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reference

ctbsvf.f

ctbsvf.f 12.39 KB

SUBROUTINE CTBSVF(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
* .. Scalar Arguments ..
 INTEGER INCX,K,LDA,N
 CHARACTER DIAG,TRANS,UPLO
* ..
* .. Array Arguments ..
 COMPLEX A(LDA,*),X(*)
* ..
*
* Purpose
* =======
*
* CTBSV solves one of the systems of equations
*
* A*x = b, or A'*x = b, or conjg( A' )*x = b,
*
* where b and x are n element vectors and A is an n by n unit, or
* non-unit, upper or lower triangular band matrix, with ( k + 1 )
* diagonals.
*
* No test for singularity or near-singularity is included in this
* routine. Such tests must be performed before calling this routine.
*
* Arguments
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the matrix is an upper or
* lower triangular matrix as follows:
*
* UPLO = 'U' or 'u' A is an upper triangular matrix.
*
* UPLO = 'L' or 'l' A is a lower triangular matrix.
*
* Unchanged on exit.
*
* TRANS - CHARACTER*1.
* On entry, TRANS specifies the equations to be solved as
* follows:
*
* TRANS = 'N' or 'n' A*x = b.
*
* TRANS = 'T' or 't' A'*x = b.
*
* TRANS = 'C' or 'c' conjg( A' )*x = b.
*
* Unchanged on exit.
*
* DIAG - CHARACTER*1.
* On entry, DIAG specifies whether or not A is unit
* triangular as follows:
*
* DIAG = 'U' or 'u' A is assumed to be unit triangular.
*
* DIAG = 'N' or 'n' A is not assumed to be unit
* triangular.
*
* 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 with UPLO = 'U' or 'u', K specifies the number of
* super-diagonals of the matrix A.
* On entry with UPLO = 'L' or 'l', K specifies the number of
* sub-diagonals of the matrix A.
* K must satisfy 0 .le. K.
* Unchanged on exit.
*
* A - COMPLEX 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 matrix of coefficients, 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 an upper
* triangular 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 matrix of coefficients, 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 a lower
* triangular 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
*
* Note that when DIAG = 'U' or 'u' the elements of the array A
* corresponding to the diagonal elements of the matrix are not
* referenced, but are assumed to be unity.
* 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 - COMPLEX array of dimension at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the n
* element right-hand side vector b. On exit, X is overwritten
* with the solution vector x.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX 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 ..
 COMPLEX ZERO
 PARAMETER (ZERO= (0.0E+0,0.0E+0))
* ..
* .. Local Scalars ..
 COMPLEX TEMP
 INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
 LOGICAL NOCONJ,NOUNIT
* ..
* .. External Functions ..
 LOGICAL LSAME
 EXTERNAL LSAME
* ..
* .. External Subroutines ..
 EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
 INTRINSIC CONJG,MAX,MIN
* ..
*
* Test the input parameters.
*
 INFO = 0
 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
 INFO = 1
 ELSE IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
 + .NOT.LSAME(TRANS,'C')) THEN
 INFO = 2
 ELSE IF (.NOT.LSAME(DIAG,'U') .AND. .NOT.LSAME(DIAG,'N')) THEN
 INFO = 3
 ELSE IF (N.LT.0) THEN
 INFO = 4
 ELSE IF (K.LT.0) THEN
 INFO = 5
 ELSE IF (LDA.LT. (K+1)) THEN
 INFO = 7
 ELSE IF (INCX.EQ.0) THEN
 INFO = 9
 END IF
 IF (INFO.NE.0) THEN
 CALL XERBLA('CTBSV ',INFO)
 RETURN
 END IF
*
* Quick return if possible.
*
 IF (N.EQ.0) RETURN
*
 NOCONJ = LSAME(TRANS,'T')
 NOUNIT = LSAME(DIAG,'N')
*
* Set up the start point in X if the increment is not unity. This
* will be ( N - 1 )*INCX too small for descending loops.
*
 IF (INCX.LE.0) THEN
 KX = 1 - (N-1)*INCX
 ELSE IF (INCX.NE.1) THEN
 KX = 1
 END IF
*
* Start the operations. In this version the elements of A are
* accessed by sequentially with one pass through A.
*
 IF (LSAME(TRANS,'N')) THEN
*
* Form x := inv( A )*x.
*
 IF (LSAME(UPLO,'U')) THEN
 KPLUS1 = K + 1
 IF (INCX.EQ.1) THEN
 DO 20 J = N,1,-1
 IF (X(J).NE.ZERO) THEN
 L = KPLUS1 - J
 IF (NOUNIT) X(J) = X(J)/A(KPLUS1,J)
 TEMP = X(J)
 DO 10 I = J - 1,MAX(1,J-K),-1
 X(I) = X(I) - TEMP*A(L+I,J)
 10 CONTINUE
 END IF
 20 CONTINUE
 ELSE
 KX = KX + (N-1)*INCX
 JX = KX
 DO 40 J = N,1,-1
 KX = KX - INCX
 IF (X(JX).NE.ZERO) THEN
 IX = KX
 L = KPLUS1 - J
 IF (NOUNIT) X(JX) = X(JX)/A(KPLUS1,J)
 TEMP = X(JX)
 DO 30 I = J - 1,MAX(1,J-K),-1
 X(IX) = X(IX) - TEMP*A(L+I,J)
 IX = IX - INCX
 30 CONTINUE
 END IF
 JX = JX - INCX
 40 CONTINUE
 END IF
 ELSE
 IF (INCX.EQ.1) THEN
 DO 60 J = 1,N
 IF (X(J).NE.ZERO) THEN
 L = 1 - J
 IF (NOUNIT) X(J) = X(J)/A(1,J)
 TEMP = X(J)
 DO 50 I = J + 1,MIN(N,J+K)
 X(I) = X(I) - TEMP*A(L+I,J)
 50 CONTINUE
 END IF
 60 CONTINUE
 ELSE
 JX = KX
 DO 80 J = 1,N
 KX = KX + INCX
 IF (X(JX).NE.ZERO) THEN
 IX = KX
 L = 1 - J
 IF (NOUNIT) X(JX) = X(JX)/A(1,J)
 TEMP = X(JX)
 DO 70 I = J + 1,MIN(N,J+K)
 X(IX) = X(IX) - TEMP*A(L+I,J)
 IX = IX + INCX
 70 CONTINUE
 END IF
 JX = JX + INCX
 80 CONTINUE
 END IF
 END IF
 ELSE
*
* Form x := inv( A' )*x or x := inv( conjg( A') )*x.
*
 IF (LSAME(UPLO,'U')) THEN
 KPLUS1 = K + 1
 IF (INCX.EQ.1) THEN
 DO 110 J = 1,N
 TEMP = X(J)
 L = KPLUS1 - J
 IF (NOCONJ) THEN
 DO 90 I = MAX(1,J-K),J - 1
 TEMP = TEMP - A(L+I,J)*X(I)
 90 CONTINUE
 IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
 ELSE
 DO 100 I = MAX(1,J-K),J - 1
 TEMP = TEMP - CONJG(A(L+I,J))*X(I)
 100 CONTINUE
 IF (NOUNIT) TEMP = TEMP/CONJG(A(KPLUS1,J))
 END IF
 X(J) = TEMP
 110 CONTINUE
 ELSE
 JX = KX
 DO 140 J = 1,N
 TEMP = X(JX)
 IX = KX
 L = KPLUS1 - J
 IF (NOCONJ) THEN
 DO 120 I = MAX(1,J-K),J - 1
 TEMP = TEMP - A(L+I,J)*X(IX)
 IX = IX + INCX
 120 CONTINUE
 IF (NOUNIT) TEMP = TEMP/A(KPLUS1,J)
 ELSE
 DO 130 I = MAX(1,J-K),J - 1
 TEMP = TEMP - CONJG(A(L+I,J))*X(IX)
 IX = IX + INCX
 130 CONTINUE
 IF (NOUNIT) TEMP = TEMP/CONJG(A(KPLUS1,J))
 END IF
 X(JX) = TEMP
 JX = JX + INCX
 IF (J.GT.K) KX = KX + INCX
 140 CONTINUE
 END IF
 ELSE
 IF (INCX.EQ.1) THEN
 DO 170 J = N,1,-1
 TEMP = X(J)
 L = 1 - J
 IF (NOCONJ) THEN
 DO 150 I = MIN(N,J+K),J + 1,-1
 TEMP = TEMP - A(L+I,J)*X(I)
 150 CONTINUE
 IF (NOUNIT) TEMP = TEMP/A(1,J)
 ELSE
 DO 160 I = MIN(N,J+K),J + 1,-1
 TEMP = TEMP - CONJG(A(L+I,J))*X(I)
 160 CONTINUE
 IF (NOUNIT) TEMP = TEMP/CONJG(A(1,J))
 END IF
 X(J) = TEMP
 170 CONTINUE
 ELSE
 KX = KX + (N-1)*INCX
 JX = KX
 DO 200 J = N,1,-1
 TEMP = X(JX)
 IX = KX
 L = 1 - J
 IF (NOCONJ) THEN
 DO 180 I = MIN(N,J+K),J + 1,-1
 TEMP = TEMP - A(L+I,J)*X(IX)
 IX = IX - INCX
 180 CONTINUE
 IF (NOUNIT) TEMP = TEMP/A(1,J)
 ELSE
 DO 190 I = MIN(N,J+K),J + 1,-1
 TEMP = TEMP - CONJG(A(L+I,J))*X(IX)
 IX = IX - INCX
 190 CONTINUE
 IF (NOUNIT) TEMP = TEMP/CONJG(A(1,J))
 END IF
 X(JX) = TEMP
 JX = JX - INCX
 IF ((N-J).GE.K) KX = KX - INCX
 200 CONTINUE
 END IF
 END IF
 END IF
*
 RETURN
*
* End of CTBSV .
*
 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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SUBROUTINECTBSVF(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
*..ScalarArguments..
INTEGERINCX,K,LDA,N
CHARACTERDIAG,TRANS,UPLO
*..
*..ArrayArguments..
COMPLEXA(LDA,*),X(*)
*..
*
*Purpose
*=======
*
*CTBSVsolvesoneofthesystemsofequations
*
*A*x=b,orA'*x = b, or conjg( A')*x=b,
*
*wherebandxarenelementvectorsandAisannbynunit,or
*non-unit,upperorlowertriangularbandmatrix,with(k+1)
*diagonals.
*
*Notestforsingularityornear-singularityisincludedinthis
*routine.Suchtestsmustbeperformedbeforecallingthisroutine.
*
*Arguments
*==========
*
*UPLO-CHARACTER*1.
*Onentry,UPLOspecifieswhetherthematrixisanupperor
*lowertriangularmatrixasfollows:
*
*UPLO='U'or'u'Aisanuppertriangularmatrix.
*
*UPLO='L'or'l'Aisalowertriangularmatrix.
*
*Unchangedonexit.
*
*TRANS-CHARACTER*1.
*Onentry,TRANSspecifiestheequationstobesolvedas
*follows:
*
*TRANS='N'or'n'A*x=b.
*
*TRANS='T'or't'A'*x = b.
*
* TRANS = 'C' or 'c' conjg( A')*x=b.
*
*Unchangedonexit.
*
*DIAG-CHARACTER*1.
*Onentry,DIAGspecifieswhetherornotAisunit
*triangularasfollows:
*
*DIAG='U'or'u'Aisassumedtobeunittriangular.
*
*DIAG='N'or'n'Aisnotassumedtobeunit
*triangular.
*
*Unchangedonexit.
*
*N-INTEGER.
*Onentry,NspecifiestheorderofthematrixA.
*Nmustbeatleastzero.
*Unchangedonexit.
*
*K-INTEGER.
*OnentrywithUPLO='U'or'u',Kspecifiesthenumberof
*super-diagonalsofthematrixA.
*OnentrywithUPLO='L'or'l',Kspecifiesthenumberof
*sub-diagonalsofthematrixA.
*Kmustsatisfy0.le.K.
*Unchangedonexit.
*
*A-COMPLEXarrayofDIMENSION(LDA,n).
*BeforeentrywithUPLO='U'or'u',theleading(k+1)
*bynpartofthearrayAmustcontaintheuppertriangular
*bandpartofthematrixofcoefficients,suppliedcolumnby
*column,withtheleadingdiagonalofthematrixinrow
*(k+1)ofthearray,thefirstsuper-diagonalstartingat
*position2inrowk,andsoon.Thetopleftkbyktriangle
*ofthearrayAisnotreferenced.
*Thefollowingprogramsegmentwilltransferanupper
*triangularbandmatrixfromconventionalfullmatrixstorage
*tobandstorage:
*
*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
*bandpartofthematrixofcoefficients,suppliedcolumnby
*column,withtheleadingdiagonalofthematrixinrow1of
*thearray,thefirstsub-diagonalstartingatposition1in
*row2,andsoon.Thebottomrightkbyktriangleofthe
*arrayAisnotreferenced.
*Thefollowingprogramsegmentwilltransferalower
*triangularbandmatrixfromconventionalfullmatrixstorage
*tobandstorage:
*
*DO20,J=1,N
*M=1-J
*DO10,I=J,MIN(N,J+K)
*A(M+I,J)=matrix(I,J)
*10CONTINUE
*20CONTINUE
*
*NotethatwhenDIAG='U'or'u'theelementsofthearrayA
*correspondingtothediagonalelementsofthematrixarenot
*referenced,butareassumedtobeunity.
*Unchangedonexit.
*
*LDA-INTEGER.
*Onentry,LDAspecifiesthefirstdimensionofAasdeclared
*inthecalling(sub)program.LDAmustbeatleast
*(k+1).
*Unchangedonexit.
*
*X-COMPLEXarrayofdimensionatleast
*(1+(n-1)*abs(INCX)).
*Beforeentry,theincrementedarrayXmustcontainthen
*elementright-handsidevectorb.Onexit,Xisoverwritten
*withthesolutionvectorx.
*
*INCX-INTEGER.
*Onentry,INCXspecifiestheincrementfortheelementsof
*X.INCXmustnotbezero.
*Unchangedonexit.
*
*
*Level2Blasroutine.
*
*--Writtenon22-October-1986.
*JackDongarra,ArgonneNationalLab.
*JeremyDuCroz,NagCentralOffice.
*SvenHammarling,NagCentralOffice.
*RichardHanson,SandiaNationalLabs.
*
*
*..Parameters..
COMPLEXZERO
PARAMETER(ZERO=(0.0E+0,0.0E+0))
*..
*..LocalScalars..
COMPLEXTEMP
INTEGERI,INFO,IX,J,JX,KPLUS1,KX,L
LOGICALNOCONJ,NOUNIT
*..
*..ExternalFunctions..
LOGICALLSAME
EXTERNALLSAME
*..
*..ExternalSubroutines..
EXTERNALXERBLA
*..
*..IntrinsicFunctions..
INTRINSICCONJG,MAX,MIN
*..
*
*Testtheinputparameters.
*
INFO=0
IF(.NOT.LSAME(UPLO,'U').AND..NOT.LSAME(UPLO,'L'))THEN
INFO=1
ELSEIF(.NOT.LSAME(TRANS,'N').AND..NOT.LSAME(TRANS,'T').AND.
+.NOT.LSAME(TRANS,'C'))THEN
INFO=2
ELSEIF(.NOT.LSAME(DIAG,'U').AND..NOT.LSAME(DIAG,'N'))THEN
INFO=3
ELSEIF(N.LT.0)THEN
INFO=4
ELSEIF(K.LT.0)THEN
INFO=5
ELSEIF(LDA.LT.(K+1))THEN
INFO=7
ELSEIF(INCX.EQ.0)THEN
INFO=9
ENDIF
IF(INFO.NE.0)THEN
CALLXERBLA('CTBSV ',INFO)
RETURN
ENDIF
*
*Quickreturnifpossible.
*
IF(N.EQ.0)RETURN
*
NOCONJ=LSAME(TRANS,'T')
NOUNIT=LSAME(DIAG,'N')
*
*SetupthestartpointinXiftheincrementisnotunity.This
*willbe(N-1)*INCXtoosmallfordescendingloops.
*
IF(INCX.LE.0)THEN
KX=1-(N-1)*INCX
ELSEIF(INCX.NE.1)THEN
KX=1
ENDIF
*
*Starttheoperations.InthisversiontheelementsofAare
*accessedbysequentiallywithonepassthroughA.
*
IF(LSAME(TRANS,'N'))THEN
*
*Formx:=inv(A)*x.
*
IF(LSAME(UPLO,'U'))THEN
KPLUS1=K+1
IF(INCX.EQ.1)THEN
DO20J=N,1,-1
IF(X(J).NE.ZERO)THEN
L=KPLUS1-J
IF(NOUNIT)X(J)=X(J)/A(KPLUS1,J)
TEMP=X(J)
DO10I=J-1,MAX(1,J-K),-1
X(I)=X(I)-TEMP*A(L+I,J)
10CONTINUE
ENDIF
20CONTINUE
ELSE
KX=KX+(N-1)*INCX
JX=KX
DO40J=N,1,-1
KX=KX-INCX
IF(X(JX).NE.ZERO)THEN
IX=KX
L=KPLUS1-J
IF(NOUNIT)X(JX)=X(JX)/A(KPLUS1,J)
TEMP=X(JX)
DO30I=J-1,MAX(1,J-K),-1
X(IX)=X(IX)-TEMP*A(L+I,J)
IX=IX-INCX
30CONTINUE
ENDIF
JX=JX-INCX
40CONTINUE
ENDIF
ELSE
IF(INCX.EQ.1)THEN
DO60J=1,N
IF(X(J).NE.ZERO)THEN
L=1-J
IF(NOUNIT)X(J)=X(J)/A(1,J)
TEMP=X(J)
DO50I=J+1,MIN(N,J+K)
X(I)=X(I)-TEMP*A(L+I,J)
50CONTINUE
ENDIF
60CONTINUE
ELSE
JX=KX
DO80J=1,N
KX=KX+INCX
IF(X(JX).NE.ZERO)THEN
IX=KX
L=1-J
IF(NOUNIT)X(JX)=X(JX)/A(1,J)
TEMP=X(JX)
DO70I=J+1,MIN(N,J+K)
X(IX)=X(IX)-TEMP*A(L+I,J)
IX=IX+INCX
70CONTINUE
ENDIF
JX=JX+INCX
80CONTINUE
ENDIF
ENDIF
ELSE
*
*Formx:=inv(A' )*x or x := inv( conjg( A'))*x.
*
IF(LSAME(UPLO,'U'))THEN
KPLUS1=K+1
IF(INCX.EQ.1)THEN
DO110J=1,N
TEMP=X(J)
L=KPLUS1-J
IF(NOCONJ)THEN
DO90I=MAX(1,J-K),J-1
TEMP=TEMP-A(L+I,J)*X(I)
90CONTINUE
IF(NOUNIT)TEMP=TEMP/A(KPLUS1,J)
ELSE
DO100I=MAX(1,J-K),J-1
TEMP=TEMP-CONJG(A(L+I,J))*X(I)
100CONTINUE
IF(NOUNIT)TEMP=TEMP/CONJG(A(KPLUS1,J))
ENDIF
X(J)=TEMP
110CONTINUE
ELSE
JX=KX
DO140J=1,N
TEMP=X(JX)
IX=KX
L=KPLUS1-J
IF(NOCONJ)THEN
DO120I=MAX(1,J-K),J-1
TEMP=TEMP-A(L+I,J)*X(IX)
IX=IX+INCX
120CONTINUE
IF(NOUNIT)TEMP=TEMP/A(KPLUS1,J)
ELSE
DO130I=MAX(1,J-K),J-1
TEMP=TEMP-CONJG(A(L+I,J))*X(IX)
IX=IX+INCX
130CONTINUE
IF(NOUNIT)TEMP=TEMP/CONJG(A(KPLUS1,J))
ENDIF
X(JX)=TEMP
JX=JX+INCX
IF(J.GT.K)KX=KX+INCX
140CONTINUE
ENDIF
ELSE
IF(INCX.EQ.1)THEN
DO170J=N,1,-1
TEMP=X(J)
L=1-J
IF(NOCONJ)THEN
DO150I=MIN(N,J+K),J+1,-1
TEMP=TEMP-A(L+I,J)*X(I)
150CONTINUE
IF(NOUNIT)TEMP=TEMP/A(1,J)
ELSE
DO160I=MIN(N,J+K),J+1,-1
TEMP=TEMP-CONJG(A(L+I,J))*X(I)
160CONTINUE
IF(NOUNIT)TEMP=TEMP/CONJG(A(1,J))
ENDIF
X(J)=TEMP
170CONTINUE
ELSE
KX=KX+(N-1)*INCX
JX=KX
DO200J=N,1,-1
TEMP=X(JX)
IX=KX
L=1-J
IF(NOCONJ)THEN
DO180I=MIN(N,J+K),J+1,-1
TEMP=TEMP-A(L+I,J)*X(IX)
IX=IX-INCX
180CONTINUE
IF(NOUNIT)TEMP=TEMP/A(1,J)
ELSE
DO190I=MIN(N,J+K),J+1,-1
TEMP=TEMP-CONJG(A(L+I,J))*X(IX)
IX=IX-INCX
190CONTINUE
IF(NOUNIT)TEMP=TEMP/CONJG(A(1,J))
ENDIF
X(JX)=TEMP
JX=JX-INCX
IF((N-J).GE.K)KX=KX-INCX
200CONTINUE
ENDIF
ENDIF
ENDIF
*
RETURN
*
*EndofCTBSV.
*
END