Task: Pascal matrix generation








VB: Option Base 1
Private Function pascal_upper(n As Integer)
    Dim res As Variant: ReDim res(n, n)
    For j = 1 To n
        res(1, j) = 1
    Next j
    For i = 2 To n
        res(i, 1) = 0
        For j = 2 To i
            res(j, i) = res(j, i - 1) + res(j - 1, i - 1)
        Next j
        For j = i + 1 To n
            res(j, i) = 0
        Next j
    Next i
    pascal_upper = res
End Function
 
Private Function pascal_symmetric(n As Integer)
    Dim res As Variant: ReDim res(n, n)
    For i = 1 To n
        res(i, 1) = 1
        res(1, i) = 1
    Next i
    For i = 2 To n
        For j = 2 To n
            res(i, j) = res(i - 1, j) + res(i, j - 1)
        Next j
    Next i
    pascal_symmetric = res
End Function

Private Sub pp(m As Variant)
    For i = 1 To UBound(m)
        For j = 1 To UBound(m, 2)
            Debug.Print Format(m(i, j), "@@@");
        Next j
        Debug.Print
    Next i
End Sub

Public Sub main()
    Debug.Print "=== Pascal upper matrix ==="
    pp pascal_upper(5)
    Debug.Print "=== Pascal lower matrix ==="
    pp WorksheetFunction.Transpose(pascal_upper(5))
    Debug.Print "=== Pascal symmetrical matrix ==="
    pp pascal_symmetric(5)
End Sub




Ada: 
with Ada.Text_IO; use Ada.Text_IO;
with Ada.Integer_Text_IO; use Ada.Integer_Text_IO;
with Ada.Float_Text_IO; use Ada.Float_Text_IO;


with Ada.Numerics.Generic_Elementary_Functions;

procedure PascalMatrix is

  type Matrix is array (Positive range <>, Positive range <>) of Natural;

  
  package Math is new Ada.Numerics.Generic_Elementary_Functions(Float_Type => Float);
  use Math;
  
  procedure Print(m: in Matrix) is
    
    w: Float := Log(Float(m'Length(1)**(m'Length(1)/2)), 10.0);
    width: Positive := Natural(Float'Ceiling(w)) + 1;
    begin
      for i in m'First(1)..m'Last(1) loop
        Put("( ");
        for j in m'First(2)..m'Last(2) loop
          Put(m(i,j), width);
        end loop;
        Put(" )"); New_Line(1);
      end loop;
    end Print;
  
  function Upper_Triangular(n: in Positive) return Matrix is
    result: Matrix(1..n, 1..n) := (
                                    1 => ( others => 1 ),
                                    others => ( others => 0 )
                                  );
    begin
      for i in 2..n loop
        result(i,i) := 1;
        for j in i+1..n loop
          result(i,j) := result(i,j-1) + result(i-1,j-1);
        end loop;
      end loop;
      return result;
    end Upper_Triangular;
  
  function Lower_Triangular(n: in Positive) return Matrix is
    result: Matrix(1..n, 1..n) := (
                                    others => ( 1 => 1, others => 0 )
                                  );
    begin
      for i in 2..n loop
        result(i,i) := 1;
        for j in i+1..n loop
          result(j,i) := result(j-1,i) + result(j-1,i-1);
        end loop;
      end loop;
      return result;
    end Lower_Triangular;
  
  function Symmetric(n: in Positive) return Matrix is
    result: Matrix(1..n, 1..n) := (
                                   1 => ( others => 1 ),
                                   others => ( 1 => 1, others => 0 )
                                  );
    begin
      for i in 2..n loop
        for j in 2..n loop
          result(i,j) := result(i,j-1) + result(i-1,j);
        end loop;
      end loop;
      return result;
    end Symmetric;
  
  n: Positive;
  
  begin
    Put("What dimension Pascal matrix would you like? ");
    Get(n);
    Put("Upper triangular:"); New_Line(1);
    Print(Upper_Triangular(n));
    Put("Lower triangular:"); New_Line(1);
    Print(Lower_Triangular(n));
    Put("Symmetric:"); New_Line(1);
    Print(Symmetric(n));
  end PascalMatrix;