Chimie Théorique » Opt'n Path

      SUBROUTINE DGBMV(TRANS,M,N,KL,KU,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)

*     .. Scalar Arguments ..

      DOUBLE PRECISION ALPHA,BETA

      INTEGER INCX,INCY,KL,KU,LDA,M,N

      CHARACTER TRANS

*     ..

*     .. Array Arguments ..

      DOUBLE PRECISION A(LDA,*),X(*),Y(*)

*     ..

*

*  Purpose

*  =======

*

*  DGBMV  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  - DOUBLE PRECISION.

*           On entry, ALPHA specifies the scalar alpha.

*           Unchanged on exit.

*

*  A      - DOUBLE PRECISION 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      - DOUBLE PRECISION 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   - DOUBLE PRECISION.

*           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      - DOUBLE PRECISION 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 ..

      DOUBLE PRECISION ONE,ZERO

      PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)

*     ..

*     .. Local Scalars ..

      DOUBLE PRECISION 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('DGBMV ',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 DGBMV .

*

      END