Threaded Mode | Linear Mode

Alireza_M · 01-01-2010, 05:55 AM

I present this program to all pro9ramming crew,specially active ones.and also good manner ones.
this program will calculate the inverse of a matrix given by you,and will check if it is the correct answer or not(if you wish).for more info about matrices and inverse of them visit : en.wikipedia.org/wiki/Matrix_(mathematics)

Code:

Program Matrixx_Inverse(input,output);

  (*This Program will Calculate the inverse of a matrix*)

  Uses CRT;

  Type

    Mat=Array[1..30,1..30] of real;

  Var

    check,counter1,D,sign,counter,help,counter2,q,p,i,j,M,ii,jj,iii,Rows:Intege​r;

    Matrix4,Matrix,Matrix3,Matrix2:mat;

    sum,K,Det,Det2,temp:Real;

    matrix22:array[1..225] of real;

  Procedure ReadingMatrix(Var Matrix:Mat;Rows:integer);

    Var

      ii,jj:integer;

      Element:real;

    Begin

      Writeln(' Please enter the elements of your ',Rows,' X ',Rows,' Matrix');

      For ii:=1 To Rows Do

        Begin

          For jj:=1 To Rows Do

            Begin

              Read(Element);

              Matrix[ii,jj]:=Element;

            End;

        End;

    End;

  Procedure PrintingMatrix(Matrix:Mat;Rows:integer);

      Var

        ii,jj:integer;

        Element:real;

    Begin

      Writeln;

      Textcolor(10);

      For ii:=1 To Rows Do

        Begin

          For jj:=1 To Rows Do

            Begin

              Write(Matrix[ii,jj]:5:2);

            End;

          Writeln;

        End;

    End;

  Procedure Determinant(Matrix:Mat;Rowss:Integer;Var Multi:Real);

    Var

      IIII,JJJJ,LLLL,MMMM:Integer;

    Begin

      For LLLL:=Rowss DownTo 2 Do

          Begin

            For IIII:=1 tO LLLL-1 Do

              Begin

                If Matrix[IIII,LLLL]=0 Then

                  Begin

                  End

                Else

                  If Matrix[LLLL,LLLL]=0 Then

                    Begin

                      For MMMM:=Rowss DownTo 1 Do

                        Begin

                          Matrix[LLLL,MMMM]:=Matrix[iiii,MMMM]+Matrix[LLLL,MMMM];

                        End;

                    End;

                  K:=0;

                  K:=(-1)*Matrix[IIII,LLLL]/Matrix[LLLL,LLLL];

                  For JJJJ:=Rowss DownTo 1 Do

                    Begin

                      Matrix[IIII,JJJJ]:=K*Matrix[LLLL,JJJJ]+Matrix[IIII,JJJJ];

                    End;

              End;

          End;

        Multi:=1;

        For D:=1 To Rowss Do

          Begin

            Multi:=Multi*Matrix[D,D];

          End;

    End;

Begin

  CLRSCR;

  textcolor(10);

  writeln('PLEASE REFER TO  WWW.PRO9RAMMING.COM  IF YOU USE THIS CODE,ENJOY!');

  writeln;

  Textcolor(yellow);

  writeln('Please enter number of rows of your matrix which you want the inverse of it');

  Readln(Rows);

  ReadingMatrix(Matrix,Rows);

  Determinant(Matrix,Rows,Det2);

  If Det2=0 Then

    Begin

      Textcolor(red);

      writeln;

      Writeln('Determinant of your matrix is Zero');

      Writeln('Can`t do this,sorry');

      delay(1000);

      Textcolor(white);

      writeln;

      Writeln('CODED BY ALIREZA_M');

      Repeat

      until keypressed;

      Halt;

    End

  Else

    Sign:=1;

    For I:=1 To Rows Do

      Begin

        For J:=1 To Rows Do

          Begin

            For P:=1 To Rows Do

              Begin

                For Q:=1 To Rows Do

                  Begin

                    If (P<>I) And (Q<>J) Then

                      Begin

                        counter:=counter+1;

                        Matrix22[Counter]:=Matrix[P,Q];

                      End;

                  End;

              End;

            counter:=1;

            For ii:=1 To rows-1 Do

              For jj:=1 to rows-1 Do

                Begin

                  matrix2[ii,jj]:=matrix22[counter];

                  counter:=counter+1;

                end;

            For iii:=1 To i+J Do

              Begin

                Sign:=Sign*(-1);

              End;

            Determinant(Matrix2,Rows-1,Det);

            Matrix3[I,J]:=(Sign*Det)/Det2;

            sign:=1;

            counter:=0;

          End;

      End;

  For i:=1 To rows Do

    Begin

      For J:=1 To Rows Do

        Begin

          If J>I THEN

            Begin

              temp:=Matrix3[i,j];

              Matrix3[i,j]:=Matrix3[j,i];

              matrix3[j,i]:=temp;

            end;

        End;

    End;

  Textcolor(Green);

  Writeln('Here`s the inverse of your matrix ->');

  writeln;

  PrintingMatrix(Matrix3,Rows);

  Writeln;

  textcolor(3);

  writeln('  If you want to check the answer ( multiplication of ');

  writeln('inverse matrix to the original matrix should give you ');

  writeln('a matrix which the elements of main diagon should be 1');

  writeln('others should be 0  then       ->             Press  1');

  Writeln('If you don`t want to check the answer Then -> Press  2');

  Writeln;

  Read(check);

  Case check of

    1: Begin

         writeln;

         For p:=1 To rows Do

           Begin

             For i:=1 To rows Do

               Begin

                 For j:=1 To Rows Do

                   Begin

                     Sum:=sum+Matrix[p,j]*matrix3[j,i];

                   End;

                 Matrix4[p,I]:=Sum;

                 sum:=0;

               End;

           End;

         printingmatrix(matrix4,rows);

         Textcolor(White);

         Delay(1500);

         writeln;

         Writeln('CODED BY ALIREZA_M');

         Repeat

         Until Keypressed;

       End;

    2: Begin

         Textcolor(White);

         Delay(100);

         Writeln('CODED BY ALIREZA_M');

         Repeat

         Until Keypressed;

       End;

  End;

End.

the length of the code is mainly for the respect to you(users) d^-^b

***drdebcol*** · (This post was last modified: 01-01-2010 06:15 AM by drdebcol.)

Well done !
Mathematically correct and in programming way it is very good and optimized.
So if determinant is zero, it is not possible to find inverse.
So when you multiplicate matrix with it's inverse you need to get Identity matrix. And when i said "multiplicate" i referred to Matrix multiplication :
http://en.wikipedia.org/wiki/Matrix_multiplication
Identity matrix I is a matrix which main diagonal elements are ones and others are zeros :

Code:

1 0 . . . 0

0 1 . . . 0

. . . . . .        

. . . . . .

0 0 . . . 1

In programming :

Code:

if i=j then

  a(i,j)=1

else

  a(i,j)=0

More about Identity matrix you have here :
http://en.wikipedia.org/wiki/Identity_matrix
Determinant of Identity matrix is 1 (det I =1).

This is just for others to see !

Alireza_M · (This post was last modified: 01-01-2010 06:49 AM by Alireza_M.)

(01-01-2010 06:14 AM)drdebcol Wrote: Well done !
Mathematically correct and in programming way it is very good and optimized.
So if determinant is zero, it is not possible to find inverse.
So when you multiplicate matrix with it's inverse you need to get Identity matrix. And when i said "multiplicate" i referred to Matrix multiplication :
http://en.wikipedia.org/wiki/Matrix_multiplication
Identity matrix I is a matrix which main diagonal elements are ones and others are zeros :

Code:

1 0 . . . 0 0 1 . . . 0 . . . . . . . . . . . . 0 0 . . . 1
In programming :

Code:

if i=j then a(i,j)=1 else a(i,j)=0
More about Identity matrix you have here :
http://en.wikipedia.org/wiki/Identity_matrix
Determinant of Identity matrix is 1 (det I =1).

This is just for others to see !

Thanks for you really fast replies and descriptions,I think if you weren't in this forum some my programs would be left non replied.i appreciate that. Wink

Alphablend · 01-26-2010, 09:30 PM

Nice code. Smile

Alireza_M · 01-26-2010, 10:44 PM

Thanks Bro Wink