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SUBROUTINE ZTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)* .. Scalar Arguments .. INTEGER INCX,K,LDA,N CHARACTER DIAG,TRANS,UPLO* ..* .. Array Arguments .. DOUBLE COMPLEX A(LDA,*),X(*)* ..** Purpose* =======** ZTBMV performs one of the matrix-vector operations** x := A*x, or x := A'*x, or x := conjg( A' )*x,** where x is an n element vector and A is an n by n unit, or non-unit,* upper or lower triangular band matrix, with ( k + 1 ) diagonals.** 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 operation to be performed as* follows:** TRANS = 'N' or 'n' x := A*x.** TRANS = 'T' or 't' x := A'*x.** TRANS = 'C' or 'c' x := conjg( A' )*x.** 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*16 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*16 array of dimension at least* ( 1 + ( n - 1 )*abs( INCX ) ).* Before entry, the incremented array X must contain the n* element vector x. On exit, X is overwritten with the* tranformed vector x.** INCX - INTEGER.* On entry, INCX specifies the increment for the elements of* X. INCX must not be zero.* Unchanged on exit.** Further Details* ===============** 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 COMPLEX ZERO PARAMETER (ZERO= (0.0D+0,0.0D+0))* ..* .. Local Scalars .. DOUBLE 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 DCONJG,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('ZTBMV ',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 sequentially with one pass through A.* IF (LSAME(TRANS,'N')) THEN** Form x := A*x.* IF (LSAME(UPLO,'U')) THEN KPLUS1 = K + 1 IF (INCX.EQ.1) THEN DO 20 J = 1,N IF (X(J).NE.ZERO) THEN TEMP = X(J) L = KPLUS1 - J DO 10 I = MAX(1,J-K),J - 1 X(I) = X(I) + TEMP*A(L+I,J) 10 CONTINUE IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J) END IF 20 CONTINUE ELSE JX = KX DO 40 J = 1,N IF (X(JX).NE.ZERO) THEN TEMP = X(JX) IX = KX L = KPLUS1 - J DO 30 I = MAX(1,J-K),J - 1 X(IX) = X(IX) + TEMP*A(L+I,J) IX = IX + INCX 30 CONTINUE IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J) END IF JX = JX + INCX IF (J.GT.K) KX = KX + INCX 40 CONTINUE END IF ELSE IF (INCX.EQ.1) THEN DO 60 J = N,1,-1 IF (X(J).NE.ZERO) THEN TEMP = X(J) L = 1 - J DO 50 I = MIN(N,J+K),J + 1,-1 X(I) = X(I) + TEMP*A(L+I,J) 50 CONTINUE IF (NOUNIT) X(J) = X(J)*A(1,J) END IF 60 CONTINUE ELSE KX = KX + (N-1)*INCX JX = KX DO 80 J = N,1,-1 IF (X(JX).NE.ZERO) THEN TEMP = X(JX) IX = KX L = 1 - J DO 70 I = MIN(N,J+K),J + 1,-1 X(IX) = X(IX) + TEMP*A(L+I,J) IX = IX - INCX 70 CONTINUE IF (NOUNIT) X(JX) = X(JX)*A(1,J) END IF JX = JX - INCX IF ((N-J).GE.K) KX = KX - INCX 80 CONTINUE END IF END IF ELSE** Form x := A'*x or x := conjg( A' )*x.* IF (LSAME(UPLO,'U')) THEN KPLUS1 = K + 1 IF (INCX.EQ.1) THEN DO 110 J = N,1,-1 TEMP = X(J) L = KPLUS1 - J IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) DO 90 I = J - 1,MAX(1,J-K),-1 TEMP = TEMP + A(L+I,J)*X(I) 90 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(A(KPLUS1,J)) DO 100 I = J - 1,MAX(1,J-K),-1 TEMP = TEMP + DCONJG(A(L+I,J))*X(I) 100 CONTINUE END IF X(J) = TEMP 110 CONTINUE ELSE KX = KX + (N-1)*INCX JX = KX DO 140 J = N,1,-1 TEMP = X(JX) KX = KX - INCX IX = KX L = KPLUS1 - J IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J) DO 120 I = J - 1,MAX(1,J-K),-1 TEMP = TEMP + A(L+I,J)*X(IX) IX = IX - INCX 120 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(A(KPLUS1,J)) DO 130 I = J - 1,MAX(1,J-K),-1 TEMP = TEMP + DCONJG(A(L+I,J))*X(IX) IX = IX - INCX 130 CONTINUE END IF X(JX) = TEMP JX = JX - INCX 140 CONTINUE END IF ELSE IF (INCX.EQ.1) THEN DO 170 J = 1,N TEMP = X(J) L = 1 - J IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*A(1,J) DO 150 I = J + 1,MIN(N,J+K) TEMP = TEMP + A(L+I,J)*X(I) 150 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(A(1,J)) DO 160 I = J + 1,MIN(N,J+K) TEMP = TEMP + DCONJG(A(L+I,J))*X(I) 160 CONTINUE END IF X(J) = TEMP 170 CONTINUE ELSE JX = KX DO 200 J = 1,N TEMP = X(JX) KX = KX + INCX IX = KX L = 1 - J IF (NOCONJ) THEN IF (NOUNIT) TEMP = TEMP*A(1,J) DO 180 I = J + 1,MIN(N,J+K) TEMP = TEMP + A(L+I,J)*X(IX) IX = IX + INCX 180 CONTINUE ELSE IF (NOUNIT) TEMP = TEMP*DCONJG(A(1,J)) DO 190 I = J + 1,MIN(N,J+K) TEMP = TEMP + DCONJG(A(L+I,J))*X(IX) IX = IX + INCX 190 CONTINUE END IF X(JX) = TEMP JX = JX + INCX 200 CONTINUE END IF END IF END IF* RETURN** End of ZTBMV .* END
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