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dsbmvf.f

dsbmvf.f 9.60 KB

SUBROUTINE DSBMVF( UPLO, N, K, ALPHA, A, LDA, X, INCX,
 $ BETA, Y, INCY )
* .. Scalar Arguments ..
 DOUBLE PRECISION ALPHA, BETA
 INTEGER INCX, INCY, K, LDA, N
 CHARACTER*1 UPLO
* .. Array Arguments ..
 DOUBLE PRECISION A( LDA, * ), X( * ), Y( * )
* ..
*
* Purpose
* =======
*
* DSBMV 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 band matrix, with k super-diagonals.
*
* Parameters
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the upper or lower
* triangular part of the band matrix A is being supplied as
* follows:
*
* UPLO = 'U' or 'u' The upper triangular part of A is
* being supplied.
*
* UPLO = 'L' or 'l' The lower triangular part of A is
* being supplied.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* K - INTEGER.
* On entry, K specifies the number of super-diagonals of the
* matrix A. K must satisfy 0 .le. K.
* Unchanged on exit.
*
* ALPHA - DOUBLE PRECISION.
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - DOUBLE PRECISION array of DIMENSION ( LDA, n ).
* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
* by n part of the array A must contain the upper triangular
* band part of the symmetric matrix, supplied column by
* column, with the leading diagonal of the matrix in row
* ( k + 1 ) of the array, the first super-diagonal starting at
* position 2 in row k, and so on. The top left k by k triangle
* of the array A is not referenced.
* The following program segment will transfer the upper
* triangular part of a symmetric band matrix from conventional
* full matrix storage to band storage:
*
* DO 20, J = 1, N
* M = K + 1 - J
* DO 10, I = MAX( 1, J - K ), J
* A( M + I, J ) = matrix( I, J )
* 10 CONTINUE
* 20 CONTINUE
*
* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
* by n part of the array A must contain the lower triangular
* band part of the symmetric matrix, supplied column by
* column, with the leading diagonal of the matrix in row 1 of
* the array, the first sub-diagonal starting at position 1 in
* row 2, and so on. The bottom right k by k triangle of the
* array A is not referenced.
* The following program segment will transfer the lower
* triangular part of a symmetric band matrix from conventional
* full matrix storage to band storage:
*
* DO 20, J = 1, N
* M = 1 - J
* DO 10, I = J, MIN( N, J + K )
* A( M + I, J ) = matrix( I, J )
* 10 CONTINUE
* 20 CONTINUE
*
* 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
* ( k + 1 ).
* Unchanged on exit.
*
* X - DOUBLE PRECISION array of DIMENSION at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the
* 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 - DOUBLE PRECISION.
* On entry, BETA specifies the scalar beta.
* Unchanged on exit.
*
* Y - DOUBLE PRECISION array of DIMENSION at least
* ( 1 + ( n - 1 )*abs( INCY ) ).
* Before entry, the incremented array Y must contain the
* 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 ..
 DOUBLE PRECISION ONE , ZERO
 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* .. Local Scalars ..
 DOUBLE PRECISION TEMP1, TEMP2
 INTEGER I, INFO, IX, IY, J, JX, JY, KPLUS1, KX, KY, L
* .. External Functions ..
 LOGICAL LSAME
 EXTERNAL LSAME
* .. External Subroutines ..
 EXTERNAL XERBLA
* .. Intrinsic Functions ..
 INTRINSIC MAX, MIN
* ..
* .. 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( K.LT.0 )THEN
 INFO = 3
 ELSE IF( LDA.LT.( K + 1 ) )THEN
 INFO = 6
 ELSE IF( INCX.EQ.0 )THEN
 INFO = 8
 ELSE IF( INCY.EQ.0 )THEN
 INFO = 11
 END IF
 IF( INFO.NE.0 )THEN
 CALL XERBLA( 'DSBMV ', 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 the array A
* are accessed sequentially with one pass through 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 upper triangle of A is stored.
*
 KPLUS1 = K + 1
 IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
 DO 60, J = 1, N
 TEMP1 = ALPHA*X( J )
 TEMP2 = ZERO
 L = KPLUS1 - J
 DO 50, I = MAX( 1, J - K ), J - 1
 Y( I ) = Y( I ) + TEMP1*A( L + I, J )
 TEMP2 = TEMP2 + A( L + I, J )*X( I )
 50 CONTINUE
 Y( J ) = Y( J ) + TEMP1*A( KPLUS1, 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
 L = KPLUS1 - J
 DO 70, I = MAX( 1, J - K ), J - 1
 Y( IY ) = Y( IY ) + TEMP1*A( L + I, J )
 TEMP2 = TEMP2 + A( L + I, J )*X( IX )
 IX = IX + INCX
 IY = IY + INCY
 70 CONTINUE
 Y( JY ) = Y( JY ) + TEMP1*A( KPLUS1, J ) + ALPHA*TEMP2
 JX = JX + INCX
 JY = JY + INCY
 IF( J.GT.K )THEN
 KX = KX + INCX
 KY = KY + INCY
 END IF
 80 CONTINUE
 END IF
 ELSE
*
* Form y when lower triangle of A is stored.
*
 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( 1, J )
 L = 1 - J
 DO 90, I = J + 1, MIN( N, J + K )
 Y( I ) = Y( I ) + TEMP1*A( L + I, J )
 TEMP2 = TEMP2 + A( L + 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( 1, J )
 L = 1 - J
 IX = JX
 IY = JY
 DO 110, I = J + 1, MIN( N, J + K )
 IX = IX + INCX
 IY = IY + INCY
 Y( IY ) = Y( IY ) + TEMP1*A( L + I, J )
 TEMP2 = TEMP2 + A( L + 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 DSBMV .
*
 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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SUBROUTINEDSBMVF(UPLO,N,K,ALPHA,A,LDA,X,INCX,
$BETA,Y,INCY)
*..ScalarArguments..
DOUBLE PRECISIONALPHA,BETA
INTEGERINCX,INCY,K,LDA,N
CHARACTER*1UPLO
*..ArrayArguments..
DOUBLE PRECISIONA(LDA,*),X(*),Y(*)
*..
*
*Purpose
*=======
*
*DSBMVperformsthematrix-vectoroperation
*
*y:=alpha*A*x+beta*y,
*
*wherealphaandbetaarescalars,xandyarenelementvectorsand
*Aisannbynsymmetricbandmatrix,withksuper-diagonals.
*
*Parameters
*==========
*
*UPLO-CHARACTER*1.
*Onentry,UPLOspecifieswhethertheupperorlower
*triangularpartofthebandmatrixAisbeingsuppliedas
*follows:
*
*UPLO='U'or'u'TheuppertriangularpartofAis
*beingsupplied.
*
*UPLO='L'or'l'ThelowertriangularpartofAis
*beingsupplied.
*
*Unchangedonexit.
*
*N-INTEGER.
*Onentry,NspecifiestheorderofthematrixA.
*Nmustbeatleastzero.
*Unchangedonexit.
*
*K-INTEGER.
*Onentry,Kspecifiesthenumberofsuper-diagonalsofthe
*matrixA.Kmustsatisfy0.le.K.
*Unchangedonexit.
*
*ALPHA-DOUBLE PRECISION.
*Onentry,ALPHAspecifiesthescalaralpha.
*Unchangedonexit.
*
*A-DOUBLE PRECISIONarrayofDIMENSION(LDA,n).
*BeforeentrywithUPLO='U'or'u',theleading(k+1)
*bynpartofthearrayAmustcontaintheuppertriangular
*bandpartofthesymmetricmatrix,suppliedcolumnby
*column,withtheleadingdiagonalofthematrixinrow
*(k+1)ofthearray,thefirstsuper-diagonalstartingat
*position2inrowk,andsoon.Thetopleftkbyktriangle
*ofthearrayAisnotreferenced.
*Thefollowingprogramsegmentwilltransfertheupper
*triangularpartofasymmetricbandmatrixfromconventional
*fullmatrixstoragetobandstorage:
*
*DO20,J=1,N
*M=K+1-J
*DO10,I=MAX(1,J-K),J
*A(M+I,J)=matrix(I,J)
*10CONTINUE
*20CONTINUE
*
*BeforeentrywithUPLO='L'or'l',theleading(k+1)
*bynpartofthearrayAmustcontainthelowertriangular
*bandpartofthesymmetricmatrix,suppliedcolumnby
*column,withtheleadingdiagonalofthematrixinrow1of
*thearray,thefirstsub-diagonalstartingatposition1in
*row2,andsoon.Thebottomrightkbyktriangleofthe
*arrayAisnotreferenced.
*Thefollowingprogramsegmentwilltransferthelower
*triangularpartofasymmetricbandmatrixfromconventional
*fullmatrixstoragetobandstorage:
*
*DO20,J=1,N
*M=1-J
*DO10,I=J,MIN(N,J+K)
*A(M+I,J)=matrix(I,J)
*10CONTINUE
*20CONTINUE
*
*Unchangedonexit.
*
*LDA-INTEGER.
*Onentry,LDAspecifiesthefirstdimensionofAasdeclared
*inthecalling(sub)program.LDAmustbeatleast
*(k+1).
*Unchangedonexit.
*
*X-DOUBLE PRECISIONarrayofDIMENSIONatleast
*(1+(n-1)*abs(INCX)).
*Beforeentry,theincrementedarrayXmustcontainthe
*vectorx.
*Unchangedonexit.
*
*INCX-INTEGER.
*Onentry,INCXspecifiestheincrementfortheelementsof
*X.INCXmustnotbezero.
*Unchangedonexit.
*
*BETA-DOUBLE PRECISION.
*Onentry,BETAspecifiesthescalarbeta.
*Unchangedonexit.
*
*Y-DOUBLE PRECISIONarrayofDIMENSIONatleast
*(1+(n-1)*abs(INCY)).
*Beforeentry,theincrementedarrayYmustcontainthe
*vectory.Onexit,Yisoverwrittenbytheupdatedvectory.
*
*INCY-INTEGER.
*Onentry,INCYspecifiestheincrementfortheelementsof
*Y.INCYmustnotbezero.
*Unchangedonexit.
*
*
*Level2Blasroutine.
*
*--Writtenon22-October-1986.
*JackDongarra,ArgonneNationalLab.
*JeremyDuCroz,NagCentralOffice.
*SvenHammarling,NagCentralOffice.
*RichardHanson,SandiaNationalLabs.
*
*
*..Parameters..
DOUBLE PRECISIONONE,ZERO
PARAMETER(ONE=1.0D+0,ZERO=0.0D+0)
*..LocalScalars..
DOUBLE PRECISIONTEMP1,TEMP2
INTEGERI,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
*..ExternalFunctions..
LOGICALLSAME
EXTERNALLSAME
*..ExternalSubroutines..
EXTERNALXERBLA
*..IntrinsicFunctions..
INTRINSICMAX,MIN
*..
*..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(K.LT.0)THEN
INFO=3
ELSEIF(LDA.LT.(K+1))THEN
INFO=6
ELSEIF(INCX.EQ.0)THEN
INFO=8
ELSEIF(INCY.EQ.0)THEN
INFO=11
ENDIF
IF(INFO.NE.0)THEN
CALLXERBLA('DSBMV ',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.InthisversiontheelementsofthearrayA
*areaccessedsequentiallywithonepassthroughA.
*
*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
*
*FormywhenuppertriangleofAisstored.
*
KPLUS1=K+1
IF((INCX.EQ.1).AND.(INCY.EQ.1))THEN
DO60,J=1,N
TEMP1=ALPHA*X(J)
TEMP2=ZERO
L=KPLUS1-J
DO50,I=MAX(1,J-K),J-1
Y(I)=Y(I)+TEMP1*A(L+I,J)
TEMP2=TEMP2+A(L+I,J)*X(I)
50CONTINUE
Y(J)=Y(J)+TEMP1*A(KPLUS1,J)+ALPHA*TEMP2
60CONTINUE
ELSE
JX=KX
JY=KY
DO80,J=1,N
TEMP1=ALPHA*X(JX)
TEMP2=ZERO
IX=KX
IY=KY
L=KPLUS1-J
DO70,I=MAX(1,J-K),J-1
Y(IY)=Y(IY)+TEMP1*A(L+I,J)
TEMP2=TEMP2+A(L+I,J)*X(IX)
IX=IX+INCX
IY=IY+INCY
70CONTINUE
Y(JY)=Y(JY)+TEMP1*A(KPLUS1,J)+ALPHA*TEMP2
JX=JX+INCX
JY=JY+INCY
IF(J.GT.K)THEN
KX=KX+INCX
KY=KY+INCY
ENDIF
80CONTINUE
ENDIF
ELSE
*
*FormywhenlowertriangleofAisstored.
*
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(1,J)
L=1-J
DO90,I=J+1,MIN(N,J+K)
Y(I)=Y(I)+TEMP1*A(L+I,J)
TEMP2=TEMP2+A(L+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(1,J)
L=1-J
IX=JX
IY=JY
DO110,I=J+1,MIN(N,J+K)
IX=IX+INCX
IY=IY+INCY
Y(IY)=Y(IY)+TEMP1*A(L+I,J)
TEMP2=TEMP2+A(L+I,J)*X(IX)
110CONTINUE
Y(JY)=Y(JY)+ALPHA*TEMP2
JX=JX+INCX
JY=JY+INCY
120CONTINUE
ENDIF
ENDIF
*
RETURN
*
*EndofDSBMV.
*
END