Data update

Task/Pascal-matrix-generation/Ada/pascal-matrix-generation.adb

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+-- for I/O
+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;
+
+-- for estimating the maximum width of a column
+with Ada.Numerics.Generic_Elementary_Functions;
+
+procedure PascalMatrix is
+
+  type Matrix is array (Positive range <>, Positive range <>) of Natural;
+
+  -- instantiate Generic_Elementary_Functions for Float type
+  package Math is new Ada.Numerics.Generic_Elementary_Functions(Float_Type => Float);
+  use Math;
+
+  procedure Print(m: in Matrix) is
+    -- determine the maximum width of a column
+    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;

Task/Pascal-matrix-generation/Pluto/pascal-matrix-generation.pluto

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+require "matrix"
+local int = require "int"
+
+local function pascal_upper_triangular(n)
+    local m = {}
+    for i = 1, n do
+        m[i] = {}
+        for j = 1, n do m[i][j] = (j >= i) ? int.binomial(j - 1, i - 1) : 0 end
+    end
+    return matrix.from(m)
+end
+
+local function pascal_symmetric(n)
+    local m = {}
+    for i = 1, n do
+        m[i] = {}
+        for j = 1, n do m[i][j] = int.binomial(i + j - 2, i - 1) end
+    end
+    return matrix.from(m)
+end
+
+local function pascal_lower_triangular(n)
+    return pascal_symmetric(n):cholesky()
+end
+
+local n = 5
+print("Pascal upper-triangular matrix:")
+print(pascal_upper_triangular(n))
+print("\nPascal lower-triangular matrix:")
+print(pascal_lower_triangular(n):format("%d"))
+print("\nPascal symmetric matrix:")
+print(pascal_symmetric(n))

Task/Pascal-matrix-generation/Uiua/pascal-matrix-generation.uiua

@@ -0,0 +1,11 @@
+# Pascal's approach.
+G! ← ⍥(˜⊂^0⊸⊣)-1⧻⊸⊢
+⍉G!(↘¯1⬚0⧈+)⬚0˜↯[1]⊂1 5
+G!(↘¯1⬚0⧈+)⬚0˜↯[1]⊂1 5
+G!(\+)˜↯1⊂1 5
+
+# Combinatorial approach.
+T ← ⧅>
+˙⊞T⇡5
+⍉˙⊞T⇡5
+≡≡T⍉↯[⟜∘]⟜⇡ ⟜(˙⊞+⇡)5

Task/Pascal-matrix-generation/VBScript/pascal-matrix-generation.vbs

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+Function pascal_upper(i,j)
+	WScript.StdOut.Write "Pascal Upper"
+	WScript.StdOut.WriteLine
+	For l = i To j
+		For m = i To j
+			If l <= m Then
+				WScript.StdOut.Write binomial(m,l) & vbTab
+			Else
+				WScript.StdOut.Write 0 & vbTab
+			End If
+		Next
+		WScript.StdOut.WriteLine
+	Next
+	WScript.StdOut.WriteLine
+End Function
+
+Function pascal_lower(i,j)
+	WScript.StdOut.Write "Pascal Lower"
+	WScript.StdOut.WriteLine
+	For l = i To j
+		For m = i To j
+			If l >= m Then
+				WScript.StdOut.Write binomial(l,m) & vbTab
+			Else
+				WScript.StdOut.Write 0 & vbTab
+			End If
+		Next
+		WScript.StdOut.WriteLine
+	Next
+	WScript.StdOut.WriteLine	
+End Function
+
+Function pascal_symmetric(i,j)
+	WScript.StdOut.Write "Pascal Symmetric"
+	WScript.StdOut.WriteLine
+	For l = i To j
+		For m = i To j
+			WScript.StdOut.Write binomial(l+m,m) & vbTab
+		Next
+		WScript.StdOut.WriteLine
+	Next
+End Function
+
+Function binomial(n,k)
+	binomial = factorial(n)/(factorial(n-k)*factorial(k))
+End Function
+
+Function factorial(n)
+	If n = 0 Then
+		factorial = 1
+	Else
+		For i = n To 1 Step -1
+			If i = n Then
+				factorial = n
+			Else
+				factorial = factorial * i
+			End If
+		Next
+	End If
+End Function
+
+'Test driving
+Call pascal_upper(0,4)
+Call pascal_lower(0,4)
+Call pascal_symmetric(0,4)