sgbmv.f

          SUBROUTINE SGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
    *     .. Scalar Arguments ..
          REAL ALPHA,BETA
          INTEGER INCX,INCY,KL,KU,LDA,M,N
          CHARACTER TRANS
    *     ..
    *     .. Array Arguments ..
          REAL A(LDA,*),X(*),Y(*)
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  SGBMV  performs one of the matrix-vector operations
    *
    *     y := alpha*A*x + beta*y,   or   y := alpha*A'*x + beta*y,
    *
    *  where alpha and beta are scalars, x and y are vectors and A is an
    *  m by n band matrix, with kl sub-diagonals and ku super-diagonals.
    *
    *  Arguments
    *  ==========
    *
    *  TRANS  - CHARACTER*1.
    *           On entry, TRANS specifies the operation to be performed as
    *           follows:
    *
    *              TRANS = 'N' or 'n'   y := alpha*A*x + beta*y.
    *
    *              TRANS = 'T' or 't'   y := alpha*A'*x + beta*y.
    *
    *              TRANS = 'C' or 'c'   y := alpha*A'*x + beta*y.
    *
    *           Unchanged on exit.
    *
    *  M      - INTEGER.
    *           On entry, M specifies the number of rows of the matrix A.
    *           M must be at least zero.
    *           Unchanged on exit.
    *
    *  N      - INTEGER.
    *           On entry, N specifies the number of columns of the matrix A.
    *           N must be at least zero.
    *           Unchanged on exit.
    *
    *  KL     - INTEGER.
    *           On entry, KL specifies the number of sub-diagonals of the
    *           matrix A. KL must satisfy  0 .le. KL.
    *           Unchanged on exit.
    *
    *  KU     - INTEGER.
    *           On entry, KU specifies the number of super-diagonals of the
    *           matrix A. KU must satisfy  0 .le. KU.
    *           Unchanged on exit.
    *
    *  ALPHA  - REAL            .
    *           On entry, ALPHA specifies the scalar alpha.
    *           Unchanged on exit.
    *
    *  A      - REAL             array of DIMENSION ( LDA, n ).
    *           Before entry, the leading ( kl + ku + 1 ) by n part of the
    *           array A must contain the matrix of coefficients, supplied
    *           column by column, with the leading diagonal of the matrix in
    *           row ( ku + 1 ) of the array, the first super-diagonal
    *           starting at position 2 in row ku, the first sub-diagonal
    *           starting at position 1 in row ( ku + 2 ), and so on.
    *           Elements in the array A that do not correspond to elements
    *           in the band matrix (such as the top left ku by ku triangle)
    *           are not referenced.
    *           The following program segment will transfer a band matrix
    *           from conventional full matrix storage to band storage:
    *
    *                 DO 20, J = 1, N
    *                    K = KU + 1 - J
    *                    DO 10, I = MAX( 1, J - KU ), MIN( M, J + KL )
    *                       A( K + 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
    *           ( kl + ku + 1 ).
    *           Unchanged on exit.
    *
    *  X      - REAL             array of DIMENSION at least
    *           ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
    *           and at least
    *           ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
    *           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   - REAL            .
    *           On entry, BETA specifies the scalar beta. When BETA is
    *           supplied as zero then Y need not be set on input.
    *           Unchanged on exit.
    *
    *  Y      - REAL             array of DIMENSION at least
    *           ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
    *           and at least
    *           ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
    *           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 ..
          REAL ONE,ZERO
          PARAMETER (ONE=1.0E+0,ZERO=0.0E+0)
    *     ..
    *     .. Local Scalars ..
          REAL TEMP
          INTEGER I,INFO,IX,IY,J,JX,JY,K,KUP1,KX,KY,LENX,LENY
    *     ..
    *     .. External Functions ..
          LOGICAL LSAME
          EXTERNAL LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC MAX,MIN
    *     ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
         +    .NOT.LSAME(TRANS,'C')) THEN
              INFO = 1
          ELSE IF (M.LT.0) THEN
              INFO = 2
          ELSE IF (N.LT.0) THEN
              INFO = 3
          ELSE IF (KL.LT.0) THEN
              INFO = 4
          ELSE IF (KU.LT.0) THEN
              INFO = 5
          ELSE IF (LDA.LT. (KL+KU+1)) THEN
              INFO = 8
          ELSE IF (INCX.EQ.0) THEN
              INFO = 10
          ELSE IF (INCY.EQ.0) THEN
              INFO = 13
          END IF
          IF (INFO.NE.0) THEN
              CALL XERBLA('SGBMV ',INFO)
              RETURN
          END IF
    *
    *     Quick return if possible.
    *
          IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
         +    ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
    *
    *     Set  LENX  and  LENY, the lengths of the vectors x and y, and set
    *     up the start points in  X  and  Y.
    *
          IF (LSAME(TRANS,'N')) THEN
              LENX = N
              LENY = M
          ELSE
              LENX = M
              LENY = N
          END IF
          IF (INCX.GT.0) THEN
              KX = 1
          ELSE
              KX = 1 - (LENX-1)*INCX
          END IF
          IF (INCY.GT.0) THEN
              KY = 1
          ELSE
              KY = 1 - (LENY-1)*INCY
          END IF
    *
    *     Start the operations. In this version the elements of A are
    *     accessed sequentially with one pass through the band part of 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,LENY
                          Y(I) = ZERO
       10             CONTINUE
                  ELSE
                      DO 20 I = 1,LENY
                          Y(I) = BETA*Y(I)
       20             CONTINUE
                  END IF
              ELSE
                  IY = KY
                  IF (BETA.EQ.ZERO) THEN
                      DO 30 I = 1,LENY
                          Y(IY) = ZERO
                          IY = IY + INCY
       30             CONTINUE
                  ELSE
                      DO 40 I = 1,LENY
                          Y(IY) = BETA*Y(IY)
                          IY = IY + INCY
       40             CONTINUE
                  END IF
              END IF
          END IF
          IF (ALPHA.EQ.ZERO) RETURN
          KUP1 = KU + 1
          IF (LSAME(TRANS,'N')) THEN
    *
    *        Form  y := alpha*A*x + y.
    *
              JX = KX
              IF (INCY.EQ.1) THEN
                  DO 60 J = 1,N
                      IF (X(JX).NE.ZERO) THEN
                          TEMP = ALPHA*X(JX)
                          K = KUP1 - J
                          DO 50 I = MAX(1,J-KU),MIN(M,J+KL)
                              Y(I) = Y(I) + TEMP*A(K+I,J)
       50                 CONTINUE
                      END IF
                      JX = JX + INCX
       60         CONTINUE
              ELSE
                  DO 80 J = 1,N
                      IF (X(JX).NE.ZERO) THEN
                          TEMP = ALPHA*X(JX)
                          IY = KY
                          K = KUP1 - J
                          DO 70 I = MAX(1,J-KU),MIN(M,J+KL)
                              Y(IY) = Y(IY) + TEMP*A(K+I,J)
                              IY = IY + INCY
       70                 CONTINUE
                      END IF
                      JX = JX + INCX
                      IF (J.GT.KU) KY = KY + INCY
       80         CONTINUE
              END IF
          ELSE
    *
    *        Form  y := alpha*A'*x + y.
    *
              JY = KY
              IF (INCX.EQ.1) THEN
                  DO 100 J = 1,N
                      TEMP = ZERO
                      K = KUP1 - J
                      DO 90 I = MAX(1,J-KU),MIN(M,J+KL)
                          TEMP = TEMP + A(K+I,J)*X(I)
       90             CONTINUE
                      Y(JY) = Y(JY) + ALPHA*TEMP
                      JY = JY + INCY
      100         CONTINUE
              ELSE
                  DO 120 J = 1,N
                      TEMP = ZERO
                      IX = KX
                      K = KUP1 - J
                      DO 110 I = MAX(1,J-KU),MIN(M,J+KL)
                          TEMP = TEMP + A(K+I,J)*X(IX)
                          IX = IX + INCX
      110             CONTINUE
                      Y(JY) = Y(JY) + ALPHA*TEMP
                      JY = JY + INCY
                      IF (J.GT.KU) KX = KX + INCX
      120         CONTINUE
              END IF
          END IF
    *
          RETURN
    *
    *     End of SGBMV .
    *
          END