PROGRAM 6


--  Filename: Matrix.ads, Matrix.adb, Program6.cpp  Author: Anthony F. Ortiz

--  This program computes the determinant and inverse of a 2 by 2 matrix,
--  adds, subtracts, and multiplies two 2 by 2 matrix, and prints the 
--  matrix with it's inverse.

with Text_IO; use Text_IO;
with Matrix; use Matrix;

procedure Main is
    package Flt_IO is new Float_IO (Float); use Flt_IO;
    A : Flt_Array;
    B : Flt_Array;
    C : Flt_Array;
    D : Flt_Array;
    E : Flt_Array;
    Inverse : Flt_Array;
    Det_A : Integer;

--  Print a 2 by 2 matrix;
procedure Print_Matrix (A : in out Flt_Array) is
begin
    for I in 1..2 loop
        for J in 1..2 loop
            Put (A (I, J), 10, 2, 0);
        end loop;
        New_Line;
    end loop;
end Print_Matrix;

--  Print the determinant.
procedure Print_Determinant (Det_A : in Integer) is
begin
    Put ("The determinant of the matrix is ");
    Put (Det_A, 10, 2, 0);
end Print_Determinant;

begin
    A := Create_Matrix (1.0, 2.0, 3.0, 4.0);
    B := Create_Matrix (2.0, 3.0, 4.0, 5.0);
    Det_A := Compute_Determinant (A);
    Inverse := Compute_Inverse (A, Det_A);
    C := Add_Matrix (A, B);
    D := Subtract_Matrix (A, B);
    E := Multiply_Matrix (A, B);
    Put ("Matrix A: ");
    New_Line;
    Print_Matrix (A);
    Put ("Matrix B: ");
    New_Line;
    Print_Matrix (B);
    Put ("Matrix C: ");
    New_Line;
    Print_Matrix (C);
    Put ("Matrix D: ");
    New_Line;
    Print_Matrix (D);
    Put ("Matrix E: ");
    New_Line;
    Print_Matrix (E);
    Put ("Inverse C: ");
    New_Line;
    Print_Matrix (Inverse);
    Print_Determinant (Det_A);
end Main;

--  Filename: Matrix.ads, Matrix.adb, Program6.cpp  Author: Anthony F. Ortiz

--  Declaration of a package called matrix.  This package contains functions
--  for computing the determinant and inverse of a 2 by 2 matrix, and perform
--  addition, subtraction, and mutliplication for two 2 by 2 matrix.

package Matrix is
    --  Holds the type the matrix cell holds.
    type Flt_Array is array (1..2, 1..2) of Float;
    --  Creates a 2 by 2 matrix.
    function Create_Matrix (C1 : in Float; C2 : in Float; C3 : in Float; C4 : in Float)
                            return Flt_Array;
    --  Computes the determinant of a 2 by 2 matrix.
    function Compute_Determinant (A : in Flt_Array) return Float;
    --  Compute the inverse of a 2 by 2 matrix.
    function Compute_Inverse (A : in Flt_Array; Det_A : in Float) return Flt_Array;
    --  Add two 2 by 2 matrix.
    function Add_Matrix (A : in Flt_Array; B : in Flt_Array) return Flt_Array;
    --  Subtract two 2 by 2 matrix.
    function Subtract_Matrix (A : in Flt_Array; B : in Flt_Array) return Flt_Array;
    --  Mutlipty two 2 by 2 matrix.
    function Multiply_matrix (A : in Flt_Array; B : in Flt_Array) return Flt_Array;
end Matrix;

--  Filename: Matrix.ads, Matrix.adb, Program6.cpp  Author: Anthony F. Ortiz

--  Implementation of a package called matrix.  This package contains functions
--  for computing the determinant and inverse of a 2 by 2 matrix, and perform
--  addition, subtraction, and mutliplication for two 2 by 2 matrix.

package body Matrix is

--  Create a 2 by 2 matrix.
function Create_Matrix(C1 : in Float; C2 : in Float; C3 : in Float;
                       C4 : in Float) return Flt_Array is
    C : Flt_Array;
begin
    C (1, 1) := C1;
    C (1, 2) := C2;
    C (2, 1) := C3;
    C (2, 2) := C4; 
    return C;
end Create_Matrix;

--  Compute the determinant of a 2 by 2 matrix.
function Compute_Determinant(A : in Flt_Array) return Float is
    Determinant : Float;
begin
    Determinant := A (1, 1) * A (2, 2) - A (1, 2) * A (2, 1);
    return Determinant;
end Compute_Determinant;

--  Compute the inverse of a 2 by 2 matrix.
function Compute_Inverse(A : in Flt_Array;
                         Det_A : in Float) return Flt_Array is
    Inverse : Flt_Array;
    Count : Integer;
begin
    Count := 2;
    for I in 1..2 loop
        for J in 1..2 loop
            if (I = J) then
                Inverse (I, J) := 1.0 / Det_A * A (Count, Count);       
                Count := Count - 1;
            else
                Inverse (I, J) := -1.0 / Det_A * A (I, J);      
            end if;
        end loop;
    end loop;
    return Inverse;
end Compute_Inverse;

--  Add two 2 by 2 matrix.
function Add_Matrix(A : in Flt_Array;
                    B : in Flt_Array) return Flt_Array is
    C : Flt_Array;
begin
    for I in 1..2 loop
        for J in 1..2 loop
            C (I, J) := A (I, J) + B (I, J);        
        end loop;
    end loop;
    return C;
end Add_Matrix;

--  Subtract two 2 by 2 matrix.
function Subtract_Matrix(A : in Flt_Array ;
                         B : in Flt_Array) return Flt_Array is
    C : Flt_Array;
begin
    for I in 1..2 loop
        for J in 1..2 loop
            C (I, J) := A (I, J) - B (I, J);        
        end loop;
    end loop;
    return C;
end Subtract_Matrix;

--  Multiply two 2 by 2 matrix.
function Multiply_Matrix(A : in Flt_Array ; 
                         B : in Flt_Array) return Flt_Array is
    C : Flt_Array;
begin
    for I in 1..2 loop
        for J in 1..2 loop
            C (I, J) := A (I, 1) * B(1, J) + A (I, 2) * B (2, J);
        end loop;
    end loop;
end Multiply_Matrix;

end Matrix

--  outfile:  prog6.out

Matrix A
      1.00      2.00
      3.00      4.00
Matrix B
      2.00      3.00
      4.00      5.00
Matrix C
      3.00      5.00
      7.00      9.00
Matrix D
     -1.00     -1.00
     -1.00     -1.00
Matrix E
     10.00     13.00
     22.00     29.00
Inverse C
     -1.13      0.63
      0.88     -0.38
The determinant of the matrix is     -0.13




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