CTM: Exercise 3-13

Posted by Urban Hafner Mon, 19 Sep 2005 10:39:50 GMT

The problem

Matrix operations. Assume that we represent a matrix as a list of lists of integers, where each internal list gives one row of the matrix. Define functions to do standard matrix operations such as matrix transposition and matrix multiplication.

My solution

Transposition

fun {Transpose Matrix}
   {List.foldR Matrix
    fun {$ R1 R2} {List.zip R1 R2 fun {$ E1 E2} E1|E2 end} end
    for E in Matrix.1 collect:C do {C nil} end}
end

Multiplication

fun {Multiply Matrix1 Matrix2}
   if {ColumnCount Matrix1}=={RowCount Matrix2} then
      TM2={Transpose Matrix2} in
      for Row1 in Matrix1 collect:R do
     {R for Row2 in TM2 collect:S do
           {S {List.foldL {List.zip Row1 Row2 fun {$ X Y} X*Y end}
           fun {$ X Y} X+Y end 0}}
        end}
      end
   else
      raise domainError end
   end
end

Addition

% Add any combination of matrices and numbers
fun {Add MN1 MN2}
   fun {AddMatrices Matrix1 Matrix2}
      {List.zip Matrix1 Matrix2
       fun {$ R1 R2} {List.zip R1 R2 fun {$ E1 E2} E1+E2 end} end}
   end
   fun {AddNumberToMatrix Matrix Number}
      for Row in Matrix collect:R do
     {R {List.map Row fun {$ E} E+Number end}}
      end
   end
in
   case MN1
   of _|_ then
      case MN2 of _|_ then
     if {RowCount MN1}=={RowCount MN2} andthen
        {ColumnCount MN1}=={ColumnCount MN2} then
        {AddMatrices MN1 MN2}
     else
        raise differentSizes end
     end
      else {AddNumberToMatrix MN1 MN2} end
   else
      case MN2 of _|_ then {AddNumberToMatrix MN2 MN1}
      else MN1 + MN2 end
   end
end

Auxiliary functions

fun {RowCount Matrix} {List.length Matrix} end
fun {ColumnCount Matrix} {List.length Matrix.1} end

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