dtbmv.f

          SUBROUTINE DTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
    *     .. Scalar Arguments ..
          INTEGER INCX,K,LDA,N
          CHARACTER DIAG,TRANS,UPLO
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION A(LDA,*),X(*)
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DTBMV  performs one of the matrix-vector operations
    *
    *     x := A*x,   or   x := 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 := 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      - 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 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      - DOUBLE PRECISION 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.
    *
    *
    *  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 ZERO
          PARAMETER (ZERO=0.0D+0)
    *     ..
    *     .. Local Scalars ..
          DOUBLE PRECISION TEMP
          INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
          LOGICAL NOUNIT
    *     ..
    *     .. External Functions ..
          LOGICAL LSAME
          EXTERNAL LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC 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('DTBMV ',INFO)
              RETURN
          END IF
    *
    *     Quick return if possible.
    *
          IF (N.EQ.0) RETURN
    *
          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.
    *
              IF (LSAME(UPLO,'U')) THEN
                  KPLUS1 = K + 1
                  IF (INCX.EQ.1) THEN
                      DO 100 J = N,1,-1
                          TEMP = X(J)
                          L = KPLUS1 - J
                          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
                          X(J) = TEMP
      100             CONTINUE
                  ELSE
                      KX = KX + (N-1)*INCX
                      JX = KX
                      DO 120 J = N,1,-1
                          TEMP = X(JX)
                          KX = KX - INCX
                          IX = KX
                          L = KPLUS1 - J
                          IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
                          DO 110 I = J - 1,MAX(1,J-K),-1
                              TEMP = TEMP + A(L+I,J)*X(IX)
                              IX = IX - INCX
      110                 CONTINUE
                          X(JX) = TEMP
                          JX = JX - INCX
      120             CONTINUE
                  END IF
              ELSE
                  IF (INCX.EQ.1) THEN
                      DO 140 J = 1,N
                          TEMP = X(J)
                          L = 1 - J
                          IF (NOUNIT) TEMP = TEMP*A(1,J)
                          DO 130 I = J + 1,MIN(N,J+K)
                              TEMP = TEMP + A(L+I,J)*X(I)
      130                 CONTINUE
                          X(J) = TEMP
      140             CONTINUE
                  ELSE
                      JX = KX
                      DO 160 J = 1,N
                          TEMP = X(JX)
                          KX = KX + INCX
                          IX = KX
                          L = 1 - J
                          IF (NOUNIT) TEMP = TEMP*A(1,J)
                          DO 150 I = J + 1,MIN(N,J+K)
                              TEMP = TEMP + A(L+I,J)*X(IX)
                              IX = IX + INCX
      150                 CONTINUE
                          X(JX) = TEMP
                          JX = JX + INCX
      160             CONTINUE
                  END IF
              END IF
          END IF
    *
          RETURN
    *
    *     End of DTBMV .
    *
          END