(******************************************************************************
 ** MATRIX.sml
 ** sml
 **
 ** Guy Blelloch
 ** Signature for the matrix library
 ******************************************************************************)

signature MATRIX =
    sig
	type matrix
	type colVec = matrix
	type rowVec = matrix

	type scalar
	type index
	type subscript = (index * index)
	type size      = (index * index)

	exception badDimension
	exception notInvertable

	val size : matrix -> size
	val nRows : matrix -> index
	val nCols : matrix -> index

	val identity : int -> matrix
	val matrix : (size * scalar) -> matrix

	val sub : (matrix * subscript) -> scalar

	val row : (matrix * index) -> rowVec
	val column : (matrix * index) -> colVec
	val rows : (matrix * index vector) -> matrix
	val columns : (matrix * index vector) -> matrix
	val subRegion : matrix * (index vector * index vector) -> matrix

	val insertElt : (matrix * subscript * scalar) -> matrix
	val insertElts : (matrix * (subscript * scalar) vector) -> matrix
	val insertRegion : matrix * (index vector * index vector) * matrix -> matrix

	val updateElt : (scalar->scalar) -> (matrix * subscript) -> matrix

	val appendCols : (matrix * matrix) -> matrix
	val appendRows : (matrix * matrix) -> matrix

	val * : (matrix * matrix) -> matrix
	val + : (matrix * matrix) -> matrix
	val - : (matrix * matrix) -> matrix
	val scale : (matrix * scalar) -> matrix

	val trans : matrix -> matrix
	val toDiag : colVec -> matrix
	val fromDiag : matrix -> colVec

	val inv : matrix -> matrix
	val det : matrix -> scalar
	val invDet : matrix -> (matrix * scalar)

	val solve : matrix * colVec -> colVec
	val crossProduct : matrix -> colVec
	val norm : matrix -> scalar

	val tabulate : (size * (subscript -> scalar)) -> matrix

	val map : (scalar -> scalar) -> matrix -> matrix
	val mapi : (subscript * scalar -> scalar) -> matrix -> matrix
	val map2 : (scalar * scalar -> scalar) -> matrix * matrix -> matrix

	val fold : (scalar * 'b -> 'b) -> 'b -> matrix -> 'b
	val foldi : (subscript * scalar * 'b -> 'b) -> 'b -> matrix -> 'b

	val fromArray2 : scalar Array2.array -> matrix
	val fromList : scalar list list -> matrix
	val toList : matrix -> scalar list list
	val toString : matrix -> string
	val toStringF : (scalar -> string) -> matrix -> string

    end