Каталог Рефератов - Программа на С++ Builder для знаходження оберненої матриці з використання елементарних перетворень

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Программа на С++ Builder для знаходження оберненої матриці з використання елементарних перетворень

ar F: Text;

I,J: Byte;

Begin

IF Errors<> [0] Then Exit;

IF Not Exist Then Begin NotExist; WriteError; Exit; End;

Assign(F,Name);

{$I-}

ReWrite(F);

IF IOResult<>0 Then Begin FileError; WriteError; Exit; End;

For I: =1 to CLines do

Begin

For J: =1 to CBars do

Begin

Write(F,GetE(I,J): F1: F2,' ');

IF IOResult<>0 Then Begin Close(F); WriteError; Exit; End;

End;

Writeln(F)

End;

Close(F);

{$I+}

End;

Procedure Tabl. TooManySize;

Begin

Errors: =Errors+ [CTooManySize] ;

AnyError

End;

Procedure Tabl. BadPosition;

Begin

Errors: =Errors+ [CBadPosition] ;

AnyError

End;

Procedure Tabl. FileNotFound;

Begin

Errors: =Errors+ [CFileNotFound] ;

AnyError

End;

Procedure Tabl. FileError;

Begin

Errors: =Errors+ [CFileError] ;

AnyError

End;

Procedure Tabl. ReadError;

Begin

Errors: =Errors+ [CReadError] ;

AnyError

End;

Procedure Tabl. WriteError;

Begin

Errors: =Errors+ [CWriteError] ;

AnyError

End;

Procedure Tabl. OutOfData;

Begin

Errors: =Errors+ [COutOfData] ;

AnyError

End;

Procedure Tabl. SearchError;

Begin

Errors: =Errors+ [CSearchError] ;

AnyError

End;

Procedure Tabl. NotExist;

Begin

Errors: =Errors+ [CNotExist] ;

AnyError

End;

Procedure Tabl. ZFE;

Begin

Errors: =Errors+ [CZFE] ;

AnyError

End;

Procedure Tabl. UnkNownError;

Begin

Errors: =Errors+ [CUnkNownError] ;

AnyError

End;

Procedure Tabl. AnyError;

Begin

End;

Constructor TAbl. VMT;

Begin

Exist: =False;

End;

Procedure Matrix. MSqr;

Var i,j: Integer;

Begin

IF Not A. Exist Then Begin A. NotExist; BadOperands; MSqrError; Exit; End;

IF A. Errors<> [0] Then Begin MsqrError; Exit; End;

IF Self. Exist Then Del;

Self. DataInit(A. CLines,A. CBars);

For i: =1 to CLines do

For j: =1 to CBars do

SetE(i,j,Sqr(A. GetE(i,j)));

Self. SelfClear;

End;

Procedure Matrix. MDg;

Var i,j: Integer;

Begin

IF Not A. Exist Then Begin A. NotExist; BadOperands; MDgError; Exit; End;

IF A. Errors<> [0] Then Begin MDgError; Exit; End;

IF A. CLines<>A. CBars Then Begin MNotSquare; MDgError; Exit; End;

IF Exist Then Del;

DataInit(A. CLines,A. CBars);

For i: =1 to A. CLines do

For j: =1 to A. CBars do

IF i=j Then SetE(i,j,A. GetE(i,j))

Else SetE(i,j,0);

Self. SelfClear;

End;

Procedure Matrix. BadOperands;

Begin

Errors: =Errors+ [CBadOperands] ;

AnyError;

End;

Procedure Matrix. MulError;

Begin

Errors: =Errors+ [CMulError] ;

AnyError;

End;

Procedure Matrix. MDgError;

Begin

Errors: =Errors+ [CMDgError] ;

AnyError;

End;

Procedure Matrix. SortError;

Begin

Errors: =Errors+ [CSortError] ;

AnyError;

End;

Procedure Matrix. DetError;

Begin

Errors: =Errors+ [CDetError] ;

AnyError;

End;

Procedure Matrix. DGaussError;

Begin

Errors: =Errors+ [CDGaussError] ;

AnyError;

End;

Procedure Matrix. MSqrError;

Begin

Errors: =Errors+ [CMSqrError] ;

AnyError;

End;

Procedure MAtrix. CuanZeeroError;

Begin

Errors: =Errors+ [CCuanZeeroError] ;

AnyError;

End;

Procedure MAtrix. SwapError;

Begin

Errors: =Errors+ [CSwapError] ;

AnyError;

End;

Procedure Matrix. MulToNumError;

Begin

Errors: =Errors+ [CMulToNumError] ;

AnyError

End;

Procedure Matrix. DegrError;

Begin

Errors: =Errors+ [CDegrError] ;

AnyError

End;

Procedure Matrix. IgError;

Begin

Errors: =Errors+ [CIgError] ;

AnyError

End;

Procedure MAtrix. SelfClear;

Begin

Lin: = [0] ;

Bar: = [0] ;

Plus: =True;

Direction: =True;

SortLines: =True;

BeginZeero: =True;

SpecialSort: =False;

Chek: =0;

Gauss: =False;

DetForRev: =False;

End;

Procedure Matrix. AllClear;

Begin

inherited AllClear;

SelfClear;

End;

Procedure Matrix. Revers;

VAr FM: Mem;

Begin

Gauss: =False;

InnerRevers(A);

End;

Procedure Matrix. RevWithGauss;

Var FM: Mem;

Begin

Gauss: =True;

InnerRevers(A);

End;

Procedure Matrix. InnerRevers;

Var P,A1: Matrix;

D: TOE;

i,j: Integer;

Var Ver: TOE;

Var FM: Mem;

Begin

IF Not A. Exist Then Begin A. NotExist; BadOperands; ReversError; Exit; End;

IF (A. Errors<> [0]) Then Begin Exit; ReversError; End;

IF (A. CBars<>A. Clines) Then Begin BadOperands; ReversError; Exit; End;

P. VMT;

P. DataInit(A. CLines,A. CBars);

A1. VMT;

A1: =A;

IF A1. CLines=31 Then Begin Matrix31(A1). VMT; A1. Exist: =True; End;

IF A1. CLines=63 Then Begin Matrix63(A1). VMT; A1. Exist: =True; End;

IF Gauss Then D: =A1. DetWithGauss;

IF D=0 Then

Begin

MDegenerate;

ReversError;

Exit;

End;

DetForRev: =True;

For i: =1 to P. Clines do

Begin

A. StepRevers;

For j: =1 to P. CBars do

Begin

A1. Lin: =A1. Lin+ [i] ;

A1. Bar: =A1. Bar+ [j] ;

IF Gauss Then Ver: =A1. DetWithGauss;

IF (A1. Errors<> [0]) or (A. Errors<> [0]) Then Begin ReversError; Exit; End;

P. SetE(j, i,(Ver) *Sign(i+j) /D);

A1. Lin: =A1. Lin- [i] ;

A1. Bar: =A1. Bar- [j] ;

End;

IF Self. Exist Then Self. del;

Self: =P;

Self. SelfClear;

End;

Procedure Matrix. SwapBars(B1,B2: Integer);

Var Prom: TOE;

i: Integer;

Begin

IF Not Exist Then BEgin NotExist; SwapError; Exit; End;

IF (Errors<> [0]) Then Begin SwapError; Exit; End;

For i: =1 to CLines do

Begin

Prom: =GetE(i,B1);

SetE(i,B1,GetE(i,B2));

SetE(i,B2,Prom)

End;

Function Matrix. CuanZeeroInBar(B1: Integer): Integer;

Var i: Integer;

Sum: Integer;

Begin

IF Not Exist Then Begin NotExist; CuanZeeroError; Exit; End;

IF (Errors<> [0]) Then Begin CuanZeeroError; Exit; End;

Sum: =0;

IF Not SpecialSort

Then

For i: =1 to CLines do IF GetE(i,B1) =0 Then Inc(Sum) else

Else

IF BeginZeero

Then

Begin

Sum: =1;

While (GetE(Sum,B1) =0) and (Sum<=CLines) do inc(Sum);

Dec(Sum);

End

Else

Begin

Sum: =CLines;

While (GetE(Sum,B1) =0) and (Sum>0) do Dec(Sum);

Sum: =Clines-Sum;

End;

CuanZeeroinBar: =Sum;

End;

Procedure Matrix. ZeeroSortBars;

Var i,j: Integer;

Max,NMax,CZ: Integer;

FM: Mem;

Begin

IF Not Exist Then Begin NotExist; Exit; End;

IF (Errors<> [0]) Then Exit;

RemSettings(FM);

SortLines: =False;

SpecialSort: =False;

UniversalSort;

RestoreSettings(FM);

End;

Function Matrix. CuanZeeroinLine(L1: Integer): Integer;

Var i: Integer;

Sum: Integer;

Begin

IF Not Exist Then Begin NotExist; CuanZeeroError; Exit; End;

IF (Errors<> [0]) Then Begin CuanZeeroError; Exit; End;

Sum: =0;

IF Not SpecialSort

Then

For i: =1 to CBars do IF GetE(L1, i) =0 Then Inc(Sum) else

Else

IF BeginZeero

Then

Begin

Sum: =1;

While (GetE(L1,Sum) =0) and (Sum<=CBars) do inc(Sum);

Dec(Sum);

End

Else

Begin

Sum: =CBars;

While (GetE(L1,Sum) =0) and (Sum>0) do Dec(Sum);

Sum: =CBars-Sum;

End;

CuanZeeroinLine: =Sum;

End;

Procedure Matrix. SwapLines(L1,L2: Integer);

Var Prom: TOE;

i: Integer;

Begin

IF Not Exist Then Begin NotExist; SwapError; Exit; End;

IF (Errors<> [0]) Then Begin SwapError; Exit; End;

For i: =1 to CBars do

Begin

Prom: =GetE(L1, i);

SetE(L1, i,GetE(L2, i));

SetE(L2, i,Prom)

End;

Procedure Matrix. ZeeroSortLines;

VAr FM: Mem;

Begin

IF Not Exist Then Begin NotExist; Exit; End;

IF (Errors<> [0]) Then Exit;

RemSettings(FM);

SortLines: =True;

SpecialSort: =False;

UniversalSort;

RestoreSettings(FM);

End;

Procedure Matrix. UniversalSort;

Var i,j: Integer;

Max,NMax,CZ: Integer;

Cuan: Integer;

Begin

IF Not Exist Then Begin NotExist; SortError; Exit; End;

IF (Errors<> [0]) Then Begin SortError; Exit; End;

IF SortLines Then Cuan: =CLines

Else Cuan: =CBars;

For i: =1 to Cuan do

Begin

IF SortLines Then Max: =CuanZeeroInLine(i)

Else Max: =CuanZeeroInBar(i);

Nmax: =i;

For j: =i to Cuan do

Begin

IF SortLines Then CZ: =CuanZeeroInLine(j)

Else CZ: =CuanZeeroInBar(j);

IF (CZ<Max) xor Direction

Then

Begin

Max: =CZ;

NMax: =j;

End;

IF i<>NMax Then

Begin

IF SortLInes Then SwapLines(i,NMax)

Else SwapBars(i,NMax);

Inc(Chek);

End;

Function Matrix. DetWithGauss: TOE;

Var i,j: Integer;

K: TOE;

P: TOE;

S: Matrix;

Si,Sj: Integer;

Procedure SortLinesOfTheBar(B1: Integer);

Var i: Integer;

Max: TOE;

nMax: Integer;

Begin

Max: =S. GetE(1,B1);

nMax: =1;

For i: =2 to S. Clines do

IF Abs(Max) <Abs(S. GetE(i,B1))

Then

Begin

Max: =S. GetE(i,B1);

nMAx: =i;

End;

IF S. Clines<>nMAx Then

Begin

S. SwapLines(S. Clines,nMAx);

Inc(S. Chek);

End;

Procedure AddLines(l1,l2: Integer; K: TOE);

Var i: Integer;

Begin

For i: =1 to S. CBars do

S. SetE(l2, i,(S. GetE(l2, i) - S. GetE(l1, i) *K));

End;

Procedure InitObject;

Var i,j: Integer;

Ver: TOE;

Begin

Si: =0;

Sj: =0;

For i: =1 to CLines do IF not (i in Lin) Then Inc(Si);

For j: =1 to CBars do IF not (j in Bar) Then Inc(sj);

S. VMT;

S. DataInit(Si,Sj);

Si: =0;

For i: =1 to CLines do

IF not (i in Lin) Then

Begin

Inc(Si);

Sj: =0;

For j: =1 to CBars do

IF not (j in Bar) Then

Begin

Inc(sj);

Ver: =GetE(i,j);

S. SetE(Si,Sj,Ver);

End

End;

Begin

IF Not Exist Then Begin NotExist; DGaussError; Exit; End;

IF (Errors<> [0]) Then Begin DGaussError; Exit; End;

IF CBars<>CLines Then Begin MNotSquare; DGaussError; Exit; End;

InitObject;

IF S. CBars<>S. CLines Then Begin MNotSquare; DGaussError; Exit; End;

For i: =Si downto 2 do

Begin

S. Clines: =i;

SortLinesOfTheBar(i);

S. Clines: =Si;

IF S. GetE(i, i) =0 Then Begin DetWithGauss: =0; Exit; End;

For j: =i-1 downto 1 do

IF S. GetE(j, i) <>0 Then

Begin

K: =S. GetE(j, i) /S. GetE(i, i);

AddLines(i,j,K);

End;

P: =1;

S. Clines: =Si;

S. CBars: =Sj;

For i: =1 to S. Clines do

P: =P*S. GetE(i, i);

DetWithGauss: =P*S. Sign(S. Chek);

S. Del;

End;

Function Matrix. Sign;

Begin

IF (C div 2) *2=C Then Sign: =1.0 Else Sign: =-1.0;

End;

Procedure Matrix. SpecialSortLines;

VAr FM: Mem;

Begin

IF Not Exist Then Begin NotExist; Exit; End;

IF (Errors<> [0]) Then Exit;

RemSettings(FM);

SpecialSort: =True;

SortLines: =True;

UniversalSort;

RestoreSettings(FM);

End;

Procedure Matrix. SpecialSortBars;

VAr FM: Mem;

Begin

IF Not Exist Then Begin NotExist; Exit; End;

IF (Errors<> [0]) Then Exit;

RemSettings(FM);

SpecialSort: =True;

SortLines: =False;

UniversalSort;

RestoreSettings(FM);

End;

Procedure RemSettings;

Begin

End;

Procedure MAtrix. MNotSquare;

Begin

Errors: =Errors+ [CMNotSquare] ;

AnyError

End;

Procedure Matrix. AddError;

Begin

Errors: =Errors+ [CAddError] ;

AnyError

End;

Procedure Matrix. ReversError;

Begin

Errors: =Errors+ [CReversError] ;

AnyError

End;

Procedure Matrix. MDegenerate;

Begin

Errors: =Errors+ [CMDegenerate] ;

AnyError

End;

Procedure Matrix. Stopped;

Begin

Errors: =Errors+ [CStopped] ;

AnyError

End;

Procedure Matrix. StepRevers;

Begin

End;

Procedure Matrix. RemSettings;

Begin

With FM do

Begin

mPlus: = Plus;

mDirection: = Direction;

mSortLines: = SortLines;

mBeginZeero: = BeginZeero;

mSpecialSort: = SpecialSort;

mGauss: = Gauss;

mDetForRev: = DetForRev;

End

End;

Procedure Matrix. RestoreSettings;

Begin

With FM do

Begin

Plus: = mPlus;

Direction: = mDirection;

SortLines: = mSortLines;

BeginZeero: = mBeginZeero;

SpecialSort: = mSpecialSort;

Gauss: = mGauss;

DetForRev: = mDetForRev;

End;

{********************************Quick metods *****************************}

Function Matrix31. DetWithGauss;

Var i,j: Integer;

K: TOE;

P: TOE;

S: Matrix31;

si,sj: Integer;

Procedure SortLinesOfTheBar(B1: Integer);

Var i: Integer;

Max: TOE;

nMax: Integer;

Begin

Max: =Ar31(S. M^) [1,B1] ;

nMax: =1;

For i: =2 to S. Clines do

IF Abs(Max) <Abs(Ar31(S. M^) [i,B1])

Then

Begin

Max: =Ar31(S. M^) [i,B1] ;

nMAx: =i;

End;

IF S. Clines<>nMAx Then

Begin

S. SwapLines(S. Clines,nMAx);

Inc(S. Chek);

End;

Procedure AddLines(l1,l2: Integer; K: TOE);

Var i: Integer;

Begin

For i: =1 to S. CBars do

Begin

Ar31(S. M^) [l2, i]: =Ar31(S. M^) [l2, i] -Ar31(S. M^) [l1, i] *K;

End;

Procedure InitObject;

Var i,j: Integer;

Ver: TOE;

Begin

S. VMT;

S. DataInit(31,31);

Si: =0;

IF DetForRev

Then

Begin

si: =31;

sj: =31;

Ar31(S. M^): =Ar31(M^)

End

Else

For i: =1 to CLines do

IF not (i in Lin) Then

Begin

Inc(Si);

Sj: =0;

For j: =1 to CBars do

IF not (j in Bar) Then

Begin

Inc(sj);

Ar31(S. M^) [Si,Sj]: =Ar31(M^) [i,j] ;

End

End;

Begin

IF Not Exist Then Begin NotExist; DGaussError; Exit; End;

IF (Errors<> [0]) Then Begin DGaussError; Exit; End;

IF CBars<>CLines Then Begin MNotSquare; DGaussError; Exit; End;

InitObject;

S. Clines: =si;

S. CBars: =sj;

IF S. CBars<>S. CLines Then Begin MNotSquare; DGaussError; Exit; End;

For i: =si downto 2 do

Begin

S. Clines: =i;

SortLinesOfTheBar(i);

S. Clines: =si;

IF Ar31(S. M^) [i, i] =0 Then Begin DetWithGauss: =0; Exit; End;

For j: =i-1 downto 1 do

IF Ar31(S. M^) [j, i] <>0 Then

Begin

K: =Ar31(S. M^) [j, i] /Ar31(S. M^) [i, i] ;

AddLines(i,j,K);

End;

P: =1;

S. Clines: =si;

S. CBars: =sj;

For i: =1 to S. Clines do

P: =P*Ar31(S. M^) [i, i] ;

DetWithGauss: =P*S. Sign(S. Chek);

S. Del;

End;

Procedure Matrix31. SwapLines(L1,L2: Integer);

Var Prom: TOE;

i: Integer;

Begin

IF Not Exist Then BEgin NotExist; SwapError; Exit; End;

IF (Errors<> [0]) Then Begin SwapError; Exit; End;

For i: =1 to CBars do

Begin

Prom: =Ar31(M^) [L1, i] ;

Ar31(M^) [L1, i]: =Ar31(M^) [L2, i] ;

Ar31(M^) [L2, i]: =Prom

End;

{-------------------------------------------------------------------------}

Function Matrix63. DetWithGauss;

Var i,j: Integer;

K: TOE;

P: TOE;

S: Matrix63;

si,sj: Integer;

Procedure SortLinesOfTheBar(B1: Integer);

Var i: Integer;

Max: TOE;

nMax: Integer;

Begin

Max: =Ar63(S. M^) [1,B1] ;

nMax: =1;

For i: =2 to S. Clines do

IF Abs(Max) <Abs(Ar63(S. M^) [i,B1])

Then

Begin

Max: =Ar63(S. M^) [i,B1] ;

nMAx: =i;

End;

IF S. Clines<>nMAx Then

Begin

S. SwapLines(S. Clines,nMAx);

Inc(S. Chek);

End;

Procedure AddLines(l1,l2: Integer; K: TOE);

Var i: Integer;

Begin

For i: =1 to S. CBars do

Begin

Ar63(S. M^) [l2, i]: =Ar63(S. M^) [l2, i] -Ar63(S. M^) [l1, i] *K;

End;

Procedure InitObject;

Var i,j: Integer;

Ver: TOE;

Begin

S. VMT;

S. DataInit(63,63);

Si: =0;

IF DetForRev

Then

Begin

si: =63;

sj: =63;

Ar63(S. M^): =Ar63(M^)

End

Else

For i: =1 to CLines do

IF not (i in Lin) Then

Begin

Inc(Si);

Sj: =0;

For j: =1 to CBars do

IF not (j in Bar) Then

Begin

Inc(sj);

Ar63(S. M^) [Si,Sj]: =Ar63(M^) [i,j] ;

End

End;

Begin

IF Not Exist Then Begin NotExist; DGaussError; Exit; End;

IF (Errors<> [0]) Then Begin DGaussError; Exit; End;

IF CBars<>CLines Then Begin MNotSquare; DGaussError; Exit; End;

InitObject;

S. Clines: =si;

S. CBars: =sj;

IF S. CBars<>S. CLines Then Begin MNotSquare; DGaussError; Exit; End;

For i: =si downto 2 do

Begin

S. Clines: =i;

SortLinesOfTheBar(i);

S. Clines: =si;

IF Ar63(S. M^) [i, i] =0 Then Begin DetWithGauss: =0; Exit; End;

For j: =i-1 downto 1 do

IF Ar63(S. M^) [j, i] <>0 Then

Begin

K: =Ar63(S. M^) [j, i] /Ar63(S. M^) [i, i] ;

AddLines(i,j,K);

End;

P: =1;

S. Clines: =si;

S. CBars: =sj;

For i: =1 to S. Clines do

P: =P*Ar63(S. M^) [i, i] ;

DetWithGauss: =P*S. Sign(S. Chek);

S. Del;

End;

Procedure Matrix63. SwapLines(L1,L2: Integer);

Var Prom: TOE;

i: Integer;

Begin

For i: =1 to CBars do

Begin

Prom: =Ar63(M^) [L1, i] ;

Ar63(M^) [L1, i]: =Ar63(M^) [L2, i] ;

Ar63(M^) [L2, i]: =Prom

End;

END.

Контрольні приклади

Дана матриця:

3 - 1 0

А= - 2 1 1

2 - 1 4

Відповідь:

1 0,8 - 0,2

А-1 = 2 2,4 - 0,6

0 0,2 0,2

Список використаної літератури
1. А.Г. Курош "курс высшей алгебры", "наука", Москва 1975.

2. С.Т. Завало, В.М. Костарчук, Б.И. Хацет "алгебра и теория чисел", Том 1,"высшая школа", Киев 1974.

3. С.Т. Завало, В.М. Костарчук, Б.И. Хацет "алгебра и теория чисел", Том 2,"высшая школа", Киев 1976.

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