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OpenBLAS

reference

ssymvf.f

ssymvf.f 7.88 KB

SUBROUTINE SSYMVF ( UPLO, N, ALPHA, A, LDA, X, INCX,
 $ BETA, Y, INCY )
* .. Scalar Arguments ..
 REAL ALPHA, BETA
 INTEGER INCX, INCY, LDA, N
 CHARACTER*1 UPLO
* .. Array Arguments ..
 REAL A( LDA, * ), X( * ), Y( * )
* ..
*
* Purpose
* =======
*
* SSYMV performs the matrix-vector operation
*
* y := alpha*A*x + beta*y,
*
* where alpha and beta are scalars, x and y are n element vectors and
* A is an n by n symmetric matrix.
*
* Parameters
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the upper or lower
* triangular part of the array A is to be referenced as
* follows:
*
* UPLO = 'U' or 'u' Only the upper triangular part of A
* is to be referenced.
*
* UPLO = 'L' or 'l' Only the lower triangular part of A
* is to be referenced.
*
* 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 - REAL .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - REAL array of DIMENSION ( LDA, n ).
* Before entry with UPLO = 'U' or 'u', the leading n by n
* upper triangular part of the array A must contain the upper
* triangular part of the symmetric matrix and the strictly
* lower triangular part of A is not referenced.
* Before entry with UPLO = 'L' or 'l', the leading n by n
* lower triangular part of the array A must contain the lower
* triangular part of the symmetric matrix and the strictly
* upper triangular part of A is not referenced.
* Unchanged on exit.
*
* LDA - INTEGER.
* On entry, LDA specifies the first dimension of A as declared
* in the calling (sub) program. LDA must be at least
* max( 1, n ).
* Unchanged on exit.
*
* X - REAL 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.
*
* BETA - REAL .
* On entry, BETA specifies the scalar beta. When BETA is
* supplied as zero then Y need not be set on input.
* Unchanged on exit.
*
* Y - REAL array of dimension at least
* ( 1 + ( n - 1 )*abs( INCY ) ).
* Before entry, the incremented array Y must contain the n
* element vector y. On exit, Y is overwritten by the updated
* vector y.
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY must not be zero.
* Unchanged on exit.
*
*
* 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 ..
 REAL ONE , ZERO
 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* .. Local Scalars ..
 REAL TEMP1, TEMP2
 INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY
* .. External Functions ..
 LOGICAL LSAME
 EXTERNAL LSAME
* .. External Subroutines ..
 EXTERNAL XERBLA
* .. Intrinsic Functions ..
 INTRINSIC MAX
* ..
* .. 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( LDA.LT.MAX( 1, N ) )THEN
 INFO = 5
 ELSE IF( INCX.EQ.0 )THEN
 INFO = 7
 ELSE IF( INCY.EQ.0 )THEN
 INFO = 10
 END IF
 IF( INFO.NE.0 )THEN
 CALL XERBLA( 'SSYMV ', INFO )
 RETURN
 END IF
*
* Quick return if possible.
*
 IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
 $ RETURN
*
* Set up the start points in X and Y.
*
 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
*
* Start the operations. In this version the elements of A are
* accessed sequentially with one pass through the triangular part
* of A.
*
* First form y := beta*y.
*
 IF( BETA.NE.ONE )THEN
 IF( INCY.EQ.1 )THEN
 IF( BETA.EQ.ZERO )THEN
 DO 10, I = 1, N
 Y( I ) = ZERO
 10 CONTINUE
 ELSE
 DO 20, I = 1, N
 Y( I ) = BETA*Y( I )
 20 CONTINUE
 END IF
 ELSE
 IY = KY
 IF( BETA.EQ.ZERO )THEN
 DO 30, I = 1, N
 Y( IY ) = ZERO
 IY = IY + INCY
 30 CONTINUE
 ELSE
 DO 40, I = 1, N
 Y( IY ) = BETA*Y( IY )
 IY = IY + INCY
 40 CONTINUE
 END IF
 END IF
 END IF
 IF( ALPHA.EQ.ZERO )
 $ RETURN
 IF( LSAME( UPLO, 'U' ) )THEN
*
* Form y when A is stored in upper triangle.
*
 IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
 DO 60, J = 1, N
 TEMP1 = ALPHA*X( J )
 TEMP2 = ZERO
 DO 50, I = 1, J - 1
 Y( I ) = Y( I ) + TEMP1*A( I, J )
 TEMP2 = TEMP2 + A( I, J )*X( I )
 50 CONTINUE
 Y( J ) = Y( J ) + TEMP1*A( J, J ) + ALPHA*TEMP2
 60 CONTINUE
 ELSE
 JX = KX
 JY = KY
 DO 80, J = 1, N
 TEMP1 = ALPHA*X( JX )
 TEMP2 = ZERO
 IX = KX
 IY = KY
 DO 70, I = 1, J - 1
 Y( IY ) = Y( IY ) + TEMP1*A( I, J )
 TEMP2 = TEMP2 + A( I, J )*X( IX )
 IX = IX + INCX
 IY = IY + INCY
 70 CONTINUE
 Y( JY ) = Y( JY ) + TEMP1*A( J, J ) + ALPHA*TEMP2
 JX = JX + INCX
 JY = JY + INCY
 80 CONTINUE
 END IF
 ELSE
*
* Form y when A is stored in lower triangle.
*
 IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
 DO 100, J = 1, N
 TEMP1 = ALPHA*X( J )
 TEMP2 = ZERO
 Y( J ) = Y( J ) + TEMP1*A( J, J )
 DO 90, I = J + 1, N
 Y( I ) = Y( I ) + TEMP1*A( I, J )
 TEMP2 = TEMP2 + A( I, J )*X( I )
 90 CONTINUE
 Y( J ) = Y( J ) + ALPHA*TEMP2
 100 CONTINUE
 ELSE
 JX = KX
 JY = KY
 DO 120, J = 1, N
 TEMP1 = ALPHA*X( JX )
 TEMP2 = ZERO
 Y( JY ) = Y( JY ) + TEMP1*A( J, J )
 IX = JX
 IY = JY
 DO 110, I = J + 1, N
 IX = IX + INCX
 IY = IY + INCY
 Y( IY ) = Y( IY ) + TEMP1*A( I, J )
 TEMP2 = TEMP2 + A( I, J )*X( IX )
 110 CONTINUE
 Y( JY ) = Y( JY ) + ALPHA*TEMP2
 JX = JX + INCX
 JY = JY + INCY
 120 CONTINUE
 END IF
 END IF
*
 RETURN
*
* End of SSYMV .
*
 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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SUBROUTINESSYMVF(UPLO,N,ALPHA,A,LDA,X,INCX,
$BETA,Y,INCY)
*..ScalarArguments..
REALALPHA,BETA
INTEGERINCX,INCY,LDA,N
CHARACTER*1UPLO
*..ArrayArguments..
REALA(LDA,*),X(*),Y(*)
*..
*
*Purpose
*=======
*
*SSYMVperformsthematrix-vectoroperation
*
*y:=alpha*A*x+beta*y,
*
*wherealphaandbetaarescalars,xandyarenelementvectorsand
*Aisannbynsymmetricmatrix.
*
*Parameters
*==========
*
*UPLO-CHARACTER*1.
*Onentry,UPLOspecifieswhethertheupperorlower
*triangularpartofthearrayAistobereferencedas
*follows:
*
*UPLO='U'or'u'OnlytheuppertriangularpartofA
*istobereferenced.
*
*UPLO='L'or'l'OnlythelowertriangularpartofA
*istobereferenced.
*
*Unchangedonexit.
*
*N-INTEGER.
*Onentry,NspecifiestheorderofthematrixA.
*Nmustbeatleastzero.
*Unchangedonexit.
*
*ALPHA-REAL.
*Onentry,ALPHAspecifiesthescalaralpha.
*Unchangedonexit.
*
*A-REALarrayofDIMENSION(LDA,n).
*BeforeentrywithUPLO='U'or'u',theleadingnbyn
*uppertriangularpartofthearrayAmustcontaintheupper
*triangularpartofthesymmetricmatrixandthestrictly
*lowertriangularpartofAisnotreferenced.
*BeforeentrywithUPLO='L'or'l',theleadingnbyn
*lowertriangularpartofthearrayAmustcontainthelower
*triangularpartofthesymmetricmatrixandthestrictly
*uppertriangularpartofAisnotreferenced.
*Unchangedonexit.
*
*LDA-INTEGER.
*Onentry,LDAspecifiesthefirstdimensionofAasdeclared
*inthecalling(sub)program.LDAmustbeatleast
*max(1,n).
*Unchangedonexit.
*
*X-REALarrayofdimensionatleast
*(1+(n-1)*abs(INCX)).
*Beforeentry,theincrementedarrayXmustcontainthen
*elementvectorx.
*Unchangedonexit.
*
*INCX-INTEGER.
*Onentry,INCXspecifiestheincrementfortheelementsof
*X.INCXmustnotbezero.
*Unchangedonexit.
*
*BETA-REAL.
*Onentry,BETAspecifiesthescalarbeta.WhenBETAis
*suppliedaszerothenYneednotbesetoninput.
*Unchangedonexit.
*
*Y-REALarrayofdimensionatleast
*(1+(n-1)*abs(INCY)).
*Beforeentry,theincrementedarrayYmustcontainthen
*elementvectory.Onexit,Yisoverwrittenbytheupdated
*vectory.
*
*INCY-INTEGER.
*Onentry,INCYspecifiestheincrementfortheelementsof
*Y.INCYmustnotbezero.
*Unchangedonexit.
*
*
*Level2Blasroutine.
*
*--Writtenon22-October-1986.
*JackDongarra,ArgonneNationalLab.
*JeremyDuCroz,NagCentralOffice.
*SvenHammarling,NagCentralOffice.
*RichardHanson,SandiaNationalLabs.
*
*
*..Parameters..
REALONE,ZERO
PARAMETER(ONE=1.0E+0,ZERO=0.0E+0)
*..LocalScalars..
REALTEMP1,TEMP2
INTEGERI,INFO,IX,IY,J,JX,JY,KX,KY
*..ExternalFunctions..
LOGICALLSAME
EXTERNALLSAME
*..ExternalSubroutines..
EXTERNALXERBLA
*..IntrinsicFunctions..
INTRINSICMAX
*..
*..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(LDA.LT.MAX(1,N))THEN
INFO=5
ELSEIF(INCX.EQ.0)THEN
INFO=7
ELSEIF(INCY.EQ.0)THEN
INFO=10
ENDIF
IF(INFO.NE.0)THEN
CALLXERBLA('SSYMV ',INFO)
RETURN
ENDIF
*
*Quickreturnifpossible.
*
IF((N.EQ.0).OR.((ALPHA.EQ.ZERO).AND.(BETA.EQ.ONE)))
$RETURN
*
*SetupthestartpointsinXandY.
*
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
*
*Starttheoperations.InthisversiontheelementsofAare
*accessedsequentiallywithonepassthroughthetriangularpart
*ofA.
*
*Firstformy:=beta*y.
*
IF(BETA.NE.ONE)THEN
IF(INCY.EQ.1)THEN
IF(BETA.EQ.ZERO)THEN
DO10,I=1,N
Y(I)=ZERO
10CONTINUE
ELSE
DO20,I=1,N
Y(I)=BETA*Y(I)
20CONTINUE
ENDIF
ELSE
IY=KY
IF(BETA.EQ.ZERO)THEN
DO30,I=1,N
Y(IY)=ZERO
IY=IY+INCY
30CONTINUE
ELSE
DO40,I=1,N
Y(IY)=BETA*Y(IY)
IY=IY+INCY
40CONTINUE
ENDIF
ENDIF
ENDIF
IF(ALPHA.EQ.ZERO)
$RETURN
IF(LSAME(UPLO,'U'))THEN
*
*FormywhenAisstoredinuppertriangle.
*
IF((INCX.EQ.1).AND.(INCY.EQ.1))THEN
DO60,J=1,N
TEMP1=ALPHA*X(J)
TEMP2=ZERO
DO50,I=1,J-1
Y(I)=Y(I)+TEMP1*A(I,J)
TEMP2=TEMP2+A(I,J)*X(I)
50CONTINUE
Y(J)=Y(J)+TEMP1*A(J,J)+ALPHA*TEMP2
60CONTINUE
ELSE
JX=KX
JY=KY
DO80,J=1,N
TEMP1=ALPHA*X(JX)
TEMP2=ZERO
IX=KX
IY=KY
DO70,I=1,J-1
Y(IY)=Y(IY)+TEMP1*A(I,J)
TEMP2=TEMP2+A(I,J)*X(IX)
IX=IX+INCX
IY=IY+INCY
70CONTINUE
Y(JY)=Y(JY)+TEMP1*A(J,J)+ALPHA*TEMP2
JX=JX+INCX
JY=JY+INCY
80CONTINUE
ENDIF
ELSE
*
*FormywhenAisstoredinlowertriangle.
*
IF((INCX.EQ.1).AND.(INCY.EQ.1))THEN
DO100,J=1,N
TEMP1=ALPHA*X(J)
TEMP2=ZERO
Y(J)=Y(J)+TEMP1*A(J,J)
DO90,I=J+1,N
Y(I)=Y(I)+TEMP1*A(I,J)
TEMP2=TEMP2+A(I,J)*X(I)
90CONTINUE
Y(J)=Y(J)+ALPHA*TEMP2
100CONTINUE
ELSE
JX=KX
JY=KY
DO120,J=1,N
TEMP1=ALPHA*X(JX)
TEMP2=ZERO
Y(JY)=Y(JY)+TEMP1*A(J,J)
IX=JX
IY=JY
DO110,I=J+1,N
IX=IX+INCX
IY=IY+INCY
Y(IY)=Y(IY)+TEMP1*A(I,J)
TEMP2=TEMP2+A(I,J)*X(IX)
110CONTINUE
Y(JY)=Y(JY)+ALPHA*TEMP2
JX=JX+INCX
JY=JY+INCY
120CONTINUE
ENDIF
ENDIF
*
RETURN
*
*EndofSSYMV.
*
END