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reference

cspr2f.f

cspr2f.f 7.15 KB

SUBROUTINE CSPR2F( UPLO, N, ALPHA, X, INCX, Y, INCY, AP )
* .. Scalar Arguments ..
 COMPLEX*8 ALPHA
 INTEGER INCX, INCY, N
 CHARACTER*1 UPLO
* .. Array Arguments ..
 COMPLEX*8 AP( * ), X( * ), Y( * )
* ..
*
* Purpose
* =======
*
* SSPR2 performs the symmetric rank 2 operation
*
* A := alpha*x*y' + alpha*y*x' + A,
*
* where alpha is a scalar, x and y are n element vectors and A is an
* n by n symmetric matrix, supplied in packed form.
*
* Parameters
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the upper or lower
* triangular part of the matrix A is supplied in the packed
* array AP as follows:
*
* UPLO = 'U' or 'u' The upper triangular part of A is
* supplied in AP.
*
* UPLO = 'L' or 'l' The lower triangular part of A is
* supplied in AP.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX*8 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* X - COMPLEX*8 array of dimension at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the n
* element vector x.
* Unchanged on exit.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* Y - COMPLEX*8 array of dimension at least
* ( 1 + ( n - 1 )*abs( INCY ) ).
* Before entry, the incremented array Y must contain the n
* element vector y.
* Unchanged on exit.
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY must not be zero.
* Unchanged on exit.
*
* AP - COMPLEX*8 array of DIMENSION at least
* ( ( n*( n + 1 ) )/2 ).
* Before entry with UPLO = 'U' or 'u', the array AP must
* contain the upper triangular part of the symmetric matrix
* packed sequentially, column by column, so that AP( 1 )
* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
* and a( 2, 2 ) respectively, and so on. On exit, the array
* AP is overwritten by the upper triangular part of the
* updated matrix.
* Before entry with UPLO = 'L' or 'l', the array AP must
* contain the lower triangular part of the symmetric matrix
* packed sequentially, column by column, so that AP( 1 )
* contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
* and a( 3, 1 ) respectively, and so on. On exit, the array
* AP is overwritten by the lower triangular part of the
* updated matrix.
*
*
* Level 2 Blas routine.
*
* -- Written on 22-October-1986.
* Jack Dongarra, Argonne National Lab.
* Jeremy Du Croz, Nag Central Office.
* Sven Hammarling, Nag Central Office.
* Richard Hanson, Sandia National Labs.
*
*
* .. Parameters ..
 COMPLEX*8 ZERO
 PARAMETER ( ZERO = 0.0E+0 )
* .. Local Scalars ..
 COMPLEX*8 TEMP1, TEMP2
 INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY
* .. External Functions ..
 LOGICAL LSAME
 EXTERNAL LSAME
* .. External Subroutines ..
 EXTERNAL XERBLA
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
 INFO = 0
 IF ( .NOT.LSAME( UPLO, 'U' ).AND.
 $ .NOT.LSAME( UPLO, 'L' ) )THEN
 INFO = 1
 ELSE IF( N.LT.0 )THEN
 INFO = 2
 ELSE IF( INCX.EQ.0 )THEN
 INFO = 5
 ELSE IF( INCY.EQ.0 )THEN
 INFO = 7
 END IF
 IF( INFO.NE.0 )THEN
 CALL XERBLA( 'SSPR2 ', INFO )
 RETURN
 END IF
*
* Quick return if possible.
*
 IF( ( N.EQ.0 ).OR.( ALPHA.EQ.ZERO ) )
 $ RETURN
*
* Set up the start points in X and Y if the increments are not both
* unity.
*
 IF( ( INCX.NE.1 ).OR.( INCY.NE.1 ) )THEN
 IF( INCX.GT.0 )THEN
 KX = 1
 ELSE
 KX = 1 - ( N - 1 )*INCX
 END IF
 IF( INCY.GT.0 )THEN
 KY = 1
 ELSE
 KY = 1 - ( N - 1 )*INCY
 END IF
 JX = KX
 JY = KY
 END IF
*
* Start the operations. In this version the elements of the array AP
* are accessed sequentially with one pass through AP.
*
 KK = 1
 IF( LSAME( UPLO, 'U' ) )THEN
*
* Form A when upper triangle is stored in AP.
*
 IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
 DO 20, J = 1, N
 IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN
 TEMP1 = ALPHA*Y( J )
 TEMP2 = ALPHA*X( J )
 K = KK
 DO 10, I = 1, J
 AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2
 K = K + 1
 10 CONTINUE
 END IF
 KK = KK + J
 20 CONTINUE
 ELSE
 DO 40, J = 1, N
 IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN
 TEMP1 = ALPHA*Y( JY )
 TEMP2 = ALPHA*X( JX )
 IX = KX
 IY = KY
 DO 30, K = KK, KK + J - 1
 AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2
 IX = IX + INCX
 IY = IY + INCY
 30 CONTINUE
 END IF
 JX = JX + INCX
 JY = JY + INCY
 KK = KK + J
 40 CONTINUE
 END IF
 ELSE
*
* Form A when lower triangle is stored in AP.
*
 IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
 DO 60, J = 1, N
 IF( ( X( J ).NE.ZERO ).OR.( Y( J ).NE.ZERO ) )THEN
 TEMP1 = ALPHA*Y( J )
 TEMP2 = ALPHA*X( J )
 K = KK
 DO 50, I = J, N
 AP( K ) = AP( K ) + X( I )*TEMP1 + Y( I )*TEMP2
 K = K + 1
 50 CONTINUE
 END IF
 KK = KK + N - J + 1
 60 CONTINUE
 ELSE
 DO 80, J = 1, N
 IF( ( X( JX ).NE.ZERO ).OR.( Y( JY ).NE.ZERO ) )THEN
 TEMP1 = ALPHA*Y( JY )
 TEMP2 = ALPHA*X( JX )
 IX = JX
 IY = JY
 DO 70, K = KK, KK + N - J
 AP( K ) = AP( K ) + X( IX )*TEMP1 + Y( IY )*TEMP2
 IX = IX + INCX
 IY = IY + INCY
 70 CONTINUE
 END IF
 JX = JX + INCX
 JY = JY + INCY
 KK = KK + N - J + 1
 80 CONTINUE
 END IF
 END IF
*
 RETURN
*
* End of SSPR2 .
*
 END

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Zhang Xianyi 提交于 2011年01月24日 22:54 +08:00 . Import GotoBLAS2 1.13 BSD version codes.

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SUBROUTINECSPR2F(UPLO,N,ALPHA,X,INCX,Y,INCY,AP)
*..ScalarArguments..
COMPLEX*8ALPHA
INTEGERINCX,INCY,N
CHARACTER*1UPLO
*..ArrayArguments..
COMPLEX*8AP(*),X(*),Y(*)
*..
*
*Purpose
*=======
*
*SSPR2performsthesymmetricrank2operation
*
*A:=alpha*x*y' + alpha*y*x'+A,
*
*wherealphaisascalar,xandyarenelementvectorsandAisan
*nbynsymmetricmatrix,suppliedinpackedform.
*
*Parameters
*==========
*
*UPLO-CHARACTER*1.
*Onentry,UPLOspecifieswhethertheupperorlower
*triangularpartofthematrixAissuppliedinthepacked
*arrayAPasfollows:
*
*UPLO='U'or'u'TheuppertriangularpartofAis
*suppliedinAP.
*
*UPLO='L'or'l'ThelowertriangularpartofAis
*suppliedinAP.
*
*Unchangedonexit.
*
*N-INTEGER.
*Onentry,NspecifiestheorderofthematrixA.
*Nmustbeatleastzero.
*Unchangedonexit.
*
*ALPHA-COMPLEX*8.
*Onentry,ALPHAspecifiesthescalaralpha.
*Unchangedonexit.
*
*X-COMPLEX*8arrayofdimensionatleast
*(1+(n-1)*abs(INCX)).
*Beforeentry,theincrementedarrayXmustcontainthen
*elementvectorx.
*Unchangedonexit.
*
*INCX-INTEGER.
*Onentry,INCXspecifiestheincrementfortheelementsof
*X.INCXmustnotbezero.
*Unchangedonexit.
*
*Y-COMPLEX*8arrayofdimensionatleast
*(1+(n-1)*abs(INCY)).
*Beforeentry,theincrementedarrayYmustcontainthen
*elementvectory.
*Unchangedonexit.
*
*INCY-INTEGER.
*Onentry,INCYspecifiestheincrementfortheelementsof
*Y.INCYmustnotbezero.
*Unchangedonexit.
*
*AP-COMPLEX*8arrayofDIMENSIONatleast
*((n*(n+1))/2).
*BeforeentrywithUPLO='U'or'u',thearrayAPmust
*containtheuppertriangularpartofthesymmetricmatrix
*packedsequentially,columnbycolumn,sothatAP(1)
*containsa(1,1),AP(2)andAP(3)containa(1,2)
*anda(2,2)respectively,andsoon.Onexit,thearray
*APisoverwrittenbytheuppertriangularpartofthe
*updatedmatrix.
*BeforeentrywithUPLO='L'or'l',thearrayAPmust
*containthelowertriangularpartofthesymmetricmatrix
*packedsequentially,columnbycolumn,sothatAP(1)
*containsa(1,1),AP(2)andAP(3)containa(2,1)
*anda(3,1)respectively,andsoon.Onexit,thearray
*APisoverwrittenbythelowertriangularpartofthe
*updatedmatrix.
*
*
*Level2Blasroutine.
*
*--Writtenon22-October-1986.
*JackDongarra,ArgonneNationalLab.
*JeremyDuCroz,NagCentralOffice.
*SvenHammarling,NagCentralOffice.
*RichardHanson,SandiaNationalLabs.
*
*
*..Parameters..
COMPLEX*8ZERO
PARAMETER(ZERO=0.0E+0)
*..LocalScalars..
COMPLEX*8TEMP1,TEMP2
INTEGERI,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
*..ExternalFunctions..
LOGICALLSAME
EXTERNALLSAME
*..ExternalSubroutines..
EXTERNALXERBLA
*..
*..ExecutableStatements..
*
*Testtheinputparameters.
*
INFO=0
IF(.NOT.LSAME(UPLO,'U').AND.
$.NOT.LSAME(UPLO,'L'))THEN
INFO=1
ELSEIF(N.LT.0)THEN
INFO=2
ELSEIF(INCX.EQ.0)THEN
INFO=5
ELSEIF(INCY.EQ.0)THEN
INFO=7
ENDIF
IF(INFO.NE.0)THEN
CALLXERBLA('SSPR2 ',INFO)
RETURN
ENDIF
*
*Quickreturnifpossible.
*
IF((N.EQ.0).OR.(ALPHA.EQ.ZERO))
$RETURN
*
*SetupthestartpointsinXandYiftheincrementsarenotboth
*unity.
*
IF((INCX.NE.1).OR.(INCY.NE.1))THEN
IF(INCX.GT.0)THEN
KX=1
ELSE
KX=1-(N-1)*INCX
ENDIF
IF(INCY.GT.0)THEN
KY=1
ELSE
KY=1-(N-1)*INCY
ENDIF
JX=KX
JY=KY
ENDIF
*
*Starttheoperations.InthisversiontheelementsofthearrayAP
*areaccessedsequentiallywithonepassthroughAP.
*
KK=1
IF(LSAME(UPLO,'U'))THEN
*
*FormAwhenuppertriangleisstoredinAP.
*
IF((INCX.EQ.1).AND.(INCY.EQ.1))THEN
DO20,J=1,N
IF((X(J).NE.ZERO).OR.(Y(J).NE.ZERO))THEN
TEMP1=ALPHA*Y(J)
TEMP2=ALPHA*X(J)
K=KK
DO10,I=1,J
AP(K)=AP(K)+X(I)*TEMP1+Y(I)*TEMP2
K=K+1
10CONTINUE
ENDIF
KK=KK+J
20CONTINUE
ELSE
DO40,J=1,N
IF((X(JX).NE.ZERO).OR.(Y(JY).NE.ZERO))THEN
TEMP1=ALPHA*Y(JY)
TEMP2=ALPHA*X(JX)
IX=KX
IY=KY
DO30,K=KK,KK+J-1
AP(K)=AP(K)+X(IX)*TEMP1+Y(IY)*TEMP2
IX=IX+INCX
IY=IY+INCY
30CONTINUE
ENDIF
JX=JX+INCX
JY=JY+INCY
KK=KK+J
40CONTINUE
ENDIF
ELSE
*
*FormAwhenlowertriangleisstoredinAP.
*
IF((INCX.EQ.1).AND.(INCY.EQ.1))THEN
DO60,J=1,N
IF((X(J).NE.ZERO).OR.(Y(J).NE.ZERO))THEN
TEMP1=ALPHA*Y(J)
TEMP2=ALPHA*X(J)
K=KK
DO50,I=J,N
AP(K)=AP(K)+X(I)*TEMP1+Y(I)*TEMP2
K=K+1
50CONTINUE
ENDIF
KK=KK+N-J+1
60CONTINUE
ELSE
DO80,J=1,N
IF((X(JX).NE.ZERO).OR.(Y(JY).NE.ZERO))THEN
TEMP1=ALPHA*Y(JY)
TEMP2=ALPHA*X(JX)
IX=JX
IY=JY
DO70,K=KK,KK+N-J
AP(K)=AP(K)+X(IX)*TEMP1+Y(IY)*TEMP2
IX=IX+INCX
IY=IY+INCY
70CONTINUE
ENDIF
JX=JX+INCX
JY=JY+INCY
KK=KK+N-J+1
80CONTINUE
ENDIF
ENDIF
*
RETURN
*
*EndofSSPR2.
*
END