135481 (Программная реализация модального управления для линейных стационарных систем), страница 4

ZeroMemory (DataPtr, FCols * FRows * SizeOf(Float));

end;

procedure TMatrix.SetSingle;

var

i: Word;

begin

if FCols <> FRows then

Raise EMatrixOperatingError.Create ('Единичная матрица должна быть '+

'квадратной')

else

begin

SetNull;

for i := 1 to FCols do SetCell (i, i, 1);

end;

end;

procedure TMatrix.SetNegative;

var

i: LongInt;

begin

for i := 1 to FCols * FRows do SetItem(i, - GetItem(i));

end;

procedure TMatrix.AddConst (AConst: Float);

var

i: LongInt;

begin

for i := 1 to FCols * FRows do SetItem (i, GetItem(i) + AConst);

end;

procedure TMatrix.AddMatrix (AMatrix: TMatrix);

var

i: LongInt;

begin

for i := 1 to FCols * FRows do SetItem (i, GetItem(i) + AMatrix.Items [i]);

end;

procedure TMatrix.MultConst (MConst: Float);

var

i: LongInt;

begin

for i := 1 to FCols * FRows do SetItem (i, GetItem(i) * MConst);

end;

procedure TMatrix.MultFromRight (MMatrix: TMatrix);

var

j, i, k: Word;

DummyRes: Float;

DummyMatrix: TMatrix;

begin

DummyMatrix := TMatrix.Create (MMatrix.ColCount, FRows);

if FCols <> MMatrix.RowCount then

Raise EMatrixOperatingError.Create ('Перемножаемые матрицы должны быть '+

'соответствующей размерности')

else

for i := 1 to FRows do

for j := 1 to MMatrix.ColCount do

begin

DummyRes := 0;

for k := 1 to FCols do

DummyRes := DummyRes + Cells[k, i] * MMatrix[j, k];

DummyMatrix[j, i] := DummyRes;

end;

Assign(DummyMatrix);

DummyMatrix.Free;

end;

procedure TMatrix.MultFromLeft (MMatrix: TMatrix);

var

j, i, k: Word;

DummyRes: Float;

DummyMatrix: TMatrix;

begin

DummyMatrix := TMatrix.Create (FCols, MMatrix.RowCount);

if MMatrix.ColCount <> FRows then

Raise EMatrixOperatingError.Create ('Перемножаемые матрицы должны быть '+

'соответствующей размерности')

else

for i := 1 to MMatrix.ColCount do

for j := 1 to FCols do

begin

DummyRes := 0;

for k := 1 to MMatrix.ColCount do

DummyRes := DummyRes + MMatrix[k, i] * Cells[j, k];

DummyMatrix[j, i] := DummyRes;

end;

Assign(DummyMatrix);

DummyMatrix.Free;

end;

procedure TMatrix.NthPower (Power: Word);

var

i: Word;

DummyMatrix: TMatrix;

begin

DummyMatrix := TMatrix.Create (FCols, FRows);

DummyMatrix.Assign (Self);

if FCols <> FRows then

Raise EMatrixOperatingError.Create ('Возводимая в степень матрица должна '+

'быть квадратной')

else

case Power of

0 : SetSingle;

1 : begin end;

else

for i := 2 to Power do MultFromRight (DummyMatrix);

end;

DummyMatrix.Free;

end;

procedure TMatrix.Transpose;

var

i, j: Word;

Dummy: Float;

begin

if FCols <> FRows then

Raise EMatrixOperatingError.Create ('Транспонируемая матрица должна быть '+

'квадратной')

else

for i := 1 to FCols do

for j := 1 to FRows do

if j > i then

begin

Dummy := GetCell(j, i);

SetCell(j, i, GetCell(i, j));

SetCell(i, j, Dummy);

end

end;

function TMatrix.Inverse: Boolean;

var

DummyMatrix: TMatrix;

Divisor, Multiplier: Float;

Row, RefRow, NewRow, Term: Word;

Singular: Boolean;

begin

Singular := False;

DummyMatrix := TMatrix.Create (FCols, FRows);

if (FCols <> FRows) or (FCols = 0) then

Raise EMatrixOperatingError.Create ('Инвертируемая матрица должна быть '+

'квадратной и ненулевого размера');

if FCols = 1 then

if ABS(GetItem(1)) < NearlyZero then Singular := True

else DummyMatrix.Items[1] := 1 / GetItem(1);

if FCols > 1 then

begin

DummyMatrix.SetSingle;

RefRow := 0;

repeat

Inc(RefRow);

if ABS(Cells[RefRow, RefRow]) < NearlyZero then

begin

Singular := TRUE;

NewRow := RefRow;

repeat

Inc(NewRow);

if ABS(Cells[RefRow, NewRow]) > NearlyZero then

begin

SwitchRows(NewRow, RefRow);

DummyMatrix.SwitchRows(NewRow, RefRow);

Singular := False;

end;

until (not Singular) or (NewRow >= FCols);

end;

if not Singular then

begin

Divisor := Cells[RefRow, RefRow];

for Term := 1 to FCols do

begin

SetCell(Term, RefRow, GetCell(Term, RefRow)/Divisor);

DummyMatrix[Term, RefRow] := DummyMatrix[Term, RefRow]/Divisor;

end;

for Row := 1 to FCols do

if (Row <> RefRow) and (ABS(Cells[RefRow, Row]) > NearlyZero) then

begin

Multiplier := - Cells[RefRow, Row] / Cells[RefRow, RefRow];

for Term := 1 to FCols do

begin

SetCell(Term, Row, GetCell(Term, Row) +

Multiplier * GetCell(Term, RefRow));

DummyMatrix[Term, Row] := DummyMatrix[Term, Row] +

Multiplier * DummyMatrix[Term, RefRow];

end

end;

end;

until Singular or (RefRow >= FCols);

end;

Assign(DummyMatrix);

DummyMatrix.Free;

if not Singular then Result := True

else Result := False;

end;

function TMatrix.Determinant: Float;

begin

Result := 0;

end;

function TMatrix.Rang: Float;

begin

Result := 0;

end;

end.

unit Operates;

interface

uses Matrix, Grids, SysUtils;

const

MaxArraySize = 30;

type

Float = Extended;

TOrder = 1..MaxArraySize;

ESingularMatrix = class (Exception);

type

TComplex = record

Re, Im : Float;

end;

TComplexVector = record

Data : array [1..MaxArraySize] of TComplex;

Dim : TOrder;

end;

function SymmetricalFunction (Roots: TComplexVector; K: byte): Float;

procedure DiffSystemSolve (matrixA,

matrixB: TMatrix;

LowerLimit,

UpperLimit: Float;

InitialValues: TMatrix;

NumReturn,

NumIntervals: Word;

SolutionValues: TMatrix);

implementation

function SymmetricalFunction (Roots: TComplexVector; K: byte): Float;

var

Z: TComplex;

function SummComplex (FirstNC, SecondNC: TComplex): TComplex;

begin

Result.Re := FirstNC.Re + SecondNC.Re;

Result.Im := FirstNC.Im + SecondNC.Im;

end;

function MultComplex (FirstNC, SecondNC: TComplex): TComplex;

begin

Result.Re := FirstNC.Re * SecondNC.Re - FirstNC.Im * SecondNC.Im;

Result.Im := FirstNC.Re * SecondNC.Im + FirstNC.Im * SecondNC.Re;

end;

function DivComplex (FirstNC, SecondNC: TComplex): TComplex;

var

Z: Float;

begin

Z := Sqr(SecondNC.Re) + Sqr(SecondNC.Im);

Result.Re := (FirstNC.Re * SecondNC.Re + FirstNC.Im * SecondNC.Im) / Z;

Result.Im := (FirstNC.Im * SecondNC.Re - FirstNC.Re * SecondNC.Im) / Z;

end;

function CombinationSumm (LowLimit, HighLimit, K: byte): TComplex;

var i: byte;

begin

Result.Re := 0;

Result.Im := 0;

if LowLimit = HighLimit then Result := Roots.Data[LowLimit]

else

for i := LowLimit to HighLimit - K + 1 do

if K = 1 then Result := SummComplex(Result, Roots.Data [i])

else Result := SummComplex(Result,

MultComplex(Roots.Data [i],

CombinationSumm(i + 1,

HighLimit, K-1)));

end;

begin

Z := CombinationSumm(1, Roots.Dim, K);

Result := Z.Re;

end;

procedure DiffSystemSolve (matrixA, matrixB: TMatrix;

LowerLimit, UpperLimit: Float;

InitialValues: TMatrix;

NumReturn, NumIntervals: Word;

SolutionValues: TMatrix);

type

Ptr = ^Data;

Data = record

Values: TMatrix;

Next: Ptr;

end;

var

ValuesStack: Ptr;

Spacing, HalfSpacing: Float;

Index, Term: Word;

F1, F2, F3, F4,

CurrentValues,

TempValues: TMatrix;

NumEquations, NumTimeCol: Word;

function TargetALL (matrixA, mayrixB: TMatrix; Values: TMatrix; KRow: Word): Float;

var

j: Word;

begin

try

Result := matrixB.Items[KRow];

for j := 1 to NumEquations do

Result := Result + matrixA[j, KRow] * Values.Items[j];

except

on EO: EOverflow do EO.Message := 'Не буду считать !!!'#10 +

'С уменьшите разброс коэффициентов в матрице А'#10 +

'либо измените опции (уменьшите их pls.)';

end;

end;

procedure Push (var ValuesStack: Ptr;

CurrentValues: TMatrix);

var

NewNode : Ptr;

begin

New(NewNode);

NewNode^.Values := TMatrix.Create(NumTimeCol, 1);

NewNode^.Values.Assign(CurrentValues);

NewNode^.Next := ValuesStack;

ValuesStack := NewNode;

end; { procedure Push }

procedure Pop (var ValuesStack: Ptr;

CurrentValues: TMatrix);

var

OldNode : Ptr;

begin

OldNode := ValuesStack;

ValuesStack := OldNode^.Next;

CurrentValues.Assign(OldNode^.Values);

OldNode^.Values.Free;

Dispose(OldNode);

end; { procedure Pop }

procedure GetValues(NumReturn, NumIntervals: Word; var ValuesStack: Ptr;

SolutionValues: TMatrix);

var

Index, Term: Integer;

j: Word;

CurrValues: TMatrix;

begin

SolutionValues.ReSize(NumTimeCol, Succ(NumReturn));

CurrValues := TMatrix.Create(NumTimeCol, 1);

Term := NumIntervals;

for Index := NumReturn downto 0 do

begin

Pop(ValuesStack, CurrValues);

Dec(Term);

while (Term / NumIntervals >= Index / NumReturn) and (Term >= 0) do

begin

Pop(ValuesStack, CurrValues);

Dec(Term);

end;

for j := 1 to NumTimeCol do

SolutionValues[j, Succ(Index)] := CurrValues.Items[j];

end;

CurrValues.Free;

end; { procedure GetValues }

procedure Step(Spacing: Float; CurrentValues: TMatrix; F: TMatrix);

var

i : byte;

begin

for i := 1 to NumEquations do

F.Items[i] := Spacing * TargetALL (matrixA, matrixB, CurrentValues, i);

end; { procedure Step }

begin

NumEquations := matrixA.RowCount;

NumTimeCol := Succ(NumEquations);

ValuesStack := nil;

Spacing := (UpperLimit - LowerLimit) / NumIntervals;

CurrentValues := TMatrix.Create(1, 1);

CurrentValues.Assign(InitialValues);

CurrentValues.ReSize(NumTimeCol, 1);

CurrentValues.Items[NumTimeCol] := LowerLimit;

TempValues := TMatrix.Create(NumTimeCol, 1);

F1 := TMatrix.Create(NumTimeCol, 1);

F2 := TMatrix.Create(NumTimeCol, 1);

F3 := TMatrix.Create(NumTimeCol, 1);

F4 := TMatrix.Create(NumTimeCol, 1);

Push(ValuesStack, CurrentValues);

HalfSpacing := Spacing / 2;

for Index := 1 to NumIntervals do

begin

{ First step - calculate F1 }

Step(Spacing, CurrentValues, F1);

TempValues.Items[NumTimeCol] := CurrentValues.Items[NumTimeCol] + HalfSpacing;

for Term := 1 to NumEquations do

TempValues.Items[Term] := CurrentValues.Items[Term] + 0.5 * F1.Items[Term];

{ 2nd step - calculate F2 }

Step(Spacing, TempValues, F2);

for Term := 1 to NumEquations do

TempValues.Items[Term] := CurrentValues.Items[Term] + 0.5 * F2.Items[Term];

{ Third step - calculate F3 }

Step(Spacing, TempValues, F3);

TempValues.Items[NumTimeCol] := CurrentValues.Items[NumTimeCol] + Spacing;

for Term := 1 to NumEquations do

TempValues.Items[Term] := CurrentValues.Items[Term] + F3.Items[Term];

{ Fourth step - calculate F4[1]; first equation }

Step(Spacing, TempValues, F4);

{ Combine F1, F2, F3, and F4 to get }

{ the solution at this mesh point }

CurrentValues.Items[NumTimeCol] := CurrentValues.Items[NumTimeCol] + Spacing;

for Term := 1 to NumEquations do

CurrentValues.Items[Term] := CurrentValues.Items[Term] +

(F1.Items[Term] + 2 * F2.Items[Term] +

2 * F3.Items[Term] + F4.Items[Term]) /6;

Push(ValuesStack, CurrentValues);

end;

GetValues(NumReturn, NumIntervals, ValuesStack, SolutionValues);

F1.Free;

F2.Free;

F3.Free;

F4.Free;

CurrentValues.Free;

TempValues.Free;

end;

end.

unit HelpUnit;