chbmv.f

          SUBROUTINE CHBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
    *     .. Scalar Arguments ..
          COMPLEX ALPHA,BETA
          INTEGER INCX,INCY,K,LDA,N
          CHARACTER UPLO
    *     ..
    *     .. Array Arguments ..
          COMPLEX A(LDA,*),X(*),Y(*)
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CHBMV  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 hermitian band matrix, with k super-diagonals.
    *
    *  Arguments
    *  ==========
    *
    *  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  - COMPLEX         .
    *           On entry, ALPHA specifies the scalar alpha.
    *           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 hermitian 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 hermitian 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 hermitian 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 hermitian 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 the imaginary parts of the diagonal elements need
    *           not be set and are assumed to be zero.
    *           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
    *           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   - COMPLEX         .
    *           On entry, BETA specifies the scalar beta.
    *           Unchanged on exit.
    *
    *  Y      - COMPLEX          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 ..
          COMPLEX ONE
          PARAMETER (ONE= (1.0E+0,0.0E+0))
          COMPLEX ZERO
          PARAMETER (ZERO= (0.0E+0,0.0E+0))
    *     ..
    *     .. Local Scalars ..
          COMPLEX 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 CONJG,MAX,MIN,REAL
    *     ..
    *
    *     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('CHBMV ',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 + CONJG(A(L+I,J))*X(I)
       50             CONTINUE
                      Y(J) = Y(J) + TEMP1*REAL(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 + CONJG(A(L+I,J))*X(IX)
                          IX = IX + INCX
                          IY = IY + INCY
       70             CONTINUE
                      Y(JY) = Y(JY) + TEMP1*REAL(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*REAL(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 + CONJG(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*REAL(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 + CONJG(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 CHBMV .
    *
          END