Matrices

This library provides support for creating and manipulating matrices of real numbers, including some math functions on matrices.

For high-performance dense matrices that support only a finite set of mathematical operations, see the GSL bindings.

Basic Usage

structure M = Mlmatrix(Mlvector);

(* Make a 3x3 matrix with all entries set to 0.0 *)
val m = M.make (3, 3, 0.0)

(* Set the diagonal to 1.0 to make the identity matrix *)
val _ = M.set (m, (0, 0), 1.0)
val _ = M.set (m, (1, 1), 1.0)
val _ = M.set (m, (2, 2), 1.0)

(* Scale m by 2 *)
val m2 = M.mulScalar (m, 2.0)

(* Create a matrix from a list of lists *)
val m3 = M.fromList
           ([[1.0, 2.0, 3.0],
             [4.0, 5.0, 6.0],
             [7.0, 8.0, 9.0]])

(* Multiply two matrices *)
val m4 = M.mul (m2, m3)

val _ = print (M.toString m4)

Interface

Types

• type scalar
  • The scalar type is a synonym for real.
• type mlvector
  • The type of rows and columns in the matrix. These are vectors.
• type mlmatrix
  • The type of the matrix itself.

Methods

• val size : mlmatrix -> (int * int)
• val makeInit : (int -> mlvector) * int -> mlmatrix
• val make : (int * int * real) -> mlmatrix
• val sub : mlmatrix * (int * int) -> scalar
• val row : mlmatrix * int -> mlmatrix
• val col : mlmatrix * int -> mlmatrix
• val onerow : mlmatrix * int -> mlvector
• val onecol : mlmatrix * int -> mlvector
• val set : mlmatrix * (int * int) * scalar -> unit
• val update : (scalar -> scalar) * mlmatrix * (int * int) -> unit
• val modify : (scalar -> scalar) * mlmatrix -> unit
• val modifyi : ((int * int * scalar) -> scalar) * mlmatrix -> unit
• val modifyrowi : ((int * mlvector) -> unit) * mlmatrix -> unit
• val copy : mlmatrix -> mlmatrix
• val vec2mat : mlvector -> mlmatrix
• val squeeze1 : mlmatrix -> mlvector
• val squeeze2 : mlmatrix -> mlvector
• val squeeze12 : mlmatrix -> scalar
• val map : (scalar -> scalar) * mlmatrix -> mlmatrix
• val mapi : ((int * int * scalar) -> scalar) * mlmatrix -> mlmatrix
• val map2 : ((scalar * scalar) -> scalar) * mlmatrix * mlmatrix -> mlmatrix
• val map2i : ((int * int * scalar * scalar) -> scalar) * mlmatrix * mlmatrix -> mlmatrix
• val foldl : (('a * scalar) -> 'a) * 'a * mlmatrix -> 'a
• val foldli : (('a * int * int * scalar) -> 'a) * 'a * mlmatrix -> 'a
• val foldRowl : ('a * mlmatrix -> 'a) * 'a * mlmatrix -> 'a
• val foldRowVecl : ('a * mlvector -> 'a) * 'a * mlmatrix -> 'a
• val transpose : mlmatrix -> mlmatrix
• val mulScalar : mlmatrix * scalar -> mlmatrix
• val mul : mlmatrix * mlmatrix -> mlmatrix
• val add : mlmatrix * mlmatrix -> mlmatrix
• val addModify : mlmatrix * mlmatrix -> unit
• val elemwise : mlmatrix * mlmatrix -> mlmatrix
• val elemwiseInplace : mlmatrix * mlmatrix -> mlmatrix
• val matMulVec : mlmatrix * mlvector -> mlvector
• val fromArray2 : scalar array array -> mlmatrix
• val fromList : scalar list list -> mlmatrix
• val toStringF : (scalar -> string) * mlmatrix -> string
• val toString : mlmatrix -> string

Method Overview

• size mat.
  • Returns the dimensions of the matrix. The resulting value is (numRows, numColumns).
• makeInit (f, height)
  • Creates a matrix where each row in the matrix is the result of applying f to the index of that row.
• make (numRows, numColumns, default)
  • Creates a numRows-by-numColumns matrix with every element set to default.
• sub (mat, (row, column)).
  • Returns the element of the matrix at the given row and column.
• row (mat, idx).
  • Returns one row of a matrix as a 1-by-n matrix.
• col (mat, idx).
  • Returns one column of a matrix as a m-by-1 matrix.
• onerow (mat, idx).
  • Like row, but converts the result to vector.
• onecol (mat, idx).
  • Like col, but converts the result to vector.
• set (mat, (row, col), r).
  • Updates the element in mat at the rowth row and colth column to be r. This modifies mat.
• update (f, mat, (idx1, idx2)).
  • Updates the element in mat at the rowth row and colth column to be the result of applying f to the original value at that index. This modifies mat.
• modify (f, mat)
  • Updates every element in mat to be the result of applying f to the original value at each index. This modifies mat.
• modifyi (f, mat)
  • Like modify, but the modification function also takes the row and column numbers as input.
• modifyrowi (f, mat)
  • Like modifyi, but f operates on a whole row at a time, with the row represented as a vector.
• copy mat
  • Creates a new matrix with the same contents as mat.
• vec2mat vec
  • Converts a vector to a 1-by-n matrix.
• squeeze1 mat
  • Extracts the first row of a matrix as a vector.
• mlvector squeeze2(mlmatrix mat)
  • Extracts the first column of a matrix as a vector.
• real squeeze12(mlmatrix mat)
  • Equivalent to sub (mat, (0, 0)).
• map (f, mat)
  • Creates a new matrix such that the value at each index in the new matrix is the result of applying f to the value at the same index in the original matrix.
• mapi (f, mat)
  • Like map, but f also takes the row and column numbers as input.
• map2 (f, mat1, mat2)
  • Map over two matrices. The resulting matrix will have the smaller size of these two matrices.
• map2i (f, mat1, mat2)
  • Like map2, but f also takes the row and column numbers as input.
• foldl (f, base, mat)
  • Combines the elements of mat using the function f, starting with base. The function f should take as an argument a tuple of the result accumulated so far and the next element of arr to process.
• foldli (f, base, mat)
  • Like fold, but f also the row and column number as input.
• foldRowl (f, base, mat)
  • Combines the rows of mat using the function f, starting with base. The function f should take as an argument a tuple of the result accumulated so far and the next row of arr, represented as a matrix, to process.
• foldRowVecl (f, base, mat)
  • Combines the rows of mat using the function f, starting with base. The function f should take as an argument a tuple of the result accumulated so far and the next row of arr to process.
• transpose mat
  • Creates a new matrix that is the transpose of mat.
• mulScalar (mat, a)
  • Creates a new matrix that is mat with each element multiplied by a.
• mul (mat1, mat2)
  • Creates a new matrix that is the product of mat1 and mat2.
• add (mat1, mat2)
  • Creates a new matrix that is the sum of mat1 and mat2.
• addModify (mat1, mat2)
  • Like add, but modifies the first matrix in-place instead of returning a new matrix. This modifies mat1.
• elemwise (mat1, mat2)
  • Creates a new matrix that is the element-wise product of mat1 and mat2.
• elemwiseInplace (mat1, mat2)
  • Like elemwise, but modifies the first matrix in-place instead of returning a new matrix. This modifies mat1.
• matMulVec (mat, vec)
  • Creates a new matrix that is the product of the mat and vec treated as a m-by-1 matrix.
• fromArray2 arr2
  • Converts an array of arrays of reals to a matrix. Modifications to the resulting matrix will modify the original array, and modifications to the array will modify the matrix.
• fromList l2
  • Converts a list of lists of reals to a matrix.
• toString mat
  • Converts a matrix to a string.