or a runtime error will be raised. > fromListsU [[1,2,3],[4,5,6]] [$mat| 1.0, 2.0, 3.0;  4.0, 5.0, 6.0 |]71Converts a matrix to a list of its rows, each as a list. > toLists [$mat|1,2,3;4,5,6|]  [[1.0,2.0,3.0] ,[4.0,5.0,6.0]]8(Interprets a vector as a 1-row matrix. > asRow [$vec|1,2,3|] [$mat| 1.0, 2.0, 3.0 |]9*Interprets a vector as a 1-column matrix. > asColumn [$vec|1,2,3|]  [$mat| 1.0;  2.0;  3.0 |]:)Constructs a matrix from a list of rows. > fromRowsU [[$vec|1,2,3|] ,[$vec|4,5,6|]] [$mat| 1.0, 2.0, 3.0;  4.0, 5.0, 6.0 |];)Converts a matrix to a list of its rows. > toRows [$mat|1,2,3;4,5,6|] [[$vec| 1.0, 2.0, 3.0 |],[$vec| 4.0, 5.0, 6.0 |]]<,Constructs a matrix from a list of columns. > fromColumnsU [[$vec|1,2,3|] ,[$vec|4,5,6|]] [$mat| 1.0, 4.0;  2.0, 5.0;  3.0, 6.0 |]=,Converts a matrix to a list of its columns. > toColumns [$mat|1,2,3;4,5,6|] [[$vec| 1.0, 4.0 |],[$vec| 2.0, 5.0 |],[$vec| 3.0, 6.0 |]]>*Returns the number of rows of the matrix. > rows [$mat|1::Double,2,3;4,5,6|] 2?-Returns the number of columns of the matrix. > cols [$mat|1::Double,2,3;4,5,6|] 3@Matrix transpose. > trans [$mat|1,2,3;4,5,6|] [$mat| 1.0, 4.0;  2.0, 5.0;  3.0, 6.0 |]A"Reshapes a vector into a matrix, 3with the specified number of columns. If the vector' s length +is not a multiple of the required columns, a runtime error is raised. > reshapeU 3 [$vecU|1,2,3,4,5,6|] [$mat| 1.0, 2.0, 3.0;  4.0, 5.0, 6.0 |]B!Flattens a matrix into a vector. > flatten [$mat|1,2,3;4,5,6|] %[$vec| 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 |]CIndexes a matrix. > [$mat|1,2,3;4,5,6|] @@> (1,2) 6.0D!Constructs a matrix from blocks. >" fromBlocksU [[[$matU|1,2,3;4,5,6|], [$matU|7,8,9;10,11,12|]], ) [[$matU|11,12,13;14,15,16|],[$matU|21,22,23;24,25,26|]]] +[$mat| 1.0, 2.0, 3.0, 7.0, 8.0, 9.0; + 4.0, 5.0, 6.0, 10.0, 11.0, 12.0; + 11.0, 12.0, 13.0, 21.0, 22.0, 23.0; + 14.0, 15.0, 16.0, 24.0, 25.0, 26.0 |]E2  for matrices. > repmatU [$mat|1;2|] 2 3 [$mat| 1.0, 1.0, 1.0;  2.0, 2.0, 2.0;  1.0, 1.0, 1.0;  2.0, 2.0, 2.0 |]FVertically flips a matrix. > flipud [$mat|1,2,3;4,5,6|] [$mat| 4.0, 5.0, 6.0;  1.0, 2.0, 3.0 |]GHorizonatlly flips a matrix. > fliprl [$mat|1,2,3;4,5,6|] [$mat| 3.0, 2.0, 1.0;  6.0, 5.0, 4.0 |]HExtracts a submatrix. >9 subMatrixU (0,1) (2,2) [$mat|1,2,3,4;5,6,7,8;9,10,11,12|] [$mat| 2.0, 3.0;  6.0, 7.0 |]I'Takes rows from the top of the matrix $until the required size is reached. > takeRows [$mat|1,2;3,4;5,6|] `atRows` d2 [$mat| 1.0, 2.0;  3.0, 4.0 |]J/Takes rows from the bottom of the matrix until the required size is reached. > dropRows [$mat|1,2;3,4;5,6|] `atRows` d2 [$mat| 3.0, 4.0;  5.0, 6.0 |]K0Takes columns from the left of the matrix until the required size is reached. > takeColumns [$mat|1,2,3;4,5,6|] `atCols` d2 [$mat| 1.0, 2.0;  4.0, 5.0 |]L+Takes columns from the right of the matrix $until the required size is reached. > dropColumns [$mat|1,2,3;4,5,6|] `atCols` d2 [$mat| 2.0, 3.0;  5.0, 6.0 |]M'Extracts the given rows from a matrix. > extractRowsU [1,0] [$mat|1,2;3,4;5,6|] [$mat| 3.0, 4.0;  1.0, 2.0 |]N2Constructs the identity matrix of any given size. > ident `atRows` d3 [$mat| 1.0, 0.0, 0.0;  0.0, 1.0, 0.0;  0.0, 0.0, 1.0 |]OBConstructs a square matrix with the given vector as its diagonal. > diag (linspace (1,3)) `atRows` d3 [$mat| 1.0, 0.0, 0.0;  0.0, 2.0, 0.0;  0.0, 0.0, 3.0 |]PGConstructs a rectangular matrix with the given vector as its diagonal. > diagRect (linspace (1,3)) `atShape` (d3,d4) [$mat| 1.0, 0.0, 0.0, 0.0;  0.0, 2.0, 0.0, 0.0;  0.0, 0.0, 3.0, 0.0 |]  > diagRect (linspace (1,3)) `atShape` (d4,d3) [$mat| 1.0, 0.0, 0.0;  0.0, 2.0, 0.0;  0.0, 0.0, 3.0;  0.0, 0.0, 0.0 |]Q"Takes the diagonal from a matrix. > takeDiag [$mat|1,2,3;4,5,6|] [$vec| 1.0, 5.0 |]RMOperations on matrices viewed as operations on the vector of their elements >, liftMatrix (+constant 2) [$mat|1,2,3;4,5,6|] [$mat| 3.0, 4.0, 5.0;  6.0, 7.0, 8.0 |]S See hmatrix's 3. T See hmatrix's 4. U See hmatrix's 5. V See hmatrix's 6. -+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUV-+,-./01235467:;<=D89>?@ABCEFGHIJKLMNOPQRSTUV,+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVportable experimental#Reiner Pope <reiner.pope@gmail.com>W"Reifies" a Vector'1s length in types. Useful when vectors of length Unknown E need to be used for a statically-sized operations. For instance, if v :: Vector Unknown Double,  then we can write   refineVec v (v -> forgetSize $ v + constant 5):to add a constant vector of 5s with the appropriate size. X5Sets an arbitrary-length vector to a specific value. > constant 1 X 5  [$vec| 1.0, 1.0, 1.0, 1.0, 1.0 |]Y5Constructs a vector from all the elements of a list. > fromListU [1,2,3,4,5]  [$vec| 1.0, 2.0, 3.0, 4.0, 5.0 |]Z Converts to a list of elements. > toList [$vec|1,2,3|]  [1.0,2.0,3.0][Vector' s length. > dim [$vec|1::Double,2,3|] 3\Indexes a vector. > [$vec|1,2,3|] @> 1 2.0]Extracts a subvector. > subVectorU 2 3 [$vec|1,2,3,4,5|] [$vec| 3.0, 4.0, 5.0 |]^Joins each vector in the list. > joinU [[$vecU|1,2,3|] , [$vecU|4,5|]]  [$vec| 1.0, 2.0, 3.0, 4.0, 5.0 |]_7Creates a constant vector of any length. The length is determined by the type. > [$vec|1,2,3|] + constant 2 [$vec| 3.0, 4.0, 5.0 |]`+Creates a vector of arbitrary length whose 1components range linearly from a to b. The vector's "length is determined by its type. > linspace (1,5)   d4 8[$vec| 1.0, 2.333333333333333, 3.6666666666666665, 5.0 |]aGives the vector's minimum entry. > vectorMin [$vec|1,2,3|] 1.0bGives the vector's maximum entry. > vectorMax [$vec|1,2,3|] 3.0cGives the index of a vector's minimum entry. > vectorMinIndex [$vec|1,2,3|] 0 dGives the index of a vector's maximum entry. > vectorMaxIndex [$vec|1,2,3|] 2e7  for vectors. > (*2) e [$vec|1,2,3|] [$vec| 2.0, 4.0, 6.0 |]f8  for vectors. > liftVector2 (+) [$vec|1,2,3|] (constant 3) [$vec| 4.0, 5.0, 6.0 |] WXYZ[\]^_`abcdefWX YZ[\]^_`abcdefWXYZ[\]^_`abcdefportable experimental#Reiner Pope <reiner.pope@gmail.com> gRequired for the m quasiquoter. See m. hRequired for the j pattern quasiquoter. See j. iRequired for the j pattern quasiquoter. See j. j6The matrix quasiquoter for expressions and patterns. 9 Elements on the same row are separated by commas; rows F themselves are separated by semicolons. All whitespace is optional 6 The expression quasiquoter allows arbitrary Haskell 8 expressions as its elements; the pattern quasiquoter - requires that each element is a variable. 6 Using the quasiquoter for patterns requires that you  use the i view pattern first (this is a + workaround since Template Haskell doesn't yet support  view patterns).  For example, A example1 :: (Element t) => Matrix (D2,D3) t -> Matrix (D2,D2) t % example1 (viewMat -> [$mat|a, b, c; $ d, e, f|]) = [$mat|a+b, b+c; : sin c, f |]k4Quasiquoter for matrices of Unknown size. We should  just use [$matU|<text>|] as shorthand for   [$mat|<text>|]. 4No pattern quasiquoter exists, and I currently have no plans to introduce one. lRequired for the m quasiquoter. See m. m=The vector quasiquoter for expressions and patterns. This is  very similar to the j quasiquoter. : Elements are separated by commas; whitespace is ignored. E The expression quasiquoter allows arbitrary Haskell expressions for H each element; the pattern quasiquoter requires that each element is  a variable pattern. 4 The pattern quasiquoter must be preceeded by a the l view pattern.  For example, ? example2 :: (Storable t, Num t) => Vector D2 t -> Vector D3 t ! example2 (viewVec -> [$vec|a, b|]) = [$vec|a*b, 5, 7|]n1Quasiquoter for vectors of unknown lengths. Like k, [$vecU|<text>|] is just shorthand for   [$vec|<text>|]. 9kDoes a simplistic parse using Parsec, which just counts brackets and escapes comments and string literals. T This parse accumulates text, which is then parsed properly using haskell-src-exts. ghijklmnjkmnhiglghijklmnportable experimental#Reiner Pope <reiner.pope@gmail.com>oCConstructs a vector from an hmatrix (dynamically-lengthed) vector. p-Gives the underlying hmatrix representation. wCConstructs a vector from an hmatrix (dynamically-lengthed) vector. x-Gives the underlying hmatrix representation. opqrstuvwxyz{|opqrstuvwxyz{|opqrstuvwxyz{|portable provisional#Reiner Pope <reiner.pope@gmail.com>      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                           ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                            ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                            ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                            ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~                            ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~        !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                           ! 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toHVectorarrayFromVectorvectorFromArraymArrayFromVectorvectorFromMArrayvectorToStorableArraystorableArrayToVector fromHMatrixU toHMatrixarrayFromMatrixmatrixFromArraymArrayFromMatrixmatrixFromMArray<|><->Mul MulResult<>matTvecTdoubleTcomplexT<.><\> linearSolveinvpinvdetrankrcondsvdfullSVD economySVDUeigeigSHqrcholhessschurluluPackedluSolveexpmsqrtmmatFunc nullspacePrec nullVectorctransepsiouter kroneckerunMatrixunVectorForeign.StorableStorable 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reifyNegative reifyPositivepow2TfacTdiv2TmodTdivTdivModTmul2TmulTsubTaddTisOddTisEvenTpredTsuccT isNegativeTisZeroT isPositiveTnegT:.Neg IsPositiveIsZero IsNegativeSuccPredIsEvenIsOdd:+::-::*:Mul2DivModDivModDiv2FacPow2NaturalT PositiveT NegativeT fromIntegerTReprIntegerT reifyIntegralIntegerRTypes.Data.BoolTrueGHC.List replicateGHC.BasemapzipWith parsecToQInfinityPNorm1PNorm2NormTypepnorm