Matrix is simply a type synonym for vector of vectors. This means that any function on Vector works also on Matrix.

Prints out to the terminal a matrix in a readable format, where all elements are right-aligned and separated by a custom separator.

>>> let m = matrix 3 3 [1,2,3,3,100,4,12,32,67]
>>> prettyMat "|" m
 1|  2| 3
 3|100| 4
12| 32|67

Checks if a matrix is null. <> and <> are both null matrices.

Returns the X and Y dimensions of matrix and checks if it is well formed.

Checks if a matrix is well-formed, meaning that all its rows are of equal length. Returns the same matrix in case it is well-formed or throws an exception if it is ill-formed.

Converts a list into a Matrix. See example from prettyMat.

Converts a matrix back to a list.

Creates a unit (i.e. singleton) matrix, which is a matrix with only one element.

Returns an infinite matrix with (X,Y) index pairs. You need to zip it against another (finite) matrix or to extract a finite subset in order to be useful (see example below).

>>> prettyMat " " $ takeMat 3 4 indexMat
(0,0) (1,0) (2,0)
(0,1) (1,1) (2,1)
(0,2) (1,2) (2,2)
(0,3) (1,3) (2,3)

Maps a function on every value of a matrix.

OBS: this function does not check if the output matrix is well-formed.

Applies a binary function pair-wise on each element in two matrices.

OBS: this function does not check if the output matrix is well-formed.

Applies a function 3-tuple-wise on each element in three matrices.

OBS: this function does not check if the output matrix is well-formed.

Reduces all the elements of a matrix to one element based on a binary function.

>>> let m = matrix 3 3 [1,2,3,11,12,13,21,22,23]
>>> reduceMat (+) m
108

Pattern implementing the template for a dot operation between a vector and a matrix.

>>> let mA = matrix 4 4 [1,-1,1,1,  1,-1,-1,-1,  1,1,-1,1,  1,1,1,-1]
>>> let y  = vector[1,0,0,0]
>>> dotVecMat (+) (*) mA y
<1,1,1,1>

Pattern implementing the template for a dot operation between two matrices.

>>> let mA = matrix 4 4 [1,-1,1,1,  1,-1,-1,-1,  1,1,-1,1,  1,1,1,-1]
>>> prettyMat " " $ dotMatMat (+) (*) mA mA
2 -2  2  2
2 -2 -2 -2
2  2  2 -2
2  2 -2  2

Returns the element of a matrix at a certain position.

>>> let m = matrix 3 3 [1,2,3,11,12,13,21,22,23]
>>> atMat 2 1 m
13

Returns the upper-left part of a matrix until a specific position.

>>> let m = matrix 4 4 [1,2,3,4,11,12,13,14,21,22,23,24,31,32,33,34]
>>> prettyMat " " $ takeMat 2 2 m
 1  2
11 12

Returns the upper-left part of a matrix until a specific position.

>>> let m = matrix 4 4 [1,2,3,4,11,12,13,14,21,22,23,24,31,32,33,34]
>>> prettyMat " " $ dropMat 2 2 m
23 24
33 34

Crops a section of a matrix.

>>> let m = matrix 4 4 [1,2,3,4,11,12,13,14,21,22,23,24,31,32,33,34]
>>> prettyMat " " m
 1  2  3  4
11 12 13 14
21 22 23 24
31 32 33 34
>>> prettyMat " " $ cropMat 2 3 1 1 m
12 13
22 23
32 33

Groups a matrix into smaller equallly-shaped matrices.

>>> let m = matrix 4 4 [1,2,3,4,11,12,13,14,21,22,23,24,31,32,33,34]
>>> prettyMat " " $ groupMat 2 2 m
  <<1,2>,<11,12>>   <<3,4>,<13,14>>
<<21,22>,<31,32>> <<23,24>,<33,34>>

Returns a stencil of neighboring elements for each possible element in a vector.

>>> let m = matrix 4 4 [1,2,3,4,11,12,13,14,21,22,23,24,31,32,33,34]
>>> prettyMat " " $ stencilMat 2 2 m
  <<1,2>,<11,12>>   <<2,3>,<12,13>>   <<3,4>,<13,14>>
<<11,12>,<21,22>> <<12,13>,<22,23>> <<13,14>,<23,24>>
<<21,22>,<31,32>> <<22,23>,<32,33>> <<23,24>,<33,34>>

Pattern which "rotates" a matrix. The rotation is controled with the x and y index arguments as following:

• (> 0) : rotates the matrix right/down with the corresponding number of positions.
• (= 0) : does not modify the position for that axis.
• (< 0) : rotates the matrix left/up with the corresponding number of positions.

>>> let m = matrix 4 4 [1,2,3,4,11,12,13,14,21,22,23,24,31,32,33,34]
>>> prettyMat " " $ rotateMat (-1) 1 m
32 33 34 31
 2  3  4  1
12 13 14 11
22 23 24 21

Reverses the order of elements in a matrix

Transposes a matrx.

Replaces a part of matrix with another (smaller) part, starting from an arbitrary position.

>>> let m  = matrix 4 4 [1,2,3,4,11,12,13,14,21,22,23,24,31,32,33,34]
>>> let m1 = matrix 2 2 [101,202,303,404]
>>> prettyMat " " $ replaceMat 1 1 m1 m
 1   2   3  4
11 101 202 14
21 303 404 24
31  32  33 34