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ru.algorithms
- RU.ALGORITHMS ----------------------------------------------------------------
From : Vova Kasatochkin 2:5020/600.3 08 Aug 2002 16:53:20
To : Vladimir Chizhov
Subject : Определитель матрицы
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31 Jul 02 02:03, you wrote to all:
VC> Hарод, есть ли какой-нить алгоритм нахождения определителя матрицы?
VC> Все умные книжки, бывшие в наличии, перерыл, ничего нет.
=== Cut ===
DECLARE FUNCTION SolveLinearEquation%(A() AS DOUBLE,b() AS DOUBLE)
DECLARE FUNCTION Determinant%(A() AS DOUBLE,det AS DOUBLE)
=== Cut ===
=== Cut ===
'$INCLUDE:'matrix.bi'
DECLARE FUNCTION UpTriangTrans%(A() AS DOUBLE)
DECLARE FUNCTION BackSolve%(A() AS DOUBLE, b() AS DOUBLE, x() AS DOUBLE)
REDIM SHARED RowIndex(0) AS INTEGER
REDIM SHARED ColIndex(0) AS INTEGER
DIM SHARED LoIndex AS INTEGER '1 normally
DIM SHARED UpIndex AS INTEGER 'N normally
DIM SHARED Sign AS INTEGER
FUNCTION UpTriangTrans%(A() AS DOUBLE)
DIM Column AS INTEGER
DIM Row AS INTEGER
DIM pvt AS INTEGER
DIM c AS INTEGER
DIM r AS INTEGER
DIM Maximum AS DOUBLE
DIM RowMax AS INTEGER
DIM ColMax AS INTEGER
DIM i AS INTEGER
DIM j AS INTEGER
DIM CPivot AS INTEGER
DIM RPivot AS INTEGER
UpTriangTrans%=-1
Sign=1
FOR pvt=LoIndex TO (UpIndex-1)
Maximum=0#
FOR i=pvt TO UpIndex
FOR j=pvt TO UpIndex
IF ABS(A(RowIndex(i),ColIndex(j)))>Maximum THEN
Maximum=ABS(A(RowIndex(i),ColIndex(j)))
RowMax=i
ColMax=j
END IF
NEXT j
NEXT i
IF Maximum=0# THEN EXIT FUNCTION
IF ColMax<>pvt THEN
SWAP ColIndex(ColMax),ColIndex(pvt)
Sign=-Sign
END IF
IF RowMax<>pvt THEN
SWAP RowIndex(RowMax),RowIndex(pvt)
Sign=-Sign
END IF
CPivot=ColIndex(pvt)
RPivot=RowIndex(pvt)
FOR r=pvt+1 TO UpIndex
Row=RowIndex(r)
A(Row,CPivot)=-A(Row,CPivot)/A(RPivot,CPivot)
FOR c=pvt+1 TO UpIndex
Column=ColIndex(c)
A(Row,Column)=A(Row,Column)+A(Row,CPivot)*A(RPivot,Column)
NEXT c
NEXT r
NEXT pvt
UpTriangTrans%=0
END FUNCTION
FUNCTION BackSolve%(A() AS DOUBLE, b() AS DOUBLE, x() AS DOUBLE)
DIM pvt AS INTEGER
DIM row AS INTEGER
DIM col AS INTEGER
DIM CPivot AS INTEGER
DIM RPivot AS INTEGER
FOR pvt=LoIndex TO (UpIndex-1)
CPivot=ColIndex(pvt)
FOR row=(pvt+1) TO UpIndex
RPivot=RowIndex(row)
b(RPivot)=b(RPivot)+A(RPivot,CPivot)*b(RowIndex(pvt))
NEXT row
NEXT pvt
FOR row=UpIndex TO LoIndex STEP -1
CPivot=ColIndex(row)
RPivot=RowIndex(row)
x(CPivot)=b(RPivot)
FOR col=(row+1) TO UpIndex
x(CPivot)=x(CPivot)-A(RPivot,ColIndex(col))*x(ColIndex(col))
NEXT col
x(CPivot)=x(CPivot)/A(RPivot,CPivot)
NEXT row
BackSolve%=0
END FUNCTION
FUNCTION SolveLinearEquation%(A() AS DOUBLE,b() AS DOUBLE)
DIM Low AS INTEGER
DIM High AS INTEGER
DIM ErrCode AS INTEGER
DIM x(0) AS DOUBLE
DIM i AS INTEGER
Low=LBOUND(A,1)
High=UBOUND(A,1)
IF LBOUND(A,2)<>Low OR UBOUND(A,2)<>High OR _
LBOUND(b)<>Low OR UBOUND(b)<>High THEN
SolveLinearEquation%=-1
EXIT FUNCTION
END IF
ON LOCAL ERROR GOTO CannotRedim
LoIndex=1
UpIndex=High-Low+1
REDIM x(LoIndex TO UpIndex) AS DOUBLE
REDIM RowIndex(LoIndex TO UpIndex) AS INTEGER
REDIM ColIndex(LoIndex TO UpIndex) AS INTEGER
FOR i=LoIndex TO UpIndex
RowIndex(i)=Low+i-LoIndex
ColIndex(i)=Low+i-LoIndex
NEXT i
ON LOCAL ERROR GOTO MAthError
ErrCode=UpTriangTrans%(A())
IF ErrCode<>0 THEN
SolveLinearEquation%=-4
ERASE RowIndex
ERASE ColIndex
ERASE x
LoIndex=0
UpIndex=0
EXIT FUNCTION
END IF
ErrCode=BackSolve%(A(),b(),x())
IF ErrCode<>0 THEN
SolveLinearEquation%=-5
ERASE RowIndex
ERASE ColIndex
ERASE x
LoIndex=0
UpIndex=0
EXIT FUNCTION
END IF
FOR i=LoIndex TO UpIndex
b(i)=x(i)
NEXT i
ERASE RowIndex
ERASE ColIndex
ERASE x
LoIndex=0
UpIndex=0
SolveLinearEquation%=0
ExitingSolveLinearEquation:
EXIT FUNCTION
CannotRedim:
SolveLinearEquation%=-2
RESUME ExitingSolveLinearEquation
MAthError:
SolveLinearEquation%=-3
RESUME ExitingSolveLinearEquation
END FUNCTION
FUNCTION Determinant%(A() AS DOUBLE,det AS DOUBLE)
DIM Low AS INTEGER
DIM High AS INTEGER
DIM ErrCode AS INTEGER
DIM i AS INTEGER
Low=LBOUND(A,1)
High=UBOUND(A,1)
IF LBOUND(A,2)<>Low OR UBOUND(A,2)<>High THEN
Determinant%=-1
EXIT FUNCTION
END IF
ON LOCAL ERROR GOTO DeterminantCannotRedim
LoIndex=1
UpIndex=High-Low+1
REDIM RowIndex(LoIndex TO UpIndex) AS INTEGER
REDIM ColIndex(LoIndex TO UpIndex) AS INTEGER
FOR i=LoIndex TO UpIndex
RowIndex(i)=Low+i-LoIndex
ColIndex(i)=Low+i-LoIndex
NEXT i
ON LOCAL ERROR GOTO DeterminantMAthError
ErrCode=UpTriangTrans%(A())
IF ErrCode<>0 THEN
Determinant%=-4
ERASE RowIndex
ERASE ColIndex
LoIndex=0
UpIndex=0
EXIT FUNCTION
END IF
det=1#
FOR i=LoIndex TO UpIndex
det=det*A(RowIndex(i),ColIndex(i))
NEXT i
det=Sign*det
ERASE RowIndex
ERASE ColIndex
LoIndex=0
UpIndex=0
Determinant%=0
ExitingDeterminant:
EXIT FUNCTION
DeterminantCannotRedim:
Determinant%=-2
RESUME ExitingDeterminant
DeterminantMAthError:
Determinant%=-3
RESUME ExitingDeterminant
END FUNCTION
=== Cut ===
VC> ЗЫ: Бэктрэкинг не предлагать, эт я и сам могу.
Vova
... np: 01 - Dazed And Confused
--- Got no time for spelling rules
* Origin: (2:5020/600.3)
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Определитель матрицы 
